Bath Applied and Interdisciplinary Mathematics Seminar - upcoming
Join us at AIMS on Tuesdays at 13.15 at 6E 2.1. All are welcome!
| Date | Speaker | Title |
| 29 Sep 2026 | Rahil Valani (University of Oxford) |
Superwalking droplets: active particles with a memory
Active particles come in many forms, from bacteria, cells and algae to synthetic colloids and microrobots, all converting energy into directed motion. Their dynamics become particularly interesting when their motion modifies the surrounding environment, which in turn acts back on them. What happens when this feedback gives an active particle a memory of its past? In this talk, I will explore this question using superwalking droplets which are millimetre-scale liquid droplets that self-propel across a vertically vibrated fluid bath through interaction with the waves they generate. The feedback between droplet and wave gives these active wave–particle entities an effective memory and produces surprisingly rich dynamics. I will discuss how this memory shapes individual locomotion, including steady walking and stop-and-go motion, before turning to wave-mediated interactions, collective behaviour, and emergent clusters formed by very large superwalkers. Finally, I will show how reduced models of memory-driven wave–particle motion lead to low-dimensional dynamical systems related to the Lorenz equations, providing a bridge between fluid mechanics, active matter and nonlinear dynamics. |
| 6 Oct 2026 | Mark Blyth (the younger) (University of Bristol) |
Why core-surface battery models fail and how to fix them
Thermal models are essential for the design, management, and control of rechargeable batteries. The simplest approach to thermal battery modelling is to assume that an entire cell is at the same temperature, leading to a so-called “lumped” model of battery temperature. In practice, the interior of a battery will heat up more than its surface because heat is generated throughout the battery but cooling can only occur at the battery surface. This led to the development of core-surface battery models where the core temperature and the surface temperature were treated as separate variables. Unfortunately, the most widely-used core-surface models lose accuracy as thermal gradients increase and they are prone to overfitting, meaning that models calibrated in one setting are hard to translate to other settings. In this talk, I will describe recent work where we explore fundamental problems with the approach used to develop core-surface models and show how an alternative approach based on a two-mode Galerkin approximation can lead to greatly-improved accuracy without increasing model complexity. |
| 13 Oct 2026 | Ed Brambley (University of Warwick) |
Mathematical Modelling of Industrial Metal Forming
Metal forming involves permanently deforming metal into a required shape. Many forms of metal forming are used in industry: rolling, stamping, pressing, drawing, etc; for example, 99% of steel produced globally is first rolled before any subsequent processing. Most theoretical studies of metal forming use Finite Elements, which is not fast enough for real-time control of metal forming processes, and gives little extra insight. As an example of how little is known, it is currently unknown whether a sheet of metal that is squashed between a large and a small roller should curve towards the larger roller, or towards the smaller roller. In this talk, I will give a brief overview of metal forming, and then some progress my group have been making on some very simplified models of cold sheet rolling in particular. The mathematics involved will include some modelling and asymptotics (including multiple scales), and should be accessible to a general applied mathematics audience. |
| 20 Oct 2026 | Marina Costa Merch Dos Santos, Shiyi Ding, Amy Darroch (University of Bath) |
PhD Student Presentations
Speaker: Marina Costa Merch Dos Santos (University of Brasilia) Title: Bifurcations in the Interaction of Two Dipoles Under the Presence of an External Magnetic Field Abstract: Consider two magnetic dipoles fixed in the plane, free to spin, separated by a distance r, subjected to a uniform external magnetic field applied with a certain orientation. This system is a non-linear dynamical system and the goal of this work is to determine and classify its equilibrium points and their bifurcations caused by changes of the applied field. Speaker: Shiyi Ding Title: Introduction to Spatial Stream-Network Models (SSN): What physical mechanisms can be incorporated? Abstract: Analysing transport processes in stream networks is challenging due to latent spatial relationships and non-Euclidean hydrologic distances. In this talk, Shiyi will introduce Spatial Stream-Network (SSN) models, which model spatial covariates by accounting for network connectivity and hydrologic metrics. The key to applying this model to her research on bacterial transport is to find the theoretical links between the statistical approach and physical mechanisms governing the growth and die-off of bacteria, which have not been addressed in the current model. Speaker: Amy Darroch Title: A mathematical model for age-related macular degeneration Abstract: Age-related macular degeneration (AMD) is the leading cause of irreversible sight loss in the UK. One of the earliest signs of the disease is the clogging of Bruch’s membrane, a thin porous layer beneath the retina, by lipoproteins and metabolic waste. Over time these deposits accumulate into drusen, which are a key clinical marker of AMD. We have developed a simple model for the clogging of Bruch’s membrane that couples fluid flow through the membrane with the advection and deposition of particles. However, this model treats the membrane as having a fixed thickness, whereas in reality Bruch’s membrane thickens with age as material builds up within it. In this talk I will present two open problems. First, how should we allow the membrane to expand as it clogs? Second, how can we extend the model to capture drusen formation, describing the transition from material trapped within the membrane to deposits growing beneath the retina? |
| 27 Oct 2026 | Ross Woods (University of Bristol) |
A Stochastic Model for Understanding How Climate Affects Snowpacks
Melting snow is a key source of water for more than 2 billion people. Changes in climate are already causing changes in the amount and timing of snowmelt, and substantial further changes are expected in future. Communicating why these changes are happening, and why they aren’t the same everywhere, will help water managers to navigate these changes. At present, we have scientific capability to calculate the expected changes in snow, but not to explain conceptually why the effects vary from place to place. The difficulty arises because snowpack dynamics are driven by nonlinear (but elementary) interactions between weather elements such as temperature and precipitation, at multiple timescales. In this talk I will (i) show some typical snow and climate data (ii) present a deterministic snowpack model and explain its strengths and weaknesses (iii) propose a non-stationary stochastic model for the snowpack, and show some preliminary results. |
| 3 Nov 2026 | Elizabeth Lewis (University of Manchester) |
Integrated water management: where can mathematics improve operational hydrology?
