Sep 25  Wed  Mr A Middleditch (Sheffield)  Applied Mathematics Colloquium  
Measuring ocean surface currents using HF radar  


Oct 2  Wed  Prof Ronald Smith (Loughborough)  Applied Mathematics Colloquium  
The optimal compact finitedifference scheme for the diffusion equation with flow  


Oct 9  Wed  Dr Makis Kappos (Sheffield)  Applied Mathematics Colloquium  
Singularities, Far and Near  


Oct 23  Wed  Dr I. Ballai (Sheffield)  Applied Mathematics Colloquium  
Coronal Seismology  


Oct 30  Wed  Dr D. Roscoe (Sheffield)  Applied Mathematics Colloquium  
Is dark matter the new phlogiston?  


Nov 6  Wed  Dr Bill Lionheart (UMIST)  Applied Mathematics Colloquium  
Anisotropic inverse boundary value problems in electromagnetics  


Nov 20  Wed  Dr V. Yudovich (Hull)  Applied Mathematics Colloquium  
Cosymmetry and its application in mechanics  


Nov 27  Wed  Mr T. Antypas (Athens)  Applied Mathematics Colloquium  
The description of concentration time series of instantaneously released gases in the atmosphere via the proper orthogonal decomposition  


Dec 4  Wed  Prof A. Hood (St. Andrews)  Applied Mathematics Colloquium  
Phase mixing: heating mechanism for coronal holes  


Dec 11  Wed  Prof Sir J. Kingman (Isaac Newton Institute)  Applied Mathematics Colloquium  
On teaching Poisson processes  


Feb 5  Wed  Dr Kristof Petrovay (Eotvos University, Budapest)  Applied Mathematics Colloquium  
Secondary shear instability in the solar tachocline  


Feb 12  Wed  Dr Stephen Belcher (Reading, Meteorology)  Applied Mathematics Colloquium  
The role of surface waves in dynamics of the ocean mixed layer  


Feb 19  Wed  Prof Ray Atkin (Sheffield)  Applied Mathematics Colloquium  
Inaugural lecture: Fluids with a future?  


Feb 21  Fri  Dr Ingo MuellerWodarg (UCL, Atmospheric Physics Laboratory)  Applied Mathematics Colloquium  
The application of General Circulation Models to terrestrial and planetary upper atmospheres  


Feb 26  Wed  Prof Vladimir Vladimirov (Hull)  Applied Mathematics Colloquium  
Virial equation in fluid dynamics  


Mar 5  Wed  Dr Christos Vassilicos (Imperial College London, Aeronautics)  Applied Mathematics Colloquium  
Turbulent diffusion  


Mar 19  Wed  Prof Alan Zinober (Sheffield)  Applied Mathematics Colloquium  
From the brachistochrone to the calculus of variations and modern control theory  


Mar 26  Wed  Prof John Gibbon (Imperial College London)  Applied Mathematics Colloquium  
Infinite energy singularity formation in a class of solutions of the 3D Euler equations  


Apr 2  Wed  Prof Farideh Honary (Lancaster)  Applied Mathematics Colloquium  
Modern Riometry: techniques and results  


May 6  Tue  Prof Xia (China)  Applied Mathematics Colloquium  
Periodic orbits arising from deltamodulated feedback control  


May 7  Wed  Prof Shadia Habbal (Aberystwyth, Physics)  Applied Mathematics Colloquium  
The solar wind and the hidden secrets of the Sun  


May 14  Wed  Dr Eleri Pryse (Aberystwyth, Physics)  Applied Mathematics Colloquium  
Imaging nearEarth space  


May 29  Thu  Dr Louise Harra (UCL, MSSL)  Applied Mathematics Colloquium  
Solar flare and Coronal Mass Ejections  


Oct 1  Wed  Dr R. Balthazor (Sheffield)  Applied Mathematics Colloquium  
Modelling the Upper Atmosphere  a historical perspective  


Oct 8  Wed  Dr N. Mole (Sheffield)  Applied Mathematics Colloquium  
Surface waves in random media: applications to solar physics  


Oct 22  Wed  Dr Kristof Petrovay (Eotvos University, Budapest)  Applied Mathematics Colloquium  
The decay of sunspots as a nonlinear turbulent erosion process  


Oct 29  Wed  Prof David Hughes (Leeds)  Applied Mathematics Colloquium  
Large and smallscale dynamo action  


Nov 5  Wed  Dr Mervyn Freeman (British Antarctic Survey)  Applied Mathematics Colloquium  
Multiscale SunEarth connections  


Nov 12  Wed  Dr John Brooke (CSAR, Manchester)  Applied Mathematics Colloquium  
Using Carrington's Legacy: analysing the spatiotemporal structure of the solar cycle from 1853 to 2003  


Nov 19  Wed  Dr Alan Aylward (UCL, Physics and Astronomy)  Applied Mathematics Colloquium  
Solar variability and climate change: what CMAT model can tell us about the possible mechanisms  


Nov 26  Wed  Dr William Wilkinson (CMIS, Brighton)  Applied Mathematics Colloquium  
The Earth's quasiparallel bow shock: review of observations and outstanding questions  


Dec 10  Wed  Prof Joe Buckley (Royal Military College of Canada, Physics)  Applied Mathematics Colloquium  
Ocean waves and microwaves  


Dec 17  Wed  Dr Michael Warby (Brunel)  Applied Mathematics Colloquium  
The computational modelling of the constrained inflation of solid polymers in the context of thermoforming  


Mar 10  Wed  Dr Itsuki Handoh (Sheffield)  Applied Mathematics Colloquium  
The midCretaceous biogeochemical cycles and climate change  


Mar 24  Wed  Dr Elizabeth Lucek (ICSTM)  Applied Mathematics Colloquium  
Cluster observations of the Earth's bow shock  


Mar 31  Wed  Dr John Porrill (Sheffield, Psychology)  Applied Mathematics Colloquium  
Why neuroscience needs mathematicians?  


Apr 28  Wed  Dr David Tsiklauri (Salford, Computer Science and Engineering)  Applied Mathematics Colloquium  
Interaction of Alfven waves with plasma structures  


May 5  Wed  Prof Slava Kurylev (Loughborough)  Applied Mathematics Colloquium  
Uniqueness and stability in multidimensional inverse problems  


May 12  Wed  Dr David Roscoe (Sheffield)  Applied Mathematics Colloquium  
Discrete dynamical states in galactic discs: New insights, new data  


May 19  Wed  Prof Viktor Shrira (Keele)  Applied Mathematics Colloquium  
Quasimodes in shear flows: a working concept  


Sep 1  Wed  Dr M. Miesch (HAO/NCAR, Boulder (USA))  Applied Mathematics Colloquium  
Behind the HYPE: A ThinShell Model for the Solar Tachocline  


Sep 17  Fri  Dr Hien Vo (Aberystwyth)  Applied Mathematics Colloquium  
Various aspects of the plasmasphere using satellite and ground data along with a study of the selforganizing criticality in using global auroral images  


Sep 29  Wed  Dr E. Benilov (Limerick)  Applied Mathematics Colloquium  
Explosive instability in linear systems with stable eigenmodes  


Oct 6  Wed  Dr R. Kerr (Warwick)  Applied Mathematics Colloquium  
Structure functions as a tool for atmospheric analysis  


Oct 13  Wed  Dr W. Chaplin (Birmingham, Physics and Astronomy)  Applied Mathematics Colloquium  
Sounding the deep solar interior: modern challenges for global Helioseismology  


Oct 20  Wed  Dr A. FerrizMas (Vigo, Spain)  Applied Mathematics Colloquium  
Fluid mechanical aspects in solar magnetism: How can magnetic fields of 100 kG be produced?  


Oct 27  Wed  Prof I. Moss (Newcastle)  Applied Mathematics Colloquium  
Warm inflation and the hot big bang  


Nov 3  Wed  Prof G. Tallents (York, Physics)  Applied Mathematics Colloquium  
The opacity of hot dense plasmas: application to laboratory and solar examples  


Nov 11  Thu  Prof S. Quegan (Sheffield)  Applied Mathematics Colloquium  
A short walk around the Carbon cycle  


Nov 18  Thu  Dr N. Mavromatos (King's College, London)  Applied Mathematics Colloquium  
CPT violation and decoherence: is there a chance of observing something?  


Nov 24  Wed  Dr P. Browning (UMIST)  Applied Mathematics Colloquium  
Heating the solar corona by nanoflares  


Nov 26  Fri  Prof P. Diamond (UCSD)  Applied Mathematics Colloquium  
Zonal flows in Laboratory plasmas  


Dec 8  Wed  Dr E. Winstanley (Sheffield)  Applied Mathematics Colloquium  
What Hawking did: why all the fuss in Dublin?  


Dec 15  Wed  Dr C. van de Bruck (Sheffield)  Applied Mathematics Colloquium  
Cosmology and Extra Dimensions  


Feb 9  Wed  Dr J. J. Healey (Keele)  Applied Mathematics Colloquium  
A strange instability with growth normal to a boundary layer  


Feb 16  Wed  Dr D. Roscoe (Sheffield)  Applied Mathematics Colloquium  
Reaction in classical electrodynamics  


Mar 2  Wed  Dr J. Kaplunov (Manchester)  Applied Mathematics Colloquium  
Explicit asymptotic models for surface elastic and electroelastic waves  


Mar 9  Wed  Dr C. Mandrini (IAFE, Argentina)  Applied Mathematics Colloquium  
Magnetic Helicity: linking solar to interplanetary phenomena  


Apr 13  Wed  Dr J. Winkler (Sheffield, Computer Science)  Applied Mathematics Colloquium  
A comparison of condition numbers of the full rank least squares problem  


Apr 20  Wed  Dr Gunnar Hornig (St. Andrews)  Applied Mathematics Colloquium  
Threedimesional magnetic reconnection  


Apr 27  Wed  Prof. Carlo Barenghi (Newcastle)  Applied Mathematics Colloquium  
The TaylorCouette problem: an old flow with new twists  


May 4  Wed  Dr Erwin Verwichte (Warwick)  Applied Mathematics Colloquium  
Transverse waves in the solar corona  


May 10  Tue  Dr Anthony Field (Culham Laboratory)  Applied Mathematics Colloquium  
How to make 100 million a day, 100 million degrees C  the temperature at which plasma burns  


May 18  Wed  Dr Sergey Nazarenko (Warwick)  Applied Mathematics Colloquium  
Turbulence of sea waves  


May 25  Wed  Dr Nils Andersson (Southampton)  Applied Mathematics Colloquium  
Gravitationalwave asteroseismology  probing the extremes of physics  


Sep 28  Wed  Dr Stephen Davies (Leiden)  Applied Mathematics Colloquium  
Constraining GaussBonnet Dark Energy  


Oct 5  Wed  Dr Steven Tobias (Leeds)  Applied Mathematics Colloquium  
The role of spectra in dynamo theory  does meanfield modelling make any sense?  


Oct 19  Wed  Karima Khusnutdinova (Loughborough)  Applied Mathematics Colloquium  
The effect of bubbles on internal waves  


Oct 26  Wed  Reza Raoufi and Alan Zinober (Sheffield)  Applied Mathematics Colloquium  
$C^3$ = Chaos, Cryptography and Control  


Nov 2  Wed  Prof. Howard Wilson (York)  Applied Mathematics Colloquium  
Explosive instabilities in laboratory fusion plasmas  


Nov 14  Mon  Prof. Stanley L Jaki (Seton Hall)  Applied Mathematics Colloquium  
A late awakening with a nightmare  


Nov 16  Wed  Dr A Thyagaraja (Culham Laboratory)  Applied Mathematics Colloquium  
Mesoscale electromagnetic turbulence in tokamaks  


Nov 23  Wed  Prof. Yurii Sergeev (Newcastle)  Applied Mathematics Colloquium  
Tracer particles in turbulent helium II at low temperatures  


Nov 30  Wed  Dr Kiril Kuzanyan (Leeds)  Applied Mathematics Colloquium  
Helicity and Solar dynamo: confront theory and observations  


Dec 13  Tue  Dr Fay Dowker (Blackett Laboratory, Imperial College)  Applied Mathematics Colloquium  
Causal Set Phenomenology  


Feb 8  Wed  Dr Thomas Neukirk (St Andrews)  Applied Mathematics Colloquium  
Current Buildup in Topologically Simple Magnetic Fields  


Feb 15  Wed  Prof Alexander B. Movchan (Liverpool)  Applied Mathematics Colloquium  
Asymptotic analysis of solutions to singularly perturbed problems in multistructures  


Feb 22  Wed  Prof Roger Grimshaw (Loughborough)  Applied Mathematics Colloquium  
Internal solitary waves and undular bores in the atmosphere and ocean  


Mar 1  Wed  Dr Andrew Soward (Exeter)  Applied Mathematics Colloquium  
Nonaxisymmetric $\alpha^2\Omega$dynamo waves in thin stellar shells  


Mar 8  Wed  Dr Robert Walsh (Central Lancashire)  Applied Mathematics Colloquium  
Taking the Sun's temperature: modelling the pros and cons of EUV rastering spectrometers vs narrowband imagers  


Mar 15  Wed  Prof Leo Brevdo (University of the Mediterranean (Marseille, France))  Applied Mathematics Colloquium  
Absolute instability of spatially developing flows and media  


Mar 29  Wed  Dr Jacques Vanneste (Edinburgh)  Applied Mathematics Colloquium  
Wave radiation by slow flows  


Apr 26  Wed  Dr Dave Roscoe (Sheffield)  Applied Mathematics Colloquium  
Redshift phenomenology: A review of Napier's analysis  


May 3  Wed  Dr Sergei Molokov (Coventry)  Applied Mathematics Colloquium  
Interfacial instability in a twolayer system with transverse electric current  


May 10  Wed  Prof Basil Hiley (Birkbeck College)  Applied Mathematics Colloquium  
Quantum Field Theory and the Bohm Model: the Role of the Photon  


May 17  Wed  Prof Chris Eilbeck (Heriot Watt)  Applied Mathematics Colloquium  
Breathers in discrete systems  


May 24  Wed  Dr David Roscoe (Sheffield)  Applied Mathematics Colloquium  
Electrodynamics: Old theory in a new light  


Jun 14  Wed  Dr Leon Ofman (NASA, USA)  Applied Mathematics Colloquium  
Waves in coronal active regions: observations and models  


Oct 4  Wed  Prof. Valentina Zharkova (Bradford)  Applied Mathematics Colloquium  
On the origin of three seismic sources in the 28 October 2003 flare  


Oct 18  Wed  Prof Dugald Duncan (HeriotWatt)  Applied Mathematics Colloquium  
Numerical analysis of a convolution model of phase separation  


Oct 25  Wed  Dr Rony Keppens (K.U.Leuven)  Applied Mathematics Colloquium  
Gridadaptive approaches for computing magnetized plasma dynamics  


Nov 1  Wed  Dr John Barrett (Nottingham)  Applied Mathematics Colloquium  
Geometry of the standard model and neutrino mass terms  


Nov 8  Wed  Dr Yasmin Andrew (JET (Culham))  Applied Mathematics Colloquium  
Experimental Studies of the LH Transition on JET  


Nov 15  Wed  Dr Konstantin Ilin (York)  Applied Mathematics Colloquium  
The stability of tangential and rotational discontinuities in MHD  


Nov 22  Wed  Dr Lisa Hall (Sheffield)  Applied Mathematics Colloquium  
Consistent modified gravity models  


Nov 29  Wed  Dr Duncan Mackay (St. Andrews)  Applied Mathematics Colloquium  
MHD Simulations of Solar Prominences  


Dec 13  Wed  Prof Koji Ohkitani (Sheffield)  Applied Mathematics Colloquium  
Blowup and regularity problems of hypoviscous fluid equations.  


Feb 7  Wed  Jitesh S.B. Gajjar (Manchester)  Applied Mathematics Colloquium  
16:00  Global stability calculations of some separated flows  


Feb 14  Wed  Rich Kerswell (Bristol)  Applied Mathematics Colloquium  
16:00  Transition to Turbulence in a Pipe  


Feb 21  Wed  Silvia Dalla (Manchester)  Applied Mathematics Colloquium  
16:00  Solar science with AstroGrid  


Feb 28  Wed  Tony Arber (Warwick)  Applied Mathematics Colloquium  
16:00  Emergence of flux through into the Solar corona: the effect of partially ionized layers  


Mar 7  Wed  T. Talipova (Institute of Applied Physics, Russian Academy of Sciences)  Applied Mathematics Colloquium  
16:00  The Gardner equation in nonlinear theory of wave motion in stratified medium  


Mar 21  Wed  MayWin Thein (New Hampshire)  Applied Mathematics Colloquium  
16:00  Celestial Navigation (CelNav): Lunar Surface Navigation  


Apr 18  Wed  Patrick Fowler (Sheffield (Chemistry Department))  Applied Mathematics Colloquium  
16:00  Mapping currents in molecules  


Apr 25  Wed  Christian Boehmer (Portsmouth)  Applied Mathematics Colloquium  
16:00  Does the cosmological constant imply the existence of a minimal energy density?  


May 2  Wed  Tom Van Doorsselaere (Warwick)  Applied Mathematics Colloquium  
15:00  Recent results in coronal loop seismology: determination of the nonideal damping mechanism and the density scale height  


May 9  Wed  Sergei Nazarenko (Warwick)  Applied Mathematics Colloquium  
16:00  Leithtype model of 2D turbulence and its predictions  


May 16  Wed  Roddy Vann (York)  Applied Mathematics Colloquium  
16:00  A burning fusion plasma: theoretical challenges  


May 23  Wed  Johan Anderson (Sheffield)  Applied Mathematics Colloquium  
16:00  Comparison of theoretical models to zonal flow generation and the effects of backreaction of zonal flows on ITG turbulence  


May 30  Wed  Daniel Brown (Aberystwyth)  Applied Mathematics Colloquium  
16:00  The onset of xray bright points in the solar corona  


Jun 6  Wed  Reza Tavakol (Queen Mary)  Applied Mathematics Colloquium  
16:00  Dynamo models and differential rotation in the Sun and latetype rapidly rotating stars  


Oct 10  Wed  Dr Matthew P.Juniper (University of Cambridge)  Applied Mathematics Colloquium  
16:00  'Absolute Stability in Fuel Injectors'  
Hicks Lecture Theatre 6  


Oct 31  Wed  Professor Alan Zinober (Sheffield)  Applied Mathematics Colloquium  
16:00  'Optimal Control and Some Applications in Operations Research'  
Hicks Lecture Theatre 6  


Nov 7  Wed  Dr C.J.Howls (Southampton)  Applied Mathematics Colloquium  
16:00  'Why is a Shock Not a Caustic?  
Hicks Lecture Theatre 6  


Nov 14  Wed  Keiichi Ueda (Kyoto University)  Applied Mathematics Colloquium  
16:00  Stripe splitting in reactiondiffusion systems on uniformly growing domains  
Hicks Lecture Theatre 6  


Nov 21  Wed  Mahesan Niranjan (Sheffield)  Applied Mathematics Colloquium  
16:00  Some fun problems that simultaneously excite Biologists, Applied Mathematicians and Computer Scientists  
Hicks Lecture Theatre 6  


Nov 28  Wed  Professor John Brown (Glasgow)  Applied Mathematics Colloquium  
15:00  \'The High Energy Sun and NASA\'s Award Winning RHESSI Mission\'  
Hicks Lecture Theatre 6  


Dec 12  Wed  Professor Steve Decent (Birmingham)  Applied Mathematics Colloquium  
16:00  Unstable Jets, Threads and Curtains  
Hicks Lecture Theatre 6  


Jan 30  Wed  Jesse Andries (Katholieke Universiteit Leuven, Belgium)  Applied Mathematics Colloquium  
14:00  Decoherence of MHD wave packets: a simple example  
Hicks Lecture Theatre A  
Abstract: Magnetohydrodynamic waves have been studied extensively in the literature. They have received much attention lately in efforts to indirectly extract information about the solar coronal plasma by combining theoretical models with data of (spaceborne) instruments that record ample evidence of MHD waves in the solar atmosphere. We will provide a rigorous treatment of linear MHD oscillations in a very simple model emphasizing the selfadjointness and the origin and implications of the existence of continuous parts in the eigenmode spectrum. This will illustrate an important idea which is mathematically and conceptually very easy to understand but which has not yet received enough attention in the context of 'coronal seismology'. Roughly speaking, the output of a system is a convolution between the input and the system. So if you want to draw conclusions based on the output of a system, either you need some information about the input which allows to determine the system, or you need some information on the system in order to draw conclusions on the input. 'Coronal seismology' has so far mainly focussed on discrete trapped waveguide modes and has therefore not payed much attention to this. However, it provides a unifying conceptual framework for the interpretation and comparison of several mechanisms which are often invoked to explain the observed wave behavior and which are often interpreted as being conceptually different (e.g. phase mixing, resonant absorption and leakage). Certainly, within the current understanding that coronal waves are coupled and driven by oscillations in the lower layers of the solar atmosphere and at the solar surface, it is important to appreciate that the characteristics of the solar coronal waves may depend crucially on the characteristics of the driver/exciter and not only on the characteristics of the medium itself. 



Feb 6  Wed  Yi Li (Sheffield)  Applied Mathematics Colloquium  
14:00  A restricted Euler model for small scale intermittency in fluid turbulence  
Hicks Lecture Theatre A  
Abstract: Smallscale intermittency in fluid turbulence refers to the infrequent but strong bursts in the signals of small scale parameters. These bursts display highly nonGaussian statistics, and its prediction poses serious challenges to turbulence research. Based on the restricted Euler approximation, we derive in this talk a simple system of equations for the shorttime Langrangian evolution of velocity and passive scalar increments. The system reproduces several important intermittency trends observed in turbulence, and thus provides a simple dynamic explanation for the observations. 



Feb 13  Wed  Philippe Caillol (Sheffield)  Applied Mathematics Colloquium  
14:00  Nonlinear singular Kelvin modes within a barotropic vortex  
Hicks Lecture Theatre A  
Abstract: This study considers the propagation of helical neutral modes within a barotropic and axisymmetric vortex with an arbitrary azimuthal velocity profile. The singular mode/mean flow interaction leads to strongly nonlinear critical layers around the radius where the angular velocity of the mean flow and the disturbance frequency are comparable. Strong analogies can be done with the theory of critical layers in a stratified flow. We formulate a theory valid when the analogous local Richardson number is small at the critical radius but is nevertheless larger than the mode amplitude, and at a long time asymptotic steady state after the formation of the critical layer. The problem is tackled by removing the apparent singularity by retaining nonlinear terms in the equations of motion inside the critical layer. Viscosity is also introduced in order to render the nonlinear critical layer solution unique, but the inviscid limit is eventually taken. The result from the interaction is the emergence of a multipolar vortex whose poles are located on the critical radius, spiral around the basic vortex axis and are embedded in a distorted mean flow caused by a slow diffusion of the threedimensional vorticity field from the critical layer in a transitional stage due to the very weak viscosity of the flow. This study gives an analytical description of these vortices. 



Feb 20  Wed  Chris Jones (Leeds)  Applied Mathematics Colloquium  
14:00  Convection driven zonal flows in giant planets  
Hicks Lecture Theatre A  
Abstract: The large scale zonal flows on Jupiter and Saturn may be due either to deep convection or to forcing in the stably stratified zone near the surface. Boussinesq simulations of deep convection in a rapidly rotating spherical shell have been successful in reproducing the strong eastward flowing current and the alternating bands of eastward and westward flow. We are currently developing an anelastic compressible model to see how the large density variation between the deep interior and the nearsurface layers affects these results. A further issue is whether the magnetic field can affect the nature of the surface flows on giant planets. 



Mar 5  Wed  Gene Ryan (Bath)  Applied Mathematics Colloquium  
13:30  InputtoState Stability of Differential Inclusions with Application to Hysteretic Feedback Systems  
Hicks Lecture Theatre 7  
Abstract: Inputtostate stability is a concept that captures ``nice'' properties of dynamical systems with input (e.g. bounded input implies bounded state, input ``eventually small'' implies state ``eventually small'', input convergent to zero implies state convergent to zero). Inputto state stability (ISS) of a class of differential inclusions is described. Every system in the class is of Lur'etype: a feedback interconnection of a linear system and a (setvalued) nonlinearity. Applications of the ISS results, in the context of feedback interconnections with a hysteresis operator in the feedback path, are developed. 



Mar 19  Wed  Anne Juel (Manchester)  Applied Mathematics Colloquium  
14:00  Interfacial wave growth in oscillating twophase flow  
Hicks Lecture Theatre A  
Abstract: When a closed vessel containing two stably stratified, immiscible liquids is oscillated sinusoidally in the horizontal direction, the at interface between the two liquids loses stability to twodimensional `frozen waves' through a mech anism analogous to that of the Kelvin{Helmholtz instability). The onset of `frozen waves' occurs through a supercritical pitchfork bifurcation, but for larger values of the forcing parameters, a qualitative change in the wave growth takes place. In terms of the inverse vibrational Froude number, W (ratio of vibrational to gravity forces, proportional to the square of the forcing velocity), there is a critical value, Wc, beyond which the experimental data collapses onto a single curve that exibits a linear dependence on W. We find that this collapse is indicative of a bifurcation to an inviscid solution at Wc. Our investigation of the evolution of the interface shape suggests that this second bifurcation is associated with a transition from gravity to capillary dominated waves, which is consistent with the wavelength reaching a minimum for W = Wc. For larger values of the forcing parameters, the twodimensional array of waves becomes unstable to threedimensional oscillatory waves through a subcritical bifurca tion. The response frequency of the threedimensional oscillatory waves is found to be locked to the forcing frequency. Secondary transition to threedimensional waves underpin the dynamics of a variety of fluid flows, e.g. the oscillatory instability of rolls in thermal convection and the formation of streamwise vortices in mixing layers. We characterise the secondary instability of our oscillating interface by comparison with these systems and discuss the physical mechanism that leads to the onset of threedimensional waves. 



Apr 9  Wed  Zhivko Stoyanov (Bath)  Applied Mathematics Colloquium  
14:00  Clustering and ordering of large networks, and sensitivity analysis  
Hicks Lecture Theatre A  
Abstract: Clustering is the problem of dividing a network into two or more balanced and wellconnected subnetworks with only a few links between them. This is a discrete problem, which is intractable for most reallife networks, due to their size. We give a brief overview of some of the methods, available in the literature, for clustering large networks. Another discrete problem on networks, which can not be solved exactly in reallife examples, is that of ordering. For example, the problem which Google solves is that of ordering the webpages in the internet, respecting the criteria of their authority, that is, how many webpages link to a given webpage. We give a brief overview of the basics of the techique, which Google uses, in order to solve the problem of ordering. In the second half of the talk we motivate the sensitivity analysis of networks and consider the effects, which small perturbations of the data can produce on the clustering of the network. 



Apr 16  Wed  A Thyagaraja (UKAEA/EURATOM Fusion Association, Culham Science Centre)  Applied Mathematics Colloquium  
14:00  Twofluid theory of axisymmetric toroidal equilibria  
Hicks Lecture Theatre A  
Abstract: An introduction to key issues in the magnetic confinement to fusion power production will be given. This is followed by an overview account of a recently developed, novel approach to axisymmetric toroidal equilibria with strong flows will be presented, essentially from an analytical point of view. 



Apr 23  Wed  Nicolas Leprovost (Sheffield)  Applied Mathematics Colloquium  
14:00  Shear stabilisation and turbulent mixing  
Hicks Lecture Theatre A  
Abstract: In order to explain the turbulent mixing in the solar tachocline and also the occurrence of differential rotation in the convection zone, we study the effect of rotation on sheared turbulence. By solving quasilinear equations for the fluctuating fields, we derive turbulence amplitude and turbulent transport coefficients (turbulent viscosity and diffusivity), taking into account the effects of shear and rotation on turbulence. The interaction between the shear and the rotation is shown to give rise to a novel nondiffusive flux of angular momentum (known as the Lambda effect), possibly offering a mechanism for the occurrence of a strong shear region in the solar interior. We also discuss the effect of stratification and magnetic fields on turbulent mixing." 



