BMC-BAMC 2025
BMC-BAMC 2025
We will be running a number of contributed talk sessions throughout the programme. The sessions and draft timings are as follows:
| CT01 (FOR/SR4) | Fluids and solids, waves and instabilities | Day1PM |
| CT02 (FOR/SR5) | Mathematical biology and medicine | Day1PM |
| CT03 (FOR/SR6) | Fluids and solids, waves and instabilities | Day1PM |
| CT04 (FOR/SR9) | Dynamics, differential equations and machine learning | Day1PM |
| CT06 (FOR/SR4) | Fluids and solids, waves and instabilities | Day2AM |
| CT07 (FOR/SR5) | Fluids and solids, waves and instabilities | Day2AM |
| CT08 (FOR/SR6) | Stochastics, dynamics, and applications | Day2AM |
| CT09 (FOR/SR9) | Fluids and solids, waves and instabilities | Day2AM |
| CT10 (FOR/SR4) | Mathematical biology and medicine | Day2PM |
| CT11 (FOR/SR5) | Mathematical biology and medicine | Day2PM |
| CT12 (FOR/SR6) | Fluids and solids, waves and instabilities | Day2PM |
| CT13 (FOR/SR9) | Dynamics, pattern formation and applications | Day2PM |
| CT14 (FOR/SR10) | Fluids and solids, waves and instabilities | Day2PM |
| CT15 (FOR/SR4) | Mathematical biology and medicine | Day3AM |
| CT16 (FOR/SR5) | Fluids and solids, waves and instabilities | Day3AM |
| CT17 (FOR/SR6) | Fluids and solids, waves and instabilities | Day3AM |
| CT18 (FOR/SR9) | Dynamics, differential equations and applications | Day3AM |
| CT19 (FOR/SR4) | Mathematical modelling | Day3PM |
| CT20 (FOR/SR5) | Mathematical biology and medicine | Day3PM |
| CT21 (FOR/SR6) | Fluids and solids, waves and instabilities | Day3PM |
| CT22 (FOR/SR9) | Dynamics, networks, and applications | Day3PM |
| CT23 (FOR/SR10) | Fluids and solids, waves and instabilities | Day3PM |
| CT24 (PCC/1.1-2) | Power diagrams and related topics | Day4AM |
| CT26 (PCC/2.1-2) | Mathematical biology and medicine | Day4AM |
| CT27 (PCC/2.5-6) | Fluids and solids, waves and instabilities | Day4AM |
| CT28 (FOR/EXP2) | Dynamics, networks, and applications | Day4AM |
| CT29 (FOR/SR7-8) | Stochastics, dynamics, and applications | Day4AM |
| CT30 (FOR/SR4) | Fluids and solids, waves and instabilities | Day4AM |
| CT31 (FOR/SR5) | Mathematical biology and medicine | Day4AM |
CT01: 15:10-17:10, 23rd June 2025, Room FOR/SR4, presentation 15:10-15:30
Paul Griffiths (Aston University)
Title: Mathematical modelling of viscoplastic surface flows
Abstract: Molten aluminium alloys, widely used for the casting of lightweight parts, tend to oxidise very quickly when first exposed to external ambient conditions. Thin oxide films, usually less than one micrometer thick, develop at the liquid metal-air interface which, in turn, affects casting processes. The oxide film can be encapsulated and further dragged away into the bulk under the effect of surface agitation. Campbell (2006) demonstrated that the encapsulation process necessarily leads to embedded oxide films (bi-films) between which air can be trapped. As a result, micro-porosities are formed after the solidification process, which can have major consequences on the quality and fatigue life of the cast parts. The selection of the right boundary condition to be applied along the surface of the liquid metal flow is not straightforward because of the complexity of the stress balance between the molten metal and the ambient surroundings (air). Irrespective of the mechanical behaviour of the oxide layer that covers the surface, one of two boundary conditions are considered by default: either a slip condition as usual for water-based flows, or a no-slip condition when the oxide film is considered to behave as a deformable wall. In fact, the reality is somewhat in between these two conditions: the continuous formation of an oxide film at the metal-air interface leads to a local and evolutive change in the boundary condition that can strongly affect the surface flow by increasing viscous dissipation. Recent experimental investigations have shed new light on the complex dynamics associated with these liquid-metal-type flow problems. Both the non-Newtonian behaviour of the oxide layer over the melted metal surface and the curvature of the interface due to wetting effects were observed via scanning electron microscopy techniques. In this study we develop a mathematical model to describe flows of this nature. Working in the low Reynolds number regime we make use of the Herschel-Bulkley fluid model in order to capture both shear-thinning and viscoplastic surface effects. In this study we develop both asymptotic and numerical analyses and report on the surface characteristics (velocity and shear profiles) as well as the important effects of surface curvature.
CT01: 15:10-17:10, 23rd June 2025, Room FOR/SR4, presentation 15:30-15:50
Orson Hart (Mathematical Institute, University of Oxford)
Title: Mathematical Modelling of Overflow Fusion
Abstract: In the modern world there is an increasing demand for ultra-thin glass sheets, for which standard glass manufacturing techniques are not well suited. One method used by glass companies such as Corning Inc. to produce ultra-thin glass sheets is known as overflow fusion. In overflow fusion, a triangular wedge shaped trough is filled with molten glass until the glass overflows and falls down the sides of the trough. The two sheets meet at the bottom of the trough, where they coalesce to form a single viscous sheet which falls under gravity until it reaches a desired thickness. We derive a mathematical model for the steady state of overflow fusion in the limit of zero wedge angle, which leads to a novel fluid mechanics problem in which a viscous fluid transitions from lubrication flow to extensional flow, under the effects of gravity and surface tension. We investigate the leading order behaviour of this model in the limit of small capillary number, and find that the fluid transitions through multiple distinct regimes where different physical effects dominate. We obtain leading order governing equations in each flow regime, and determine the leading order behaviour in each region using the method of matched asymptotic expansions.
