Semester 1, Week 7: Prof Valery Nakariakov, University of Warwick
2025-10-31 14:05 - 14:55 (Europe/London)
Academic webpage
Title: Decayless kink oscillations of solar coronal loops as a self-oscillatory process
Abstract:
Kink oscillations of the decayless class are detected as small amplitude (< 1 Mm) persistent transverse repetitive displacements of solar coronal plasma loops, occurring without any association with solar flares, eruptions, or other impulsive energy releases. The linear correlation of the oscillation periods with the lengths of the oscillating loops demonstrates that the oscillations are natural modes of the loops. The statistical distribution of oscillation amplitudes with the periods shows no pronounced peaks, suggesting the lack of a periodic driver. Together with the lack of an impulsive excitation, it suggests that the energy losses are compensated by the interaction of the loop with either quasi-steady or random external plasma flows. In this study, the decayless regime is associated with the energy supply from coronal plasma flows via the negative friction, i.e., self-oscillations, and/or random movements of footpoints of the oscillating loop.

The kink oscillation period is found to be practically independent of noise, which justifies seismological estimations of the coronal magnetic field. The transition from the large-amplitude rapidly-decaying regime to the low-amplitude decayless oscillations demonstrates that the decay pattern differs from the usually assumed exponential decay.

Implications of this finding for magnetohydrodynamic seismology of the solar corona, based on the effect of resonant absorption are discussed.

Semester 1, Week 6: Independent Learning Week, No Seminar
2025-10-24 14:05 - 14:55

Semester 1, Week 5: Dr Omar Lakkis, University of Sussex
2025-10-17 14:05 - 14:55
Academic webpage
Title: Adaptive methods and explicit time-stepping
Abstract:
Aposteriori error analysis for Galerkin finite element methods have proven very successful tool in developing mathematically rigorous adaptive mesh refinement algorithms for implicit/space-time evolution equations. In this work we extend rigorous adaptivity principles to explicit time-stepping for the wave equation.
I will review in the first part of the talk the state of the art for the wave equation. In the second part, I will present recent work in connection to fully practical explicit schemes such as the Leapfrog method and local time step variants thereof.

This talk is mostly based on joint work with M Grote, C Santos.
Location: TBD

Semester 1, Week 4: Prof Fabian Spill, University of Birmingham
2025-10-10 14:05 - 14:55
Academic webpage
Title: The Role of Geometry, Topology and Mechanics in Physiology and Disease
Abstract:
Molecular networks underpin all cellular functions, including metabolism, division, and migration. These networks are frequently altered in disease and are common targets for therapeutic intervention. Many key molecular components are associated with the plasma membrane or are localized within organelles such as mitochondria and the endoplasmic reticulum (ER). Notably, the spatial, geometrical, and topological organization of cells and organelles is highly dynamic and varies with cell type, physiological state, and environmental context. For instance, mitochondria can exist as discrete, spherical structures or as extensive, fused networks, while the ER can adopt sheet-like or tubular morphologies.

A major open question is how the organization of cellular and subcellular structures contributes to physiological regulation and how disruptions in this organization influence disease progression and therapeutic response.

In this talk, I will present recent and ongoing work demonstrating that spatial organization is a key determinant of cellular function. First, I will discuss how mitochondrial architecture influences metabolic pathway activity in the context of diabetes. Next, I will explore how metabolic interactions between cancer cells and stromal cells drive tumour progression. Finally, I will show how the structural organization of the ER into sheets and tubules regulates collective cell migration during wound healing, in a manner that is dependent on cell morphology.

