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Mathematics Institute

Applied Mathematics Seminars

Organisers: Clarice Poon and Ellen Luckins

The Applied Maths Seminars are held on Fridays 12:00-13.00. This year the seminar will be hybrid (at least for Term 1): you can choose to attend in person in room B3.02 or on MS Teams. The team for the seminar is the same as last year, but if you are not a member, you can send a membership request via MS Teams or email the organisers.

Please contact Clarice Poon or Ellen Luckins if you have any speaker suggestions for future terms.

Seminar Etiquette: Here is a set of basic rules for the seminar.

  • Please keep your microphone muted throughout the talk. If you want to ask a question, please raise your hand and the seminar organiser will (a) ask you to unmute if you are attending remotely or (b) get the speaker's attention and invite you to ask your question if you are in the room.
  • If you are in the room with us, the room microphones capture anything you say very easily, and this is worth keeping in mind 鈽猴笍.
  • You can choose to keep your camera on or not. Colleagues in the room will be able to see the online audience.
  • Please let us know if you would like to meet and/or have lunch with any of the speakers who are coming to visit us so that I can make sure you have a place in the room.

Term 3

Term 2

Term 1

Abstracts

Term 3

Week 1. Jinglai Li (Birmingham) -- Nemytskii neural operator: a nonlinear model reduction method for parametrized partial differential equations
In this talk, we introduce a Nemytskii neural operator framework for nonlinear model reduction of parametrized steady-state partial differential equations. The method generalizes reduced basis approaches by replacing linear combinations of basis functions with a structured nonlinear mapping via a pointwise Nemytskii operator acting on fixed feature functions. Feature functions are learned offline via nonlinear dimension reduction from high-fidelity snapshots. A lightweight reconstruction network is first trained offline and refined online using physics-informed residual minimization. The Nemytskii structure preserves analytical regularity and enables efficient evaluation of spatial and parametric derivatives, leading to fast online adaptation. Numerical experiments are provided to demonstrate the performance of the proposed method.
Week 2. Tobias Grafke (Warwick) -- Extreme events in atmosphere and ocean via sharp large deviations estimates
Rare and extreme events are notoriously hard to handle in any complex stochastic system: They are simultaneously too rare to be reliably observable in experiments or numerics, but at the same time often too impactful to be ignored. Large deviation theory provides a classical way of dealing with events of extremely small probability, but generally only yields the exponential tail scaling of rare event probabilities. In this talk, I will discuss theory, and algorithms based upon it, that improve on this limitation, yielding sharp quantitative estimates of rare event probabilities from a single computation and without fitting parameters. Notably, these estimates require the computation of determinants of differential operators, which in relevant cases are not traceclass and require appropriate renormalization. We demonstrate that the Carleman--Fredholm operator determinant is the correct choice. Throughout, I will demonstrate the applicability of these methods to high-dimensional real-world systems, for example coming from atmosphere and ocean dynamics.
Week 3. Desmond Higham (Edinburgh) --Generalized Friendship Paradoxes in Network Science

The original Friendship Paradox dates back to the work of the sociologist Scott Feld, who showed that, on average, our friends have at least as many friends as us. In graph theory terms, for any graph, neighbours have a degree at least as high as nodes, on average. Feld discussed two types of averaging, which may be viewed as global and local. These paradoxes have attracted attention in academia and beyond. They are relevant to many aspects of human interaction, notably in social science, epidemiology and healthcare intervention. Generalized friendship paradoxes occur when degree is replaced by some other attribute. I will focus on the case of network centrality, where we ask whether, on average, our friends are more influential than us. I will present some new results concerning the inevitability of network centrality paradoxes arising. The analysis brings together a surprisingly wide range of ideas; from linear algebra, matrix polynomials, number theory, mathematical physics and chemical graph theory. I will also point out some open questions. This is based on joint work with Francesco Hrobat and Francesco Tudisco.

Week 5. Wadim Gerner (Genoa) -- An optimal trace inequality and its applications

I will present an optimal quantitative homogeneous trace inequality which reflects the geometry of an underlying Euclidean domain. In the second part of this talk I will discuss some applications of this inequality in the context of electromagnetism and elasticity theory. In particular, I will provide explicit geometric estimates for constants appearing in Gaffney's inequality and Korn's second inequality under appropriate boundary conditions.