Apr 30  Wed  Robert Rothschild (Lancaster)  Applied Mathematics Colloquium  
14:00  Should airlines codeshare or should they merge?  
Hicks Lecture Theatre A  
Abstract: This seminar compares the profits from 'contractual' relationships amongst competing firms, with those obtainable when the parties formally merge. The emphasis throughout is on the essentially gametheoretic nature of the decision, and the strategic equilibria that result. 



May 7  Wed  Remi Tailleux (Reading)  Applied Mathematics Colloquium  
14:00  Are incompressible NavierStokes equations valid for describing turbulent diabatic motions?  
Hicks Lecture Theatre A  
Abstract: According to classical turbulence theory, there exists two possible pathways to dissipation for kinetic energy in a turbulent stratified fluid, a viscous and a diffusive one. The viscous pathway is well known and associated with the work of molecular viscous stresses. The second one is envisioned as a two steps process. In the first step, kinetic energy is converted into available potential energy (APE) adiabatically, without modification of the mean gravitational potential energy (GPEr). In a second step, lateral molecular diffusion is thought to irreversibly convert the APE into GPEr. Thus, according to the diffusive pathway, kinetic energy is dissipated into mean GPE. In this talk, I will present different line of arguments aiming at demonstrating that this view is invalid. Ultimately, the arguments will lead to the conclusion that the incompressible description of hydrodynamics of fluid flows at low Mach number must be invalid too for representing diabatic irreversible motions. A modification of the incompressible NavierStokes equations will be proposed that is more physically consistent, and how existing incompressible hydrodynamics codes can be modified will be discussed. We will also show that the above results provide a simple solution to the existing ``ocean heat engine controversy". 



May 28  Wed  Rekha Jain (Sheffield)  Applied Mathematics Colloquium  
14:00  Interaction of p Modes with a Thin Magnetic Flux Tube  
Hicks Lecture Theatre A  
Abstract: The Sun's magnetic active regions, composed of sunspots and plage, are topologically complex. The magnetic field is highly structured, forming a tangle of fibrils within the plage and more compact, regimented bundles within sunspot umbrae. The fragmented nature of the field makes helioseismic observations within active regions rather difficult to interpret. We choose to study the propagation of acoustic waves through regions of plage, modelling the magnetic field therein as a collection of thin flux tubes. In this talk I will present the first results of this research; the computation of the absorption coefficient from a single tube. The incoming acoustic waves interact with the flux tube, exciting sausage and kink tube waves which propagate downward and upward carrying away energy, thereby producing absorption. The tube response further scatters the incoming wave into a variety of f modes and p modes. We treat plage as a collection of noninteracting flux tubes. I will present the resulting theoretically calculated absorption coefficients and compare with the most recent observations. 



May 28  Wed  Rekha Jain (Sheffield)  Applied Mathematics Colloquium  
14:00  tbd  
Hicks Lecture Theatre A  


Jun 4  Wed  Yuri Shtessel (Alabama)  Applied Mathematics Colloquium  
14:00  Higher Order Sliding Mode Control with Application to Blood Glucose Level Regulation  
Hicks Lecture Theatre A  
Abstract: Control under uncertainty is one of the main topics of the modern control theory. In spite of the extensive and successful development of robust adaptive control and backstepping technique, sliding mode control (SMC) stays, probably, the main choice in handling bounded uncertainties/disturbances and unmodeled dynamics. The idea is in stirring the system trajectory to properly chosen constraints (sliding manifold) and keeping it thereafter by means of highfrequency switching control, exploiting the main features of the sliding mode: its insensitivity to external and internal disturbances matched by control and ultimate accuracy and finitetime reaching transient. Stabilization of the sliding variable in SISO systems by means of the traditional SMC, designed as a switching control with respect to the socalled sliding variable, requires the system relative degree to be equal to one with respect to the sliding variable. Also, high frequency control switching leads to the socalled chattering effect, which is exhibited by high frequency vibration of the controlled plant that can be dangerous in applications and difficult to avoid or attenuate. The intrinsic difficulties of the traditional SMC are mitigated by the higher order sliding mode control (HOSM) that stabilizes at zero not only the sliding variable, but also its successive derivatives (kth order HOSM). HOSM is a new generation of SMC that is based on a general discontinuouscontrol approach. The unique power of the approach is revealed by the development of practical arbitraryorder realtime robust exact differentiator, which performance is proved to be asymptotically optimal in the presence of small Lebesguemeasurable input noises. 1k Applications of HOSM control and observation to blood glucose regulation (diabetes control) are discussed. 



Sep 25  Thu  Brian Sawford (Monash)  Applied Mathematics Colloquium  
14:00  Relative Dispersion and Richardson's Constant  
Hicks Lecture Theatre 5  
Abstract: This talk will describe some very recent analysis of Direct Numerical Simulation results for turbulent relative dispersion over a wide range of Reynolds numbers. We will start with some background discussion of the nature and significance of relative dispersion and of the role of Kolmogorov's similarity theory, leading to the introduction of Richardson's constant as a fundamental parameter of relative dispersion. Although it is of great fundamental and practical significance, Richardson's constant has not been wellquantified, and model estimates for it range from 0.01 to 4. We will describe first a traditional analysis of relative dispersion data, concluding that this approach does not yield a good estimate for Richardson's constant even at the highest Reynolds number currently available. We then use a modified version of a new approach developed by Ott and Mann (JFM, 422, 207, (2000)) to show that a welldefined Richardson scaling range exists in our data. We estimate Richardson's constant over a range of Reynolds numbers showing that it decreases weakly with Reynolds number to an asymptotic value at large Reynolds number of 0.55  0.57. 



Oct 1  Wed  Professor Keke Zhang (Exeter)  Applied Mathematics Colloquium  
14:00  Linear and nonlinear instabilities in rotating cylindrical RayleighBénard convection  
Hicks Lecture Theatre A  
Abstract: Motivated by the wish to understand the fundamental dynamics taking place in planetary/stellar fluid interiors and atmospheres, convection in rotating cylindrical geometry has been extensively studied. We shall present some new analytical and numerical results on linear and nonlinear convection in cylindrical systems heated from below and rotating about its vertical axis. In particular, we shall discuss asymptotic solutions of inertial convection in rotating cylinders and nonlinear countertraveling waves in connection with the EckhausBenjaminFeirtype instability and with the saddlenodetype bifurcation in rotating cylindrical channels. 



Oct 22  Wed  Dr Rosa DiazSandoval (Sheffield)  Applied Mathematics Colloquium  
14:00  Solar activity and human health  
Hicks Lecture Theatre A  
Abstract: We will show the most important results of statistical studies regarding the relationship between solar activity and cardiac and mental diseases, as well as the physiological parameters of healthy individuals. In order to establish a plausible physical mechanism, the whole system from the sun to the human body is studied. The methodology used to find correlations between solar and health parameters is based mainly upon the spectral analysis of solar and medical data because it has been suggested that a possible physical mechanism might be related to solar periodicities. To compare the geomagnetic activity, caused by the solar activity itself, and health parameters, the Superposed Epochs Method is used. The Forbush decreases in cosmic rays and the geomagnetic index Ap are the phenomena most commonly analyzed because of previous results reported in the literature. We will show, based on the Mexican results, that solar activity could well be a risk factor that affects the vulnerable population by a factor of 2 in the occurrence of myocardial infarction diseases. 



Oct 29  Wed  Elizabeth Winstanley (Sheffield)  Applied Mathematics Colloquium  
14:00  Furry black holes  
Hicks Lecture Theatre A  
Abstract: My aim in this seminar is to explain what furry black holes are, and why they might be interesting. There will not be a lot of detail on the relativity side of things, but I will explain the mathematics behind the proof of the existence and stability of furry black holes in a particular matter model. 



Nov 5  Wed  Peter Constantin (Chicago)  Applied Mathematics Colloquium  
14:00  Complex Fluids  
LTA  
Abstract: I will describe recent results concerning melts of complex particles. Time permitting, I will describe some mathematical results concerning suspensions in fluids. 



Nov 12  Wed  Jennifer Waters (Sheffield)  Applied Mathematics Colloquium  
14:00  Data Assimilation into the Wavewatch III model  
Hicks Lecture Theatre A  
Abstract: The assimilation of data into wave models aims to improve the performance of the model by correcting the model state with observations. The area considered in this study is the Celtic Sea region off the coast of South Wales were a Pisces HF radar was deployed between 2002 and 2005. The ultimate aim is to assimilate the HF radar data into Wavewatch III and an initial study is presented where perturbed buoy data is assimilated into the model to test the assimilation scheme configuration. 



Nov 12  Wed  Noel Robertson (SheffieldSheffield)  Applied Mathematics Colloquium  
14:00  Modelling of the effect of snow on the hydrology and carbon budget of boreal regions  
Hicks Lecture Theatre A  
Abstract: In the study of global carbon dynamics, the carbon and water cycles are closely related. In order to act as an effective carbon sink, plants must have water as well as sunlight to perform photosynthesis. In cold boreal regions, where some of the world's largest forests are located, we therefore need to quantify the role of snow water dynamics in the carbon cycle. In this talk I particularly discuss the effect of climatedriven model predictions of snow water equivalent on the hydrology and carbon budget of boreal zones such as Siberia. 



Nov 19  Wed  Francesca Ticconi (Universita degli Studi Roma Tre)  Applied Mathematics Colloquium  
14:00  Synthetic aperture radar: its role in remote sensing  
Hicks Lecture Theatre A  
Abstract: The Synthetic Aperture Radar (SAR) is an active sensor that transmits a beam of electromagnetic radiation, in the microwave region of the electromagnetic spectrum, providing high quality image of the Earth's surface, with a fine resolution independent of the sensor altitude or wavelength. By proper selection of operating frequency, the microwave signal can penetrate clouds, haze, rain, fog and precipitation with very little attenuation, thus allowing operation in unfavourable weather conditions that preclude the use of visible/infrared system. Being an active sensor, that is providing its own source of illumination, SAR is not dependent on light from Sun and therefore it can operate day or night. Moreover, it is able to illuminate with variable look angle and can select wide area coverage. The net result is an instrument that is capable of continuously monitoring geophysical parameters related to the structural and electrical properties of Earth's surface and also it is capable of observing dynamic phenomena, such as ocean currents, sea ice motion or changing of land cover vegetation. In addition, the topography change can be derived from phase difference between measurement using radar interferometry, achievable due the coherent character of the SAR system that retains both phase and magnitude of the backscattered echo signal. Even if the interpretation on the SAR images is less intuitive compared to the optical ones, SAR has been shown to be very useful over a wide range of applications, including sea and ice monitoring, oil pollution monitoring, oceanography, snow monitoring, forest monitoring and classification of Earth terrain. 



Nov 26  Wed  Dr Balazs Pinter (Aberystwyth)  Applied Mathematics Colloquium  
14:00  Local Helioseismology  How far can we see?  
Hicks Lecture Theatre A  
Abstract: We can see clusters of galaxies millions of light years away in the deep space. However, looking into the interior of the nearest star is impossible even to the deservedly celebrated Hubble Space Telescope. Helioseismology is the only field of physics which offers means to discover the hidden world of the Sun. We will briefly review different techniques together with the greatest results of local helioseismology. The power of observing and analysing oscillations will be apparent also in the second part, which will be a case study in coronal seismology. A filament was visible in the Sun's atmosphere on 15th October 2002. A part of it was clearly oscillating until the filament erupted. The spatial structure and the temporal variation of the filament oscillations will be studied by using the techniques of wavelet analysis. 



Dec 10  Wed  Dr Anne Juel (Manchester)  Applied Mathematics Colloquium  
14:00  Steep capillarygravity waves in oscillatory shear flows  
LTA  
Abstract: Nonlinear waves in uids are associated with a rich variety of dynamics that often underpin important natural phenomena. Examples range from internal solitarylike waves that are ubiquitous features of coastal oceans to the surface ocean spectra, whose interpretation relies on the nonlinear interaction between surface water waves and wind. We study steep capillarygravity waves that form at the interface between two stably stratied layers of immiscible liquids in a horizontally oscillating vessel, and are commonly referred to as frozen waves. The oscillatory nature of the external forcing prevents the waves from over turning, and thus enables the development of steep sheardriven waves at large forcing. The onset of `frozen waves' occurs through a supercritical pitchfork bi furcation, with a nonmonotonic dependence on the viscosity ratio between the layers. Thus, increasing the viscosity of one of the uids often results in a more unstable interface. For larger values of the forcing parameters, a qualitative change in the wave growth takes place. Beyond a critical value of Wc (ratio of vibrational to gravity forces, proportional to the square of the forcing velocity), the experimental data collapses onto a single curve that exibits a linear depen dence on W. The evolution of the interface shape suggests a transition from gravity to capillary dominated waves, which is consistent with the wavelength reaching a minimum for W = Wc. For larger values of the forcing parameter, the twodimensional array of waves becomes unstable to threedimensional oscil latory waves through a subcritical bifurcation that exhibits a viscosity depen dence opposite to the primary instability. The existence of a global bifurcation point is investigated. 



Dec 17  Wed  Dr Dave Roscoe (Sheffield)  Applied Mathematics Colloquium  
14:00  Via Aristotle, Leibniz, Berkeley and Mach to necessarily largescale fractal structure in the Universe  
Hicks Lecture Theatre A  
Abstract: Abstract The claim that the large scale structure of the Universe is hierarchical has a very long history going back at least to Charlier's papers of the early 20th century. In recent years, the debate has centered largely on the works of Sylos Labini, Joyce, Pietronero and others, who have made the quantative claim that the large scale structure of the Universe is quasifractal with fractal dimension D=2. There is now a concensus that this is the case on medium scales, with the main debate revolving around what happens on the scales of the largest available modern surveys. Apart from the (essentially sociological) problem that their thesis is in absolute conflict with any concept of a Universe with an age of 14 billion years or, indeed, of any finite age, the major generic difficulty faced by the proponents of the hierarchical hypothesis is that, beyond hypothesizing the case (eg: Nottale's Scale Gravity), there is no obvious mechanism which would lead to large scale structure being nontrivially fractal. This talk describes a surprising resolution to this problem: in effect, the conflict between a homogeneous vs fractal universe is shown, at root, to be a conflict between two opposing views of ``space". One has its roots in ideas which can be traced from Democritus, through Newton to Einstein whilst the other has its roots in ideas which can be traced from Aristotle through Leibniz, and Berkeley to Mach. 



Feb 11  Wed  Philippa Browning (Manchester)  Applied Mathematics Colloquium  
14:00  Magnetic reconnection and the active solar corona  
Hicks Lecture Theatre A  
Abstract: Magnetic reconnection is a process by which the topology of magnetic fields can change, even in a highly conducting plasma, and which allows efficient dissipation of magnetic energy. One of the major outstanding problems in solar physics is to explain the high temperature of coronal plasma, and a strong candidate is the dissipation of free magnetic energy by magnetic reconnection. The physical process is then essentially the same as in solar flares  dramatic energyreleasing events in the solar atmosphere  and coronal heating can be viewed as a superposition of many small flarelike events. A key feature of solar flares is the presence of nonthermal high energy charged particles, and understanding the origin of these is a challenge for theorists. These high energy particles provide an important diagnostic of the magnetic reconnection process. After an introduction to coronal heating and solar flares, some recent work concerning acceleration of high energy particles by magnetic reconnection in solar flares will be presented. Also, a new model of coronal heating by reconnection, occurring during the nonlinear phase of kink instability of coronal loops, will be described. A theoretical model based on a minimum energy principle will be described, complemented by numerical simulations. 



Feb 18  Wed  Alice Courvoisier (Leeds)  Applied Mathematics Colloquium  
14:00  The Mean Field Approach to the Transport of Magnetic Fields  
Hicks Lecture Theatre A  
Abstract: The Sun's global magnetic field is believed to be the result of a `largescale dynamo', whereby inductive motions within the solar convection zone are able to generate and sustain a magnetic field on scales larger than their own. Mathematically, the evolution of the Sun's largescale magnetic field is conveniently described using mean field electrodynamics, a turbulence closure theory that relies on the parametrisation of smallscale effects by transport coefficients. Among these, the socalled `alphaeffect' is responsible for the growth of the mean magnetic field and will be the focus of my talk. Trying to understand how this coefficient depends on the turbulent motions within the solar plasma is tricky. Instead, we construct simpler models based on 2D motions for which the alphaeffect can be unambiguously determined and we study systematically how the spatial and temporal coherence of the flows influence it. I will start by introducing the alphaeffect from a phenomenological and mathematical point of view before presenting the results of our calculations and discussing their implications. 



Mar 4  Wed  Dr Takashi Sakajo (Hokkaido)  Applied Mathematics Colloquium  
14:00  Dynamics of pointvortices in multiply connected domains  
Hicks Lecture Theatre A  
Abstract: The motion of incompressible and inviscid flow is described by the twodimensional Euler equations. According to Kelvin's theorem, the circulation is conserved along the path of a fluid particle and thus the vorticity neither generates nor disappears during its evolution. Hence in order to solve the Euler equations, we have only to investigate the evolution of the nonzero vorticity domain at the initial moment. Based on this observation, we discretize the initial nonzero vorticity domain with a set of $N$ points, called point vortices, whose strengths are determined by the circulation around these points. Then we track the evolutions of the $N$ point vortices. This discretization method for the Euler equations is known as the vortex method, which reduces the Euler equations to a system of ordinary differential equations for the N point vortices. The present talk gives the equation of motion for $N$ point vortices in a bounded planar multiply connected domain inside the unit circle that contains many circular obstacles. The equation not only describes fundamental interactions between solid obstacles and fluids, but also contributes toward understanding of geophysical flows with many islands and artificial obstacles such as lakes, inland seas and coastal region. As an example, we consider the motion of a vortex dipole that consists of two point vortices with the unit strength of the opposite signs. When the multiply connected domain is symmetric with respect to the real axis, the motion of the vortex dipole is integrable for the initial configuration with the same symmetry. We investigate the integrable system in detail and discuss a nonintegrable motion of the vortex dipole without the reflectional symmetry. 



Mar 11  Wed  Youra Taroyan (Sheffield)  Applied Mathematics Colloquium  
14:00  Alfven instability in a compressible flow  
Hicks Lecture Theatre A  
Abstract: Abstract: Macroscopic instabilities have important energetic and dynamic consequences in space plasmas and laboratory devices. Well known examples include the current pinch, RayleighTaylor and shear flow instabilies which can be studied using the magnetohydrodynamic approach. A brief introduction will be followed by a presentation of a new magnetohydrodynamic instability. It will be demonstrated that linear incompressible Alfvenic disturbances can become exponentially amplified in compressible plasma flows. The instability does not require high flow speeds or shear. The amplification process is based on the mechanism of overreflection wellknown from previous studies of shear flows. A transparent stability criterion can be derived for a simple twolayer model. The instability may arise in both open and closed magnetic structures. An application to a solar coronal loop model with a siphon flow will be presented. Theoretical and observational implications of the Alfven instability will be discussed. 



Mar 25  Wed  Alan Hood (St Andrews)  Applied Mathematics Colloquium  
14:00  Heating the solar corona by nanoflares triggered by a kink instability  
Hicks Lecture Theatre A  
Abstract: The heating of solar coronal plasma to millions of degrees may be due to the superposition of many small energyreleasing events, known as nanoflares. Nanoflares dissipate magnetic energy through magnetic reconnection. It is proposed that heating is triggered by the onset of an ideal MHD instability, with energy release occurring in the nonlinear phase due to fast magnetic reconnection. Numerical simulations are used to investigate the energy release and the heating process. 



Apr 1  Wed  Steve Cowley (Director of the UKAEA, Culham Laboratory)  Applied Mathematics Colloquium  
14:00  Fusion  the Theoretical Challenge  
Hicks Lecture Theatre A  
Abstract: The international fusion experiment ITER will start operating in the south of France late in the next decade. This historic experiment will generate up to 500 megawatts of fusion power and provide a proof of principle for fusion energy. The theoretical description of fusion plasmas is very challenging and there are many unanswered questions. For example, the plasma is permeated with small scale turbulence that determines the confinement and the evolution. But, a full predictive model of the turbulence is still unavailable. I will outline the challenges and the progress that has been made. 



May 6  Wed  D Kurtz (Central Lancashire)  Applied Mathematics Colloquium  
14:00  Songs of the Stars  
Student Union Auditorium  


May 6  Wed  Mike Thompson (Sheffield)  Applied Mathematics Colloquium  
15:30  Helioseismology  
Student Union Auditorium  


May 6  Wed  Roger Webster (Sheffield)  Applied Mathematics Colloquium  
16:30  The tail of Pi  
Student Union Auditorium  


May 13  Wed  Jamie Douglas (Sheffield)  Applied Mathematics Colloquium  
14:00  An examination of the linear structure of the CUTIE plasma turbulence code  
Hicks Lecture Theatre A  


May 20  Wed  Carsten van de Bruck (Sheffield)  Applied Mathematics Colloquium  
14:00  Dark Energy in the Cosmos and the Laboratory  
Hicks Lecture Theatre A  
Abstract: According to observations the expansion of the universe seems to be speeding up, instead of slowing down. To explain this observation, one is either forced to introduce a new energy component (dark energy) with strange properties (such as negative pressure) or to change the laws of gravity. In this talk I will focus on the former possibility and describe theoretical models for dark energy and how to test these with cosmological observations or even in the laboratory. 



May 27  Wed  Alice Robinson (Sheffield)  Applied Mathematics Colloquium  
14:00  HF Radar and Wind turbine interaction in Liverpool Bay  
Hicks Lecture Theatre A  
Abstract: HF radar has become accepted over the last 50 years as a key tool in remote sensing of ocean currents and waves. It is favoured for excellent spatial and temporal coverage, and ease of access compared to more traditional buoy's and ADCP's. Data is available in near to real time and is well used by the maritime industry. The Proudman Oceanographic Laboratory operates a 13MHz HF WERA radar in Liverpool Bay. It is by nature sensitive to RFI and clutter which can degrade the accuracy and availability of the current and wave measurements. Liverpool Bay is undergoing extensive wind farm development which will present problems for any radar system due to their large radar cross sections. It is important to understand and mitigate any effects of the wind turbines on data accuracy and availability to achieve maximum performance from the HF radar. 



May 27  Wed  Andrew Newton (Sheffield)  Applied Mathematics Colloquium  
14:30  Numerical Investigation into sheared MHD turbulence  
Hicks Lecture Theatre A  
Abstract: Shear flows and magnetic fields are ubiquitous in astrophysical plasmas, playing a crucial role in turbulent transport. Here, we present the first numerical results of the suppression of magnetic diffusion by a shear flow in 2D MHD turbulence. For a very strong magnetic field, a new scaling regime of magnetic diffusion quenching by magnetic fields is found, with a stronger dependence on magnetic field strength compared to the previous result [1]. Furthermore, we show the first numerical evidence of enhanced transport due to the interaction between shear flow and magnetic field via resonances,which weakens the magnetic diffusion quenching. Similar results are also presented for momentum transport. These results highlight the importance of shear flows, (Alfven) waves, and resonances in understanding turbulent dissipation of magnetic fields. We discuss important implications of these results in turbulent magnetic reconnection and dynamos. [1] F. Cattaneo and S.I. Vainshtein, Astrophys. J. Lett. 376. L21 (1991) 



Jun 10  Wed  Christoffer Karoff (Birmingham)  Applied Mathematics Colloquium  
14:00  Flares, oscillations and cycles in the Sun and other stars  
Hicks Lecture Theatre A  
Abstract: We recently presented evidence of a strong correlation between the energy in the highfrequency part of the acoustic spectrum of the Sun and the solar Xray flux (Karoff and Kjeldsen, 2008). The discovery indicates that flares drive global oscillations in the Sun. If this indication turns out to be true we might be able to use the relation between flares and the energy in the highfrequency part of the acoustic spectrum to detect e.g. flares on the far side of the Sun and flares on other solarlike stars. The last possibility will be tested with observations from the nearly launched Kepler satellite as part of a larger project of sounding stellar cycles with asteroseismology. Asteroseismology can sound stellar cycles by studying periodic changes, in the amplitudes and frequencies of the oscillation modes in the stars, that follow the stellar cycles. By comparing these measurements with conventional groundbased chromospheric activity measurements we might be able to increase our understanding of the relation between the chromospheric changes and the changes in the oscillation modes. Also, asteroseismic measurements of e.g. the depth of the convection zone and internal differential rotation could enable us to answer the question: Are the stellar cycles driven at the top or the base of the convection zone? 



Sep 17  Thu  David Southwood (European Space Agency)  Applied Mathematics Colloquium  
14:00  Magnetism and Rotation at Saturn: the puzzles produced by the Cassini space mission  
LT7  
Abstract: The planet Saturn has for long had properties that defied expectations concerning planetary magnetism. A fast rotating gas giant, it was hardly surprising it had a dipolar magnetic field but it was surprising when early spacecraft flybys revealed that the dipole seemed almost perfectly aligned with the rotation axis. More surprises were to come. In the early nineties, measurements of the radio signals with the sensitive Ulysses spacecraft antenna revealed the Saturn kilometric radio signal was pulsing with a rate that varied slowly with time (~few times 0.1% change per year), drawing into doubt the longassumed link between radio pulsing and deep planetary rotation. Then, just before the arrival of Cassini reanalysis of the Voyager spacecraft magnetic data by a student at Imperial College showed there was a signature present in the Voyager spacecraft magnetic data at the planetary rotation period but one unambiguously associated with a source external to the planet! Each of the magnetic and radio oddities of Saturn was borne out once Cassini was in orbit but that was not the end of the surprises. Early in 2009, members of the Cassini radio team determined that the period of the radio pulsing which originated from the northern hemisphere differed from the period of the signal from the south. Subsequently, it has been firmly determined that the magnetic field measured above the northern Saturnian polar cap appears to be rotating at a rate 0.3% slower than the south. A review will be given of the present knowledge of the Saturn magnetic field and some speculations given on the implications of the results. 



Sep 30  Wed  Dave Roscoe (Sheffield)  Applied Mathematics Colloquium  
14:00  The conflict between realism and the scalar potential in electrodynamics  
Hicks Lecture Theatre A  


Oct 14  Wed  Edmund Chadwick (Salford)  Applied Mathematics Colloquium  
14:00  Oscillatory oseenlets  
LT A  
Abstract: Consider uniform flow past an oscillating body. Assume that the resulting farfield flow consists of both steady and time periodic components. The time periodic components can be decomposed into a Fourier expansion series of time harmonic components. The form of the steady component in terms of the steady oseenlet is wellknown. However, the timeharmonic components in terms of oscillatory oseenlet does not yet appear to be in the literature. 



Oct 21  Wed  Chutiphon Pukdeboon  Applied Mathematics Colloquium  
14:00  Optimal Sliding Mode Controllers for Attitude Tracking of Spacecraft  
LT A  
Abstract: This research studies two optimal sliding mode control laws using integral sliding mode control (ISM) for some spacecraft attitude tracking problems. Integral sliding mode control combining the first order sliding mode and optimal control is applied to quaternionbased spacecraft attitude tracking manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state dependent Riccati equation (SDRE) and Control Lyapunov function (CLF) approaches are used to solve the infinitetime nonlinear optimal problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify the usefulness of these controllers. 



Oct 21  Wed  Lawrence Chan (Sheffield)  Applied Mathematics Colloquium  
14:30  The relationship between concentration and its dissipation rate in turbulent dispersion  
LTA  
Abstract: To model the probability distribution of concentration in turbulent dispersion it is necessary to make closure assumptions. One aspect of interest in looking for reasonable closure assumptions is the relationship between concentration and its dissipation rate. Here it is assumed that Taylor's frozen turbulence hypothesis can be used to approximate the dissipation rate of concentration using the time derivative of concentration at a fixed point in space. I then use measurements of concentration from line source experiments in wind tunnel gridturbulence to examine the behaviour of the joint and marginal distributions of concentration and its dissipation rate. A simple stochastic process model is constructed for the concentration time series, from which these distributions are also derived , and then compared with those from the experiments. 



Oct 28  Wed  Elizabeth Winstanley (Sheffield)  Applied Mathematics Colloquium  
14:00  Black holes at the LHC  
LT A  
Abstract: Brane world models in string theory suggest that our universe is a slice, or 'brane', of a higherdimensional spacetime. In this talk we will discuss why one consequence of these models is that copious numbers of mini black holes may be formed by collisions at the Large Hadron Collider (LHC) at CERN. We will describe how these mini black holes are created, and what happens to them once they have been produced. In particular, we discuss why these black holes will not swallow up the entire Earth. 