Semester 1, Week 3: Unassigned
2025-10-03 14:05 - 14:55
Academic webpage
Title: TBA
Abstract: TBA
Location: TBD

Prof. Denise Kirschner, University of Michigan
2025-05-30 14:00 - 15:00

Dr Eric William Hester, University of Bath
2025-05-02 14:00 - 15:00 | MAT Theatre D
Academic webpage
Title: Modelling multiphase matter: from microparticles to mega-icebergs
Abstract: The world is multiphase. Water and ice, rock and lava, nucleus and cytoplasm. How can we model these systems, and simulate them efficiently? I’ll start with three examples from my research, boat drag in dead water, melting icebergs in salty oceans, and phase-separating polymers in microparticle experiments. The same patterns recur. A seemingly simple partition into PDEs and boundary conditions belies the murky interface between them. This diffuse interface in turn motivates a host of numerical schemes and mathematical questions. The bulk of my talk will discuss the mathematical tools we need to understand these methods. Signed-distance coordinates give a straightforward vector calculus around arbitrary submanifolds, and matched asymptotics describes the resulting solutions to arbitrary order. I’ll show how we can use this knowledge to design more accurate and efficient numerical schemes, and thereby achieve a better understanding of our motivating problems, before concluding with some bigger questions for multiphase methods.

Prof. Peter Davidson, University of Cambridge
2025-04-25 14:00 - 15:00 | MAT Theatre D
Academic Webpage
Title: Reversals of the Geodynamo
Abstract: Somewhat surprisingly, there is still no convincing model, or even cartoon, for reversals of the earth’s magnetic field. This is because the underlying mechanisms are still not understood. While numerical simulations of the geodynamo are, perhaps, finally beginning to approach a dynamically relevant regime, they still cannot reproduce realistic reversals of the terrestrial field. In this talk a new model of reversals is presented, a model whose predictions are reasonably earth like.

Prof. Patrick Farrell, University of Oxford
2025-03-28 14:00 - 15:00 | MAT Theatre D
Academic webpage: https://www.maths.ox.ac.uk/people/patrick.farrell
Title: Designing conservative and accurately dissipative numerical integrators in time
Abstract: Numerical methods for the simulation of transient systems with structure-preserving properties are known to exhibit greater accuracy and physical reliability, in particular over long durations. These schemes are often built on powerful geometric ideas for broad classes of problems, such as Hamiltonian or reversible systems. However, there remain difficulties in devising higher-order-in-time structure-preserving discretizations for nonlinear problems, and in conserving non-polynomial invariants.
In this work we propose a new, general framework for the construction of structure-preserving timesteppers via finite elements in time and the systematic introduction of auxiliary variables. The framework reduces to Gauss methods where those are structure-preserving, but extends to generate arbitrary-order structure-preserving schemes for nonlinear problems, and allows for the construction of schemes that conserve multiple higher-order invariants. We demonstrate the ideas by devising novel schemes that exactly conserve all known invariants of the Kepler and Kovalevskaya problems, arbitrary-order schemes for the compressible Navier-Stokes equations that conserve mass, momentum, and energy, and provably dissipate entropy, and helicity-conservative/energy-dissipative schemes for the Parker problem of magnetohydrodynamics.

Dr Christopher Prior, Durham University
2025-03-14 14:05 - 15:00 | MAT Theatre D
Academic webpage: https://www.durham.ac.uk/staff/christopher-prior/
Title: Predicting protein dynamics using writhe
Abstract: The advent of AlphaFold has steered the fundamental questions on protein structure towards understanding their dynamics in their native state, rather than the static crystal states routinely predicted. One critical tool in our arsenal is small angle x-ray scattering (SAXS) which allows, with significant modelling, for the imaging of protein dynamics in solution. However, modelling proteins by standard force field methods is inhibitively computationally expensive, so alternative methods are required for effective and routine interpretation of SAXS data. I will present a method and code for SAXS interpretation (Carbonara), which used constraints on the geometry and topology of proteins which we have derived from structural data. Hopefully it will be of interest for the potential audience at St Andrews that the fundamental underlying quantity in this method is the writhe, a quantity routinely used in solar and astrophysical modelling to quantify and constrain the topology of magnetic flux ropes. In doing so I will briefly highlight the interesting history of how the fields of long chain biology and solar magnetic fields have both provided insight to each other.