Week 6. Smita Sahu (Portsmouth) -- A simplified blended electrode model for lithium-ion batteries

Blended electrodes, containing two or more electrochemically distinct active materials, offer a practical route to improving lithium-ion battery performance by combining materials that individually excel in different respects, such as rate capability or energy density. Simulating such electrodes with the standard Newman model is computationally expensive, a difficulty that is compounded in the blended electrode setting by the need to solve a separate particle diffusion equation for each active material species. This motivates us to derive a systematic asymptotic reduction of a Newman-type model for blended electrodes, yielding a reduced-order model that we term the simplified blended electrode model (SBEM).

The SBEM has comparable complexity to the widespread single particle model, yet is able to accurately describe the behaviour of blended electrodes. Our derivation exploits the disparity between the thermal voltage and the characteristic cell voltage, which gives rise to the large dimensionless parameter. The SBEM is validated against experimental data for cathodes containing lithium nickel cobalt aluminum oxide (NCA) and lithium manganese oxide (LMO), and shows good agreement with experiments across a range of discharge rates. We anticipate that the SBEM will serve as a useful tool for guiding the design of better blended electrodes.

Week 7. Katerina Kaouri (Cardiff) -- From embryos to epidemics: mathematical modelling across scales and disciplines

In this talk, I will present a selection of interdisciplinary modelling challenges that I have worked on, in collaboration with experimentalists, clinicians, architects and policymakers. I will begin with mathematical models of calcium signalling in in vitro fertilization (IVF) and embryogenesis, illustrating how multiscale approaches can connect molecular and cellular processes to early embryo development. I will then discuss our ongoing work on modelling viral transmission in indoor environments, developed in collaboration with architects and public health stakeholders, with the aim of informing evidence-based policy and preparedness for future epidemics. Throughout the talk, I will highlight the role of mathematical modelling as a bridge across scientific disciplines and scales, from intracellular dynamics to population-level phenomena.

Term 2

Week 1. Marine Fontaine (Warwick) -- Dynamic landscape analysis and neural tube patterning
Single-cell RNA sequencing (scRNA-seq) generates high-dimensional gene-expression datasets that capture cell states during fate decisions. I will discuss our recent work on dynamic landscape analysis, a framework that combines dynamical systems and bifurcation theory to build quantitative, predictive models from these datasets. We have developed a dimension reduction approach for time-series scRNA-seq data that enables the identification of stable cell states and the dynamical transitions between them. This method provides a qualitative perspective on the decision-making landscape that guides the differentiation of ventral progenitors through to their maturation into neurons under the influence of the morphogen Sonic Hedgehog in the early formation of the neural tube. Next, we constructed a theory-based dynamical model that reproduces the key patterns of the fate decision and behaves sensibly when we simulate perturbations. The model is fitted to experimental data, linking theory to observations and motivating new experimental protocols.
Week 2. Dan Hill (Oxford) -- Think Global, Act Local: Inducing Fully Localised 2D Patterns via Spatial Heterogeneity
The existence of localised two-dimensional patterns has been observed and studied in numerous experiments and simulations: ranging from optical solitons, to patches of desert vegetation, to fluid convection. And yet, our mathematical understanding of these emerging structures remains extremely limited beyond one-dimensional examples.
In this talk I will discuss how adding a compact region of spatial heterogeneity to a PDE model can not only induce the emergence of fully localised 2D patterns, but also allows us to rigorously prove and characterise their bifurcation. The idea is inspired by experimental and numerical studies of magnetic fluids and tornados, where our compact heterogeneity corresponds to a local spike in the magnetic field and temperature gradient, respectively. In particular, we obtain local bifurcation results for fully localised patterns both with and without radial or dihedral symmetry, and rigorously continue these solutions to large amplitude. Notably, the initial bifurcating solution (which can be stable at bifurcation) varies between a radially-symmetric spot and a 'dipole' solution as the width of the spatial heterogeneity increases.
This work is in collaboration with David J.B. Lloyd and Matthew R. Turner (both University of Surrey).
Week 3. Robyn Edge (Exeter) -- Engineering Dispersion Relations with Beyond Nearest Neighbour Couplings
Endeavours to obtain enhanced control over wave dynamics has driven a vast amount of research. The
emergence of metamaterial structures has facilitated unprecedented wave manipulation, offering transformative solutions to both theoretical and practical research challenges. A prominent theme within elastic
media is the incorporation of non-local connections into lattice frameworks, giving rise to exotic dispersion
phenomena [Nat. Comms. 12.1 (2021)]. In canonical 1D lattice toy models, systems typically consist of
nearest-neighbour couplings that provide strictly local interactions. In the non-local regime, additional connections extend beyond the confines of the unit cell, significantly influencing lattice dynamics. This extended
configuration provides an effective platform for probing exotic dispersion characteristics and forms a promising basis for tailoring and engineering wave behaviour.
Exploring 1D periodic toy models, we demonstrate the theoretical freedom afforded over dispersion
phenomena, illustrating how the manipulation and tuning of lattice configurations can predictably modify
wave behaviour towards target dispersion profiles. In passive, discrete mass–beam lattice systems with
multiple degrees-of-freedom, beyond-nearest-neighbour connections between junctions affords control over
the locality of extrema in reciprocal space. We demonstrate that competing power channels drive the position
and existence of zero group velocity modes within the first Brillouin zone, while the additional coupling
between degrees-of-freedom provides enhanced flexibility over the dispersive properties, extending beyond
the confines of extraordinary Bragg reflections [New J. Phys. 27, 023007 (2025)]. Leveraging conservative
mass–spring lattices, we implement a non-Hermitian inverse-design protocol to engineering wave propagation
in non-local configurations. By extending the inverse-design method to complex frequencies, incorporating
velocity-dependent, non-conservative behaviours into the governing equations, both the real band structures
and attenuation can be precisely tailored [Phys. Rev. B, 112, 014304 (2025)]. Demonstrating apparent
wavenumber band gaps and compact Fourier representations of target functions, suitable for both passive
and active systems.
Week 4. Estefania Loayza-Romero (Strathclyde) -- Gradient-based training for multilevel optimal control problems with neural surrogate models