Nov 11  Wed  Judith Wolf (POL)  Applied Mathematics Colloquium  
14:00  WaveCurrent Interaction in Liverpool Bay  
tbd  
Abstract: Waves in shallow water are strongly controlled by the water level as well as the wind forcing and can be refracted by strong current shear. Theory suggests that the mechanisms by which waves and the winddriven mean flow are generated are closely interconnected in the surface layer through the windstress. Also there is evidence that the bottom friction experienced by waves and nearbed currents are mutually enhanced. New theoretical work has been implemented in the POLCOMSWAM coupled hydrodynamic and wave model system to include the effect of 3D currents, allowing the vertical current shear to affect wave propagation and accounting for 3D radiation stress and Stokes' drift. We investigate the occurrence of typical and extreme wave conditions in Liverpool Bay and the adjacent estuaries and assess which areas may be prone to flooding and erosion due to waves in combination with high water levels. This is a macrotidal environment prone to storm surges and moderate storm waves with occasional flooding in lowlying areas. Data from the POL Coastal Observatory, including the HF radar system which simultaneously measures waves and currents, have been employed to validate wave, tide and surge models for this area. We have also used the SWAN model in oneway coupled mode in comparison with the POLCOMSWAM model to investigate the magnitude of interactions between waves, tides and surges. Here we review the physical mechanisms, their effects, and the implications for our understanding of coastal processes, and discuss where further development is still needed in shallow water wave models. 



Nov 18  Wed  Colin Steele (Manchester)  Applied Mathematics Colloquium  
14:00  Tadpoles, Horseshoes and the Trojan Wars: the restricted 3body problem in the Solar System  
LT A  
Abstract: The twobody problem in Celestial Mechanics has been solved to give orbits in the form of conic sections (ellipses etc.). The introduction of a third body, however, disallows any algebraic solutions and numerical work is required in order to follow the motion of the objects. The restricted three body problem assumes that one of the three objects is of negligible mass i.e. the third body responds to the gravitational attraction of the first two bodies but does not itself influence the motion of these first two bodies. In the solar system, with there being a wide range of masses of Sun, planets, satellites, minor planets, comets etc, this restricted threebody problem is certainly relevant. Under the restricted threebody problem, the third (light) body can be followed through a wide variety of situations. Without retracting from dynamical solutions, this talk will concentrate on cases close to equilibria and/or involving cycles. Such cases will be modelled including an analysis of the linear stability and a numerical simulation. Particular real cases in the solar system involve minor planets with orbits affected by Jupiter and the motions of some of the inner satellites of Saturn. 



Nov 25  Wed  Alan Zinober (Sheffield)  Applied Mathematics Colloquium  
14:00  A New NonClassical Class of Optimal Variational Problems  
LT A  
Abstract: The Calculus of Variations was developed in the 18th Century and forms a basic foundation of modern optimal (maximising or minimising) variational problems, nowadays often called optimal control. An introduction to the Calculus of Variations with some sample examples will be presented. This will include the EulerLagrange and Hamiltonian formulation together with the associated final boundary value conditions. Maple or the numerical shooting method can be used to solve the resulting Two Point Boundary Value Problem (TPBVP), a set of differential equations. A new nonclassical class of variational problems has been motivated by recent research on the nonlinear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the Calculus of Variations (CoV) or Optimal Control. However, the state value at the final fixed time, $y(T)$, is a priori\/ unknown and the integrand to be maximised is also a function of the unknown $y(T)$. This is a nonstandard CoV problem that has not been studied before. New final value costate boundary conditions will be presented for this CoV problem and some results will be shown. 



Dec 9  Wed  David Pontin (Dundee)  Applied Mathematics Colloquium  
14:00  Magnetic reconnection in three dimensions  
LT A  
Abstract: Magnetic reconnection is of fundamental importance in many plasmas, for example the Solar corona. It plays a role in heating the corona and is thought to be responsible for many dynamic phenomena observed there. The magnetic field in the corona has a highly complex structure that is clearly threedimensional. Furthermore, recent advances in theory and computational experiments have shown that the nature of reconnection in 3D is fundamentally different from 2D models. Here we discuss the underlying theory of threedimensional magnetic reconnection. We also review a selection of new 3D reconnection models that illustrate the current state of the art, as well as highlighting the complexity of the process in complicated 3D magnetic fields. 



Dec 16  Wed  Yi Li (Sheffield)  Applied Mathematics Colloquium  
14:00  tbd  
LT A  


Jan 1  Fri  Alice Courvoisier (Leeds)  Applied Mathematics Colloquium  
14:00  The Mean Field Approach to the Transport of Magnetic Fields  
Hicks Lecture Theatre A  


Feb 10  Wed  Mitchell Berger (Exeter)  Applied Mathematics Colloquium  
14:00  Applications of Braid Theory  
LTA  
Abstract: Two great puzzles in solar astrophysics concern the source of coronal heating and the distribution of solar flares. The atmosphere of the sun is heated to one million degrees or more, possibly by swarms of tiny flares. These tiny flares could be consequences of the braiding of magnetic field lines. Reconnection between braided threads of magnetic flux can release energy stored in the braid. The larger flares exhibit a power law energy distribution. Several authors have suggested that a selforganization process in the solar magnetic field could lead to such a distribution. Here we show how reconnection of braided lines can organize the small scale structure of the field, leading to power law energy release. An application of braids to mixing theory will also be discussed. 



Feb 17  Wed  Martin Whittle (SheffieldSheffield)  Applied Mathematics Colloquium  
14:00  Dissipative Particle Dynamics Simulation of Colloids  
LTA  
Abstract: Clearing legacy radioactive sludge from cooling ponds is a priority for the nuclear industry in its current renaissance. To develop and optimise the necessary machinery it is relying heavily on simulation to model flow and part of this programme involves the incorporation of mesoscopic simulations directed at the rheology of colloids. Here we look at one such approach using Dissipative Particle Dynamics (DPD). DPD was developed in the 1990's and is one of a steadily increasing number of mesoscopic simulation techniques that has been used to model complex fluids and flows in microchannels. Here we discuss methods of modelling colloids using DPD and compare the results of simulations with some other approaches. Although DPD has an inbuilt thermostat this becomes ineffective at high shear rates and we will explore some methods of applying auxiliary thermostatting for nonequilibrium simulations. The results display several classic features of colloidal rheology including evidence of pseudoplasticity at high volume fraction. Nevertheless, despite the advantages of simplicity, the model still presents a number of challenges that will be discussed. 



Mar 3  Wed  Marina Skender (Leuven)  Applied Mathematics Colloquium  
14:00  Quasiequlibrium current sheet and the onset of impulsive bursty reconnection  
LT A  
Abstract: A twodimensional reconnecting current sheet is studied numerically in the MHD approach. Different simulation setups are employed in order to follow the evolution of the formed current sheet in diverse configurations: Two types of initial equilibria, Harris and forcefree, two types of boundary conditions, periodic and open, with uniform and nonuniform grid set, respectively. All the simulated cases are found to exhibit qualitatively the same behavior in which a current sheet evolves slowly through a series of quasiequilibria; eventually it fragments and enters a phase of fast impulsive bursty reconnection. In order to gain more insight on the nature and characteristics of the instability taking place, physical characteristics of the simulated current sheet are related to its geometrical properties. The aspect ratio of the current sheet is observed to increase slowly in time up to a maximum value at which it fragments. Additional turbulence introduced to the system is shown to exhibit the same qualitative steps, but with the sooner onset of the fragmentation and at smaller aspect ratio. 



Mar 17  Wed  Michael Proctor  Applied Mathematics Colloquium  
14:00  Fully consistent mean field MHD  
tbd  
Abstract: We consider the linear stability of twodimensional nonlinear magnetohydrodynamic basic states to longwavelength threedimensional perturbations. Following the work of Hughes and Proctor the 2D basic states are obtained from a specific forcing function in the presence of an initially uniform mean field of strength B. By extending to the nonlinear regime the kinematic analysis of Roberts, we show that it is possible to predict the growth rate of these perturbations by applying mean field theory to both the momentum and the induction equations. If B = 0, these equations decouple and largescale magnetic and velocity perturbations may grow via the kinematic effect and the AKA instability respectively. However, if the imposed field is nonzero, the momentum and induction equations are coupled by the Lorentz force; in this case, we show that four transport tensors are now necessary to determine the growth rate of the perturbations. We illustrate these situations by numerical examples; in particular, we show that a mean field description of the nonlinear regime based solely on a quenched coefficient is incorrect. 



Apr 21  Wed  Tatiana Talipova (Nizhny Novgorod, Russia )  Applied Mathematics Colloquium  
14:00  Avalanche and Landslide Dynamics  
LT A  
Abstract: The SavageHutter model is applied to describe the gravity driven shallowwater flows in inclined channels of paraboliclike shapes modeling the avalanches moved in the mountain valleys or the landslide motions in underwater canyons. The Coulomb (sliding) friction term is included in model. The Riemann invariants are found for this hyperbolic system. Several analytical solutions described the nonlinear dynamics of avalanche are obtained: Riemann wave, dambreak problem, selfsimilar solutions and the CarrierGreenspanlike solutions. Some of them extend the known solution for inclined plate (1D geometry). They can be used to test the 2D numerical models of debris volcano avalanches, mountain flanks and landslides in submarine continental slopes. 



Apr 28  Wed  Francesca Ticconi (DLR  German Aerospace Center)  Applied Mathematics Colloquium  
14:00  SAR Polarimetry  
LT A  
Abstract: The direction of the electric field vector, describing an ellipse in a plane transverse to propagation, plays an essential role in the interaction of electromagnetic waves with material bodies and the propagation medium. This polarisation transformation behaviour is denoted as "Polarimetry" in radar and synthetic aperture radar (SAR) sensing and imaging. A fully polarimetric radar transmits two orthogonal polarisations and receives the backscattered wave on the same two polarisations. This results in four received channels where both the amplitude and relative phase are measured. The measured signals in these four channels represent all the information needed to measure the polarimetric scattering properties of the target. Such information is necessary for the estimation of soil moisture and surface roughness parameters, since a major problem in this estimation is the separation of soil moisture and surface roughness contributions to the backscattered radar signal. A set of methods known as target decomposition theorems have been developed for the interpretation of polarimetric SAR data and two different approaches will be shown based respectively on a physicalbased model decomposition and on the eigenvectorbased target decomposition. For the soil moisture content retrieval, an inversion model, based on this latter decomposition, has been applied on Lband airborne SAR data and the result of the inversion will be shown. 



May 5  Wed  Richard Morton (Sheffield)  Applied Mathematics Colloquium  
14:00  Oscillations in solar plasma with variable background  
LT A  
Abstract: The solar atmospheric plasma is an extremely dynamic medium threaded by a complex magnetic field that is constantly subject to heating and cooling processes. The magnetic field provides the foundations for a wide variety of plasma fine structure in the solar atmosphere, e.g. coronal loops, coronal holes, prominences. Each of these features in the solar atmosphere can support an array of magnetohydrodynamic (MHD) oscillatory modes. We present here a first study of the propagation of MHD waves in a magnetised plasma environment that is cooling due to radiation. Previous investigations have concentrated on the affect of radiation on the perturbations only. An approximate radiation function that has the form of Newtonian cooling is used for the sake of simplicity. We find that the cooling of the plasma leads to a time dependent frequency of MHD waves (or oscillations) and causes both damping and amplification of these periodic phenomena. This result could have important implications for various aspects of magnetoseismology in the solar atmosphere. 



May 12  Wed  Vladimir Vladimirov (York)  Applied Mathematics Colloquium  
14:00  
LT A  


Oct 13  Wed  Jamie Douglas (Sheffield)  Applied Mathematics Colloquium  
14:00  Linear eigenspectra in tokamak fusion plasmas  
tbd  
Abstract: Nuclear fusion has become one of the "hot" topics in recent years, with the likes of Prof. Stephen Hawking and Prof. Brian Cox offering their own perspective on the issue (see below). Although many of the applied mathematical and theoretical physics aspects of maintaining a fusion plasma are well understood, some aspects of linear theory remain unexplored. Using the CUTIE tokamak fusion plasma simulation code developed at the Culham Science Centre, which has successfully reproduced many nonlinear features of tokamak plasmas, we are now investigating the linear properties of these plasmas. This seminar will cover an introduction to nuclear fusion, tokamak reactors and the CUTIE code, before outlining some of the linear modes we have investigated using a linear version of the CUTIE code which employs two new techniques for finding linear modes: the resolvent eigenvalue technique which reveals the entire linear spectrum; and the nonlinearisation technique for finding the dominant linear mode. \par Prof. Stephen Hawking, quoted in the Guardian newspaper 11th September 2010: "Nuclear fusion...would provide an inexhaustible supply of energy without pollution or global warming. Many badly needed goals, like fusion and cancer cures, would be achieved much sooner if we invested more." \par Prof. Brian Cox quoted in the same article: "The provision of clean energy is of overwhelming importance. What frustrates me is that we know how to do [fusion] as physicists, and how it works. It is an engineering solution that is within our grasp. I think the most important practical problem, which may be more of an engineering challenge than a scientific one, is to build economically viable nuclear fusion power stations. If we haven't dealt with our world's increasing appetite for energy by the end of this century, I think we will be in very deep trouble indeed." 



Oct 20  Wed  Peter Haynes (Cambridge)  Applied Mathematics Colloquium  
14:00  What controls the rate of mixing of passive scalars in smooth flows?  
LTA  
Abstract: Stirring and mixing of chemical and biological species is an important in atmospheric and oceanic flows and in many other contexts. Some aspects of stirring and mixing can be captured by 'Lagrangian stretching theories' which essentially consider evolution in small fluid elements in which the flow may be approximated as a linear function of space coordinates, but time varying. This is a great simplification to solving the full advectiondiffusion equation and potentially gives a practical approach to calculation. It also motivates an examination of whether 'Lagrangian stretching theories' are always correct. Solution of a suitable idealised problem shows that Lagrangian stretching theories make correct predictions (for an initial value problem) if the advection diffusion operator, which always has a continuous spectrum in the limit of vanishing diffusivity, has no discrete eigenvalues. 



Nov 3  Wed  Joel Weller (Sheffield)  Applied Mathematics Colloquium  
14:00  Cosmological inflation with a DiracBornInfeld field  
LTA  
Abstract: Our understanding of the cosmos is underpinned by precision observations on very large and very small scales, and theoretical models must not only be wellmotivated but also consistent with the wealth of data available. The inflationary paradigm, in which the universe experiences a period of rapid expansion early in its history, stands as a crowning example of this principle, in that it leaves observable traces in the distribution of structure on large scales and the cosmic microwave background (CMB) radiation that can be explained in terms of the microscopic quantum fluctuations of the field(s) driving inflation. The availability of high precision observational data in cosmology means that it is possible to go beyond the simple descriptions of cosmic inflation in which the expansion is driven by a single scalar field. One set of models of particular interest involve the DiracBornInfeld (DBI) action, arising in string cosmology, in which the dynamics of the field are affected by a speed limit in a manner akin to special relativity. In this talk, I will discuss how the problems faced by the standard hot big bang model are resolved by introducing an inflationary period, and describe the mathematical treatment of the standard and DBI scenarios. 



Nov 10  Wed  Ashley Willis (Sheffield)  Applied Mathematics Colloquium  
14:00  Charting the phasespace of transitional fluid flow  
LTA  
Abstract: In 1883, Reynolds observed a transition from laminar to turbulent flow in a pipe. Although more than 125 years have passed, fundamental questions on the nature of this transition remain. All evidence to date suggests that laminar pipe flow (Hagen Poiseuille flow) is linearly stable, but it has only been proved rigorously for special cases. At the modest flow rates examined by Reynolds, it is now clear the finite amplitude disturbances to the laminar are required to trigger the transition to turbulence. Recently, a host of finiteamplitude solutions for pipe flow has been discovered (Faisst & Eckhart 2004; Pringle, Duguet & Kerswell 2008). While a few have been shown to be embedded within the 'laminarturbulent boundary', the role of the vast majority of solutions is yet to be determined. In this talk, evidence for the appearance of travelling waves during transition is presented, plus a method for projection of the underlying dynamics. 



Nov 17  Wed  Edmund Ryan (Sheffield)  Applied Mathematics Colloquium  
14:00  Improving estimates of atmosphereland carbon flux by assimilating satellite observations of biomass  
LTA  
Abstract: There are large uncertainties in estimates of the atmosphereland exchange of carbon by natural processes (photosynthesis and respiration). Accurate estimates are crucial for better understanding of the global carbon cycle and climate modelling. Traditonally the models we use to get these estimates are tested for their ability to reproduce reallife processes by comparing model output with observations. However, a more useful way of using the observations, which takes into account the observational error, is to assimilate the observations into the model. This is called Data Assimilation or DA. We can use DA to estimate the states of the system or to estimate some or all of the parameters to the model. While DA has been generally performed on small models, some recent work is using it on the larger ones for example JULES (Joint Uk Land Surface Simulator) which is the land part to the climate model used by the met office. However, up till now, DA has been mainly carried out using ground observations. In this PhD, I am exploring the value of using satellite observations instead, due to the major advantages such observations have over ground based ones (ie more frequent observations and more observations on the spatial scale). 



Nov 24  Wed  Nils Mole (Sheffield)  Applied Mathematics Colloquium  
14:00  Modelling the moments of the expected mass fraction for a line source in decaying grid turbulence  
LTA  
Abstract: To assess hazards resulting from dispersing clouds or plumes of toxic or flammable gases, one would like to know the probability density function (pdf) of concentration, including its dependence on space and time. The expected mass fraction (EMF) provides a spaceintegrated equivalent of the pdf. Here I develop a model for the moments of the EMF, which I apply to the particular case of a plume dispersing from a steady line source in decaying grid turbulence. The results will be compared with measurements from some laboratory experiments in wind and water tunnels. 



Jan 1  Sat  Ian (Waikato)  Applied Mathematics Colloquium  
14:00  Exact models for magnetic reconnection in coronal plasmas  
tbd  
Abstract: An introduction to magnetic reconnection in coronal plasmas is given. Some exact analytic solutions are presented that describe recent 'fan' and 'spine' reconnection models. 



Jan 1  Sat  Ata S Sharma (Sheffield)  Applied Mathematics Colloquium  
14:00  Predicting structure in turbulence  
tbd  
Abstract: *Predicting structure in turbulence * How to find a simple model that predicts the important structural and statistical features of turbulence is a central unsolved problem in classical physics. Most commonly found flows are turbulent, for instance flow of air over an aeroplane wing or water past a ship's hull, flow of oil through an transcontinental pipeline, or the movement of the atmosphere. All these flows experience chaotic threedimensional motion, but nonetheless show persistent, repeating structure. This talk will cover significant new advances, involving the application of systemstheoretic ideas to the equations governing turbulence, which predict these structures. The computationally cheap approach explains and predicts structures and velocity statistics that have previously been identified only in experiments or by direct numerical simulation. Short Biography: After graduating as a physicist from UCL, Dr Sharma completed his doctoral thesis in control engineering at Imperial College, London on the modelling and control of tokamak nuclear fusion reactors. Following two years in industry, he returned to academia as a postdoc to work on fluid flow control, and was then awarded an Imperial College Junior Research Fellowship in that area. Dr Sharma joined ACSE as a lecturer in July. 



Jan 26  Wed  Phil Livermore (Leeds)  Applied Mathematics Colloquium  
14:00  Inviscid dynamos: evolving a magnetic field subject to a continuum of constraints  
LT A  
Abstract: The geomagnetic field is generated in Earth's liquid core by a dynamo process, a complex nonlinear system described by a collection of partial differential equations. In the last few decades, running numerical models of the geodynamo has become fairly widespread, although these are so complex and run with parameters so many orders of magnitude different from Earth's core that there remains large gap between the current state of the art and models that are defensibly realistic. Since 1963 it has been known how to model the slow time evolution of the geodynamo system with zero viscosity, arguably one of the the simplest realistic descriptions of the system. However, this limit has associated a continuum of constraints that the magnetic field must satisfy, a stumbling block that has hindered progress on this front for 48 years. In this talk, I shall summarise recent work that allows, on the adoption of a suitable numerical method, this continuum of constraints to collapse to a finite number and therefore admits the possibility of numerical models that evolve whilst simultaneously satisfying these constraints. I will describe some basic time evolution models that exploit these developments. 



Feb 2  Wed  Sandra Chapman (Warwick)  Applied Mathematics Colloquium  
14:00  Quantifying and understanding the statistical properties of turbulence  what we have learned from the solar wind  
LTA  
Abstract: The solar wind exhibits fluctuations over a broad range of timescales characteristic of magnetohydrodynamic (MHD) turbulence evolving in the presence of structures of coronal origin. In situ spacecraft observations of plasma parameters are at minute (or below) resolution for intervals spanning the solar cycle and provide a large number of samples for statistical studies. The magnetic field power spectrum typically has an inertial range of turbulence over several orders of magnitude with approximately Kolmogorov power law and at lower frequencies, an approximately '1/f' energy containing range believed to be of direct coronal origin and at higher frequencies, a kinetic range of turbulence. With a magnetic Reynolds number estimated to be of order 10^5 the solar wind provides a unique 'laboratory' for the study of MHD turbulence, and dissipation processes. Recent results however also suggest that in the ecliptic, signatures of scaling which are of direct coronal origin are embedded in the inertial range of turbulence of the solar wind, and as a consequence these show solar cycle and latitudinal dependence. At high latitudes, in uninterrupted streams of fast solar wind flow, and with recent high cadence observations of coronal structures there is the opportunity to study evolving finite range turbulence which can also inform our understanding of turbulence in boundary layers. This talk will survey quantitative statistical methods that can be used to distinguish these distinct physical processes in the solar wind and offer connections to a wider class of nonlinear systems approaches. 



Feb 9  Wed  Jesse Andries (Monash)  Applied Mathematics Colloquium  
14:00  Some theoretical considerations on magnetohydrodynamical waves in shear flows  
LT A  
Abstract: The theoretical foundation of the study of linear MHD waves and instabilities in stationary equilibria, is much less developed than its counterpart in static equilibria. For static equilibria a sound theory is based on the eigenmodes of a selfadjoint force operator, which can be equivalently expressed by a variational principle (RayleighRitz) for the quadratic potential energy functional. Such an approach seems impossible for stationary equilibria. While some relations between the eigenfrequencies and a number of quadratic functionals have long been known (Frieman and Rotenberg, 1960), those do not straightforwardly allow to construct a corresponding variational principle. Attempts so far involved the generalisation to a bilinear functional (where the energy interpretation is absent), and the associated doubling of the dimensionality of the variational space, or the assumption of some symmetry in the equilibrium. We will discuss the central problem and show that, contrary to what is often believed and claimed, many results do generalise to stationary media (shear flows). In particular, we focus on the clear interpretation of the energy functionals as they appear in a generalised variation principle that we formulated recently (Andries 2010, Physics of Plasmas, 17, 2106). 



Feb 16  Wed  Eduard Kontar (Glasgow)  Applied Mathematics Colloquium  
14:00  
LTA  


Mar 2  Wed  Erwin Verwichte (Warwick)  Applied Mathematics Colloquium  
14:00  Observations of MHD wave activity in the solar corona  
LTA  
Abstract: The advent of extremeultraviolet and xray imagers and spectrometers in the last decade has brought overwhelming observational evidence of magnetohydrodynamic wave activity in the solar corona. Such waves carry in their signatures valuable information about the structures along which they travel and has given birth to the field of coronal seismology that aims to extract this information. In this seminar I will highlight some of the key discoveries and discuss the nature of these waves, taking examples from established and new instruments such as TRACE, Hinode and SDO. 



Mar 16  Wed  Ineke de Moortel (St Andrews)  Applied Mathematics Colloquium  
14:00  Coupled Kink and Alfvén Mode Propagation in the Solar Corona  
LTA  
Abstract: Observations have revealed ubiquitous transverse velocity perturbation waves propagating in the solar corona. We perform 3D numerical simulations of broadband footpointdriven transverse waves propagating in a low Î² plasma. When density structuring is present, mode coupling in inhomogeneous regions leads to very efficient coupling of the kink mode to the Alfvén mode. The frequencydependent decay of the propagating kink wave is observed as energy is transferred to the local Alfvén mode. For all density structures considered, modest changes in density were capable of efficiently converting energy from the driving footpoint motion to localised Alfvén modes. Hence, transverse footpoint motions at the base of the corona will transfer energy to Alfvén modes in the corona. 



Mar 23  Wed  Christian Beck (Queen Mary, UL)  Applied Mathematics Colloquium  
14:00  Superstatistical techniques for complex systems with time scale separation  
tbd  
Abstract: Many complex driven nonequilibrium systems are effectively described by a superposition of several statistics on different time scales, in short a `superstatistics'. Superstatistical techniques have recently been successfully applied to a variety of complex systems, for example turbulence (Lagrangian, Eulerian, environmental), hydroclimatic fluctuations, pattern formation, mathematical finance, traffic delay statistics, random matrix theory, networks, scattering processes in high energy physics, as well as medical and biological applications. In this talk I will first give a general overview of this concept and its recent applications, and then discuss three examples is somewhat more detail: Train delay statistics on the British railway network, accelerations of tracer particles in turbulent flows, and cancer survival statistics. 



May 4  Wed  James Douglas (Sheffield)  Applied Mathematics Colloquium  
14:00  Linear stability analysis of non ideal tokamak plasma fluid models  
LT A  
Abstract: As the price of energy increases in an age of austerity, it is proper to invest in alternate energy sources. A tokamak is a magnetic confinement fusion device which seeks to maintain a burning plasma at temperatures comparable to the core of the Sun, thus harnessing the energy released during fusion reactions. Although many of the applied mathematical and theoretical physics aspects of maintaining a fusion plasma are well understood, some aspects of linear theory remain unexplored. Using the CUTIE tokamak fusion plasma simulation code developed at the Culham Science Centre, which has successfully reproduced many nonlinear features of tokamak plasmas, a thorough investigation of the linear properties of these plasmas is presented. This investigation includes reduced models, such as RMHD, and pertinent extensions covering the role of advective flows and toroidal curvature on linear stability. An introduction to nuclear fusion, tokamak reactors and the CUTIE code is discussed, before outlining some of the linear modes we have investigated using a linear version of the CUTIE code. This linear code employs two powerful new techniques for finding linear modes: the resolvent eigenvalue technique which reveals the entire linear spectrum; and the nonlinearisation technique for finding the dominant linear mode. 



May 11  Wed  Inigo Arregui (Universitat de les Illes Balears, Palma de Mallorca, Spain)  Applied Mathematics Colloquium  
14:00  Prominence thread oscillations: seismology and dynamics of transverse kink waves  
LT A  
Abstract: Quiescent prominences are large clouds of plasma suspended against gravity in the solar atmosphere, by forces thought to be of magnetic origin. High resolution observations show that prominences consist of fine threads. Transverse oscillations in prominence threads and their temporal damping are a common feature in a number of recent observations obtained by, e.g., the Swedish Solar Telescope (SST) in La Palma. Consider cylindrically symmetric magnetic flux tubes in the zero plasma beta approximation. Physical models for prominence threads can then be constructed by specifying particular density distributions. By analyzing the oscillatory properties of transverse kink waves in rather general twodimensional density models, we provide insight to both seismology of transversely oscillating structures and to the physics of resonantly damped kink modes. Concerning the inversion of physical parameters using transverse kink waves, we find that the details of longitudinal density structuring have a significant impact on the inferred values of the AlfvÃ©n speed in those structures, while they are almost irrelevant when determining their transverse density structuring. On the subject of the physics of resonantly damped kink modes, we show the potential of combining the information from the spatial distribution of eigenfunctions together with energy arguments to better understand the energy transfer between kink waves of global character and oscillations at small spatial scales around the resonance. A detailed examination of the timeaveraged Poynting flux in a twodimensional region around the resonance shows how and where energy is fed into the resonance and the way it is thereafter distributed along the magnetic field lines. The use of the governing equations in the form of energy conservation laws and the computation of the different terms informs us about the spatial distribution of relevant quantities, such as the kinetic and magnetic energies, the generated current densities, and the associated resistive heating. The method and results here reported are also applicable to coronal loops and their transverse oscillations. 