Dr Robert Teed, University of Glasgow
2025-02-28 14:05 - 15:00 | MAT Theatre D
Academic webpage: https://www.gla.ac.uk/schools/mathematicsstatistics/staff/robertteed/
Title: Numerically modelling the magnetic field generation of Earth’s core
Abstract:
Planetary magnetic fields are produced by dynamo action through turbulent motions of an electrically conducting fluid within the interior of the planet. Numerical experiments of dynamo action relevant to Earth’s magnetic field have produced different regime branches identified within bifurcation diagrams [1].

Notable are distinct branches in which the resultant magnetic field is either weak or strong (when compared with the fluid flow). Such branches can be found within a small window of parameter space, as long predicted [2]. Weak field solutions can be identified by the prominent role of viscosity on the motion whereas the magnetic field has a leading order effect on the flow in strong field solutions. One measure of the success of numerical models of the geodynamo is the ability to replicate the expected balance between forces operating within Earth’s core; Coriolis (rotational) and Lorentz (magnetic) forces are predicted to be most important. The value of considering lengthscale dependent force balances [3] and ‘gradient-free’ solenoidal forces has been highlighted recently [4].

I will review the approach in numerically modelling the geodynamo and the challenges in doing so. I will discuss the branches/bifurcations of dynamo action previously explored in numerical simulations. Furthermore, in new results, I shall highlight that the expected force balance of Earth’s core can be preserved as input parameters of numerical simulations are moved towards more realistic values.

[1] E. Dormy et al, Fluid Dynamics Res. 50, 011415 (2018)
[2] P. Roberts, In: Cupal, I. (ed.), Proc. First Int. Workshop on Dynamo Theory and the Generation of the Earth’s Magnetic Field pp. 7–12. Czech. Geophys. Inst. Rep (1979)
[3] T. Schwaiger et al, Geophys. J. Inter. 219, S101–S114 (2019)
[4] R. J. Teed & E. Dormy, J. Fluid Mech. 964, A26 (2023)

Prof Pavel S. Berloff, Imperial College London
2025-02-21 14:05 - 15:00 | MAT Theatre D
Academic webpage: https://www.ma.imperial.ac.uk/~pberloff/
Title: Oceanic Vortex Pulsars

Abstract: Theoretical studies of coherent vortices have a half-century history and in many ways have become classics of geophysical fluid dynamics. Some recent results will be presented on a new class of stable and ever-living coherent vortices on stratified background shears. These features, referred to as “vortex pulsars”, are fundamentally non-isolated, and also asymmetric and nonstationary. Two distinctly different families of solutions — “strong” and “weak” — will be discussed.

Dr Gabriel Barrenechea, University of Strathclyde
2025-02-14 14:05 - 15:00 | MAT Theatre D
Affiliation: University of Strathclyde, UK
Academic Webpage
Title: A reduced model for a problem in non-Newtonian fluid mechanics
Abstract: We propose a finite element discretisation of a three-dimensional non-Newtonian flow whose dynamics are described by an Upper Convected Maxwell model.
First, a one-directional simplification of the UCM problem is made, so the main
variables are velocity, pressure, and one vector which acts as the “square root”
of the stress tensor. For this model a finite element method is proposed and analysed.
The scheme preserves structure in the sense that the velocity is divergence-free and the overall discretisation is energy consistent with the underlying
problem. We investigate the problem’s complexity and devise relevant timestepping strategies for effcient solution realisation. We showcase the method with several numerical experiments, confirm the theory and demonstrate the efficiency of the scheme.

Prof. José A. Carrillo, University of Oxford
2024-11-29 14:05 - 15:00 | Physics Theatre C
Affiliation: University of Oxford, UK
Academic webpage
Title: Aggregation-Diffusion Equations for Collective Behaviour in the Sciences