In this talk, we will consider multilevel optimisation framework for optimal actuator and control design in semi-discretised dynamical systems, where the actuator placement is optimised based on the performance of the underlying optimal control problem. To address the computationally challenging evaluation of the value function for a given actuator realisation, we develop gradient-based neural network surrogates within a supervised learning paradigm. This choice enables the use of efficient consensus-based optimisation methods to determine the optimal actuator design. We validate our approach by solving problems associated with the heat equation with space-dependent diffusion parameter and the viscous Burgers鈥� equation.

Week 5. Claire Boyer (Orsay) -- How Learning Rates & Latent Spaces Shape Diffusion Generative Models
This talk explores two surprising mechanisms that shape the behavior of diffusion-based generative models. First, we uncover an implicit regularization effect in denoising score matching: large learning rates prevent models from overfitting the training data, mitigating memorization without explicit constraints. Second, we show that in Latent Diffusion Models, running the diffusion too long can worsen sample quality, a phenomenon rooted not in numerical instability, but in the dimensionality reduction of the latent space. We derive conditions linking optimal stopping time to latent dimension, revealing it as a key hyperparameter for generation quality. Together, these findings highlight how early (diffusion) stopping and optimization dynamics jointly govern generalization in modern diffusion models.
Week 6: Julian Braun (Heriot Watt) -- On elastic far-fields induced by crystal defects and the incompleteness of Sinclair flexible boundary conditions.

The elastic field around a defect in a crystalline material is known to be described by continuum linearised elasticity in leading order away from the defect core for dislocations or crack openings. For point defects, the leading order instead is given by a defect-dipole tensor. If both approaches are combined and generalised, one can derive higher order asymptotic expansions of the elastic far-field as well. These can be used as high accuracy boundary conditions for atomistic defect computations. I will showcase an outline of the theory and specific resulting numerical methods for point defects, dislocations, and a Mode III crack. In the latter case, this will show the incompleteness of the classical ansatz for flexible boundary conditions by Sinclair.