May 18  Wed  Ben Shepherd (Sheffield)  Applied Mathematics Colloquium  
14:00  Holographic Superconductivity  
LT A  
Abstract: Superconductors are materials which have zero electrical resistance below a certain critical temperature. However, there is no theory in condensed matter physics to describe the best superconductors, i.e. those with the highest critical temperature. The AdS/CFT correspondence provides a way to investigate these high temperature superconductors, in which we consider a higher dimensional gravitational theory with a black hole in anti de Sitter (AdS) space. The theory describing our superconductor is then given by the boundary of AdS. After introducing superconductivity and the AdS/CFT correspondence, we will show that a planar black hole with an SU(N) gauge field gives the correct properties associated with high temperature superconductors. 



Jun 8  Wed  Georg Struth (Sheffield)  Applied Mathematics Colloquium  
14:00  Algebraic Methods for Developing and Analysing Computing Systems  
LT A  
Abstract: Programs without bugs is one of the grand ideals of computer science. It has stimulated decades of research, resulted in a number of Turing Awards, and has significant, and increasing, societal and economic relevance. It is widely accepted that mathematical methods are essential for analysing computing systems, and that new methods need to be developed to deal with their discrete, often nondeterministic nature. In turn, it has been claimed that these methods are increasingly relevant to other disciplines, such as physics, biology or economics. In this talk I will introduce variants of semirings, iteration algebras and relation algebras as fundamental structures of computing which are applicable to a variety of program analysis tasks. I will show how such algebraic methods can be used for proving theorems about programs that appear, for instance, in compiler optimisation, and how they provide frameworks in which the correctness of programs can be analysed. I will demonstrate that automated theorem provers and counterexample generators are instrumental both for program analysis and the development of algebraic methods. I will show how decision procedures and representation theorems for (fragments) of these algebras further support program analysis tasks. If time permits I will report on ongoing work on algebraic methods for concurrent and probabilistic systems, and mention some mathematically interesting open questions in these areas. 



Oct 12  Wed  Pieter Kok (Sheffield)  Applied Mathematics Colloquium  
14:00  The ultimate limits to quantum measurements  
LT10  
Abstract: Precision measurements are the cornerstone of the scientific enterprise, and whenever new measurement techniques have become available, new natural phenomena were discovered. One important question is therefore what the ultimate limits to precision measurements are. In particular, what is the best precision we can achieve with a particular quantum mechanical setup given a certain amount of resources? Traditionally, this question is answered in quantum mechanics by the socalled Heisenberg limit. However, there have been recent claims that this limit is broken. We demonstrate that the Heisenberg limit is in fact optimal for all parameter estimation procedures in quantum metrology, but it requires careful consideration as to which resource is appropriate for expressing the scaling behaviour of the precision. 



Oct 19  Wed  John Billingham (Nottingham)  Applied Mathematics Colloquium  
14:00  How do droplets climb up a vibrating hill?  
LT10  
Abstract: Recent experiments by Phillipe Brunet have shown that when a millimetric droplet of fluid is placed on a slope that strongly vibrates vertically it can climb up the slope. In this talk I will present some shallow water models for this phenomenon. I will begin with a model that includes just surface tension and the applied acceleration, but which can be solved numerically in its threedimensional form. This model cannot capture the phenomenon. I will then include the effect of inertia in a twodimensional model. The interaction of swaying and spreading modes of oscillation can cause the droplet to rise. However, we find that the behaviour of the moving contact lines is not realistic. Finally, we include the effect of viscosity, and model the moving contact lines more carefully. 



Oct 26  Wed  Rekha Jain (Sheffield)  Applied Mathematics Colloquium  
14:00  Absorption and scattering of acoustic waves by thin magnetic flux tubes in a gravitationally stratified atmosphere  
LT10  
Abstract: The sun's acoustic oscillations, pmodes, are observed to have more than half of their power absorbed by sunspots and almost 2030% by plages. Sunspots are also observed to have strong phase shifts but plages lack measurable phase shifts. The magnetic field within these structures is complex and highly structured which makes helioseismic observations troublesome to interpret and model. We study the propagation of acoustic waves through regions of plage, modeling the magnetic field therein as a collection of thin flux tubes. In this talk, I will present the background to this problem followed by the computation of the absorption and scattering coefficients arising from a single, axisymmetric magnetic tube. Implications for the measured absorption and phase shifts will also be discussed. 



Nov 2  Wed  William George (Chalmers)  Applied Mathematics Colloquium  
14:00  Reconsidering Kolmogov for Nonstationary Turbulent Flows  
LT10  
Abstract: One of the most important contributions to turbulence over the past century was the theory of Kolmogorov 1941. Since its introduction to the western world by Batchelor in 1946 it has dominated turbulence, both the interpretation of experiments and the development of turbulence models and scaling laws. It has been commonly assumed since the tidal channel measurements of Grant et al. 1961 that experiments have been uniformly supportive and that the coefficients are universal. Unfortunately the most important parameter, the turbulent dissipation, can almost never be measured directly and quite frequently is determined by `fitting' the measured data to the `established' results. Thus the `perfect' agreement is largely illusory, and in fact there is a considerable disagreement about what the `universal' constants are (or even if they are universal). Also it is seldom pointed out that almost all of the experiments cited are in statistical equilibrium, so that Kolmogorov's crucial first hypothesis of `local' equilibrium is statisfied identically. Thus none of these experiments can be regarded as a test of its generality. Worse, recent experiments and DNS in nonstationary turbulence show significant departures from Kolmolgorov behavior. These nonstationary homogeneous experiments are, however, consistent with the equilibrium similarity theory of George 1992 for these flows. So together the nonstationary theory and experiments together provide some confidence in these iconoclastic results. Therefore they present by counterexample a challenge to the Kolmogorovbased ideas for nonstationary flows, suggesting that we need to modify at least one of our fundamental beliefs. 



Nov 9  Wed  Johan Anderson (Chalmers)  Applied Mathematics Colloquium  
14:00  
LT10  


Nov 16  Wed  Chuong Van Tran (St Andrews)  Applied Mathematics Colloquium  
14:00  A dynamical systems approach to fluid turbulence  
LT10  
Abstract: This seminar presents an analytic approach to fluid turbulence as an alternative to Kolmogorov's phenomenology. The new approach uses basic elements and concepts in dynamical systems theory and applies to a variety of fluid models, allowing us to recover key predictions made by the classical method. These include the number of degrees of freedom, the dissipation wavenumber and the exponent of the powerlaw energy spectrum of the inertial range. The twodimensional surface quasigeostrophic and magnetohydrodynamic systems are used as illustrative examples, with the theoretical predictions corroborated by numerical results. 



Nov 23  Wed  Zhivko Stoyanov (Reading)  Applied Mathematics Colloquium  
14:15  Communicability in the brain  
LT10  
Abstract: Given a network of relationships between people, we naturally want to find the "big players" in the network. Furthermore, with the constant progress in technology, we are now able to capture the interactions between people in real time. We no longer have a static, but an evolving network of relationships. So we can now trace the flow of information on the network (passing of rumours, etc.). Therefore the term "big players" could have different meanings: it might mean people who are great broadcasters, but it could also mean people who are great receivers. Marketing companies, for example, might want to find the most influential people in the network, while the MoD could be interested in approaching the people with most information about the network. I will be interested in both: broadcasters and receivers, but instead of a social network, I shall be looking at the brain. In this talk I will suggest a simple way of using fMRI data to represent the brain as an evolving network. Then, using Network Theory and, in particular, a recently introduced notion of communicability, I will show a way to calculate the communicability score of each voxel (the 3D version of a pixel) in the brain. This score, which might be seen as a possible generalisation of PageRank, determines the extent to which a particular voxel is a broadcaster or a receiver. However, in our case there are around one million voxels in the brain. So there is little use in knowing the score for each voxel. Therefore, I shall discuss our attempt at summarising this information using the Discrete Fourier Transform. Furthermore, once we have "compressed" the communicability of the brain, I will try to discriminate between brains with a clinically diagnosed condition and healthy brains, using simple tools from Bayesian Statistics. 



Dec 14  Wed  Stephen Coombes (Nottingham)  Applied Mathematics Colloquium  
14:00  Patterns and waves in cortical models  
LT10  
Abstract: The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this talk I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. These models typically take the form of nonlinear integrodifferential equations. Their nonlocal nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. Here I will present an overview of these techniques, and discuss the relevance of neural field models for describing the brain at the large scales necessary for interpreting EEG data. I will also discuss recent results on an interface approach for describing the evolution of intricate labyrinthine structures seen in planar neural field models. 



Feb 8  Wed  Paul Linden (Cambridge)  Applied Mathematics Colloquium  
14:20  Gravitydriven flows in stratified fluids  
LT6  
Abstract: This talk will describe experiments on flows driven by horizontal density gradients in fluids which are stably stratified. Examples are intrusions on density interfaces or in stratified ambient fluids, and cases where the intruding fluid is also stably stratified. Traditional approaches that have been applied to unstratified fluids have been to use ideas of energy conversion from available potential energy to kinetic energy to predict the speeds of the gravitydriven flows, which in this simple case are gravity currents. I will explore how well these approaches work in systems which can support internal waves and discuss the resulting dynamics. 



Feb 29  Wed  Ati Sharma (Sheffield)  Applied Mathematics Colloquium  
14:00  Predicting structure in turbulence  
LT6  
Abstract: How to find a simple model that predicts the important structural and statistical features of turbulence is a central unsolved problem in classical physics. Most commonly found flows are turbulent, for instance flow of air over an aeroplane wing or water past a ship's hull, flow of oil through an transcontinental pipeline, or the movement of the atmosphere. All these flows experience chaotic threedimensional motion, but nonetheless show persistent, repeating structure. This talk will cover significant new advances, involving the application of systemstheoretic ideas to the equations governing turbulence, which predict these structures. The computationally cheap approach explains and predicts structures and velocity statistics that have previously been identified only in experiments or by direct numerical simulation. Short Biography After graduating as a physicist from UCL, Dr Sharma completed his doctoral thesis in control engineering at Imperial College, London on the modelling and control of tokamak nuclear fusion reactors. Following two years in industry, he returned to academia as a postdoc to work on fluid flow control, and was then awarded an Imperial College Junior Research Fellowship in that area. Dr Sharma joined ACSE as a lecturer in July. 



Mar 7  Wed  John Hinch (Cambridge)  Applied Mathematics Colloquium  
14:00  Large drops of a powerlaw fluid in a thin film on a vertical fibre  
Abstract: We study a thin liquid film on a vertical fibre. Without gravity, there is a RayleighPlateau instability in which surface tension reduces the surface area of the initially cylindrical film. Spherical drops cannot form because of the fibre, and instead, the film forms bulges of roughly twice the initial thickness. Large bulges then grow very slowly through a ripening mechanism. A small nondimensional gravity moves the bulges. They leave behind a thinner film than that in front of them, and so grow. As they grow into large drops, they move faster and grow faster. When gravity is stronger, the bulges grow only to finite amplitude solitary waves, with equal film thickness behind and in front. We study these solitary waves, and the effect of shearthinning and shearthickening of the fluid. In particular, we will be interested in solitary waves of large amplitudes, which occur near the boundary between large and small gravity. Frustratingly, the speed is only determined at the third term in an asymptotic expansion. The case of Newtonian fluids requires four term. 



Mar 14  Wed  Joab Winkler (Sheffield)  Applied Mathematics Colloquium  
14:00  The computation of multiple roots of polynomials whose coefficients are inexact  
LT6  
Abstract: This lecture will show by example some of the problems that occur when the roots of a polynomial are computed using a standard polynomial root solver. In particular, polynomials of high degree with a large number of multiple roots will be considered, and it will be shown that even roundoff error due to floating point arithmetic, in the absence of data errors, is sufficient to cause totally incorrect results to be obtained. Since data errors are usually larger than roundoff errors (and fundamentally different in character), the errors encountered with real world data are significant and emphasise the need for a computationally robust polynomial root solver. The inability of commonly used polynomial root solvers to compute high degree multiple roots correctly requires investigation. A method developed by Gauss for computing the roots of a polynomial will be discussed, and it will be shown that it has an elegant geometric interpretation in terms of pejorative manifolds, which were introduced by William Kahan (Berkeley). Polynomials defined by points on these manifolds satisfy properties that are fundamentally different from the properties of polynomials defined by points that are not on these manifolds. The numerical interpretation of this difference provides the motivation for the method of Gauss, and the geometric properties of pejorative manifolds will therefore be emphasised and considered in detail. Furthermore, these properties explain why multiple roots are preserved in a floating point environment when the coefficients of the polynomial are corrupted by noise. This numerical interpretation leads naturally to a discussion of a structured condition number of a root of a polynomial, where structure refers to the form of the perturbations that are applied to the coefficients. It will be shown that this structured condition number, where the perturbations are such that the multi plicities of the roots are preserved, differs significantly from the standard componentwise and normwise condition numbers, which refer to random (unstructured) perturbations of the coefficients. Several ex amples will be given and it will be shown that the condition number of a multiple root of a polynomial due to a random perturbation in the coefficients is large, but the structured condition number of the same root is small. This large difference is typically several orders of magnitude. The computational implementation of the method of Gauss raises some nontrivial issues  the determi nation of the rank of a matrix in a floating point environment and the quotient of two inexact polynomials  and they will be discussed because they are illposed operations. They must be implemented with care because simple methods will necessarily lead to incorrect results. Furthermore, problems occur when the coefficients of the polynomial span several orders of magnitude, in which case the polynomial must be processed before its roots are computed in order to guarantee computationally reliable arithmetic operations. I will finish the talk by demonstrating Matlab code that implements the method on several high degree polynomials whose coefficients have been corrupted by noise and whose theoretically exact forms have multiple roots of high degree. 



Mar 21  Wed  Alex Best (Sheffield)  Applied Mathematics Colloquium  
14:00  Modelling the coevolution of parasites and their hosts  
LT6  
Abstract: Understanding the dynamics of infectious diseases in human, animal and plant hosts is one of the biggest challenges for modern science, with considerable health, social and financial implications. Mathematical models of these hostparasite interactions can allow us to understand and predict the behaviour of many disease systems. Here I shall focus on the evolutionary dynamics of parasites and hosts, applying the evolutionary framework of adaptive dynamics to a classic model of hostparasite interactions. I shall show how parasite infectivity and host defence may be expected to evolve, both in isolation and when they coevolve with one another. Throughout I shall highlight the important role of the evolutionary tradeoffs on the eventual outcome, particularly focussing on the potential for variation to arise through evolutionary branching. 



Apr 25  Wed  Nick Monk (Sheffield)  Applied Mathematics Colloquium  
14:00  Modelling decision making in multicellular tissues.  
LT6  
Abstract: During the development of multicellular organisms, cells need to make decisions about their fate by integrating information from their neighbours, their surroundings, and their history. I will describe mathematical models of cellular decision making that reveal how cells can adopt different strategies depending on their setting, allowing them to make either rapid coordinated decisions or more measured decisions that provide more scope for the generation of cellular diversity. 



May 9  Wed  Anantanarayanan Thyagaraja (Bristol)  Applied Mathematics Colloquium  
14:00  A KdVlike advectiondiffusion equation with remarkable properties  
LT6  
Abstract: Nonlinear partial differential equations which arise naturally in the theory of wave propagation in many branches of physics have both a rich history and wealth of novel properties, not shared by their linearized equivalents. The Kortewegde Vries Equation (KdVE), which is now more than 100 years old, occupies a special place in this class, along with the complex Nonlinear Schrödinger Equation (NLSE), and forms the core of the modern theory of the InverseScatteringTransform technique of solving equations of this type. Some colleagues and I have recently encountered a close ''cousin'' of this equation [cf. Abhijit Sen et al, (2012), in press, Communications in Nonlinear Science and Numerical Simulations, also available as an ArXiv preprint] which has novel and interesting properties. It arose in a curious way during a ''genetic programming'' search looking for equations which share solutions in common with the KdVE. In this talk, I will outline some of the more in teresting features of this equation which also serves as a counterexample to some commonly held views about recurrent solutions in certain con servative nonlinear dispersive wave equations. The new equation also has some properties which are not shared by the KdVE and appears to define a new class of interesting nonlinear partial differential equations describing wave motions. 



May 23  Wed  Jingsong He (Ningbo University, China)  Applied Mathematics Colloquium  
14:00  Some new patterns of the higher order rogue waves of the NLS equation  
Lecture Theatre 10  
Abstract: The rogue wave of the Nonlinear Schrodinger equation is one kind of hot topic in the studies of water wave, plasma, nonlinear optics and mathematical physics. One core problem is the generating mechanism of this very novel phenomenon. In this talk I shall discuss how to make different patterns (including circular, triangle and their combinations) of the higher order rogue waves of the NLS from breather solutions, which provides a new insight of the mechanism of the rogue wave. I also hope to show similar results of Hirota equation if the time is sufficient. 



May 30  Wed  Tobias Galla (Manchester)  Applied Mathematics Colloquium  
14:00  Agentbased modelling of the nestsite choice by honeybee swarms  
LT10  
Abstract: In a recent paper List, Elsholtz and Seeley [Phil. Trans. Roy. Soc. B. 364, 755 (2009)] have devised an agentbased model of the the nestchoice dynamics in swarms of honeybees, and have concluded that both interdependence and independence are needed for the bees to reach a consensus on the best nest site. I here present a simplified version of the model which can be treated analytically with the tools of statistical physics and which largely has the same features as the original dynamics. Based on analytical approaches it is possible to characterize the coordination outcome exactly on the deterministic level, and to a good approximation if stochastic effects are taken into account, reducing the need for computer simulations on the agentbased level. In the second part of the talk I will discuss a spatial extension, and show that transient nontrivial patterns emerge, before consensus is reached. Reference: T. Galla, Independence and interdependence in the nestsite choice by honeybee swarms: Agentbased models, analytical approaches and pattern formation, J. Theor. Biol. 262 (2010) 186 



Sep 20  Thu  Jose M Redondo (UPC)  Applied Mathematics Colloquium  
11:00  Dispersion in Coastal/complex flows  
LT9  
Abstract: Experimental and numerical KS results of turbulent flows in the sea surface near the coastline have been performed using both Lagrangian and Eulerian methods, field tests are presented using video recordings and velocity sensors. The spatial and temporal resolution is limited by the measuring instruments, which results in "filtering" out the very small scales. The experimental fieldresults obtained during the largescale surf zone experiments carried out in the Ebro Delta, Vilanova and Recife (Spain), under spilling/plunging breaking waves are compared with experiments performed at the enclosed Barcelona and Olinda harbours. The fieldmeasurements include several tests across the surf zone with high vertical resolution measuring dispersion coefficients both in time and space. The measured turbulent properties are compared with turbulence characteristics and length parameterisations. Diffusion from KS models, applied to oil slicks and buoy tracers is evaluated and compared with measurements in a complex nonhomogeneous parameter space. The Diffusivity dependence with time D = c t^n is related to the local velocity spectra so that a generalized Richardson law may be used and evaluated as a function of local parameters such as distance from the coast. 



Oct 24  Wed  David Smith (Birmingham)  Applied Mathematics Colloquium  
13:50  The fluid mechanics of sperm motility  
LT9  


Nov 14  Wed  Shigeo Kida (Kyoto)  Applied Mathematics Colloquium  
14:00  What does the flake pattern represent in flows?  
LT9  
Abstract: Tiny and thin reflective flakes, such as aluminum powders, mica flakes or Kalliroscope, are widely used to visualize the flow structure in a closed container. From their brightness distribution we may obtain useful information on the flow, such as the occurrence of instability, the location of turbulent/nonturbulent boundaries, etc. However, it is not straightforward to identify which properties of the flow are reflected in the visualized patterns. We should note that it is not the orientation itself of the flake surface but its timederivative that responds instantaneously to the velocity gradient. The orientation of flake surface has history effect and may not represent the local flow structure. In this talk we consider the mechanism of formation of brightness distribution of reflective flakes in flows in a precessing spherical cavity. 



Nov 28  Wed  Sam Dolan (SoMaS, Sheffield)  Applied Mathematics Colloquium  
14:00  Black hole instabilities: a cure for baldness?  
LT9  
Abstract: 'A black hole has no hair', suggested John Wheeler in 1973, summarizing the standard view that black holes have just three 'bald' characteristics: mass, electric charge and angular momentum. All other information is rapidly lost beyond the blackhole event horizon. In this talk, I will argue that in fact 'black holes are hirsute', if there exists in nature an ultralight bosonic field with a Compton wavelength similar to the event horizon radius. If so, the black hole's 'hair' (i.e. certain modes in the bosonic field) will regrow exponentiallyfast in the linear regime. Hairgrowth is generated by a phenomenon known as superradiance, which leads to stimulated extraction of rotational energy from the black hole. Through a variety of simulations I will explore the superradiant instability in detail to show how it may generate a 'black hole bomb': a radical cure for blackhole baldness! 



Dec 21  Fri  Eamon Scullion (University of Oslo)  Applied Mathematics Colloquium  
13:00  TypeII spicule heating and magnetic fields  
LT 09  
Abstract: Over the past decade there has been a resurgence in the study of smallscale chromospheric jets known, classically, as spicules. Recent observations have lead us to conclude that there are two distinct varieties of spicule, namely, slower typeI (i.e. mottles, dynamic fibrils, Halpha spicules etc.) and faster typeII (RBEs: Rapid Blueshift Excursions ondisk). Such events dominate the dynamics of the chromosphere. Joint SDO (Solar Dynamics Observatory) and Hinode observations have revealed that fast spicules are the source of hot plasma channelling into the corona. Here we report on the properties of this widespread heating with observations from the high resolution CRISP (CRisp Imaging SpectroPolarimeter) instrument at the SST (1m Swedish Solar Telescope, La Palma) and coaligned NASA/SDO data. We reveal new insight into the formation mechanism of typeII spicules through considering the distribution of RBEs with respect to their magnetic fields rooted in the photosphere. 



Jan 30  Wed  Yohann Duguet (LIMSICNRS, Orsay)  Applied Mathematics Colloquium  
14:00  Oblique laminarturbulent interfaces in wallbounded shear flows  
LT9  
Abstract: The onset of transition to turbulence in subcritical wallbounded flows is characterised by largescale localised structures such as turbulent spots or turbulent stripes. Interestingly, the laminarturbulent interfaces associated with these structures always display obliqueness with respect to the mean direction of the flow. We will attempt to explain this phenomenon using an assumption of scale separation between large and small scales, and we can show analytically that the corresponding laminarturbulent interfaces are always oblique with respect to the mean direction of the flow. In the case of plane Couette flow, the mismatch between the streamwise flow rates near the boundaries of a single turbulence patch generates a largescale flow with a nonzero spanwise component. Advection of the smallscale turbulent fluctuations by the corresponding largescale flow distorts the shape of the turbulence patch and is responsible for its oblique growth. This mechanism can be easily extended to other flows such as Plane Poiseuille flow or TaylorCouette flow. 



Mar 6  Wed  Peter Lewis (Imperial)  Applied Mathematics Colloquium  
14:00  Are quantum states real?  
LT9  
Abstract: Perhaps quantum states represent only the information available to an agent, or incomplete information about a real state of affairs. Thisthe psiepistemic view of quantum statesis an attractive idea because if quantum states represent only information then measurement induced collapse, for example, is analogous to (and only as confusing as) the Bayesian updating of a probability distribution given new data. Recently, however, a few theorems (most notably by Pusey, Barrett and Rudolph) have been proven demonstrating that indeed the quantum state must play a role in the description of the real state of affairsthe psiontic view. Making use of the â€˜ontological modelsâ€™ formalism, we demonstrate that models can be constructed such that more than one quantum state is consistent with a single underlying real state. Thus all PBRlike theorems, and the restrictions they place on recovering quantum theory from a deeper theory, necessarily require assumptions beyond those required for a welldefined ontological model. 



Mar 13  Wed  Xuesong Wu (Imperial)  Applied Mathematics Colloquium  
14:00  Freestream turbulence, streaks and bypass transition  
LT9  
Abstract: Bypass transition of boundarylayer flows occurs in the presence of relatively strong turbulence in the free stream, and the ensuing transition location depends directly on the turbulence level. It is generally accepted that freestream turbulence penetrates into the boundary layer to generate streaks, which amplify downstream and become unstable thereby causing onset of turbulence. Therefore accounting for the entrainment of freestream turbulence is a crucial step towards understanding and predicting bypass transition. A popular approach adopted in most previous studies, especially in DNS (direct numerical simulations), of bypass transition, is to use continuous spectra of the OS and Squire operators. In this talk, I will argue that this approached is flawed by showing that continuous spectra and entrainment are fundamentally different. An alternative and appropriate mathematical approach, which describes in a selfconsistent manner the entrainment, formation and instability of streaks, will be presented. This framework allows for, in principle, a physicsbased prediction of bypass transition. 



Apr 10  Wed  Gordon Ogilvie (DAMTP, Cambridge)  Applied Mathematics Colloquium  
14:00  Local dynamics and hydrodynamic instability of warped astrophysical discs  
LT9  
Abstract: Astrophysical discs, which include circumstellar discs in which planets are formed and highenergy accretion discs around black holes, consist of a continuous distribution of material in orbital motion around a central massive body. In a general Keplerian disc, this orbital motion can have variable eccentricity and inclination. A warped disc is one in which the orbital plane varies with radius and possibly with time. There is strong theoretical and observation motivation for considering warped discs in several situations. Current interest, for example, focuses on black holes in galactic nuclei, which grow by accreting gas that is supplied in different orientations, and protoplanetary systems, where spinorbit misalignments have been discovered, suggesting that a warped disc may have been involved. We introduce a new local model for the study of warped astrophysical discs. This generalizes the shearing sheet of Goldreich & LyndenBell (1965) by imposing the local curvature of the orbital plane in addition to shear and rotation. The simplest hydrodynamic solutions in the local model are horizontally uniform laminar flows that oscillate at the orbital frequency. These determine the largescale evolution of the shape and mass distribution of the disc through their hydrodynamic stresses. We present a simpler and independent derivation of the basic equations for warped discs obtained by Ogilvie (1999). We also analyse the hydrodynamic stability of the laminar flows and find widespread instability deriving from parametric resonances of inertial waves. Very small warps in nearly Keplerian discs of low viscosity can be expected to generate hydrodynamic turbulence by this mechanism. As well as modifying the dynamics of the warp, this could have important consequences for planet formation. 



May 8  Wed  Jingsong He (Ningbo)  Applied Mathematics Colloquium  
14:00  
LT10  


May 15  Wed  Ben Wright (Harrison Goddard Foote)  Applied Mathematics Colloquium  
14:00  [*Seminar has been postponed*] Overview of intellectual property  
LT10  


May 22  Wed  Alan Zinober (Sheffield)  Applied Mathematics Colloquium  
14:00  A Brief History of Optimal Variational Problems and Some Recent Research  
LT9  
Abstract: The Calculus of Variations was initiated in the 17th Century and forms a basic foundation of modern optimal (maximising or minimising) variational problems, nowadays often called optimal control. An introduction to the Calculus of Variations with some sample examples will be presented. This will include the EulerLagrange and Hamiltonian formulation together with the associated final boundary value conditions. A numerical shooting method can be used to solve the resulting Two Point Boundary Value Problem (TPBVP), a set of differential equations. There are many interesting applications including the optimal spending of capital, reservoir control, maintenance and replacement policy of vehicles and machinery, optimal delivery of medicines, drug bust strategies, study for examinations and optimal presentation of a lecture like this one. A new nonclassical class of variational problems has been motivated by research on the nonlinear revenue problem in the field of economics. This class of problem can be set up as a maximising problem in the Calculus of Variations (CoV) or Optimal Control. However, the state value at the final fixed time, $y(T)$, is {em a priori} unknown and the integrand to be maximised is also a function of the unknown $y(T)$. This is a nonstandard CoV problem that has not been studied before. New final value costate boundary conditions will be presented for this CoV problem and some results will be shown. 



Oct 2  Wed  Gabriel Lord (HeriotWatt)  Applied Mathematics Colloquium  
14:00  Computing Stochastic Travelling Waves  
LT9  
Abstract: This talk will introduce stochastic differential equations from scratch and develop from there to discuss stochastic partial differential equations (SPDEs). From there we will discuss how to compute travelling waves for SPDEs and discuss a technique that freezes the wave and stops it from moving. 