Abstract:
Many phenomena in the life sciences, ranging from the microscopic to macroscopic level, exhibit surprisingly similar structures. Behaviour at the microscopic level, including ion channel transport, chemotaxis, and angiogenesis, and behaviour at the macroscopic level, including herding of animal populations, motion of human crowds, and bacteria orientation, are both largely driven by long-range attractive forces, due to electrical, chemical or social interactions, and short-range repulsion, due to dissipation or finite size effects. Various modelling approaches at the agent-based level, from cellular automata to Brownian particles, have been used to describe these phenomena. An alternative way to pass from microscopic models to continuum descriptions requires the analysis of the mean-field limit, as the number of agents becomes large. All these approaches lead to a continuum kinematic equation for the evolution of the density of individuals known as the aggregation-diffusion equation. This equation models the evolution of the density of individuals of a population, that move driven by the balances of forces: on one hand, the diffusive term models diffusion of the population, where individuals escape high concentration of individuals, and on the other hand, the aggregation forces due to the drifts modelling attraction/repulsion at a distance. The aggregation-diffusion equation can also be understood as the steepest-descent curve (gradient flow) of free energies coming from statistical physics. Significant effort has been devoted to the subtle mechanism of balance between aggregation and diffusion. In some extreme cases, the minimisation of the free energy leads to partial concentration of the mass. Aggregation-diffusion equations are present in a wealth of applications across science and engineering. Of particular relevance is mathematical biology, with an emphasis on cell population models. The aggregation terms, either in scalar or in system form, is often used to model the motion of cells as they concentrate or separate from a target or interact through chemical cues. The diffusion effects described above are consistent with population pressure effects, whereby groups of cells naturally spread away from areas of high concentration. This talk will give an overview of the state of the art in the understanding of aggregation-diffusion equations, and their applications in mathematical biology.

Dr. Niklas Kolbe, RWTH Aachen
2024-11-22 14:05 - 15:00 | Physics Theatre C
Affiliation: RWTH Aachen
Academic Webpage
Title: Central finite volume schemes for coupled hyperbolic models
Abstract: Various real-world problems in two-phase dynamics, multi-scale processes and networks can be addressed by coupling hyperbolic models at a static interface. We propose a new relaxation based approach for the coupling of general hyperbolic systems, in which the Lax curves of the coupled systems are not required. The approach is based on a relaxation limit taken at the coupling interface and embedded in an asymptotic preserving finite volume method. The role of the modified coupling condition is discussed and applications in traffic flow and vascular networks are presented.

Dr. Cathal Cummins, Heriot-Watt University
2024-11-15 14:05 - 15:00 | Phys Theatre A
Affiliation: Heriot Watt University
Academic webpage
Title: Resonance and viscous losses in wave energy systems
Abstract:
Wave Energy Converters (WECs) harness the motion of ocean waves to generate renewable energy, with sometimes complex dynamics underlying their performance. This talk explores the mathematical modelling of two leading types of WECs, built here in Scotland. Each has distinct characteristics, and each exhibits resonance. While resonance is beneficial for one of the WECs, it is something to be avoided in the other. We will examine the underlying principles of these resonances and reveal how the standard mathematical framework (inviscid potential flow) breaks down under conditions of resonance, partly due to viscous dissipation. A method will be introduced to account for viscous damping within a potential flow framework, known as viscous potential flow.