Water management is a substantial practical challenge. Because rain falls everywhere, water can be managed anywhere, and both the complexity of the system and the number of possible interventions are very large. Producing evidenced management plans is therefore difficult, and we rely on models and data to lay out evidence in a structured way, explore options, and support decisions with critical scrutiny. In practice, water is managed at different scales and in separate silos: in England, surface water flooding is the responsibility of local authorities, river flooding of the Environment Agency, water supply of regional water companies, and water quality of several organisations. These elements are, however, parts of one interacting system, and implementation of interventions, and the funding of them, could be considerably more efficient if their benefits were assessed together. Managing water in an integrated way has long been an ambition, but technical and logistical barriers have so far limited progress. There is now both political momentum, through the government’s water reform programme, and technological capability for integrating evidence systems. We have been working with the Greater Manchester Integrated Water Management team, who are leading this approach, to design and develop the informatics infrastructure that supports it. This seminar presents that work: mapping the complex system of water processes, establishing a data catalogue, reviewing evidence on which important processes are missing from current modelling frameworks, and designing an integrated modelling system, including where AI can usefully be applied. The breadth of this work provides a basis for discussing where mathematics could improve operational hydrology. Topics will include formulating well-posed questions, scenario testing and optioneering, information theory and its relationship to data availability, model selection and benchmarking, sensitivity analysis, calibration and validation strategies, and the quantification and reduction of uncertainty. |
| 10 Nov 2026 | Simon Mathias (Durham University) |
Mathematical aspects of the power-law discharge function used in rainfall-runoff modelling
Power-law relationships between catchment storage and discharge are widely used in conceptual rainfall-runoff models and provide a simple means of representing nonlinear catchment response. Despite their apparent simplicity, these relationships have a number of interesting mathematical properties and can be interpreted in terms of several familiar hydraulic systems. This seminar explores the mathematical basis and practical implications of the power-law discharge function. The relationship with the master recession curve is first considered, before examining how different power-law exponents can arise from physical arguments based on Poiseuille flow, Manning’s equation and groundwater drainage from an unconfined aquifer. The limiting behaviour of the power-law formulation as the power-law exponent tends to infinity is also explored through its relationship with the exponential storage model. Attention is then given to the solution of the resulting storage equations. Analytical solutions are presented for several special cases, alongside numerical solutions using explicit time-stepping, implicit time-stepping and MATLAB’s ode45. The stability constraints associated with explicit time-stepping are examined and used to motivate a maximum-discharge formulation that avoids numerical instability. Finally, it is shown how streamflow recessions can be isolated from observed river-flow data using a modified implementation of GR4J incorporating the PDM rainfall-runoff model. Linear regression of individual recession periods is then used to illustrate the range of power-law exponents inferred from catchment data and to consider what these values imply for the representation of nonlinear storage-discharge behaviour in rainfall-runoff models. |
| 17 Nov 2026 | David Sibley (Loughborough University) |
Coexisting multiphase and interfacial behaviour of ouzo
Multi-component liquid mixtures can be both complex and fascinating, with some systems being amenable to simple experimentation at home, giving valuable insight into fundamental aspects of bulk and interfacial phase behaviour. One particularly interesting mixture is the popular drink ouzo, which has charmed both the general public and scientists by virtue of its ability to display spontaneous emulsification when water is added. When these two clear (and drinkable) liquids are poured into each other, a single milky-coloured liquid is formed. In this seminar I will discuss some collaborative work over recent years finding the equilibrium phase-diagram for the stable liquid phases of ouzo via experiment and modelling and extensions for when the two liquid phases also coexist with a vapour phase (i.e., along a line of triple points) and within our model uncover the complex bulk phase behavior for this simple beverage. As a consequence, this leads to some interesting observations that also apply more widely, about visualising phase diagrams in ternary systems of this type. Our modelling relies on a relatively simple lattice density functional theory model but captures physical reality surprisingly well. We also examine the interfacial behaviour, connecting microscopic density functional theory results with macroscopic (Neumann) predictions for the shape of droplets at interfaces. |
| 24 Nov 2026 | AIMS members (University of Bath) |
PhD project proposals
Project proposals from AIMS group members |
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https://bath-ac-uk.zoom.us/j/99753762534?pwd=4gMpJvORysHydzEzym33HsBuS0Vg2H.1
Meeting ID: 997 5376 2534
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