Oct 23  Wed  Monica Oliveira (Strathclyde)  Applied Mathematics Colloquium  
14:00  Extensional flows of complex fluids at the microscale  
LT9  
Abstract: The nonlinear rheological properties of complex fluids often impart a rich set of unusual characteristics to flow systems. When these fluid properties, such as viscoelasticity, are combined with the small scales of microfluidics, the nonlinearities are enhanced and may dominate the flow dynamics. In this presentation, we will discuss some of our experimental and numerical investigation highlighting the elastic effects that arise in viscoelastic microfluidic flows with a strong extensional contribution, and the use and optimisation of microfluidic devices for rheometry purposes. 



Oct 30  Wed  Rainer Hollerbach (Leeds)  Applied Mathematics Colloquium  
14:00  Magnetorotational Instabilities in TaylorCouette Flow  
LT9  
Abstract: [APW: The flow in accretion discs has been observed to be turbulent, but according to the Rayleigh Criterion, hydrodynamic Kepler flows should be linearly stable. The existence of a subcritical nonlinear is debated, but appears to be unlikely. That turbulence in these flows originates via a magnetic instability looks more 'PROMISE'ing.] 



Nov 6  Wed  Michele Bartuccelli (Surrey)  Applied Mathematics Colloquium  
14:00  Obtaining estimates of the norm for solutions of dissipative partial differential equations  
LT9  
Abstract: In this talk we will address the problem of obtaining explicit and accurate estimates of the supnorm for solutions of dissipative partial differential equations such as the Swift–Hohenberg Equation and the NavierStokes equations in one and two space dimensions. By using the best (so far) available estimates of the embedding constants which appear in the classical functional interpolation inequalities used in the study of solutions of dissipative partial differential equations, we will evaluate in an explicit manner the values of the supnorm of the solutions of the PDE under investigation. In addition (time permitting) we will compute the socalled timeaveraged dissipative length scale associated to the solutions of the PDE. 



Nov 20  Wed  Mohammed Afsar (Imperial)  Applied Mathematics Colloquium  
14:00  Nonhomogeneous Rapiddistortion theory on transversely sheared flows  
LT9  
Abstract: We are concerned with the small amplitude unsteady motion of an inviscid nonheat conducting compressible fluid on a transversely sheared mean flow. We show that the hydrodynamic component of the motion is determined by two arbitrary convected quantities in the absence of solid surfaces and hydrodynamic instabilities. These results can be used to specify appropriate upstream boundary conditions for unsteady surface interaction problems on transversely sheared mean flows in the same way that the vortical component of the Kovasznay (1953) decomposition is used to specify these conditions for surface interaction problems on uniform mean flows. But unlike Kovasznay’s (1953) result the arbitrary convected quantities no longer bear a simple relation to the physical variables. We complete the formalism developed in Goldstein (1978 & 1979) by obtaining the necessary relations between these quantities and the physically measurable flow variables. The results are important because they enable the complete extension of Nonhomogeneous Rapid Distortion Theory to transversely sheared mean flows. We use these results to derive a generalization of the famous Ffowcs Williams and Hall (1970) formula for the sound produced by the interaction of turbulence with an edge that is frequently used as a starting point for predicting sound generation by turbulence/solid surface interactions. We illustrate the utility of this result by using it to calculate the sound radiation produced by the interaction of a twodimensional jet with the downstream edge of a flat plate. 



Nov 27  Wed  Bill Chaplin (Birmingham)  Applied Mathematics Colloquium  
14:00  Sounding stars and the search for exoplanets  
LT9  
Abstract: We are in a golden era for stellar physics driven by new satellite and telescope observations of unprecedented quality and scope. Thanks to the launch of the NASA Kepler Mission the past four years has seen dramatic progress in the study of other stellar systems in our galaxy. Kepler has revolutionized the field of asteroseismology, the study of stars by observation of their natural oscillations. In this seminar I will discuss the asteroseismic study of solartype stars, including characterisation of exoplanet host stars which provides essential information for constraining the properties of the detected planets (including information on spinorbit alignment of the systems). Finally, I will touch on what the future holds for Kepler (following the recent failure of a second of its reaction wheels). 



Dec 4  Wed  Tony Padilla (Nottingham)  Applied Mathematics Colloquium  
14:00  Sequestering the Standard Model Vacuum Energy  
LT9  
Abstract: We propose a very simple reformulation of General Relativity, which completely sequesters from gravity all of the vacuum energy from a matter sector, including all loop corrections and renders all contributions from phase transitions automatically small. The idea is to make the dimensional parameters in the matter sector functionals of the 4volume element of the universe. For them to be nonzero, the universe should be finite in spacetime. If this matter is the Standard Model of particle physics, our mechanism prevents any of its vacuum energy, classical or quantum, from sourcing the curvature of the universe. The mechanism is consistent with the large hierarchy between the Planck scale, electroweak scale and curvature scale, and early universe cosmology, including inflation. Consequences of our proposal are that the vacuum curvature of an old and large universe is not zero, but very small, that wDE≃−1 is a transient, and that the universe will collapse in the future. 



Feb 12  Wed  Christopher Nelson; Schuyler Nicholson (Sheffield)  Applied Mathematics Colloquium  
14:00  SN: Implications regarding statistical distances in nonequilibrium systems;
CN: The formation of Ellerman bombs in the lower solar atmosphere. 

LT9  
Abstract: Implications regarding statistical distances in nonequilibrium systems Statistical mechanics seeks to use the small scale dynamics of a system to derive its large scale outcomes, for example the macroscopic observables such as temperature, energy or pressure. This goal is hampered for nonequilibrium systems using traditional Statistical mechanics, as fundamental quantities such as the work done, or the equation of motion for the system’s ensemble are not always well deﬁned. As a useful tool in understanding nonequilibrium systems, we investigate the metric distance in probability space given by the Thermodynamic length (L). For a system represented by a probability distribution that is changing in time, L lends a notion of distance that the system travels in its evolution. By utilizing this measure we show how the Thermodynamic length is actually a measure of work done by the system in its evolution. This result is interesting because of the generality in which the thermodynamic length is deﬁned. The Logistic map is then used to numerically illustrate the thermodynamic length. Here the system is shown to often take the path of minimum work. The unstable ﬁxed points of the Logistic map are also identiﬁed using our methodology as the major drivers of the system towards equilibrium, i.e. they most efficiently use the available work of the system. The formation of Ellerman bombs in the lower solar atmosphere We discuss the solar phenomena known as Ellerman bombs. These smallscale events form in the photosphere and are thought to be observational evidence of magnetic reconnection. A basic overview of Ellerman bombs is presented highlighting the key traits which are widely linked to magnetic reconnection, before a brief discussion about the mathematical modelling of these events is undertaken. 



Feb 18  Tue  Mitsuaki Funakoshi (Kyoto)  Applied Mathematics Colloquium  
14:00  The onset of thermal convection in a rectangular container  
LT2  
Abstract: The widely known problem of onset of thermal convection in a container is examined in detail with high accuracy. That is, the onset of threedimensional thermal convection of a fluid in a rectangular cavity is examined for various values of its aspect ratios under the assumption of rigid walls with perfect thermal conductance. The critical Rayleigh number, at which a motionless state becomes unstable, and the flow patterns of most unstable modes are calculated numerically with high accuracy using a Galerkin spectral method. A few interesting results on the dependences of critical Rayleigh number and flow patterns of most unstable modes on the aspect ratios are reported in this talk. 



Mar 5  Wed  Silke Weinfurtner (Nottingham)  Applied Mathematics Colloquium  
14:00  Measurement of Stimulated Hawking Emission in an Analogue System  
LT9  
Abstract: Hawking argued that black holes emit thermal radiation via a quantum spontaneous emission. To address this issue experimentally, we utilize the analogy between the propagation of fields around black holes and surface waves on moving water. By placing a streamlined obstacle into an open channel flow we create a region of high velocity over the obstacle that can include surface wave horizons. Long waves propagating upstream towards this region are blocked and converted into short (deepwater) waves. This is the analogue of the stimulated emission by a white hole (the time inverse of a black hole), and our measurements of the amplitudes of the converted waves demonstrate the thermal nature of the conversion process for this system. Given the close relationship between stimulated and spontaneous emission, our findings attest to the generality of the Hawking process. 



Mar 12  Wed  Andy White (HeriotWatt)  Applied Mathematics Colloquium  
14:00  Diseasemediated replacement of native species: UK red/grey squirrels as a case study  
LT9  
Abstract: Since its introduction into the UK, c1900, the grey squirrel has replaced the native red squirrel throughout most of England and Wales, and in parts of Scotland and Ireland. There is strong evidence that grey squirrels are superior competitors in many habitats and also that a shared virus, squirrelpox, plays a critical role in red squirrel decline. ODE and PDE frameworks, parameterised to represent the red/grey/squirrelpox system, will be examined to understand the impact of squirrelpox on red and grey squirrel population dynamics and the spread of squirrelpox following grey invasion. Squirrelpox is endemic in grey populations in England and Wales but has only recently been reported in Southern Scotland. A spatial, individual based version of the model will be outlined and used to assess the spread of squirrelpox through squirrel populations in Southern Scotland. These findings are being used to inform current red squirrel conservation policy. 



Mar 26  Wed  Shigeo Kida (Doshisha)  Applied Mathematics Colloquium  
14:00  A new instability to Steady Flow in a Precessing Sphere  
LT9  
Abstract: We consider the ﬂow structure and its stability in a rapidly rotating sphere with weak precession. This work is motivated by a recent laboratory experiment by Goto et al. (2011). They observed that the ﬂow is unstable for $Po > O(Re−\alpha)$ with $\alpha = 0.8 \sim 0.9$ at large $Re$ (Reynolds number) and small $Po$ (Poincare number). However, this value of $\alpha$ is a bit surprising because it is long known (Greenspan 1968) that the decay rates of eigenmodes in a precessing sphere are proportional to $Re^{−0.5}$ and the precession, whose eﬀects on the ﬂow are proportional to $Po$, may destabilize the ﬂow for $Po > O(Re^{−0.5})$. In fact we have shown by a linear stability analysis (Kida 2013) that the steady ﬂow in a precessing sphere is unstable for $Po > 7.9\, Re^{−0.5}$ for the global disturbances (oscillating over the whole sphere) at $Re>>1$ and $Po<<1$. Since these unstable modes do not explain the experimental observation, we searched another mode and found that a local disturbance which is limited in the critical regions gives the stability curve $Po = 21.25\,Re^{−0.8}$. This curve agrees excellently with the abovementioned laboratory experiment. Furthermore, it would be interesting to note that the stability curve for global disturbances coincides with that in a slightly oblate spheroid (Goto et al. 2011). 



Apr 30  Wed  Jonathan Pearson (Durham)  Applied Mathematics Colloquium  
14:00  Constraining properties of the dark universe  
LT9  
Abstract: When recent observational evidence and the GR+FRW+CDM model are combined we obtain the result that the Universe is accelerating, where the acceleration is due to some notyetunderstood "dark sector". There has been a considerable number of theoretical models constructed in an attempt to provide an "understanding" of the dark sector: dark energy and modified gravity theories. The proliferation of modified gravity and dark energy models has brought to light the need to construct a "generic" way to parameterize the dark sector. I will discuss our way of approaching this problem: constructing equations of state for perturbations. Our approach is inspired by that taken in particle physics, where the most general modifications to the standard model are written down for a given field content that is compatible with some assumed symmetries. Our emphasis is on constructing a theoretically motivated toolkit which can be used to meaningfully transcribe from experimentally obtained observations into well defined statements about the allowed properties of the dark sector. It is key to use meaningful models of the perturbed universe when analysing data sets which are sensitive to the clustering of the dark sector. I will present our observational constraints (using e.g., Planck CMB temperature and lensing, CFHTLenS data) on the parameters in the equations of state for perturbations. If I get time, I shall briefly discuss “material models of dark energy”, where the theory of relativistic solids can be used to formulate a dark energy theory which can naturally be compared to data. 



May 14  Wed  Chris Fewster (York)  Applied Mathematics Colloquium  
14:00  Quantum Energy Inequalities  
LT9  
Abstract: Classical physics typically assumes that energy density is everywhere nonnegative, as measured by any observer. This is responsible for the tendency of matter tends to collapse under its own gravity, which is the underlying physics of the famous singularity theorems of general relativity due to Hawking and Penrose. However, as I will describe, quantum theory is incompatible with the demand for everywherenonnegative energy densities and even allows arbitrarily negative energy densities. Instead, classical positivity is replaced by Quantum Energy Inequalities (QEIs) which are lower bounds on local averages of the energy density. I will describe the status of QEIs and some of their consequences, including applications to the Casimir effect, and constraints on `designer spacetimes' containing wormholes or other exotic objects. I also describe related results in other parts of quantum theory, including the `backflow' phenomenon, in which state with momentum in one direction manges to reverse for a short while. The talk will also touch on (but not assume prior knowledge of) some of the mathematical tools used to investigate these ideas, which include microlocal analysis and sharp Gaarding inequalities. 



May 21  Wed  Jack Morrice (Sheffield)  Applied Mathematics Colloquium  
14:00  Dark energy  
LT9  


Jul 2  Wed  Johan Andersson (Chalmers, Göteborg)  Applied Mathematics Colloquium  
14:00  Statistical analysis and modeling of intermittent transport events in the tokamak SOL  
LT5  
Abstract: In the tokamak scrapeoff layer (SOL), anomalous heat and particle transport arise as a consequence of a competition between particle and heat injection from the plasma core, perpendicular transport driven by turbulence, and plasma losses at the sheaths where the magnetic field lines intersect the vacuum vessel. Turbulent modes are ubiquitous in the SOL, and they are excited by a combination of effects, most notably the combination of unfavorable magnetic field curvature, a short pressure gradient scale $L_p=p/\nabla p\sim 1$cm, and adiabaticity breaking through parallel dynamics effects. The resulting turbulent dynamics is characterized by the large fluctuations with a significant radial extension. In particular, both experimental measurements and nonlinear simulations reveal the presence of radially propagating, coherent mesoscale modes, the socalled blobs, with amplitudes several times larger than the rootmeansquare (RMS) fluctuation level. These intermittent plasma transport events manifests a patchy spatial and bursty temporal structure, pertaining to radially propagating coherent structures, and have been suggested to carry a significant fraction of the total transport. The likelihood of these intermittent events are described by probability density functions (PDFs) which significantly deviate from Gaussian predictions. In particular a major goal would be to control the edge heat flux loads, which depend on the instant amplitude of fluctuations, as opposed to the mean load, which can be calculated by quasilinear theory. 



Oct 15  Wed  Vasilis Archontis (St. Andrews)  Applied Mathematics Colloquium  
14:00  Magnetic flux emergence as a driver of solar dynamic events: jets, eruptions and flares  
LT B  
Abstract: We present a series of 3D MHD numerical simulations on magnetic flux emergence in the Sun. We focus on the onset of jets, eruptions and flares on various scales, after the emergence of magnetic flux from the solar interior into the highly stratified atmosphere of the Sun. 



Oct 22  Wed  Takeshi Akinaga (Aston)  Applied Mathematics Colloquium  
14:00  Sequential bifurcation approach for the transition of flow in the TaylorCouette system  
LT B  
Abstract: We have studied transitions of flows to turbulence by sequential bifurcation approach, whereas multilateral researches are required in order to comprehend the structure of turbulence. Recently we utilised the approach to the TaylorCouette system with two simplifications: narrow gap limit and corotation, as an extensional work of Weisshaar et al.[1]. The results will be shared and be compared with experimental results obtained by Hegseth et al.[2] in a consistent manner, as a connection between numerical and experimental studies. References: [1] E Weisshaar, FH Busse & M Nagata: Twist vortices and their instabilities in the TaylorCouette system. J. Fluid Mech. 226 (1991), 549564. [2] JJ Hegseth, GW Baxter & CD Andereck: Bifurcations from Taylor vortices between corotating concentric cylinders. Phys. Rev. E 53 (1996), 507521. # This work is a collaboration between Dr Takeshi Akinaga, Dr Sotos Generalis (Aston) and Prof. Friedrich Busse (Bayreuth). ## FB is a Leverhulme Trust Visiting Professor and TA is a Marie Curie International Incoming Fellow. 



Oct 29  Wed  Robert Poole (Liverpool)  Applied Mathematics Colloquium  
14:00  Hibernating Turbulence  
LT B  
Abstract: The asymptotic upper limit of turbulent drag reduction with polymer additives – often termed Virk’s Maximum Drag Reduction (MDR) asymptote [1] – is a wellknown phenomenon in the turbulent flow of complex fluids. One of the most intriguing features of MDR is its universality. Recent direct numerical simulations [2, 3] have identified time intervals showing key features of MDR. These intervals have been termed ‘hibernating turbulence.’ They are a weak turbulence state which is characterised by low wallshear stress and extremely weak vortical flow structures. Here we report the results of an experimental investigation which appears to confirm that the streamwise velocity of a turbulent channel flow collapses to an MDRlike asymptote, even in the absence of a polymer additive, during intervals of hibernating turbulence. Our experiments are conducted in a fully developed turbulent channel flow of a Newtonian fluid at Reynolds numbers of Re_τ = u_τ h / ν = 70, 85, 100 and 120 where uτ is the friction velocity, h is channel halfheight and ν is the kinematic viscosity. We measure the instantaneous wallshear stress with a flushmounted hotfilm probe, which we use as an indicator for hibernating turbulence, whilst simultaneously sampling the streamwise velocity component with Laser Doppler Velocimetry. We also use stereoscopic Particle Image Velocimetry to probe the dynamics of individual hibernation events.
[1] P.S. Virk, AIChE J. 21, 625 (1975) 



Nov 19  Wed  Jonathan Potts (Sheffield)  Applied Mathematics Colloquium  
14:00  The scale of animal movement decisions and consequences for continuumlimit modelling  
LT B  


Nov 26  Wed  Bogdan Hnat (Warwick)  Applied Mathematics Colloquium  
14:00  Large scale flows in magnetically confined plasmas: Geodesic Acoustic Mode at the edge region of Mega Amp Spherical Tokamak.  
LT B  
Abstract: B. Hnat1, J. R. Robinson1, A. Kirk2, P. Tamain3, A. Thyagaraja4, K. G. McClements2, P. J. Knight2, and the MAST Team 1 Physics Department, University of Warwick, Coventry, CV4 7AL, UK. 2 EURATOM/CCFE Fusion Association, Culham Science Centre, Abingdon, OX14 3DB, UK. 3 Association Euratom/CEA, CEA Cadarache, F13108 St. PaullezDurance, France 4 University of Bristol, H.H. Wills Physics Laboratory, Bristol BS8 1TL. The development of magnetically confined fusion (MCF) plasma into a viable energy source rests on our ability to control the stability of a plasma heated to 200 million Kelvin. Hot plasmas are complex systems with dynamics driven by collective interactions of particles with the fields through a plethora of modes. Even when globalscale instabilities are eliminated, microinstabilities drive turbulent plasma transport and this is the main obstacle in achieving selfsustained fusion reaction in a tokamak at the present time. Turbulent fluctuations can also selforganize through nonlinear processes into largescale, linearly stable zonal flows, which act as a sink of energy for turbulence. A large body of evidence suggests that zonal flows are instrumental in achieving a highconfinement mode (Hmode): a basic operating scenario for ITER. In toroidal geometry, zonal flows couple to compressive modes, called Geodesic Acoustic Modes (GAM) and acquire a finite frequency, which allows for their identification in experimental data. We report recent observation of the GAM at the edge of the Mega Amp Spherical Tokamak (MAST). A shift in frequency with plasma rotation is found, and a rapid suppression of the mode is observed when magnetic configuration is modified. Nonlinear coupling to high wave number turbulence is evident, and an increase in power of turbulence fluctuations is seen after suppression. The mode is then studied numerically using the two fluid, global simulation CENTORI. We examine mode localisation and effects of magnetic geometry, given by aspect ratio, elongation and safety factor, on the observed frequency of the mode. An excellent agreement between simulations and experimental data is found for simulation plasma parameters matched to those of MAST. 



Dec 3  Wed  Victor Ambrus (Sheffield)  Applied Mathematics Colloquium  
14:00  Quadrature methods in lattice Boltzmann modelling  
LT B  


Dec 10  Wed  Aditi Sood (Sheffield)  Applied Mathematics Colloquium  
14:00  MHD  
LT B  


Dec 19  Fri  Jingsong He (Ningbo)  Applied Mathematics Colloquium  
13:00  Rogue waves  
LT 10  


Feb 11  Wed  Sylvain Laizet (Imperial)  Applied Mathematics Colloquium  
14:00  Incompact3d: a highorder flow solver to tackle turbulence problems using supercomputers  
LT 10  
Abstract: Simulating and understanding turbulent flows remains one of the most challenging problems in mechanics. Significant progress has been made recently using high performance computing, and computational fluid dynamics (CFD) is now a critical complement to experiments and theories in order to understand turbulent flows and how to apply them in various engineering contexts. Only very few codes for Direct and Large Eddy Simulations (DNS/LES) are capable of undertaking massive simulations with several billion mesh nodes on thousands of computational cores. Most of them are simulating idealized homogeneous, isotropic turbulence, using spectral methods with periodic boundary conditions in at least two spatial directions. Engineering problems have more complex geometries and full spectral approaches are not practical. In conventional CFD, especially in an industrial context, complex geometries are usually treated using nonstructured element meshes, requiring loworder schemes and sophisticated tools for the generation of highly distorted meshes. The resulting accuracy is most of the time incompatible with a detailed analysis of engineering problems. Note that the spectral element method seems to be a very promising strategy to undertake complex problems with the spectral accuracy. However, using this technique on thousands of computational cores is a challenging task that requires important numerical developments to conciliate accuracy, efficiency and scalability. In this talk, I will present an innovative numerical method which can reconcile accuracy, efficiency, versatility and scalability using a Cartesian grid. Various examples will be shown in this talk such as fractalgenerated turbulence, gravity currents in an open basin, impinging jets on a heated plate and a microjet device to control a turbulent jet. 



Feb 18  Wed  Chris Keylock (Civil Eng., Sheffield)  Applied Mathematics Colloquium  
14:00  Velocity Increments in Turbulent Wakes  
LT 10  
Abstract: (with Joachim Peinke and Robert Stresing, University of Oldenburg) A traditional approach to studying turbulence is by linking the moments of the velocity increments to dissipation. This then leads to models such as those of Kolmogorov (1941,1962), Frisch et al. (1978) and She and Leveque (1994) for the scaling of the moments. An alternative approach was proposed by Peinke and coworkes in 1997 based on studying the full distribution function for the increments. If a Markovian property holds, a FokkerPlanck equation can be written for the evolution of the increment distribution function, parameterised by drift and diffusion coefficients. An issue of contemporary interest is the effect that multiple scales of forcing has on the structure of turbulence. Peinke, Stresing and Vassilicos published a paper in Physical Review Letters in 2010 arguing that the drift and diffusion coefficients behaved differently under multiscale forcing. Here we combine the FokkerPlanck approach with the data from the PRL paper, and a method we have developed for controlled randomisation of datasets (called Gradual Wavelet Reconstruction). We show using this technique that we can explore the higher order expansions of the diffusion coefficient to gain a richer understanding of turbulence from the perspective of the FokkerPlanck model. An explanation is proposed for the differing behaviour of wakes produced by forcing at single and multiplescales. The content of this talk is based on a paper accepted in Physics of Fluids 



Mar 4  Wed  Jeremy Sakstein (Portsmouth)  Applied Mathematics Colloquium  
14:00  Astrophysical tests of gravity  
LT 10  
Abstract: The puzzling nature of the latetime acceleration of the cosmological expansion has prompted a recent interest in alternate theories of gravity. Any theory that can drive the acceleration must include a mechanism that recovers GR in the solar system, a screening mechanism. In this talk I will describe how astrophysical objects such as stars and galaxies can act as new and novel probes of these theories. 



Mar 11  Wed  Takashi Sakajo (Kyoto)  Applied Mathematics Colloquium  
14:00  Word representations of structurally stable Hamiltonian flows in multiply connected domains and its applications  
LT 10  
Abstract: We are concerned with Hamiltonian vector fields with a dipole singularity satisfying the slip boundary condition in twodimensional multiply connected domains. One example of such a Hamiltonian vector field is the incompressible and inviscid flow in an exterior multiply connected domain with a uniform flow whose Hamiltonian is called the stream function. They are regarded as mathematical models for biofluids such as insect flights and vertical descend of rotating plant seeds and for environmental flows in rivers and coastal flows. Here, we consider structurally stable Hamiltonian vector fields and their streamline topologies. We introduce an encoding procedure to assign a unique sequence of words to these patterns, owing to which one can identify every streamline pattern with its representing sequence of words. Based on the theory of word representations, we can determine all possible structurally stable streamline patterns in a combinatorial manner. Moreover, we describe transitions between two different structurally stable patterns only from their word representations without specifying the Hamiltonian. We also demonstrate how the present theory is applied to fluid flow problems with vortex structures. 



Mar 18  Wed  ZhengTong Xie (Southampton)  Applied Mathematics Colloquium  
14:00  Fluids  
LT 10  


Apr 29  Wed  Peter Schmid (Imperial)  Applied Mathematics Colloquium  
14:00  Dynamic mode decomposition  
LT 10  


May 8  Fri  Duncan Mackay (St. Andrews)  Applied Mathematics Colloquium  
13:00  Data Driven NonLinear ForceFree Models of the Sun’s Magnetic Field  
LT 10  
Abstract: The talk will discuss the application of both global and local data driven nonlinear forcefree models of the Suns magnetic field. The construction of the models will first be discussed. Following this the models will be tested against observations of solar filaments, Open Magnetic Flux and CMEs. It will be shown that the nonlinear forcefree models reproduce many features of the solar corona and can be used in future to predict and understand space weather events. 



May 13  Wed  Lucy Wyatt (Sheffield)  Applied Mathematics Colloquium  
14:00  Fisheries, swimmers and a severed head  my Australian (radar) adventure  
LT 10  


May 20  Wed  Anthony Yeates (Durham)  Applied Mathematics Colloquium  
14:00  IMPACT OF MAGNETIC TOPOLOGY ON PLASMA DYNAMICS  
LT 10  
Abstract: How is a plasma's evolution affected by its global magnetic field structure? I will focus on trying to understand the selforganisation of turbulently relaxing plasma  a phenomenon observed in laboratory devices and hypothesised to occur in astrophysical plasmas such as stellar atmospheres. If these plasmas were perfect electrical conductors, their magnetic topology (linkage and connectivity of their magnetic field lines) would be perfectly frozenin for all time. In reality, the turbulent flows lead to very sharp layers of electric current where even a very small resistivity allows for fieldline reconnection. Nevertheless, it is wellknown that the total magnetic helicity  an overall measure of the topology  remains a robust invariant. Thus the magnetic energy released during the relaxation may be limited by the conservation of total magnetic helicity. Our work goes further: we focus on the possible relevance of additional topological constraints beyond total magnetic helicity. In a turbulently relaxing plasma, we propose that the leading order behaviour is a reorganisation of fieldline helicity, which in general will put additional constraints on the dynamics. If the region of turbulent reconnection is localised, one such constraint may be expressed as conservation of the topological degree of the magnetic fieldline mapping. Joint work with Gunnar Hornig and Alexander Russell (University of Dundee). 