Prof. Jacek Banasiak, University of Pretoria
2024-10-11 14:00 - 15:00 | Phys Theatre A
Academic Webpage
Title: Life cycle of mosquitoes and malaria – a journey through asymptotic analysis and monotone systems
Authors: J. Banasiak, S. Y. Tchoumi and M. Bime Ghakanyuy, University of Pretoria
Abstract:
Due to the presence of populations with widely different vital rates, such as mosquitoes and humans, malaria dynamics offers rewarding examples of multiscale models represented by regularly and singularly perturbed systems of differential equations [3,5,6]. Recent improvements in their analysis [1,2] allow for significantly simplifying such models without losing salient features and their original long-term dynamics. Moreover, in many cases, the application of the singular perturbation theory leads to simplified models that are monotone and thus allow for an even more comprehensive analysis. We illustrate the theoretical results with concrete models describing the spreading of malaria [3] and the gonotrophic cycle of mosquitoes [4,7].
Literature
[1] F.C. Hoppensteadt, Singular perturbations on the infinite interval, Trans. Amer. Math. Soc. 123 (1966) 521–535.
[2] J. Banasiak, A note on the Tikhonov theorem on an infinite interval, Vietnam J. Math. 49 (2021), no. 1, 69–86.
[3] J. Banasiak, S.Y. Tchoumi, Multiscale malaria models and their uniform in-time asymptotic analysis, Mathematics and Computers in Simulation, 221 (2024), 1 – 18.
[4] G.A. Ngwa, M.I. Teboh-Ewungkem, Y. Dumont, R. Ouifki, J. Banasiak, On a three-stage structured model for the dynamics of malaria transmission with human treatment, adult vector demographics and one aquatic stage, J. Theoret. Biol. 481 (2019) 202–222.
[5] P. Rashkov, B.W. Kooi, Complexity of host-vector dynamics in a two-strain dengue model, J. Biol. Dyn. 15 (1) (2021) 35–72.
[6] P. Rashkov, E. Venturino, M. Aguiar, N. Stollenwerk, B.W. Kooi, On the role of vector modeling in a minimalistic epidemic model, Math. Biosci. Eng. 16 (5) (2019) 4314–4338.
[7] J. Banasiak, G. Ngwa, M. Bime, The Impact of Mating on Modeling Mosquito Dynamics: A Mathematical Investigation, in preparation.

Dr. Karen Meyer, University of Dundee
2024-10-04 14:00 - 15:00 | Phys Theatre A
Academic webpage
Title: Persistence in Solar Physics

Abstract:

Persistence, or long memory, is of longstanding interest in solar physics, having first been identified in time series of sunspot numbers in the seminal paper by Mandelbrot and Wallis (1969): “Some long‐run properties of geophysical records”. They used a method called Rescaled Range Analysis (R/S) to determine a Hurst exponent, H=0.93, which is indicative of strong persistence. It has since been suggested that for sunspot numbers, and indeed most times series of solar quantities, R/S is not an appropriate method for estimating persistence due to the non-stationary nature of the time series. Detrended fluctuation analysis (DFA) has been proposed as a more suitable method for estimating persistence, and has since been widely used in the analysis of solar and geo-physical time series. However, DFA is known to introduce uncontrolled bias and is in fact inappropriate for non-stationary processes (Bryce & Sprague, 2012).

Here, we assume an alternative class of long-memory models, more commonly found in statistics and econometrics: fractionally integrated processes. We revisit solar physics time series such as sunspot number and total solar irradiance with more robust estimators, and identify higher persistence than previous studies, as well as persistence over timescales significantly shorter than previously identified.

We also consider persistence in time series of quantities derived from solar physics simulations, demonstrating that these simulations capture the memory structure that is present in the observational input data. Further, we provide an algorithm for the quantitative assessment of simulation burn-in: the time after which a quantity has evolved away from its arbitrary initial condition to a physically more realistic state.

Dr. Enrico Camporeale, Queen Mary
2024-05-03 11:00 - 12:00 | MAT Theatre B
Affiliation: Queen Mary University
Academic Webpage

Title: Data-Driven Discovery of Fokker-Planck Equation for the Earth’s Radiation Belts Electrons Using Physics-Informed Neural Networks
Abstract: We use the framework of Physics-Informed Neural Network (PINN) to solve the inverse problem associated with the Fokker-Planck equation for radiation belts’ electron transport, using 4 years of Van Allen Probes data. Traditionally, reduced models have employed a diffusion equation based on the quasilinear approximation. We show that the dynamics of “killer electrons” is described more accurately by a drift-diffusion equation, and that drift is as important as diffusion for nearly-equatorially trapped ∼1 MeV electrons in the inner part of the belt. Moreover, we present a recipe for gleaning physical insight from solving the ill-posed inverse problem of inferring model coefficients from data using PINNs. Furthermore, we derive a parameterization for the diffusion and drift coefficients as a function of L only, which is both simpler and more accurate than earlier models. Finally, we use the PINN technique to develop an automatic event identification method that allows identifying times at which the radial transport assumption is inadequate to describe all the physics of interest.