Week 7: Gyula Toth (Loughborough) -- Diffuse interface modelling of pattern formation phenomena in liquid mixtures
We present a diffuse–interface formulation for the dynamics of isothermal multicomponent liquid mixtures, derived within the Ginzburg–Landau framework for first-order phase transitions. Starting from the principles of classical fluid mechanics, we first construct a thermodynamically consistent convection–diffusion model for incompressible multicomponent fluids. Constitutive relations for diffusion fluxes and capillary stresses are obtained using variational principles, leading to a unified description that couples hydrodynamics, diffusion, and interfacial effects.
A key aspect of the model is the treatment of incompressibility in the presence of interfaces of finite width between non-mixing liquids with different bulk densities. The approach is based on a generalization of the definition of incompressibility for multicomponent systems, which is then incorporated systematically through a Lagrange multiplier formulation, yielding a closed set of evolution equations with consistent constraints.
The resulting model is analysed numerically in the context of a quaternary Cahn–Hilliard system. The simulations demonstrate that density variations do not affect equilibrium states when the free-energy functional satisfies appropriate structural conditions, but can strongly influence transient dynamics and pattern formation far from equilibrium. These results highlight the importance of density effects in multicomponent phase separation and provide a modelling framework suitable for further analytical and numerical investigation.
Week 8: Anna Scaife (Manchester) -- Learning foundational representations in astrophysics
Pre-trained representations from large volumes of unlabelled data, known as foundation models, are rapidly emerging as a key AI technology in scientific research. I will review some of the recent applications of these models in astrophysics, highlight their advantages, and some of the potential challenges. I will also describe our recent work looking at recovering calibrated uncertainties from such models and how we can use related metrics to understand the diversity of astrophysical sources in our data, identify varying types of distributional shift - and preserve the potential for discovery. Data is central to both the development and exploitation of large AI models, and I will conclude with a future outlook that focuses on how data usage and access may evolve as AI tools become increasingly mainstream in science.
Week 9: Duncan Hewitt (Cambridge) -- Stuck in the mud? Channelling and swimming in viscoplastic fluids

Numerous natural and industrial materials, ranging from lava and mud to cosmetics, foodstuffs, blood and mucus, exhibit both fluid-like and solid-like behaviour: they can flow like a viscous fluid under sufficient force, but withstand deformation at lower stresses. Clogging and flow localisation in such materials is a generic feature of their mechanics: it underlies the triggering of mudslides, catastrophic liquefaction of mining waste, blood jamming in sickle cell disease, and numerous issues in industrial processing and cleaning. The problem of locomotion through such materials – encountered, for example, by worms moving through soil or sediment – is also controlled by these features of flow and stress localisation.

In this talk, I will explore some basic fluid mechanical behaviour of idealised viscoplastic materials, illustrating some ways in which channelling and clogging can generically occur. To further illustrate some of these features, I will particularly focus on the problem of undulatory 鈥榮wimming鈥� through such materials, with the development of a viscoplastic slender-body theory and an explanation of how the rheology allows for a 鈥榖urrowing鈥� mechanism of locomotion.

Term 1

Week 1. Mohit Dalwadi (Oxford) -- Emergent phenomena from multiscale heterogeneity: losing symmetry and causing chaos
In this talk I use hybrid multiscale techniques to understand emergent phenomena arising in two fundamental problems in fluids and biology.
In the first part, I investigate an overarching question in developmental biology: how are cells able to decode spatio-temporally varying signals into functionally robust patterns in the presence of confounding effects caused by complex heterogeneous environments? This is linked to the general idea first explored by Alan Turing in the 1950s. I present a general theory of pattern formation in the presence of spatio-temporal input variations, and use multiscale mathematics to show how delayed bifurcations (via 鈥楻-tipping鈥�) can allow biological systems to generate non-standard dynamic robustness for 鈥榝ree鈥� over physiologically relevant timescales. This work also has applications in pattern formation more generally.
In the second part, I investigate how the rapid motion of 3D microswimmers affects their emergent trajectories in viscous shear flow. This can be considered an active version of the classic fluid mechanics result of Jeffery鈥檚 orbits for inert spheroids, first explored in the 1920s. I show that the rapid short-scale motion exhibited by many microswimmers can have a significant effect on longer-scale trajectories, despite the common neglect of this motion in some mathematical models. I further demonstrate that fast-scale yawing can generate emergent asymmetry and subsequent chaos, in stark contrast to constant fast-scale rotation.
Week 2. Marcus Webb (Manchester) -- Low-rank approximation of analytic kernels
Many algorithms in scientific computing and data science take advantage of low-rank approximation of matrices and kernels, and understanding why nearly-low-rank structure occurs is essential for their analysis and further development. In this talk I will discuss a new framework for bounding the best low-rank approximation error of matrices arising from samples of a kernel that is analytically continuable in one of its variables to an open region of the complex plane. Elegantly, the low-rank approximations used in the proof are computable by rational interpolation using the roots and poles of Zolotarev rational functions, leading to a fast algorithm for their construction. A preprint can be found at .
Week 3. Tristan Lawrie (Exeter) -- A Quantum Graph Model for Static and Time-Varying Metamaterials

Since the turn of the 21st century, metamaterials have garnered significant attention for their potential to exhibit highly nontrivial and exotic properties, such as cloaking or perfect lensing. This has driven substantial efforts to develop reliable mathematical models that accurately predict the required material compositions. In this work, we present a quantum graph approach to metamaterial design. Wave transport in the material is modelled as a network of vertices connected by one-dimensional edges governed by the wave equation. By varying the graph topology, edge lengths, and vertex boundary conditions, we demonstrate a range of nontrivial effects, including negative refraction, discrete angular filtering, and beam forming and steering. We compare the model's predictions with experimental results from both acoustic and electromagnetic networks, finding excellent agreement. These results establish quantum graph theory as an ideal mathematical framework for studying metamaterials.