Oct 14  Wed  SURE students: Samuel Hayes, James Heseltine, Richard Molyneux, Janith Petangoda, Ashleigh Randall (SoMaS)  Applied Mathematics Colloquium  
14:00  
Hicks, LT 11  


Oct 28  Wed  Matthew Juniper (Cambridge)  Applied Mathematics Colloquium  
14:00  Nonlinear Thermoacoustics: flames on the edge of chaos  
Hicks, LT 11  
Abstract: Thermoacoustic oscillations occur in combustion chambers when heat release oscillations lock into pressure oscillations. They were first observed in lamps in the 18th century, in rockets in the 1930s, and are now one of the most serious problems facing gas turbine manufacturers. Most analysis of thermoacoustic oscillations has been linear and has considered the point at which the oscillations become unstable. Nonlinear studies have usually assumed that, once linearly unstable, a thermoacoustic system grows to limit cycle oscillations. Recent experiments, however, show that limit cycle oscillations in thermoacoustics are the exception rather than the rule. They also show that thermoacoustic oscillations can sometimes be triggered by little more than background noise. These experiments motivate the current study. In this study, a premixed flame in a tube is modelled using a levelset approach. The flame dynamics is coupled to the acoustics. This system, although relatively simple, exhibits much of the elaborate nonlinear behaviour found in experiments, such as biperiodic, quasiperiodic, multiperiodic and chaotic oscillations. This raises questions, and some answers, about how thermoacoustic oscillaions should be modelled in the nonlinear regime. This study also shows how triggering in thermoacoustics is related to bypass transition to turbulence in hydrodynamics. 



Nov 18  Wed  Alex Hague + Freddie Mather (SoMaS)  Applied Mathematics Colloquium  
14:00  (Solar physics)  
Hicks, LT 11  
Abstract: Alex: BuoyancyDriven Magnetohydrodynamic Waves in a TwoLayer Solar Atmosphere: In this talk we look at magnetohydrodynamic (MHD) waves in a gravitationally stratified plasma embedded in a vertical magnetic field. We consider waves where buoyancy plays a key role in the motion. In a nonmagnetic model, such waves are internal gravity waves (IGWs). Using appropriate simplifying assumptions we show that the magnetic counterparts to IGWs are slow MHD waves. We will study propagating waves, standing waves in a onelayer cavity, and waves in a twolayer semiinfinite atmosphere. Freddy: Stability of Magnetohydrodynamic surface waves at a tangential discontinuity in a viscous plasma with shear flow:
Background flows are ubiquitous in many physical plasma's. These flows can lead to Doppler shifting of MHD waves. Without a flow, in linear MHD, a surface wave can have a forward and backward propagating solution, traveling with equal phase speed but in opposite directions. With the addition of a strong enough shear flow, this backward wave can reverse it's direction of propagation. 



Nov 25  Wed  Richard Mann (Leeds)  Applied Mathematics Colloquium  
14:00  Maximum Entropy Production in Collective Animal Behaviour  
Hicks, LT 11  
Abstract: Maximum Entropy Production (MEP) is a powerful tool for deriving steadystate flows in nonequilibrium physical systems, such as energy flows in the earth’s climate [1]. Flows of energy and material through the system are assumed to take values that maximise the production of entropy, much as in equilibrium systems are assumed to exist in a state of maximum entropy, subject to any known constraints. Recently the ‘causal entropic principle’ has been proposed as an analogous concept for intelligent systems [2]. In this talk I will discuss our application [3] of the causal entropic principle to collective decisionmaking and collective motion. Our analysis shows that agents in groups that are maximally entropic over their possible paths through future statespace must obey Weber's law interactions over discrete choices, and linearly additive social forces in continuous motion. This provides both a novel derivation of these commonly observed interactions and a new perspective on grouplevel behaviour. [1] R. K. Niven, Phys. Rev. E 80, 021113 (2009) [2] A. WissnerGross and C. Freer, Phys. Rev. Lett. 110, 168702 (2013) [3] R.P. Mann and R. Garnett, J. R. Soc. Interface 12, 20150037 (2015) 



Dec 2  Wed  Miguel Teixeira (Reading)  Applied Mathematics Colloquium  
14:00  Two mechanisms for free surface deformation over a flowing stream: subsurface turbulence and bottom topography  
Hicks, LT 11  
Abstract: The surface of a stream, particularly when this is shallow and flows fast, is characterized by deformations on a wide range of scales. Whereas in the deep ocean, such deformations are mostly free surface waves forced by the wind, in a fast shallow stream they result primarily from subsurface turbulence, which can generate both free and forced waves, and from bottom topography, which generates stationary waves. In this talk I will focus on these two mechanisms, showing some results from linear theories that capture essential aspects of each of them. The first theory is Rapid Distortion Theory (RDT), where the pressure disturbances that deform the free surface result from the interaction between the mean shear in the stream and subsurface turbulence. The second theory uses the fact that the stationary waves on the free surface are analogous to atmospheric waves trapped at a temperature inversion. The pressure disturbances that force them are thus due to interaction of the flow with bottom topography, and, for an isolated obstacle, produce a pattern reminiscent of Kelvin's ship waves. 



Dec 9  Wed  Amirul Khan (Leeds)  Applied Mathematics Colloquium  
14:00  CFDbased optimisation of ventilation systems  
Hicks, LT 11  
Abstract: Airflow, contaminant concentration and temperature distribution in a multibed hospital ward represented by a simple model room with multiple inlet and outlet vents, have been studied using computational fluid dynamics (CFD). Our work is concerned with the development and implementation of a practical and robust response surface based multiobjective optimization (MOP) scheme, with the aim of assisting hospital ward designers and managers /operators to enhance infection control (i.e. reduce the risk of airborne transmission) without compromising patient comfort and environmental impact. 



Feb 10  Wed  Andrew Hillier (DAMTP, Cambridge)  Applied Mathematics Colloquium  
14:00  Investigating MHD turbulence in solar prominences  
Hicks, LT 9  
Abstract: The motions of plasma in quiescent prominences, as revealed by Hinode observations, display highly complex flows across a wide range of spatial and temporal scales, and with the small diffusivity and viscosity of the system, it is no surprise that prominences host turbulence. In this talk I will present my analysis of Hinode SOT dopplergrams of a quiescent prominence observed on the 20080927. By investigating the spatial and temporal correlations between the lineofsight velocity fluctuations, it was possible to determine the scaling of the power laws up to highorder in the velocity difference, which display powers that are at some scales consistent with weak MHD turbulence, and at others is consistent with strong MHD turbulence. I will present some interpretation of these results based on the current theoretical understanding of turbulence, but also highlight areas in which they do not match with theory, and hopfully provide satisfactory explanations as to why this is the case. These results present another piece of the puzzle that is understanding the complex nature of quiescent prominences, and also on the role how turbulence plays in the complex magnetic field found in the solar atmosphere. 



Feb 12  Fri  Chris Jones (Leeds)  Applied Mathematics Colloquium  
13:00  Joint AM Colloquium + SP2RC Seminar Waves in the Earth's Core  
Hicks, LT 11  
Abstract: The Earth contains a liquid iron core 2,900 km below its surface. The Earth's magnetic field is generated by convective stirring in this electrically conducting core. Slow waves with periods of a several years can occur in the core, due to the interaction of rotational and magnetic forces. These waves can be detected in two different ways. They disturb the geomagnetic field, giving it a timedependent character, known as the magnetic secular variation, and this variation is being monitored by geomagnetic satellites. The waves can also transport angular momentum, and as they interact with the Earth's mantle, they lead to small but observable changes in the length of the day. The nature of both the axisymmetric and nonaxisymmetric wave modes that can occur in the core will be discussed. Axisymmetric torsional oscillations have been found in dynamo and magnetoconvection simulations, and this has enabled us to identify the excitation mechanism generating these waves, at least in the models. The waves originate primarily from the tangent cylinder, the cylinder coaxial with the rotation axis that encloses the solid inner core. Nonaxisymmetric waves are also seen in simulations, and these can be used to suggest which parts of the secular variation are likely dominated by wave propagation. Waves can also potentially shed light on the question of whether some parts of the core are stably stratified, as has been recently suggested. 



Mar 2  Wed  Kensuke Yokoi (Cardiff)  Applied Mathematics Colloquium  
14:00  Numerical simulations of free surface flows based on CLSVOF method, multimoment methods and densityscaled balanced CSF model  
Hicks, LT 9  
Abstract: In this presentation, we propose a practical numerical framework for free surface flows. The numerical framework consists of the CLSVOF (coupled level set and volumeoffluid) method, the THINC/WLIC (tangent of hyperbola for interface capturing/weighted line interface calculation) scheme, multimoment methods (CIPCSL and VSIAM3) and the densityscaled balanced CSF (continuum surface force) model. The framework is validated through several benchmark problems and comparisons with an experiment of droplet splashing. The numerical results have shown that the numerical framework is highly reliable and can well capture free surface flows with complex interface geometries like droplet splashing. 



Mar 4  Fri  Andrew Soward (Newcastle)  Applied Mathematics Colloquium  
13:00  Joint AM Colloquium + SP2RC. The Equatorial Ekman Layer  
Hicks, LT 11  
Abstract: This talk concerns a very old classic problem in rotating (incompressible) viscous fluids of the linear steady flow between two spheres caused by rotating them rapidly with slightly different rates about a common axis. The problem goes back to Proudman but was made famous by Stewartson through his resolution of the many free shear layers in the vicinity of the tangent cylinder (generators parallel to the rotation axis) to the inner sphere. I shall discuss the one he did not solve for, i.e., the limiting form of the Ekman layer on the inner sphere at the equator, where the tangent cylinder touches. 



Mar 9  Wed  Mat Hunt (hyperkahler.co.uk)  Applied Mathematics Colloquium  
14:00  3D surface and interfacial waves in MHD  
Hicks, LT 9  
Abstract: We present results on weakly nonlinear surface waves in 2+1 dimensions. Several cases are examined with and without a magnetic field above the plasma. We also present a derivation of the dispersion relation for two non interacting plasmas with different depths to get an interesting dispersion relation with lots of subcases. 



Mar 16  Wed  Andy Hoyle (Stirling)  Applied Mathematics Colloquium  
14:00  The short and longterm effects of parasite outbreaks to Salmon populations  
Hicks, LT 9  
Abstract: The UK Salmon industry is worth over £1bn per annum, but as with all ecological systems, it is under constant threat from disease outbreaks. One major threat is a macroparasite, G. salaris. Initially, I will use an ODEbased model to determine the impact of such a parasite outbreak to a host population in the shortterm. Then, by allowing the host to evolve a resistance mechanism, I will start to look at the longerterm effects, such as the time until we are likely to see host populations recover without intervention. Finally, by taking an adaptive dynamics style of approach, I can demonstrate under what conditions will a high level resistance evolve, as those seen in salmon population in other Baltic countries. 



Mar 18  Fri  David Southwood (Imperial)  Applied Mathematics Colloquium  
13:00  Joint AM Colloquium+SP2RC Seminar: The MHD kink mode and angular momentum transfer  
Hicks, LT 11  
Abstract: Storage and/or transmission of angular momentum in twisted magnetic fields is of fundamental interest in astrophysical problems. The transmission of angular momentum by waves from a rotating conducting object embedded in a stationary plasma is investigated. Our model is simple but enough to suggest a radical conclusion that in many circumstances where the magnetic field in a dissipationfree plasma is being twisted by a torque from a conductor threaded by the same field, kinking of the magnetic column that threads the rotating conductor is inherent. The kinking is produced by a wave with spiral phase characteristics that is standing in the rotating frame. On the outer edges of the distorted column currents flow along the characteristics connecting the rotating source to the wave front established when the rotation started. An immediate motivation was to explain the 10.7 hr magnetic pulsations that are seen to originate in the polar regions of the magnetosphere of Saturn. However, the idea potentially explains the longstanding puzzle as to why pulsars pulse as well as having applications in the solar atmosphere. 



Apr 20  Wed  Nikos Kavallaris (Chester)  Applied Mathematics Colloquium  
14:00  On a nonlocal parabolic problem arising in game theory  
Hicks, LT 9  
Abstract: In the current talk we first present the construction of a degenerate nonlocal equation which arises in the replicator dynamics system coming from the evolutionary game theory. Once the local existence is established we study the longtime behaviour of the preceding equation. Depending on the total mass of the initial data we either prove globaltime existence or finitetime blowup. For total mass equal to 1 then also the convergence towards the steadystates (Nash equilibria) is proven. 



Apr 27  Wed  Andrew Gilbert (Exeter)  Applied Mathematics Colloquium  
14:00  Fluids/MHD  
Hicks, LT 9  


May 11  Wed  Mike Jolly (Indiana)  Applied Mathematics Colloquium  
14:00  Turbulence of passive tracers  
Hicks, LT 9  
Abstract: We study the influence that fluid turbulence has on passive tracer turbulence. In particular, we consider the effect the inverse cascade in 2D can have on the tracer cascade. In this case, we assume two power laws for the tracer which are consistent with the power laws of the fluid. We show that the tracer cascade range can extend up to the dissipation wave number of the fluid under certain reasonable constraints on the Grashof number of the fluid, and the gap between the injection of the tracer and the energy. For moderate Prandtl numbers the diffusive wave number is comparable to the dissipation wave number, so this provides an optimal tracer cascade range. For 3D flows we can extend the tracer cascade range up to a power of 2/3 of the diffusion wave number, which is analogous to a result for the fluid cascade in previous work. 



May 18  Wed  Steve Tobias (Leeds)  Applied Mathematics Colloquium  
15:00  Direct Statistical Simulation of wallbounded, geophysical and astrophysical flows  
Hicks, LT 9  
Abstract: Fluid flows are often turbulent owing to the extreme values of the Reynolds numbers. A description of these ﬂows via direct numerical simulation (DNS) would therefore have to be able to resolve a huge range of spatial and temporal scales, which, for certain problems, is clearly beyond the capability of current algorithms and computational resources (and indeed those of the immediate future). However these flows often display remarkable organisation. The jets on Jupiter, the differential rotation of the Sun and the solar activity cycle are all examples of this "order from chaos". Laboratory flows are likewise characterised by an interaction between systematic flows and turbulent motions. Owing to the presence of rotation and stratiﬁcation ﬂows are often (if not always) inhomogeneous and anisotropic.Here I shall describes a new programme, which we term Direct Statistical Simulation (DSS) that attempts to calculate directly the loworder statistics of such ﬂows (such as mean ﬂows and twopoint correlation functions). DSS respects the inhomogeneity and anisotropy of the fluid systems, and is predicated on an expansion in cumulants. I shall further discuss generalisations of the quasilinear approximation that lead to new closure schemes for these ﬂows. As examples I shall use models for the formation of jets on giant planets and the problem of rotating couette flow. 



May 25  Wed  Adam Pound (Southampton)  Applied Mathematics Colloquium  
14:00  Gravitational selfforce and the future of binary inspiral modelling  
Hicks, LT 9  
Abstract: The recent observation of the black hole binary GW150914 has inaugurated the era of gravitational wave astronomy. Current, groundbased detectors are expected to primarily observe more binaries of the same sort as GW150914, composed of comparablemass compact objects. However, planned spacebased detectors will be able to observe other classes of binaries, with intermediate and extreme mass ratios, which will serve as unheralded probes of strongfield geometry and dynamics. Presently, the only viable method of modeling those binaries is provided by gravitational selfforce theory, which uses tools from singular perturbation theory to construct an asymptotic approximation in the extrememassratio limit. Remarkably, by interfacing with other methods, selfforce theory can also be used to improve models of comparablemass binaries. In this talk, I discuss the foundations of selfforce theory, its successes in assisting comparablemass models, and recent progress in overcoming the largest remaining obstacle to accurate extrememassratio models: extending selfforce computations to second perturbative order. 



Oct 26  Wed  Robert Kerr (Warwick)  Applied Mathematics Colloquium  
14:00  Scaling of NavierStokes trefoil reconnection  
Hicks, LT 10  
Abstract: The reconnection of a trefoil vortex knot is examined numerically to determine how its helicity and two vorticity norms behave. During an initial phase, the helicity is remarkably preserved, as reported in recent experiments (Scheeler et al. 2014a). Equally unexpected is selfsimilar growth in the volumeintegrated vorticity squared or enstrophy Z, growth where (√ν)Z(tx) is independent of the viscosity at a configuration dependent time txtx which will be interpreted as the end of first reconnection. By rescaling tx−t for times t 



Nov 2  Wed  Peter Taylor (Conell/Dublin)  Applied Mathematics Colloquium  
14:00  New modesum prescriptions for quantum stressenergy tensor regularization  
Hicks, LT 10  
Abstract: Quantum gravity remains one of the most important outstanding problems in physics. In the absence of a full theory, one must rely on approximations. One particularly important approximation is semiclassical gravity, which is the treatment of quantum fields interacting with a classical spacetime metric via the semiclassical Einstein equations. Solving the semiclassical Einstein equations is notoriously difficult. The first major obstacle one encounters is that the source term  which is the expectation value of the stressenergy tensor for some quantum fields  is divergent. While this may be handled by normal ordering in Minkowski spacetime, the situation is more complicated in curved spacetime where there is no preferred vacuum. A formal prescription to regularize the quantum stressenergy tensor  known as the pointsplitting scheme  dates back to DeWitt and Christensen's seminal work in the 1970s. However, applying the pointsplitting scheme in a way that is amenable to numerical evaluation has remained a challenge; the first work in this direction was the work of Candelas and Howard in the 1980s. Despite some serious drawbacks, the CandelasHoward approach has remained more or less the standard prescription for several decades. In recent years, advances in numerical relativity and new techniques for modesum regularization developed within the selfforce community has made a fully selfconsistent semiclassical evolution a realistic goal, which has given new impetus to developing practical and efficient modesum schemes in the quantum field theory context. I will discuss two recent independent endeavours in this direction: the first by Taylor, Ottewill and Breen and the other by Levi and Ori. 



Nov 10  Thu  Thomas Michelitsch (CNRS, Paris)  Applied Mathematics Colloquium  
14:00  Fractional Lattice Dynamics: Nonlocal constitutive behavior generated by power law matrix functions and their fractional continuum limit kernels  
Hicks, LT 10  
Abstract: We introduce positive elastic potentials in the harmonic approximation leading by Hamilton's variational principle to fractional Laplacian matrices having the forms of power law matrix functions of the simple local Bornvon Karman Laplacian. The fractional Laplacian matrices are well defined on periodic and infinite lattices in n=1,2,3,.. dimensions. The present approach generalizes the central symmetric second difference operator (Born von Karman Laplacian) to its fractional central symmetric counterpart (Fractional Laplacian matrix). For noninteger powers of the Born von Karman Laplacian, the fractional Laplacian matrix is nondiagonal with nonzero matrix elements everywhere, corresponding to nonlocal behavior: For large lattices the matrix elements far from the diagonal expose power law asymptotics leading to continuum limit kernels of Riesz fractional derivative type. We present explicit results for the fractional Laplacian matrix in 1D for finite periodic and infinite linear chains and their Riesz fractional derivative continuum limit kernels. The approach recovers for α=2 the well known classical Born von Karman linear chain (1D lattice) with local next neighbor springsleading in the well known continuum limit of classic local standard elasticity, and for other integer powers to gradient elasticity.We also present a generalization of the fractional Laplacian matrix to ndimensional cubic periodic (nD tori) and infinite lattices. For the infinite nD lattice we deduce a convenient integral representation.We demonstrate that our fractional lattice approach is a powerful tool to generate physically admissible nonlocal lattice material models and their continuum representations. 



Nov 16  Wed  Vassilios Dallas (Leeds)  Applied Mathematics Colloquium  
14:00  Can we predict the large scales of turbulence?  
Hicks, LT 10  
Abstract: Absolute equilibrium (zero flux) statistical mechanics have been used effectively in the ideal case of zero viscosity to predict the cascade (finite flux) of ideal invariants across scales in dissipative turbulence. We show numerically that the statistical properties of helical hydrodynamic (HD) and helical MHD turbulence at scales larger than the forcing scale can be described to a large degree by the truncated Euler and ideal MHD equations, respectively. Therefore, the functional shape of the large scale spectra can be predicted using absolute equilibrium theory. Provided that scales sufficiently larger than the forcing scale but also sufficiently smaller than the box size are examined, then $E(k) \propto k^2$ and $H_u(k)/(kE(k)) \propto k$ in HD turbulence while $E(k) \propto k^2$ and $kH_b/E(k) \propto k^{1}$ in MHD turbulence. In these turbulent systems equilibrium and outofequilibrium statistical mechanics coexist though instantaneous fluctuations of fluxes towards large and small scales. 



Nov 23  Wed  Chuong Tran (St. Andrews)  Applied Mathematics Colloquium  
14:00  The pressure force in NavierStokes flows: Depletion of nonlinearity versus regularity  
Hicks, LT 10  
Abstract: The issue of solution regularity of the threedimensional NavierStokes equations is a longstanding problem in mathematical fluid mechanics. It is well known that classical solutions exist locally in time for sufficiently smooth initial velocity fields. The question is whether such solutions remain regular globally. Active research since Leray's seminal work in the 1930s appears to have suggested a negative answer to this question. Indeed, the volume of results on partial regularity in the literature unmistakably casts doubt on the capability of viscous effects in controlling the NavierStokes nonlinearity. The pressure force driving NavierStokes flows apparently exhibits some depletion of nonlinearity. It is possbile that such depletion is sufficient to allow for a balance between nonlinear and viscous effects, thereby ensuring global regularity. This seminar presents results from recent investigations into this possibility. Regularity criteria in terms of pressure and velocity gradients along streamlines are derived and discussed. 



Nov 30  Wed  John Gibbon (Imperial)  Applied Mathematics Colloquium  
14:00  Analysis of PDEs involving the RayleighTaylor instability  
Hicks, LT 10  
Abstract: The phenomenon of the RayleighTaylor instability (RTI), involving the mixing of a heavy fluid overlaying a lighter, has a long history, not least because it occurs in laboratory tank and plasma fusion experiments, multiphase physics and astrophysical phenomena. The approach taken by different schools varies widely. We will briefly review this work but spend most of the talk on what is known as the variable density model (VDM) pioneered by Cook and Dimotakis (2001) and Livescu and Ristorcelli (2007). The PDEs, coupled to the 3D NavierStokes equations, have a remarkably elegant nature but pose hard technical challenges. Our analysis uses the data generated by Daniel Livescu (LANL) and available on the Johns Hopkins Turbulence database (JHTDB). If time permits I will briefly discuss the occurrence of the RTI at interfaces in multiphase physics which involves the coupling of the 3D NavierStokes equations to the 3D CahnHilliard equations. 



Feb 8  Wed  George Papadakis (Imperial)  Applied Mathematics Colloquium  
14:00  Nonlinear optimal control of bypass transition in a boundary layer flow  
Hicks, LT 10  
Abstract: We apply and assess a nonlinear optimal control strategy to suppress bypass transition in a zeropressuregradient boundary layer. To this end, a Lagrange variational formulation is employed that results in a set of adjoint equations. The optimal wall actuation (blowing and suction from a control slot) is found by solving iteratively the nonlinear NavierStokes and the adjoint equations in a forward/backward loop using DNS. The optimization is performed in a finite time horizon. Large values of optimization horizon result in instability of the adjoint equations. The control slot is located exactly in the region of transition. The results show that the control is able to significantly reduce the objective function, which is defined as the spatial and temporal integral of the quadratic deviation from the Blasius profile plus a term that quantifies the control cost. The physical mechanism with which the actuation interacts with the flow field is investigated and analysed in relation to the objective function employed. The spanwise averaged velocity is distorted by the control action, resulting in a significant reduction of the skin friction coefficient. We performed simulations with and without zeronet mass flow constraint of the actuation velocity. Results are also compared with uniform blowing using the same timeaverage velocity obtained from the nonlinear optimal algorithm. 



Feb 15  Wed  Felix Ng (Department of Geography, Sheffiled)  Applied Mathematics Colloquium  
15:00  Grainscale processes in the Earth's polar ice sheets  
Hicks, LT 10  
Abstract: The spreading of the Antarctic and Greenland Ice Sheets is a slow viscous flow with nonlinear rheology. Besides temperature, grain sizes and crystal orientation within the polycrystalline ice are important factors behind the rheology. After giving this glaciological background, I will describe two mathematical models recently built to understand grainsize evolution. The first model is formulated to capture the observed grainsize profiles in ice cores. The second model tackles the fundamental process of normal grain growth (NGG), a coarsening process that occurs in metals as well as ice. 



Mar 22  Wed  Abraham Harte (Dublin City University)  Applied Mathematics Colloquium  
14:00  Metricindependence of electromagnetic fields  
Hicks, LT 10  


Apr 26  Wed  Cedric Beaume (Leeds)  Applied Mathematics Colloquium  
14:00  From convectons to complexity in doubly diffusive convection  
Hicks, LT 10  
Abstract: Doubly diffusive convection arises frequently in natural phenomena and industrial processes. It occurs in systems where heat and another quantity diffuse at different rates. Wellknown examples are provided by thermohaline convection and the salt finger instability. In this talk, we consider threedimensional thermohaline convection where a binary mixture is confined between vertical walls maintained at different temperatures and salinities. In this configuration, we found stationary spatially localised solutions consisting of spots of convection embedded in a background conduction state. These convectons are formed through a subcritical bifurcation from the conductive state (motionless fluid) and display a variety of patterns while simulations above onset reveal chaotic dynamics. 



May 10  Wed  Schuyler Nicholson (U Mass Boston)  Applied Mathematics Colloquium  
14:00  Information, patterns, and learning the rules of an explosion  
Hicks, LT 10  
Abstract: At the right pressures and temperatures, gaseous mixtures of hydrogen and oxygen explode. Experimental advances continue to extract chemical processes at ever shorter timescales. The goal of these experiments is to transform this data into chemical mechanisms which describe the sequences of transient chemical species formed during an explosion. Constructing this chemical mechanism will enhance the eciency, reliability, and safety of hydrogen technologies from combustion engines to fuel cells. However, this need to learn the basic rules of combustion is hampered by constraints on the experimentally accessible information. In this talk, I will introduce our recent work applying theoretical tools from information theory and statistical mechanics, which respects these constraints and allows for the systematic discovery of chemical mechanisms. 



May 24  Wed  Alvar Daza (Universidad Rey Juan Carlos)  Applied Mathematics Colloquium  
14:00  Fractal basins and unpredictability in dynamical systems  
Hicks, LT 10  
Abstract: Basins of attraction take its name from hydrology, and in dynamical systems they refer to the set of initial conditions that lead to a particular final state. When different final states are possible, the predictability of the system depends on the structure of these basins. In this talk, we will revise the main kinds of fractal basin boundaries appearing in dissipative and Hamiltonian systems. Finally, we will introduce the concept of basin entropy in order to answer an apparently naïve question: how can we say that one basin is more unpredictable than another? 



Sep 27  Wed  Matthew Allcock/Mihai Barbulescu (Sheffield)  Applied Mathematics Colloquium  
14:00  Magnetoacoustic waves in asymmetric solar waveguides: magnetoseismology and the KelvinHelmholtz instability  
Hicks, LT 9  
Abstract: Matthew Allcock's abstract  Our Sun is a restless plasma with a strong and evolving magnetic field, making magnetohydrodynamics (MHD) an essential tool to describe its behaviour. The Sun’s atmosphere, where magnetic forces dominate, is permeated by MHD waves that can be used as an indirect method for diagnosing difficulttomeasure parameters of the solar plasma. This technique is known as solar magnetoseismology. In this talk, we will introduce a novel equilibrium structure consisting of two parallel discontinuities with a uniform magnetic field in the central region. We perturb the system and illustrate the eigenmodes using 3D animations to demonstrate the change in character of symmetric MHD wave modes when the system is asymmetric. We derive two methods that use this asymmetry to estimate the strength of the background magnetic field. This advances the field of solar magnetoseismology in locally asymmetric structures in the solar atmosphere. Mihai Barbulescu's abstract  Solar plasma is highly dynamic and subject to various kinetic and magnetic forces. Many of these forces create bulk flows which need to be included in analytical models, especially when studying time dependent phenomena. Building up from the previous talk, we study the effects that a steady flow has on wave propagation in an asymmetric waveguide, and on its stability. When flow speeds are high enough, they force perturbations of the waveguide to steepen, and the KelvinHelmholtz instability (KHI) occurs. We calculate the critical values required by the KHI under different parameter regimes and discuss how these results may change how we view various solar phenomena. 