Prof Emmanuil Georgoulis, Heriot Watt and NTU Athens
2024-04-19 14:00 - 15:00 | MAT Theatre B
Affiliation: Heriot Watt and National Technical University Athens
Academic Webpage
Title: Discontinuous Galerkin methods on arbitrarily-shaped elements: stability, analysis, and adaptivity
Abstract: I will present a recent generalisation of the popular interior-penalty discontinuous Galerkin (dG) method discretizing general classes of linear and nonlinear advection-diffusion-reaction problems to meshes comprising extremely general, essentially arbitrarily-shaped element shapes. In particular, our analysis allows for curved element shapes, without the use of non-linear elemental maps. The feasibility of the method relies on the definition of a suitable choice of the discontinuity-penalisation, which turns out to be explicitly dependent on the particular element shape, but essentially independent on small shape variations. A priori error bounds for the resulting method will be given, under very mild structural assumptions restricting the magnitude of the local curvature of element boundaries. In the second part of the talk, I plan to present new, rigorous, a posteriori error estimates in various norms for the above method for elliptic as well as a class of semilinear parabolic problems. The key challenge of robustness with respect to local element shape variations. I will present some ideas on how this is addressed theoretically, by generalising existing concepts of proof of a posteriori error estimates for non-conforming Galerkin methods. Numerical experiments will be also presented throughout the talk aiming to motivate and showcase the practicality and the potential advantages of the proposed numerical framework.

Prof Joseph Henry Lacasce, Oslo
2024-04-05 14:00 - 15:00 | WRL Theatre B
Affiliation: University of Oslo, Norway
Academic Webpage
Title: Vortices over bathymetry
Abstract: In many regions of the ocean, the flow is dominated by surface-intensified vortices with scales of 10s of kilometers. These interact with bottom topography, often non-intuitive ways. It is possible to predict the mean flow generated by such “geostrophic turbulence” using a simple variational argument. With a single fluid layer, the predicted flow is correlated with the bathymetry, with cyclonic flow around basins, but with the small scales smoothed out. With two fluid layers, the flow is bottom-intensified, with the same sense of circulation. Interestingly, at larger energies the deep flow is strong enough that the deep potential vorticity is “homogenized”. In such cases, the topographic effect vanishes and the flow is effectively like that over a flat bottom.
We examine a range of numerical turbulence simulations in light of the predictions. The basin-scale flow is as predicted, bottom-intensified with the correct circulation. But in addition, an oppositely-signed (anticyclonic) vortex is often observed at the surface. Such vortices are also seen in the ocean, notably a semi-permanent feature in the Lofoten Basin west of Norway. We consider possible explanations for this, and also how bottom friction modifies the different components of the flow. With the addition of the planetary beta effect, the resulting surface vortices closely resemble those in the ocean, as seen by satellite.

Dr Wessel Woldman, Univ. of Birmingham & Neuronostics Ltd
2024-03-29 14:00 - 15:00 | MAT Theatre B
Affiliation: University of Birmingham and Neuronostics Ltd
Academic Webpage
Title: Computational biomarkers for epilepsy from clinically non-informative EEG
Abstract: In this talk, I will provide an overview of several studies where computational analysis of routine clinical recordings has led to novel set of candidate biomarkers for seizures and epilepsy. By using a dynamic network model approach, I will show how we can systematically explore how changes to network structure or model parameters influence the seizure-likelihood in model simulations. Finally, I will discuss how we are currently aiming to assess the potential added value and robustness of these candidate markers in clinical studies.