Week 4. Audrey Repetti (Heriot Watt) -- Analysis and synthesis approximated denoisers for forward-backward plug-and-play algorithms

In this presentation we will study the behaviour of the forward-backward (FB) algorithm when the proximity operator is replaced by a sub-iterative procedure to approximate a Gaussian denoiser, in a Plug-and-Play (PnP) fashion. Specifically, we consider both analysis and synthesis Gaussian denoisers within a dictionary framework, obtained by unrolling dual-FB iterations or FB iterations, respectively. We analyse the associated global minimization problems as well as asymptotic behaviour of the resulting FB-PnP iterations. For each case, analysis and synthesis, we show that the FB-PnP algorithms solve the same problem whether we use only one or an infinite number of sub-iteration to solve the denoising problem at each iteration. We will illustrate our theoretical results on numerical simulations, considering an image restoration problem in a deep dictionary framework. Joint work with Matthieu Kowalski, Benoit Malezieux and Thomas Moreau.

Week 5. Albane Th茅ry (Warwick) -- Single-cell models for bacterial motility in complex environments

Understanding and preventing bacterial infections requires insight into how microorganisms move and interact within realistic, structured environments such as biofilms or tissues. From a modelling perspective, these systems can be studied across multiple scales — from continuum PDEs approaches and agent-based models to single-cell descriptions. In this talk, we focus on this latter class of single-cell models, and study the coupling between individual motile bacteria and their environment.