Oct 4  Wed  Zijing Ding (Bristol)  Applied Mathematics Colloquium  
14:00  Thin liquid film flowing down a vertical fibre  
Hicks, LT 9  
Abstract: We consider the motion of a gravitydriven flow coating a vertical fibre rotating about its axis. This flow exhibits rich dynamics including the formation of droplets, or beads, driven by a RayleighPlateau mechanism modified by the presence of gravity and rotation. We derived an evolution equation for the film thickness using a longwave approximation. We focus on the effect of rotation on the linear stability, absoluteconvective instabilities (CI/AI), nonlinear evolution and the travelling solutions. The results of the linear stability analysis show that the effect of rotating is destabilizing. A spatialtemporal stability analysis is performed to investigate the convectiveabsolute instability characteristics of the problem. We also perform a numerical simulation on the nonlinear evolution of the film to examine the transition from CI to AI regime. It has been shown that the effect of rotation enhances the absolute instability and promotes the breakup of the film into smaller droplets. The travelling wave solutions of the evolution equation yield information regarding the shape of the interface and propagation speed of the disturbance 



Oct 25  Wed  James Mather (Sheffield)  Applied Mathematics Colloquium  
14:00  Flow Instabilities in Partially Ionised Plasmas: Dissipative and Resonant Instabilities  
Hicks, LT 9  
Abstract: The solar atmosphere is a vastly complex and dynamic area, containing many different magnetic structures. The temperature can vary from approximately 4500 K at the temperature minimum to over 10 MK in parts of the solar corona. This temperature stratification affects how ionised the solar plasma is at different layers. Prominences are largely characterised as chromospheric material, at approximately 10000 K, suspended within the coronal plasma and, therefore, may not be fully ionised. They are also very dynamic and may exhibit bulk flows, with observations showing the presence of numerous instabilities. In this talk we firstly briefly introduce the fully ionised magnetic plasma slab moving under. Next, we investigate a plasma slab that has a uniform background bulk flow in the single fluid approximation, where partial ionisation is considered in Cowling’s resistive term in the induction equation, modelling a prominence surrounded by a viscous corona. We study the dissipative instability that can occur at flow speeds that match the internal tube/slow speed. Secondly, we set up a completely two fluid magnetic slab (ions and neutrals) moving under a bulk flow and investigate, in both the compressible and incompressible cases, a quasiresonant instability that occurs between a new mode, that appears due to neutral molecules, which is always KHI unstable for any shear in flow and the normal magnetoacoustic modes of a slab moving under a uniform bulk flow. 



Nov 15  Wed  Rebecca Hoyle (Southampton)  Applied Mathematics Colloquium  
14:00  Maternal effects and environmental change  
Hicks, LT 9  
Abstract: Maternal effects are influences of the maternal phenotype on offspring phenotypes by routes other than direct genetic transmission. Potentially they provide an additional means of adaptation to changing environmental conditions over and above that afforded by withingeneration phenotypic plasticity. However, maternal effects have also been implicated in the risks of heart disease, diabetes and obesity. I will show how mathematical modelling can provide insight into the interaction of maternal effects and phenotypic plasticity under different patterns of environmental change and suggest when maternal effects might be expected to evolve and why. 



Nov 22  Wed  Jonathan Sherratt (HeriotWatt)  Applied Mathematics Colloquium  
14:00  Using Mathematics to Infer the Historical Origin of Vegetation Patterns in SemiDeserts  
Hicks, LT 9  
Abstract: Landscapescale patterns of vegetation occur worldwide at interfaces between semiarid and arid climates. They are important as potential indicators of climate change and imminent regime shifts, and arise from positive feedback between vegetation and infiltration of rainwater. On gentle slopes the typical pattern form is bands (stripes), oriented parallel to the contours, and their wavelength is probably the most accessible statistic for vegetation patterns. I will discuss the use of mathematical models to investigate different possible mechanisms for the origin of these patterns. I will show that patterns can arise either from degradation of uniform vegetation, or from the colonisation of bare ground. Most significantly, I will show that these two mechanisms can be distinguished by the relationship between pattern wavelength and slope gradient: degradation of uniform vegetation generates patterns whose wavelength increases with slope, while colonisation of bare ground gives the opposite trend. This makes it possible to infer the historical origin of the patterns. Specifically, for subSaharan Africa (the "Sahel" region) model predictions and historical rainfall data together imply that vegetation patterns originated by the colonisation of bare ground, either during c.17601790 or since c.1850. 



Nov 29  Wed  Ricardo GarciaMayoral (Cambridge)  Applied Mathematics Colloquium  
14:00  Alteration of nearwall turbulence by textured surfaces  
Hicks, LT 9  
Abstract: The structure of turbulence near walls can be altered by the presence of surface features such as roughness or texturing, providing opportunities to control the flow passively. The surface texture can induce a coherent component in the flow, as well as a shift in the 'virtual origin' experienced by the overlying turbulence. We will illustrate these mechanisms using the examples of transitionally rough and superhydrophobic textures. 



Dec 6  Wed  Kenta Ishimoto (Oxford)  Applied Mathematics Colloquium  
14:00  Hydrodynamics of sperm rheotaxis and guidance of microswimmers  
Hicks, LT 9  
Abstract: Sperm cells swim against a flow  just as salmon swimming in the river. This sperm rheotacic behaviour was first observed more than a century ago, and recently, it has been hypothesised to be a mechanism of sperm guidance in female reproductive tract. In this talk, we present simple hydrodynamic simulations and theoretical models that could explain this phenomenon, and proceed to consider mathematical structures of the hydrodynamic interactions of a microswimmer in a flow. Possible engineering applications for guidance of microswimmeres will also be discussed. 



Feb 7  Wed  Dan Lucas (Keele)  Applied Mathematics Colloquium  
14:00  A dynamical systems perspective on layers and mixing in stratified turbulence  
Hicks, LT 9  
Abstract: Stably stratified flows, with dense fluid underlying lighter fluid, are commonly observed in nature and industry. In the oceans the behaviour of turbulence when the fluid is strongly stratified is of great importance if we are to understand fundamental processes such as layer formation and mixing. In this work we approach these issues from the socalled ‘dynamical systems perspective’ where we seek unstable simple solutions, or “exact coherent structures”, which are embedded in the chaos of the turbulent flow. First we show that when forcing the flow with a horizontal shear, spontaneous layers form. We are able to associate the coherent structures responsible for the layers with steady states which a bifurcation analysis shows are the finite amplitude product of a sequence of stratified linear instabilities [1]. Secondly we attack the problem of mixing in stratified turbulence by locating unstable periodic orbits embedded in the turbulence in two parameter regimes; one where the mixing is quite efficient and another where the mixing is weak. The periodic orbits represent a reduced description of the flow which we are able to examine in detail, and compare the processes involved in rearranging the buoyancy field in each case [2]. [1] Lucas, Caulfield & Kerswell 2017 J. Fluid Mech. 832 pp 409437 [2] Lucas & Caulfield 2017 J. Fluid Mech. 832 R1, 



Feb 26  Mon  Dwight Barkley (Warwick)  Applied Mathematics Colloquium  
15:00  Recent Advances in the subcritical transition to turbulence  
Hicks, LT E  
Abstract: Explaining the route to turbulence in wallbounded shear flows has been a long and tortuous journey. After years of missteps, controversies, and uncertainties, we are at last converging on a unified and fascinating picture of transition in flows such as pipes, channels, and ducts. Classically, subcritical transition (such as in a pipe), was thought to imply a {\em discontinuous} route to turbulence. We now know that this is not the case  subcritical shear flows may, and often do, exhibit continuous transition. I will discuss recent developments in experiments, simulations, and theory that have established a deep connection between transition in subcritical shear flows and a class of nonequilibrium statistical phase transitions known as directed percolation. From this we understand how to define precise critical points for systems without linear instabilities and how to characterize the onset of turbulence in terms of nontrivial, but universal power laws. I will discuss the physics responsible for the complex turbulent structures ubiquitously observed near transition and end with thoughts on outstanding open questions. 



Feb 26  Mon  Laurette Tuckerman (ESPCI Paris)  Applied Mathematics Colloquium  
15:45  Exotic patterns of Faraday waves  
Hicks, LT E  
Abstract: When a fluid layer is vibrated at a sufficiently high amplitude, a pattern of standing waves appears at its surface. Because of the imposed periodicity, this is a Floquet problem, but we explain how to easily solve it. Classically, the pattern takes the form of stripes, squares or hexagons, but we also look at more exotic patterns like quasipatterns, heteroclinic orbits, supersquares, and Platonic polyhedra. (Longer version) A standing wave pattern appears on the free surface of a fluid layer when it is subjected to vertical oscillation of sufficiently high amplitude. Like TaylorCouette flow (TC) and RayleighBenard convection (RB), the Faraday instability is one of the archetypical patternforming systems. Unlike TC and RB, the wavelength is controlled by the forcing frequency rather than by the fluid depth, making it easy to destabilize multiple wavelengths everywhere simultaneously. Starting in the 1990s, experimental realizations using this technique produced fascinating phenomena such as quasipatterns and superlattices which in turn led to new mathematical theories of pattern formation. Another difference is that the Faraday instability has been the subject of surprisingly little numerical study, lagging behind TC and RB by several decades. The first 3D simulation reproduced hexagonal standing waves, which were succeeded by longtime recurrent alternation between quasihexagonal and beaded striped patterns, interconnected by spatiotemporal symmetries. In a large domain, a supersquare is observed in which diagonal subsquares are synchronized. A liquid drop subjected to an oscillatory radial force comprises a spherical version of the Faraday instability. Simulations show Platonic solids alternating with their duals while drifting. 



Feb 28  Wed  Peter Millington (Nottingham)  Applied Mathematics Colloquium  
14:00  Energyparity from a bicomplex algebra  
Hicks, LT 9  
Abstract: There is a long history of attempts to alleviate the sensitivity of quantum field theory to vacuum fluctuations and ultraviolet divergences by introducing states of negative norm or states of negative energy. This history involves early works by Dirac, Pauli, Pontrjagin and Krein, as well as more recent suggestions by Linde, Kaplan and Sundrum, and ‘t Hooft and Nobbenhuis. In this talk, we will attempt to construct viable scalar quantum field theories that permit positive and negativeenergy states by replacing the field of complex numbers by the commutative ring of bicomplex numbers. The two idempotent zero divisors of the bicomplex numbers partition the algebra into two ideal subalgebras, and we associate one with positiveenergy modes and the other with negativeenergy modes. In so doing, we avoid destabilising, negativeenergy cascades, while realising a discrete energyparity symmetry that eliminates the vacuum energy. The probabilistic interpretation is preserved by associating expectation values with the Euclidean inner product of the bicomplex numbers, and both the positive and negativeenergy Fock states have positivedefinite Euclidean norms. We consider whether this construction can yield transition probabilities consistent with the usual scattering theory and highlight potential limitations. We conclude by commenting on the extension to spinor, vector and tensor fields. 



Apr 18  Wed  Elena Marensi (Sheffield)  Applied Mathematics Colloquium  
14:00  Calculation of minimal seeds in stabilised pipe flows  
Hicks, LT 9  
Abstract: Turbulent wall flows exert a much higher friction drag than laminar flows, with consequent increase in energy consumption and carbon emissions. Considerable research effort is thus directed towards the design of control strategies to reduce the turbulent drag or delay the transition to turbulence. Of fundamental interest from this viewpoint is the socalled minimal seed, i.e. the initial perturbation of lowest energy capable to trigger transition. In this talk, variational methods are used to construct fully nonlinear optimisation problems that seek the minimal seed in stabilised pipe flows. The question of how representative the minimal seed is of typical ambient disturbances is addressed here for the first time by performing a statistical study of the critical initial energies for transition with different initial perturbations. A set of initial conditions are thus generated to investigate the stabilising effect of a simple model for the presence of a baffle in the core of the flow. Significant increases in the critical energy and drag reductions are found to be possible. The relevance of the minimal seed in realistic scenarios will be further discussed, as well as a closelyrelated variational problem for the control of transition. 



May 9  Wed  Riccardo Vanon (Sheffield)  Applied Mathematics Colloquium  
14:00  The role of zonal flows in selfgravitating astrophysical disc turbulence  
Hicks, LT 9  
Abstract: Astrophysical discs whose mass is not negligible compared to their central object (ie. selfgravitating discs) can be induced to fragment or settle into a turbulentlike state due to the destabilising action of selfgravity. Although the fragmentation process is well studied, the mechanism allowing the gravitational turbulent state to sustain itself is poorly understood, as this requires a continuous extraction of energy from the background flow to prevent its decay. In this talk I will present numerical simulations, carried out using a bespoke pseudospectral code, that will show how the gravitational turbulent state and the formation of zonal flows in the disc are strongly connected thanks to the action of axisymmetric and nonaxisymmetric instabilities. 



May 16  Wed  Ati Sharma (Southampton)  Applied Mathematics Colloquium  
14:00  Some recent developments in the loworder modelling of fluid flows  
Hicks, LT 9  
Abstract: Modelling fluid flows is a difficult problem. Fluid flows are well described by the NavierStokes equations, but these are nonlinear PDEs, which are difficult to solve in a general way. Much recent work has focused on finding lowdimensional approximations to fluid flow systems, either by abstracting them from data generated from experiment and simulation or by finding suitable approximations to the equations. This talk will discuss two such approaches, Dynamic Mode Decomposition (DMD) and resolvent analysis. The approaches will be explained, and a variety of recent applications to flow analysis and estimation will be presented. 



Sep 26  Wed  Yang Zhang (Sheffield (Mech Eng))  Applied Mathematics Colloquium  
14:00  Imaging based flame diagnostics and its quantitative analysis  
Hicks, LT 9  
Abstract: In this talk, a brief history of photography and their application in combustion studies will be given, which actually goes back to the 19th century. Then case studies will be shown on digital flame imaging, especially high speed imaging for the tracking of the fast flame dynamics. It will demonstrate that selective digital imaging enhancement is essential in observing the drastically different flame light intensities of the soot and chemical species. Through digital image processing, quantitative and useful information can be extracted from the flame image database. The simultaneous imaging of visible and infrared light emissions from the ignition of a flame using a single high speed colour digital camera will also be demonstrated which also poses a challenge in spectroscopic study on how to identify this infrared only emissions. 



Oct 3  Wed  Priya Subramanian (Leeds)  Applied Mathematics Colloquium  
14:00  Pattern formation in systems with multiple scales  
Hicks, LT 9  


Oct 24  Wed  Istvan Cziegler (York)  Applied Mathematics Colloquium  
14:00  Turbulence and phase transitions in tokamak plasmas  
Hicks, LT 11  
Abstract: The transition from the low to the highconfinement operation is one of the most important phenomena in magnetic confinement fusion. The highconfinement regime, known as Hmode, leads to a vastly increased plasma density and temperature, which equates to a significant gain in fusion power. Since the dominant transport across the confining magnetic field is due to turbulence, the LH transition can be thought of as a phase transition to suppressed turbulence. It is known that both the quality of global confinement and the threshold of the transition depend on macroscopic parameters, such as plasma density, magnetic topology and geometry near particle exhaust areas called divertors. The talk will connect the various scales of dynamics with this phenomenology and some broader context in physics. 



Oct 31  Wed  Miguel Teixeira (Reading)  Applied Mathematics Colloquium  
14:00  A physicallybased model for the winddriven current in the wavy oceanic surface layer  
Hicks, LT 9  
Abstract: A simple analytical model is developed for the current induced by the wind and modified by surface windwaves in the oceanic surface layer, based on a firstorder turbulence closure and including the effect of a vortex force representing the Stokes drift of the waves. The shear stress is partitioned between a component due to shear in the current and a waveinduced component, which decays over a depth proportional to the wavelength. The model reproduces the apparent reduction of the friction velocity and enhancement of the roughness length estimated from current profiles, detected in a number of studies. The current profile becomes flatter for strong wave forcing owing to a smaller fraction of the total shear stress being supported by the current shear. These effects are entirely attributed to nonbreaking surface waves, and predicted to increase with wave forcing. A version of the model where the shear stress decays to zero with depth is able to adequately predict the surface current speed. 



Nov 14  Wed  James McLaughlin (Northumbria)  Applied Mathematics Colloquium  
14:00  Modelling QuasiPeriodic Pulsations in Solar and Stellar Flares  
Hicks, LT 9  
Abstract: Solar flare emission is detected in all EM bands and variations in flux density of solar energetic particles. Often the EM radiation generated in solar and stellar flares shows a pronounced oscillatory pattern, with characteristic periods ranging from a fraction of a second to several minutes. These oscillations are referred to as quasiperiodic pulsations (QPPs), to emphasise that they often contain apparent amplitude and period modulation. We review the current understanding of quasiperiodic pulsations in solar and stellar flares. In particular, we focus on the possible physical mechanisms, with an emphasis on the underlying physics that generates the resultant range of periodicities. These physical mechanisms include MHD oscillations, selfoscillatory mechanisms, oscillatory reconnection/reconnection reversal, wavedriven reconnection, two loop coalescence, MHD flow overstability, the equivalent LCRcontour mechanism, and thermaldynamical cycles. We also provide a histogram of all QPP events published in the literature at this time. The occurrence of QPPs puts additional constraints on the interpretation and understanding of the fundamental processes operating in flares, e.g. magnetic energy liberation and particle acceleration. Therefore, a full understanding of QPPs is essential in order to work towards an integrated model of solar and stellar flares. Based on McLaughlin et al., 2018, Space Science Review, 214, 45, https://doi.org/10.1007/s1121401804785 



Nov 21  Wed  Simon Malham (HerrotWatt)  Applied Mathematics Colloquium  
14:00  Partial differential equations with nonlocal nonlinearities: Generation and solution  
Hicks, LT 9  
Abstract: We present a programme for generating the solutions of large classes of nonlinear partial differential equations, by pulling the equations back to a linear system of equations. The idea underlying this programme is to lift the standard relation between Riccati equations and linear systems to the infinite dimensional setting. This generalisation is wellknown in optimal control theory where the offline Riccati solution mediates the optimal current state feedback. The solution procedure can be presented at an elementary level and many examples will be included. Such example applications are partial differential equations with nonlocal nonlinearities, for example the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation and Smoluchowski's coagulation equation and, by association, the inviscid and viscous Burgers equations with local advective nonlinearities. 



Dec 5  Wed  Jake Shipley (SoMaS)  Applied Mathematics Colloquium  
14:00  Strongfield gravitational lensing by black holes  
Hicks, LT 11  
Abstract: A key prediction of Einstein's theory of general relativity (GR) is the bending of light due to gravity, a phenomenon known as gravitational lensing. In 1919, Eddington's observation of light deflection by the Sun – weakfield gravitational lensing – played a key role in the establishment of GR as our best theory of gravitation. Almost 100 years later, we are on the verge of a new era in the field of gravitational lensing. Using the Event Horizon Telescope (EHT), an Earthscale virtual telescope which employs verylongbaseline interferometry, astronomers will soon directly observe the supermassive black hole at the galactic centre. The highresolution images formed by the EHT will allow us to test GR in the strongfield regime. In this talk, I will review the subject of gravitational lensing, before presenting an overview of the EHT's main aims and objectives. I will conclude with a review of some recent theoretical work on the subject of strongfield gravitational lensing by black holes. 



Feb 20  Wed  Heather Harrington (Oxford)  Applied Mathematics Colloquium  
14:00  Comparing models and biological data using computational algebra and topology  
Hicks, LT 9  
Abstract: Many biological problems, such as tumorinduced angiogenesis (the growth of blood vessels to provide nutrients to a tumor), or signaling pathways involved in the dysfunction of cancer (sets of molecules that interact that turn genes on/off and ultimately determine whether a cell lives or dies), can be modeled using differential equations. There are many challenges with analyzing these types of mathematical models, for example, rate constants, often referred to as parameter values, are difficult to measure or estimate from available data. I will present mathematical methods we have developed to enable us to compare mathematical models with experimental data. Depending on the type of data available, and the type of model constructed, we have combined techniques from computational algebraic geometry and topology, with statistics, networks and optimization to compare and classify models without necessarily estimating parameters. Specifically, I will introduce our methods that use computational algebraic geometry (e.g., Gröbner bases) and computational algebraic topology (e.g., persistent homology). I will present applications of our methodology on datasets involving cancer. Time permitting, I will conclude with our current work for analyzing spatiotemporal datasets with multiple parameters using computational algebraic topology. Mathematically, this is studying a module over a multivariate polynomial ring, and finding discriminating and computable invariants. 



Mar 6  Wed  Rachael Hardman (SoMaS)  Applied Mathematics Colloquium  
14:00  Measuring the Ocean Spectrum using HF Radar Data and a Neural Network  
Hicks, K14  
Abstract: High frequency, or HF, coastal radars can provide continuous high resolution measurements of ocean surface currents, winds and waves. First derived in 1972, the expected radar signal when electromagnetic waves are scattered by the ocean surface can be modelled by the radar cross section, a nonlinear integral equation which enables us to predict the radar output for any ocean state. Methods for inverting the radar cross section  which ultimately permit us to measure ocean parameters from HF radar data  have been developed over the last few decades; however there are times when the measured data cannot be modelled by the mathematical equations and are therefore not suitable for inversion using the existing methods. Using a neural network, trained on simulated radar data, we have successfully inverted HF radar data not modelled by the radar cross section. In this talk, I will give an overview of how HF radar is used in ocean sensing before introducing neural networks. I will finish by presenting the results of a validation experiment, showing how a neural network can learn the complex inverse relationship between HF radar and the ocean surface. 



Mar 13  Wed  Tobias Grafke (Warwick)  Applied Mathematics Colloquium  
14:00  Hydrodynamic instantons and the universal route to rogue waves  
Hicks, LT 9  
Abstract: In stochastic systems, extreme events are known to be described by "instantons", saddle point configurations of the action of the associated stochastic field theory. In this talk, I will present experimental evidence of a hydrodynamic instanton in a real world fluid system: A 270m wave channel experiment in Norway. The experiment attempts to model conditions on the ocean in order to observe socalled rogue waves, realisations of extreme ocean surface elevation out of relatively calm surroundings. These rogue waves are also observed in the ocean, where they are rare and hard to predict but pose significant danger to naval vessels. We show that the instanton approach, which is rigorously grounded in large deviation theory, offers a unified description of rogue waves in the water tank, covering the entire range of parameters for deep water waves in the ocean. In particular, this approach allows for a unified description of both the predominantly linear and the highly nonlinear regimes, and is able to explain the experimental data in the tank regardless of the strength of the nonlinearity. 



Mar 22  Fri  Steffen Gielen (Nottingham)  Applied Mathematics Colloquium  
14:00  The universe as a condensate of spacetime atoms  
TBA  
Abstract: In the standard picture of cosmology, the Universe began at the Big Bang; the Big Bang itself is a singularity where the laws of physics break down. A quantum theory of gravity should resolve this singularity and help in understanding the initial state of the Universe needed to account for present observations. I will present some progress towards this goal in the group field theory approach to quantum gravity, using the idea of a universe formed as a "condensate", i.e. a very homogeneous quantum configuration, from a large number of discrete building blocks of geometry. I will show how this setting produces new cosmological models without an initial singularity; demanding that such models be both theoretically selfconsistent and potentially compatible with observation then gives new ways for constraining theories of quantum gravity. 



Mar 27  Wed  Daniele Avitabile (Nottingham)  Applied Mathematics Colloquium  
14:00  Interfacial dynamics for neurobiological networks: from excitability thresholds to localised spatiotemporal chaos  
Hicks, LT 9  
Abstract: We will discuss levelset based approaches to study the existence and bifurcation structure of spatiotemporal patterns in biological neural networks. Using this framework, which extends previous ideas in the study of neural field models, we study the first example of canards in an infinitedimensional dynamical system, and we give a novel characterisation of localised structures, informally called “bumps”, supported by spiking neural networks. We will initially consider a spatiallyextended network with heterogeneous synaptic kernel. Interfacial methods allow for the explicit construction of a bifurcation equation for localised steady states. When the model is subject to slow variations in the control parameters, a new type of coherent structure emerges: the structure displays a spatiallylocalised pattern, undergoing a slowfast modulation at the core. Using interfacial dynamics and geometric singular perturbation theory, we show that these patterns follow an invariant repelling slow manifold, hence we name them "spatiotemporal canards". We classify spatiotemporal canards and give conditions for the existence of foldedsaddle and foldednode canards. We also find that these structures are robust to changes in the synaptic connectivity and firing rate. The theory correctly predicts the existence of spatiotemporal canards with octahedral symmetries in a neural field model posed on a spherical domain. We will then discuss how the insight gained with interfacial dynamics may be used to perform coarsegrained bifurcation analysis on neural networks, even in models where the network does not evolve according to an integrodifferential equation. As an example I will consider a wellknown eventdriven network of spiking neurons, proposed by Laing and Chow. In this setting, we construct numerically travelling waves whose profiles possess an arbitrary number of spikes. An open question is the origin of the travelling waves, which have been conjectured to form via a destabilisation of a bump solution. We provide numerical evidence that this mechanism is not in place, by showing that disconnected branches of travelling waves with countably many spikes exist, and terminate at grazing points; the grazing points correspond to travelling waves with an increasing number of spikes, a welldefined width, and decreasing propagation speed. We interpret the so called “bumps” and “meandering bumps”, supported by this model as localised states of spatiotemporal chaos, whereby the dynamics visits a large number of unstable localised travelling wave solutions. 



Apr 3  Wed  Matt Turner (Surrey)  Applied Mathematics Colloquium  
14:00  Dynamic sloshing via timedependent conformal mappings  
Hicks, LT 9  
Abstract: In this talk we examine twodimensional, inviscid, irrotational fluid sloshing in both fixed and moving vessels. In particular we focus on a numerical scheme which utilizes timedependent conformal mappings of doublyconnected domains to produce a scheme which is fast and efficient. Results are presented for flows in a fixed vessel, a moving vessel with bottom topography, a coupled pendulum slosh problem and a fixed vessel with multiple horizontal baffles. The application of this work is to the modelling of offshore wave energy converters. 



May 1  Wed  Sam Falle (Leeds)  Applied Mathematics Colloquium  
14:00  Shock structures described by hyperbolic balance laws  
Hicks, LT 9  
Abstract: In this talk I will consider shock structures that arise in systems of hyperbolic balance laws, i.e. hyperbolic systems of conservation laws with source terms. I show how the Whitham criterion for the existence of such shock structures can be extended to systems with more than one relaxation variable. In addition, I descibe a method based on the HermiteBiehler theorem that is useful for determining the stability of the equilibrium states of such systems. The utility of this method is illustrated by a number of examples: ideal gas with two internal degrees of freedom, two fluid magnetohydrodynamics and magnetohydrodynamics with tensor resistivity. 



May 8  Wed  Kasia Rejzner (York)  Applied Mathematics Colloquium  
14:00  Perturbative algebraic QFT  Example of the sineGordon model  
Hicks, LT 9  
Abstract: In this talk I will present recent results on the construction of the net of local algebras for the sineGordon model. The approach I will present is that of perturbative algebraic QFT, in which the interacting fields are constructed using formal Smatrices. It has been shown that in sineGordon model these formal Smatrices can be realized as unitary operators in certain Hilbert space representation, appropriate for massless scalar field in 2 dimensions. 



May 13  Mon  Yuri M. Pismak (St. Petersburg State University)  Applied Mathematics Colloquium  
14:00  Modelling the interaction of the quantum electrodynamics fields with extended material bodies  
Hicks, LT 9  
Abstract: The method proposed by K. Symanzik for constructing quantum field models in an inhomogeneous spacetime is used to describe the interaction of the quantum electrodynamics (QED) fields with material objects. It is carried out within the framework of quantum field models in which the QED Lagrangian is modified according to the QED basic principles (locality, gauge invariance, renormalizability) and taking into account the properties of the material medium interacting with QED fields. Models with interactions of electromagnetic and Dirac fields with twodimensional materials of flat, spherical and cylindrical shape are considered. The results obtained in such models for the Casimir effect, scattering processes and bound states are discussed. 