Dr Susanne Horn, Coventry
2024-03-15 14:00 - 15:00 | MAT Theatre B
Affiliation: Coventry University
Academic Webpage
Title: Generating tornado-like vortices in Coriolis-centrifugal convection
Abstract: Tornadoes are the most intense atmospheric vortices and have been observed on all continents of Earth (except Antarctica), and even on Mars. The most dangerous tornadoes
develop within the mesocyclone of supercell thunderstorms. But what makes a mesocyclone tornadic or not remains one of the greatest mysteries of tornado research, with less than 25%
of mesocyclones producing tornadoes. Magnetic tornadoes have also been observed in the solar atmosphere and are believed to be crucial for coronal heating. Yet, also in the Sun, the
formation mechanisms are far from being fully understood. Thus, the generation of tornadoes and tornado-like vortices is a major and sometimes controversial subject in planetary,
atmospheric, and solar science. Here, I will explore how tornadoes are self-consistently generated in Coriolis-centrifugal convection, that is rotating Rayleigh-Benard convection with ´
the explicit inclusion of centrifugal buoyancy. Turbulent Coriolis-centrifugal convection in a cylindrical domain constitutes an idealised model system of tornadic storms, where the
rotating cylinder represents the mesocyclone of a supercell thunderstorm. I will discuss possible explanations for why seemingly similar mesocyclones may or may not spawn
tornadoes, and how varying boundary conditions and magnetic fields affect the morphology and other flow characteristics. I will show that centrifugal buoyancy is indeed highly relevant
for the understanding of these planetary and solar atmospheric vortices, and likely a key component in next-generation models of tornado physics.

Prof Cleopatra Christoforou, Cyprus
2024-02-16 14:00 - 15:00 | MAT Theatre B
Affiliation: University of Cyprus
Academic webpage
Title: An exposition on hyperbolic balance laws with application to an Euler-type flocking model
Abstract. Mathematical models introduced to capture the emergent behavior of self-organized systems have brought new mathematical challenges and most studies on flocking models investigate so far smooth solutions. In this talk, we will first have an overview of the theory of entropy weak solutions to hyperbolic balance laws and then describe an Euler-type flocking problem with an all-to-all interaction kernel. We will discuss how the theory of balance laws is further developed to establish the global existence of entropy weak solutions to Euler-type flocking systems with arbitrary initial data and also capture unconditional time-asymptotic flocking behavior for weak solutions.

Dr Irene Kyza, Dundee
2023-12-08 14:00 - 15:00 | MAT Theatre B
Academic webpage
Affiliation: University of Dundee (soon to be in St Andrews)
Seminar title: A posteriori error Control and Adaptivity for problems with Finite Time Blowup
Abstract: In this talk we discuss numerical strategies inspired by problems exhibiting very sharp concentrations, e.g., tumor growth and chemotaxis. More specifically, we present results on the a posteriori error control and adaptivity for a semilinear parabolic evolution problem with possible blowup in finite time. In particular, we rigorously derive a posteriori error estimators in various norms for finite element-type schemes. The obtained estimates are conditional, i.e., they are valid under verifiable conditions. Utilising the obtained estimates we design space-time adaptive strategies, that allow us to enter the blowup regime and approximate the blowup time. Furthermore, we compare the different a posteriori error estimators and the proposed adaptive strategies, and we discuss advantages and disadvantages. This is joint work with A. Cangiani (SISSA, Italy), E.H. Georgoulis (Heriot-Watt University and NTUA, Greece) and S. Metcalfe (McGill University, Canada).

Dr Andrew Krause, Durham
2023-11-24 14:00 - 15:00 | MAT Theatre B
Affiliation: Durham University
Academic Webpage
Title: Dynamical Systems Approaches and Interactive Visualisations for Pattern Formation
Abstract: Natural patterns, such as those created during embryological development, can arise from enormously complex processes occurring across vast scales of space and time. A key scientific challenge is to conceptually map out these processes in terms of distinct mechanisms, and their interplay. Dynamical systems theory provides several tools for developing hypotheses regarding such processes, and for understanding the limitations of potential mechanisms.
We will discuss the uses and limitations of linear and nonlinear analyses of reaction-transport models in the context of understanding problems of multiscale periodic patterning. A focus will be on understanding robustness and the ability for ‘generic’ models to exhibit different patterning behaviours, without having to quantify molecular details of a particular system. We will aim to demonstrate how these kinds of models and ideas can help generalize insights from specific systems and numerical simulations, while also discussing fundamental limitations to this kind of modelling. VisualPDE.com will be introduced as a tool to rapidly prototype simple models, as well as to teach and communicate aspects of PDEs more generally. We will end with a range of open problems, both technical and conceptual.