We first examine how suspended particles influence the swimming of flagellated bacteria, combining analytical and semi-analytical results to explain the experimentally observed speed increase in suspensions. We then turn to microorganisms for which motility relies on elasto-hydrodynamic instabilities and such minimal models cannot capture key features of their motility. We present elasto-hydrodynamic simulations for the swimming of the oral pathogen Selenomonas sputigena and the gliding motion of filamentous cyanobacteria.
Week 6. Scott McCue (QUT) -- Complex-plane behaviour for nonlinear reaction diffusion models
This talk concerns solutions of nonlinear reaction diffusion models in the complex plane, which are a) interesting in their own right, and b) related to the crucial real-line behaviour. For example, a power series expansion in time will be divergent and break down at a complex singularity of the pde's initial condition, leading to an inner analysis that reveals information about time-dependent complex singularities. When one of these singularities hits the real axis, the real-valued solution undergoes finite-time blow-up. Thus, it is fruitful to track these singularities using analytical and numerical methods. In this talk, a family of semi-linear diffusion models will be discussed as prototype examples. Asymptotic limits of small time, small diffusion, near-blow-up and large time will be mentioned if time permits. This is work in progress done in collaboration with Prof John King from Nottingham and PhD student Daniel VandenHeuvel from Imperial College London.
Week 7. Maciej Buze (Lancaster) -- Barycenters in unbalanced optimal transport
A central challenge in many applications of optimal transport concerns finding a representative (probability) distribution of a given set of distributions. The basic optimal transport approach to this problem is to find the so-called barycenter, which is done by minimizing the sum of weighted two-marginal optimal transport costs between the barycenter and each input distributions. In a seminal contribution [1], it was subsequently shown that an equivalent and computationally favourable approach is to instead solve a single least-cost multi-marginal optimal transport problem.
If the input distributions do not all have equal mass, an unbalanced barycenter can be found via a recourse to the emerging theory of unbalanced optimal transportation. This, however, can be done in a number of ways, depending on how one penalises mass deviations, what cost function is employed and whether one wishes to consider the conic formulation --- see the detailed discussion in [2].
In this talk, following a gentle introduction to the topic, I will present several results on how to recover the celebrated least-cost multi-marginal formulation of Agueh and Carlier in the unbalanced setting [3] and discuss on-going work on generalising such results to unbalanced settings where such a reformulation is not possible.
Lastly, I will also touch upon applications of this and related results in the context of modelling of polycrystalline materials [4].
[1] Agueh, M., & Carlier, G. (2011). Barycenters in the Wasserstein space. SIAM Journal on Mathematical Analysis, 43(2), 904-924.
[2] Liero, M., Mielke, A., & Savar茅, G. (2018). Optimal entropy-transport problems and a new Hellinger–Kantorovich distance between positive measures. Inventiones mathematicae, 211(3), 969-1117.
[3] Buze, M. (2025). Constrained Hellinger–Kantorovich barycenters: least-cost soft and conic multimarginal formulations. SIAM Journal on Mathematical Analysis, 57(1), 495-519.
[4] Buze, M., Feydy, J., Roper, S. M., Sedighiani, K., & Bourne, D. P. (2024). Anisotropic power diagrams for polycrystal modelling: Efficient generation of curved grains via optimal transport. Computational Materials Science, 245, 113317.
Week 8. James Griffin (Coventry) -- Automated Manufacturing and Control through Non-Destructive Testing (NDT) Methods: Pattern Recognition of Grinding Phenomena and In-situ Quality Monitoring of Laser Shock Peening
This titled work details the application of sensitive Acoustic Emission (AE) sensing and Machine Learning (ML) techniques for automated manufacturing and control using Non-Destructive Testing (NDT) methods. The focus encompasses pattern recognition within both grinding processes and Laser Shock Peening (LSP) quality control. For grinding, the research identifies and classifies micro and macro phenomena, including cutting, ploughing, and rubbing, alongside anomalies such as burn and chatter. Utilising Neural Networks (NN) and Genetic Algorithm (GA) optimised Fuzzy-clustering, the classification of grinding mechanics achieved accuracies between 82% and 96%. The work also examines the use of AE for in-situ quality monitoring during Laser Shock Peening (LSP), a surface strengthening technology. AE data is analysed to understand how process parameters, such as confinement layers (air, gel, water) and power densities (15% to 98%), influence the AE output, which correlates well with resulting surface modifications and residual stress detected by methods like Barkhausen noise. This generic strategy, leveraging signal extraction techniques like Short-time Fourier Transform (STFT), provides a foundation for developing intelligent, real-time ML models for automated process monitoring and quality control.
Week 9. Bernhard Schmitzer (Gottingen) -- The Riemannian geometry of Sinkhorn divergences
Optimal transport provides an intuitive and robust way to compare probability measures with applications in many areas of mathematics. This holds in particular for the Wasserstein-2 distance with its formal Riemannian structure.
While entropic regularization of optimal transport has several favourable effects, such as improved statistical sample complexity, it destroys this metric structure. The de-biased Sinkhorn divergence is a partial remedy, as it is positive, definite, and its sublevel sets induce the weak* topology. However, it does not satisfy the triangle inequality. We resolve this issue by considering the Hessian of the Sinkhorn divergence as a Riemannian tensor and study the induced distance. In this talk we outline the key steps of this construction, the corresponding induced notion of tangent space, some early results on the distance, and open directions for future work.
Week 10. Daniel Ratliff (Northumbria) -- What Can Ocean Waves Teach Us About Space Plasmas? An interdisciplinary Journey
In the near-Earth space environment, the trapped plasma (known as the Van Allen Radiation Belts) creates a dynamic which is a host to a who zoo of electromagnetic waves. One family of these, Whistler-mode Chorus waves are of particular interest not only due to their fascinating sonorous bird-like chirping behaviour but also for the role they play in particle energisation events. Such wave-particle interactions can even cause electrons in the radiation belt to reach levels that can damage satellites and spacecraft, so understanding the dynamics of this interplay (particularly from the wave perspective) is imperative to our ability to predict where and when such hazards may occur.
That sounds interesting鈥� but why is Dan, notoriously obsessed with water waves, studying these? And better yet, how is he even able to?
This talk documents the interdisciplinary journey I鈥檝e taken to use nonlinear approaches from water waves to understand Whistler-mode Chorus (WMC). By leveraging the similarities between the mathematical structure of wave-particle interactions in WMC and those of wave-mean flow in water waves, we are able to derive an extended envelope equation for the dynamics of WMC wave packets. By doing so, we are able to not only provide a self-consistent route to chirping behaviour in these waves but provide a mathematical basis for the often-seen bandgap at half the electron gyrofrequency seen within the in-situ data. In tandem, these results into wave-particle mediated frequency changes shed light on why water waves are able to 鈥渄ownshift鈥� – the process in which water waves increase their period and amplitude to stabilise a modulation instability. This talk concludes by presenting some ongoing work extends these parallels to the dynamics of wave spectra which uses the well-established approaches of WAVEWATCH and the ECMWF ocean wave models to construct similar dynamical model for WMC wave spectra.

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