Aug 22  Thu  Jason Green (Massachusetts Boston)  Applied Mathematics Colloquium  
11:00  The struggle between order and chaos in atomistic fluids  
Hicks, K14  
Abstract: Molecular motion in fluids is a consequence of wellknown physical laws, but in diverse soft matter contexts, it is challenging to construct predictions of bulk properties directly from the nonlinear intermolecular forces. The difficulty is that molecules in liquids are constantly moving, in a perpetual state of collision and chaos. As a result, their dynamics sit balanced at the knifeedge between the sharp, welldefined collisions in gases and the ordered oscillations in crystalline solids. That is, the disordered liquid state reflects a tension between order and chaos. This tension is especially heightened at the liquidvapor critical point where strong statistical correlations imply structural organization that is intrinsically opposed by the chaotic dynamics. The goal of this talk will be to explain some recent developments coupling nonlinear dynamics and statistical physics and how these advances are beginning to offer a mechanistic view of longstanding paradigms in liquid state theory and critical phenomena. Critical fluctuations and slowing down of chaos Moupriya Das, Jason R. Green Nat. Commun. 2019 10(1) p. 2155 Selfaveraging fluctuations in the chaoticity of simple fluids Moupriya Das, Jason R. Green Phys. Rev. Lett. 2017 119(11), p. 115502 Extensivity and additivity of the KolmogorovSinai entropy for simple fluids Moupriya Das, Anthony B. Costa, Jason R. Green Phys. Rev. E 2017 95(2), p. 022102 



Sep 11  Wed  Baofang Song (Center for Applied Mathematics, Tianjin University)  Applied Mathematics Colloquium  
14:00  The transition to turbulence and turbulence control in pipe flow  
Hicks, K14  
Abstract: The transition to turbulence in wallbounded shear flows, such as pipe, channel, and Couette flows, is a fundamental problem of fluid dynamics. The questions of when and how turbulence rises in these flows, as Reynolds number increases, have challenged scientists and engineers for over a century and have not been fully understood till today. The complexity lies in the subcritical nature of the transition in these flows and the coexistence of various turbulent states and the quiescent laminar state during the transition process. Nevertheless, in recent years, significant advancements in this research area have been made. In this talk, I will present some results of our team on the transition to turbulence as well as turbulence control in pipe flow. 



Oct 2  Wed  Bartek Protas (McMaster/INI Cambridge)  Applied Mathematics Colloquium  
14:00  Maximum Amplification of Enstrophy in NavierStokes Flows and the Hydrodynamic BlowUp Problem  
Hicks, LT 9  
Abstract: In the presentation we will discuss our research program focused on a systematic search for extreme, potentially singular, behaviors in the NavierStokes system and in other models of fluid flow. Enstrophy and enstrophylike quantities serve as convenient indicators of the regularity of solutions to such system  as long as these quantities remains finite, the solutions are guaranteed to be smooth and satisfy the equations in the classical (pointwise) sense. However, there are no available estimates with finite a priori bounds on the growth of enstrophy in 3D NavierStokes flows and hence the regularity problem for this system remains open. While the 1D Burgers and the 2D NavierStokes system are known to be globally well posed, the question whether the corresponding estimates on the instantaneous and finitetime growth of various enstrophylike quantities is quite relevant. We demonstrate how new insights concerning such questions can be obtained by formulating them as variational PDE optimization problems which can be solved computationally using suitable discrete gradient flows. More specifically, such an optimization formulation allows one to identify "extreme" initial data which, subject to certain constraints, leads to the most singular flow evolution which can then be compared with upper bounds obtained using rigorous methods of mathematical analysis. In order to quantify the maximum possible growth of enstrophy in 3D NavierStokes flows, we consider a family of such optimization problems in which initial conditions with prescribed enstrophy E_0 are sought such that the enstrophy in the resulting NavierStokes flow is maximized at some time T. By solving these problems for a broad range of values of E_0 and T, we demonstrate that the maximum growth of enstrophy is in fact finite and scales in proportion to E_0^{3/2} as E_0 becomes large. Thus, in such worstcase scenario the enstrophy still remains bounded for all times and there is no evidence for formation of singularity in finite time. We also analyze properties of the NavierStokes flows leading to the extreme enstrophy values and show that this behavior is realized by a series of vortex reconnection events. 



Oct 16  Wed  Nathan JohnsonMcDaniel (Cambridge)  Applied Mathematics Colloquium  
14:00  Testing general relativity with gravitational wave observations: From numerical analysis to Bayesian statistics  
Hicks, LT 9  
Abstract: Gravitational waves carry information directly to us from some of the most violent events in the universe, such as the mergers of binaries of black holes or neutron stars. Observations of such gravitational wave signals allow us to extract considerable information about the binaries that generate them. In particular, we can test whether general relativity (GR) is still a good description of gravity in such extreme situations. I will give an overview of the mathematics and statistics used in the analysis of gravitational wave data, from the analytical and numerical methods used to solve the field equations of GR and obtain model waveforms, to the Bayesian methods used to compare the data to these models. As an illustration, I will describe the tests of general relativity carried out on the compact binary signals detected by Advanced LIGO and Advanced Virgo during their first two observing runs. These tests did not reveal any deviation from the predictions of GR and have allowed us to put the most stringent constraints to date on possible deviations from these predictions in the strong field, highly dynamical regime. 



Oct 23  Wed  Takashi Sakajo (Kyoto/INI Cambridge)  Applied Mathematics Colloquium  
14:00  Topological Flow Data Analysis  Theory and Applications  
Hicks, LT 9  
Abstract: We have investigated a mathematical theory classifying the topological structures of streamline patterns for 2D incompressible (Hamiltonian) vector fields on surfaces such as a plane and a spherical surface, in which a unique combinatorial structure, called partially Cyclically Ordered rooted Tree (COT), associated with a symbolic expression (COT representation) is assigned to every streamline topology. With the COT representations, one can identify the topological streamline structures without ambiguity and predict the possible transition of streamline patterns with a mathematical rigor. In addition, we have recently developed a software converting the values of stream function on structured/nonstructured grid points in the plane into the COT representation automatically. It enables us to conduct the classification of streamline topologies for a large amount of flow datasets and the snapshots of timeseries of flow evolutions obtained by measurements and numerical simulations, which we call Topological Flow Data Analysis (TFDA). The combinatorial classification theory of flow topologies is now extended to the flow of finite type, which contains MorseSmale vector fields, compressible flows and 2D slices of 3D vector fields. I will present an overview of basic theory and its applications to atmospheric data and engineering problem. 



Oct 30  Wed  Xin Huang (NAOC Beijing)  Applied Mathematics Colloquium  
14:00  Solar flare forecasting models from the perspective of machine learning: past, present and future  
Hicks, LT 9  
Abstract: Solar flares are intense flashes of radiation emanating from the Sun. A strong solar flare and it’s related eruptive events can interfere with high frequency radio communication, satellite operation, navigation equipment and so on. Furthermore, effects of solar flares could reach the earth within approximately 8 minutes. Therefore, solar flare forecast has caused longterm concern in the field of space weather. Solar flares originate from the release of the energy stored in the magnetic field of solar active regions, the triggering mechanism for these flares, however, remains unknown. Hence the statistical and machine learning methods are used to build the solar flare forecasting model. From the perspective of machine learning, we review the solar flare forecasting models and try to discuss the possible directions to build more powerful solar flare forecasting models. 



Nov 6  Wed  Nobert Magyar (Warwick)  Applied Mathematics Colloquium  
14:00  Waves and turbulence in the solar corona and solar wind  
Hicks, LT 9  
Abstract: The solar corona and solar wind are still enigmatic from a physical standpoint. The coronal heating problem and the solar wind acceleration are one of the most important unsolved probems in astrophysics. Waves, which are omnipresent in the inner heliosphere, are strong candidates that might solve these conundrums. Just to make it even more difficult, the presence of waves might lead to the generation of turbulence, which is an unsolved problem on its own right. In this talk, we will explore what we know (and what we don't), first observationally and then by theory, about waves and turbulence in the extended solar corona. We will present the current magnetohydrodynamical (MHD) understading of turbulence generation in a plasma, which will be supplemented by my recent findings in the field. 



Nov 13  Wed  Tom Morley (SoMaS)  Applied Mathematics Colloquium  
14:00  A quantum tour of antide Sitter spacetime  
Hicks, LT 9  
Abstract: In General Relativity, the rate of expansion of the universe is governed by the cosmological constant. We know, from observations, that our universe is expanding at an accelerated rate, so the cosmological constant is usually taken to be positive. What happens if we choose the cosmological constant to be negative instead? Then we find ourselves in the weird and wonderful antide Sitter universe, a universe with a timelike boundary and closed timelike curves. And if we try to define a quantum field theory in this spacetime, we find some very surprising results indeed. In this talk, I will show how the vacuum polarisation, a divergent quantity associated with the local temperature of a quantum field, is affected by varying conditions imposed on the adS boundary. 



Nov 20  Wed  Dongho Chae (ChunAng)  Applied Mathematics Colloquium  
14:00  Liouville type theorems in the stationary NavierStokes and related equations  
Hicks, LT 9  
Abstract: We consider the stationary NavierStokes equations in $ \Bbb R^{3}$ \begin{align} \Delta u + (u \cdot \nabla) u =  \nabla p ,\quad \qquad\qquad \nabla \cdot u=0. \hspace{1cm}(1) \end{align} The standard boundary condition to impose at the spatial infinity is \begin{equation} u(x)\to 0 \quad \text{as} \quad x\to 0 . \hspace{4.5cm} (2) \end{equation} We also assume finiteness of the Dirichlet integral, \begin{equation} \int_{\Bbb R^3} \nabla u^2 dx <+\infty. \hspace{5cm} (3) \end{equation} Obviously $(u,p)$ with $u=0$ and $p=$constant is a trivial solution to (1)(3). A very challenging open question is if there is another nontrivial solution. This Liouville type problem is wide open, and has been actively studied recently in the community of mathematical fluid mechanics. The explicit statement of the problem is written in Galdi's book [1][Remark X. 9.4, pp. 729], where under the stronger assumption $u\in L^{\frac{9}{2}} (\Bbb R^3)$ he concludes $u=0$. After that many authors deduce sufficient conditions stronger than (2) and/or (3) to obtain the Liouville type result. In this talk we review various previous results and present recent progresses in getting sufficient condition in terms of the potential functions of the velocity. We also show that similar method can applied to prove Liouville type theorems for the other related equations such as the magnetohydrodynamic equations(MHD), HallMHD and the nonNewtonian fluid equations.




Dec 4  Wed  1. Farhad Allian / 2. Hope Thackray (SoMaS)  Applied Mathematics Colloquium  
14:00  1. A New Analysis Procedure for Detecting Periodicities within Complex Solar Coronal Arcades 2. Fast Magnetohydrodynamic Modes of a Semicylindrical Waveguide  
Hicks, LT 9  
Abstract: 1. Coronal loop arcades form the building blocks of the hot and dynamic solar atmosphere. In particular, their oscillations serve as an indispensable tool in estimating the physical properties of the local environment by means of seismology. However, due to the nature of the arcade's complexity, these oscillations can be difficult to analyze. In this talk, I will present a novel imageanalysis procedure based on the spatiotemporal autocorrelation function that can be utilized to reveal 'hidden' periodicities within EUV imagery of complex coronal loop systems. 2. Coronal loop models have often been used as a diagnostic tool for plasma properties in the Sun's corona. In particular, the oscillations triggered by nearby eruptive events may be modelled with a 3D semicylindrical waveguide. We investigate the resulting eigenfunctions for a “twoshell” (and later “threeshell”) density profile model that introduces sharp density contrast. We find that waves are elliptically polarised, but the eigenmodes can differ significantly when considering small changes to density profile. Such behaviour necessitates careful choice of density structure for understanding observational data. 



Feb 12  Wed  Lyuba Chumakova (Edinburgh)  Applied Mathematics Colloquium  
14:00  Why are we not falling apart: cytoskeleton selforganization and some results on intracellular transport  
Hicks, LT 9  
Abstract: For cells and organism to function correctly, cellular components must be robustly delivered to their biologically relevant location. This is achieved through intracellular transport, where vesicles and organelles are transported like cargo via cars (molecular motors) along highways (the microtubule cytoskeleton). Failure of this process can result in pathologies. In this talk I will present a series of studies of microtubule selforganisation and the resulting intracellular transport in epithelium, one of the four fundamental tissue types in all animals. In particular, I will address the questions of the selforganisation of the microtubule network, and how to determine the molecular motor type from the distribution of the cargo it distributes. This will be shown with stochastic simulations, in vivo experiments, and simple probabilistic models, which uncover the mathematical basis of the underlying biological phenomena 



Feb 19  Wed  Mitchell Berger (Exeter)  Applied Mathematics Colloquium  
14:00  Localized measures of magnetic helicity and helicity flux  
Hicks, LT 9  
Abstract: Magnetic helicity is an ideal MHD invariant; it measures geometric and topological properties of a magnetic field. The talk will begin by reviewing helicity and its mathematical properties. It can be decomposed in several ways (for example, self and mutual helicity, Fourier spectra, field line helicity, linking, twist, and writhe). The talk will also review methods of measuring the helicity flux. Applications in solar and stellar astrophysics will be reviewed. I will then discuss some new developments in measuring localized concentrations of helicity in a welldefined, gauge invariant manner. One method involves absolute measures of helicity (rather than relative to a vacuum field), based on generalizations of the ToroidalPoloidal decomposition in spherical geometries. A second method involves employing wavelets and multiresolution analysis 



Apr 24  Fri  Martin Saal (Pisa/Darmstadt)  Applied Mathematics Colloquium  
14:00  White noise solutions for (m)SQG  
Google Hangout Meet  
Abstract: The inviscid surface quasigeostrophic equation (SQG) describes (roughly speaking) the temperature in a rapidly rotating stratified fluid which is transported by the velocity field. The velocity field is connected to the temperature via Riesztransform, which are singular integral operators. It has applications in both meteorological and oceanic flows, while in mathematics it is often used as a toy model for the 3D Euler equations due to some structural similarities of these equations. We give a brief overview on versions of the SQG equation and of the known mathematical results. For a modified version (mSQG) with a smoother velocity field, which links the SQG equation to the vorticity formulation of the 2D Euler equations, we will show that by using a special Symmetrie in the kernel a white noise solution to mSQG can be constructed and give some comments on Further results. Finally, we outline the difficulties of our approach in the case of SQG itself. 



May 6  Wed  Matt Rosenzweig (Texas Austin)  Applied Mathematics Colloquium  
14:00  From Point Vortices to 2D Fluids: Back and Forth  
Google Meet  
Abstract: In this talk, we will discuss the connection between twodimensional (2D) fluid equations, such as the incompressible Euler or surface quasigeostrophic (SQG) equations, and systems of interacting particles, which are known as point vortex models. We consider this topic from two angles determined by different scaling limits. The first is localization, where one passes from a fluid equation to a point vortex model. The second is meanfield limit, where one passes from a point vortex model to a fluid equation. Time permitting, we will also discuss these connections in the stochastic setting, where multiplicative noise has been added to the dynamics. 



May 13  Wed  Silvia Gazzola (Bath)  Applied Mathematics Colloquium  
14:00  Iterative regularization methods for largescale linear inverse problems  
Google Meet  
Abstract: Inverse problems are ubiquitous in many areas of Science and Engineering and, once discretized, they lead to illconditioned linear systems, often of huge dimensions: regularization consists in replacing the original system by a nearby problem with better numerical properties, in order to find a meaningful approximation of its solution. After briefly surveying some standard regularization methods, both iterative (such as many Krylov methods) and direct (such as Tikhonov method), this talk will introduce a recent class of methods that merge an iterative and a direct approach to regularization. In particular, strategies for choosing the regularization parameter and the regularization matrix will be emphasized, eventually leading to the computation of approximate solutions of Tikhonov problems involving a regularization term expressed in some pnorms. 



May 20  Wed  Didier Leibovici (SoMaS)  Applied Mathematics Colloquium  
14:00  On spatiotemporal entropy based methods for data science  
Google Meet  
Abstract: The entropy, as a metric to describe if a distribution tends to be uniform (high entropy) or not can be useful in data science to highlight spatiotemporal structures (low entropy). The seminar looks into complementary aspects of multiway data analysis deriving from a tensor decomposition and the use of entropy within a spatiotemporal context. Derived from practices in landscape ecology, a framework based on size and shapes of patches within a spatiotemporal context is used in conjunction with the entropy decomposition theorem or with a tensor decomposition approach. Combined with statistics, such as cooccurrences of observations or specific distance ratios instead of occurrence counts, to define pseudodistributions to derive spatiotemporal entropies, the framework allows a range of analyses. Along the path some examples are illustrating involved connexe methods, some of which can be found in the references below. Leibovici DG and Claramunt C (2019) On Integrating Patch Size and Shape Distributions into a SpatioTemporal Information Entropy Framework Entropy, 21(11):1112 (special issue) Leibovici DG, Brosset D, Claramunt C, and Jackson M (2015 ) kCooccurrences Density Map Estimation. Spatial Statistics Conference: Emerging Patterns, 912th of June 2015, Avignon, France, Procedia Environmental Sciences, 26: 105109. Leibovici DG, and Birkin MH (2015) On Geocomputational Determinants of Entropic Variations for Urban Dynamic Studies. Geographical Analysis, 47 (3): 193218 Leibovici DG, Bastin L, and Jackson M (2011) " HigherOrder Cooccurrences for Exploratory Point Pattern Analysis and Decision Tree Clustering on Spatial Data." Computers & Geosciences: 37(3): 382389 Leibovici DG, (2010) " Spatiotemporal Multiway Decomposition using Principal Tensor Analysis on kmodes: the R package PTAk." Journal of Statistical Software, 34(10), 134 



Nov 4  Wed  JeanLuc Lehners (MaxPlanckInstitute, Potsdam)  Applied Mathematics Colloquium  
14:00  Path integrals, black holes and the beginning of the universe  
Google Meet  
Abstract: Quantum gravity promises to unveil the deepest mysteries about space, time and matter. But that is for the far future. In this talk, I will review recent progress in a less ambitious setting, namely in semiclassical gravity, which may be thought of as the leading order in hbar approximation to quantum gravity. I will discuss techniques for evaluating gravitational path integrals, both in the context of black holes and regarding the implications for the HartleHawking noboundary proposal. This not only shows a close relation between black holes and the big bang, but also provides clues for an effective description of the quantum origin of the universe. 



Nov 18  Wed  Andreagiovanni Reina (CS, Sheffield)  Applied Mathematics Colloquium  
14:00  Collective Decision Making: From Bees to Robots via Multiscale Modelling  
Google Meet  
Abstract: I will give an overview of my studies on modelling and simulating collective decision making in distributed systems. Such systems, found in biology, sociology, and engineering, are composed of a large number of interacting individuals that coordinate in order to reach a consensus. The main phases of the collective decision making process consist of identifying the available options, estimating their quality, and selecting the best option or any of them. I will present the main results of my research in understanding and designing each of these phases. Collective systems are inherently difficult to analyse as the stochastic nonlinear interactions between individuals can give rise to complex emergent dynamics. Therefore, I employ a collection of advanced techniques, commonly defined as multiscale modelling. Relying on a set of methods, rather than a single one, gives the benefit of having complementary techniques addressing one another's limitations. In fact, through multiscale modelling, it is possible to analyse the systems at various levels of complexity and detail, from macroscopic grouplevel dynamics to microscopic individuallevel behaviour, and from noisefree deterministic models to stochastic spatial descriptions. I finally shed a light on the recently developed opensource software for automated multiscale modelling. This software, called MuMoT, can also be a useful resource for remote teaching. For more info on MuMoT see (Marshall et al. PlosOne 2019) or MuMoT live notebook (https://mumot.readthedocs.io/). Bio: Dr Andreagiovanni Reina is a Research Fellow in Collective Robotics at the University of Sheffield, UK. He is currently working on the DiODe project (Distributed Algorithms for Optimal DecisionMaking) led by Prof. James Marshall, and is the Principal Investigator of the Swarm Awareness project (https://swarmawareness.group.shef.ac.uk/). Andreagiovanni is the researcher responsible for more than 900 Kilobot robots and the related Augmented Reality for Kilobot (ARK) infrastructure at Sheffield Robotics. He holds a PhD in applied sciences from IRIDIA (Marco Dorigo's AILaboratory) of the Université Libre de Bruxelles, Belgium, and an M.Sc. in computer engineering from Politecnico di Milano, Italy. He has been a researcher in five European projects on distributed robotic systems since 2009. In December 2020, he plans to return to Brussels with an FNRS Fellowship on modelling heterogeneity in decentralised consensus. Full info at http://areina.staff.shef.ac.uk. 



Dec 2  Wed  Andrew Krause (Oxford)  Applied Mathematics Colloquium  
14:00  Recent Progress & Open Frontiers in TuringType Morphogenesis  
Google Meet  
Abstract: Motivated by recent work with biologists, I will showcase some mathematical results on Turing instabilities in complex domains. This is scientifically related to understanding developmental tuning in the whiskers of mice, and more generally pattern formation on multiple scales and evolving domains. Such phenomena are typically modelled using reactiondiffusion systems of morphogens, and one is often interested in emergent spatial and spatiotemporal patterns resulting from instabilities of a homogeneous equilibrium, which have been wellstudied. In comparison to the wellknown effects of how advection or manifold structure impacts unstable modes in such systems, I will present results on instabilities in heterogeneous systems, as well as those arising in the setting of evolving manifolds. These contexts require novel formulations of classical dispersion relations, and may have applications beyond developmental biology, such as in population dynamics (e.g. understanding colony or niche formation of populations in heterogeneous environments). These approaches also help close the vast gap between the simple theory of diffusiondriven pattern formation, and the messy reality of biological development, though there is still much work to be done in validating even complex theories against the rich dynamics observed in nature. 



Dec 9  Wed  Gary Mirams (Nottingham)  Applied Mathematics Colloquium  
14:00  Selecting and parameterising a model for a potassium ion channel's dynamics  
Google Meet  
Abstract: There are a wide range of suggested models in the literature for how the hERG potassium channel opens and closes in response to changes in the voltage across cell membranes. These are typically ODE models with a handful of state variables and up to tens of parameters. Experiments can clamp voltage and measure the resulting current, but we'd like to be able to predict the current in new (unseen) situations that might occur in different cells, people and conditions. In this talk, I'll describe our efforts to choose and parameterise a model, by using novel experimental designs with rapidly fluctuating input waveforms, as well as a strict separation between training and validation of the models. The rapid experiments have allowed us to make cellspecific models and to create a parameterisation for a mutant channel which sheds light on why the mutant may increase the risk of cardiac arrhythmias. We've also used highthroughput measurements to look at cellcell variability and to examine the temperaturedependence of channel opening. I'll discuss some of the open challenges in tying together experimental design for ion channel models with selection, parameterisation, validation and assessment of discrepancy/misspecification. 



Dec 16  Wed  Konstantinos Zygalakis (Edunburgh)  Applied Mathematics Colloquium  
14:00  Hybrid modeling for the stochastic simulation of multiscale chemical kinetics  
Google Meet  
Abstract: It is well known that stochasticity can play a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, wellmixed systems can be adequately modeled by Markov processes and, for such systems, methods such as Gillespie’s algorithm are typically employed. While such schemes are easy to implement and are exact, the computational cost of simulating such systems can become prohibitive as the frequency of the reaction events increases. This has motivated numerous coarsegrained schemes, where the “fast” reactions are approximated either using Langevin dynamics or deterministically. While such approaches provide a good approximation for systems where all reactants are present in large concentrations, the approximation breaks down when the fast chemical species exist in small concentrations, giving rise to significant errors in the simulation. This is particularly problematic when using such methods to compute statistics of extinction times for chemical species, as well as computing observables of cell cycle models. In this talk, we present a hybrid scheme for simulating wellmixed stochastic kinetics, using Gillespie–type dynamics to simulate the network in regions of low reactant concentration, and chemical Langevin dynamics when the concentrations of all species are large. These two regimes are coupled via an intermediate region in which a “blended” jumpdiffusion model is introduced. Examples of gene regulatory networks involving reactions occurring at multiple scales, as well as a cellcycle model are simulated, using the exact and hybrid scheme, and compared, both in terms of weak error, as well as computational cost. If there is time, we will also discuss the extension of these methods for simulating spatial reaction kinetics models, blending together partial differential equation with compartment based approaches, as well as compartment based approaches with individual particle models. 



Feb 10  Wed  Kevin Painter (Politecnico di Torino)  Applied Mathematics Colloquium  
14:00  Sticking together by going against the flow  
Google Meet  
Abstract: The formation of swarms, schools, flocks, herds, aggregates etc is a classical example of selforganisation, with the benefits of forming a high density group ranging from efficient migration to higher fecundity. Often, groups form through a mechanism of chemical signalling between population members, an evolutionary ancient communication used by both microscopic and macroscopic species. Populations in fluid environments, though, must contend with complex and turbulent flows, potentially detrimental (e.g. splitting up groups) or beneficial (e.g. coalescing individuals) to the formation and maintenance of a group. As a counter to flow, rheotaxis describes a behaviour in which individuals orient their body axis with respect to the current and is observed in both unicellular and multicellular organisms . Here we investigate the extent to which rheotaxis and flow impact on chemicallymediated aggregation, revealing these can impact both negatively and positively according to the population state and flow conditions. A hypothesised densitydependent rheotaxis appears capable of optimising group formation and maintenance, exploiting the positive benefits from each of flow and rheotaxis. The results are discussed in the context of broadcast swarming phenomena in marine invertebrates. 



Mar 3  Wed  Valerio Lucarini (Reading)  Applied Mathematics Colloquium  
14:00  Fingerprinting Heatwaves and Cold Spells and Assessing Their Response to Climate Change using Large Deviation Theory  
Google Meet  
Abstract: Extreme events provide relevant insights on the dynamics of the climate system and their understanding is key to defining useful strategies for mitigating the impact of climate variability and climate change. Here we approach the study of persistent weather extremes using the lens of large deviation theory. We first consider a simplified yet Earthlike general circulation model of the atmosphere and numerically estimate large deviation rate functions of nearsurface temperature in the midlatitudes. We find that, after a renormalisation based on the integrated autocorrelation, the rate function one obtains at a given latitude by looking, locally in space, at long time averages agrees with what is obtained, instead, by looking, locally in time, at large spatial averages along the latitude. This is a result of scale symmetry in the spatialtemporal turbulence and of the fact that advection is primarily zonal. This agreement hints at the universality of large deviations of the temperature field. Furthermore, we discover that the obtained rate function is able to describe spatially extended and temporally persistent heat waves or cold spells, if we consider temporal averages of spatial averages over intermediate spatial scales. We then extend our analysis by looking at the output of a stateoftheart climate model and at observational data. We show how to const ruction in a mathematically rigorous way the climatology of persistent heatwaves and cold spells in some key target regions of the planet by constructing empirically the corresponding rate functions for the surface temperature, and we assess the impact of increasing CO2 concentration on such persistent anomalies. In particular, we can better understand the increasing hazard associated to heatwaves in a warmer climate. We show that two 2010 high impact events  summer Russian heatwave and winter Dzud in Mongolia  are associated with atmospheric patterns that are exceptional compared to the typical ones, but typical compared to the climatology of extreme events. Finally, we propose an approximate formula for describing large and persistent temperature fluctuations from easily accessible statistical properties. Refs: V. Galfi, V. Lucarini, Fingerprinting Heatwaves and Cold Spells and Assessing Their Response to Climate Change using Large Deviation Theory, PRL, in review (2020) V. Galfi, V. Lucarini, J. Wouters, A Large Deviation Theorybased Analysis of Heat Waves and Cold Spells in a Simplified Model of the General Circulation of the Atmosphere, J. Stat. Mech. 033404 doi: 10.1088/17425468/ab02e8 (2019) 



Apr 21  Wed  Peter Clarkson (University of Kent)  Applied Mathematics Colloquium  
14:00  Rational solutions of three integrable equations and applications to rogue waves  
Google Meet  
Abstract: In this talk I shall discuss rational solutions of the Boussinesq equation, the focusing nonlinear Schrodinger (NLS) equation and the KadomtsevPetviashvili I (KPI) equation, which are all soliton equations solvable by the inverse scattering. The Boussinesq equation was introduced by Boussinesq in 1871 to describe the propagation of long waves in shallow water. Rational solutions of the Boussinesq equation, which are algebraically decaying and depend on two arbitrary parameters, are expressed in terms of special polynomials that are derived through a bilinear equation, have a similar appearance to roguewave solutions of the focusing NLS equation and have an interesting structure. Conservation laws and integral relations associated with rational solutions of the Boussinesq equation will also be discussed. Rational solutions of the KPI equation will be derived in three ways: from rational solutions of the NLS equation; from rational solutions of the Boussinesq equation; and from the spectral problem for the KPI equation. It'll be shown that these three families of rational solutions are fundamentally different. 