Prof Mitchell Berger, Exeter
2023-11-17 14:00 - 15:00 | MAT Theatre B
Affiliation: University of Exeter
Academic webpage
Title: Characterization of winding and entanglement in spherical and cubic volumes
Abstract: It is often useful to quantify the topological complexity of magnetic fields (as well as polymer entanglements). Simulations and observations of magnetic fields often involve spherical volumes (either interior, exterior, or a spherical shell. Some simulations involve the interiors of cubes or cuboids. I will describes general procedures for working in such volumes. There will be a brief excursion to Borromean winding, and, along the way, a mention of Gauss-Bonnet.

Dr Tom Elsden, St Andrews
2023-11-10 14:00 - 15:00 | MAT Theatre B
Affiliation: University of St Andrews
Personal webpage
Title: Ultra Low Frequency Waves of Earth’s Magnetosphere

Abstract:
My research focusses on magnetohydrodynamic (MHD) waves which manifest in Earth’s magnetosphere, known as ultra low frequency (ULF) waves (frequencies ~1mHz – 1Hz). Some of the first measurements by ground magnetometers of ULF waves date back to 1859 following the Carrington event (a large geomagnetic storm triggered by a coronal mass ejection). They communicate large scale disturbances in Earth’s magnetic field, generally caused by the interaction with the solar wind. Over the last 20 years or so, there has been a resurgence in the study of ULF waves, due to their critical effect on energetic particles in the Earth’s magnetosphere, which play an important role in space weather.

In this talk, I’ll provide a broad introduction to the magnetosphere and describe the what, where, when and why of ULF waves. I realise that many members of the applied division will not be familiar with this area, so I will treat this more as a general overview of some topics I’ve worked on, with an emphasis on explaining the big picture ideas. I study ULF waves using numerical MHD modelling, and I’ll discuss the approach I’ve taken to this and how that fits in to the broader landscape of magnetospheric MHD modelling. For members of the solar group, this talk will be rather similar to the seminar I gave to the group last year!

Prof Moira Jardine, St Andrews
2023-11-03 14:00 - 15:00
Affiliation: University of St Andrews
Academic Webpage:
Title “The space weather of other stars“
Abstract:
“Our understanding of stellar activity and its impact on exoplanets has been transformed by the bringing together of two complementary types of studies. Detailed spectropolarimetric studies that map the surface magnetic fields of individual stars now number more than 100 stars. They have revealed surprising trends in fundamental parameters such as stellar mass and rotation rate. These studies have now been placed in a broader context however by large-scale studies of flaring and stellar rotational evolution. These observational advances can now be used both as inputs and as tests of sophisticated 3D MHD models of stellar coronae and winds. In this talk I will describe the results of recent studies of the “space weather” that is driven by stellar magnetic activity and its variation over stellar magnetic cycles. This can have a significant impact on the structure and evolution of a star’s corona and on the types of ejecta it might produce. Recent results from Parker Solar Probe on the “breathing” of the solar corona over the course of a cycle give us some ground truth with which to interpret these stellar observations. Finally I will touch on the observed trends in stellar magnetic helicity density (which can now be mapped across stellar surfaces) and speculate on its role in the relationship between stellar flares and mass ejections.“

Dr Richard Mann, Leeds
2023-10-27 14:00 - 15:00
Affiliation: University of Leeds
Academic webpage
Title: Collective decision-making by rational agents

Abstract:
The decisions made by others are a valuable source of social information about the world, because they may have knowledge that we lack. This means that when one agent makes a given choice, it can induce others to do so as well. In this talk I will describe a theory of rational agents who optimally utilise the social information provided by others, and explore the dynamics this produces at the individual and group level. In particular, I will show how the implicit beliefs such agents hold about the physical and social environment shape their response to each other, and how changes to the environment that conflict with these beliefs can dramatically alter collective behaviour and impact the success of groups.