CT01: 15:10-17:10, 23rd June 2025, Room FOR/SR4, presentation 15:50-16:10
Anand Kumar Yadav (Shishu Niketan Model Sr. Sec. School, Sector 22 D, Chandigarh, India)
Title: Waves in thermoelastic layer loaded over a hygro-thermoelastic solid half-space with Klein-Gordon time nonlocality effects.
Abstract: The investigation of the waves speed at interface of thermoelastic layer and hygro-thermal solid in fractional order derivative. The governing equations are formulated for thermoelastic layer and a hygro-thermoelastic material in Klein-Gordon nonlocality with new concept of time nonlocality. Mathematical expression for nonlocal dispersive equations of wave speed is obtained. Effect of Eringen nonlocality and Klein-Gordon nonlocality are examined. The effect of hygrothermal conditions is displayed graphically.
CT01: 15:10-17:10, 23rd June 2025, Room FOR/SR4, presentation 16:10-16:30
Mukul Yadav (Department of Chemical Engineering, IIT Kharagpur, Kharagpur, West Bengal, India.)
Title: Diffusion of concentration potential in a porous elastic medium in context of Klein-Gordon time nonlocality.
Abstract: The investigation of the diffusion process of concentration potential in a porous elastic material in context of Klein-Gordon time nonlocality theory. The governing equations are formulated for a porous elastic material in Klein-Gordon nonlocality with new concept of time nonlocality theory. The expression for nonlocal dispersive equations of wave speed is obtained. Effect of Klein-Gordon nonlocality, diffusion parameter and porosity are examined. These effects are displayed graphically. (with Anand Kumar Yadav)
CT01: 15:10-17:10, 23rd June 2025, Room FOR/SR4, presentation 16:30-16:50
Matthew Turner (University of Surrey)
Title: Coupled fluid/vessel sloshing interaction in the presence of porous baffles
Abstract: In this talk we consider two-dimensional coupled sloshing in a rectangular vessel. The vessel is free to move in one horizontal space direction and is attached via a linear spring to a solid wall, which provides a restorative force on the system. The vessel is partially filled with an inviscid, incompressible, irrotational fluid, and the interior of the vessel is divided into regions via infinitely thin porous baffles. The vessel is displaced, such that the spring extends, and then released from this position giving a coupled motion where the vessel motion induces the fluid to move, which in turn exerts a force on the vessel walls and baffles, causing the motion of the vessel to change. By considering linear motions we identify the modal structure of this system showing that the system contains neutral symmetric modes, where the vessel is at rest, and decaying antisymmetric modes which couple to the vessel motion. The shallow-water form of the governing equations are solved numerically in the weakly nonlinear regime where no overturning or wave-breaking occurs, using a numerical scheme based on a Lagrangian Particle Path formulation. The scheme utilises a symplectic discritization to capture, in an essential way, the energy exchange between the fluid and the vessel. We investigate the effect of time-periodic variations in baffle porosity on the energy dissipation of the system and show that by manipulating the frequency and magnitude of this variability, a greater amount of energy can be extracted from the system compared with the optimal constant porosity baffle.
CT01: 15:10-17:10, 23rd June 2025, Room FOR/SR4, presentation 16:50-17:10
Jack Keeler (University of East Anglia)
Title: Eliminating the nonlinear Kelvin wake
Abstract: Everyone has seen the v-shaped Kelvin wake-pattern visible in the wake of a moving object on the surface of water. These patterns are a rare example of a fluid dynamics phenomenon well-known to scientists and laymen alike. However, the wake is undesirable for several reasons; it can cause erosion to river banks and cause wave-drag, thus reducing the fuel efficiency. Therefore, the design of a moving body that can reduce or even eliminate these waves is important for sustainability. A typical approach is to model the boat by an imposed pressure distribution in the free-surface Bernouilli condition. In this talk we show, using a simple mathematical argument, that by a judicious choice of a pressure distribution, wave-free solutions are possible in the context of a model system; the forced Kadometsev-Petviashvili equation. Strikingly, we show that these solutions are stable, so they could potentially be visualised in a physical experiment.
CT02: 15:10-17:10, 23rd June 2025, Room FOR/SR5, presentation 15:10-15:30
Victor Applebaum (University of Exeter)
Title: A Model for Tissue Adrenal Steroid Trajectories and How They are Affected by Physiological Variables
Abstract: The mechanisms of tissue adrenal steroid cycles over daily cycles, and how they are affected by physiological variables, such as age, smoking status and blood pressure, are little understood. In order to advance our understanding of these, we construct an explainable autoregressive-style Bayesian hierarchical model for trajectories of seven hormones: cortisol, cortisone, 18-hydroxycortisol, tetrahydrocortisol, allo-tetrahydrocortisol, corticosterone and aldosterone. The model is fitted with a recent data set of healthy individuals. By placing physiological variables into the model, we are able to pinpoint their effects on interpretable parameters and the overall trajectories. In addition to enhancing our understanding of these mechanisms, the model can be used to infer trajectories of other hormones, when only one is available. It can additionally be used to create synthetic data sets. We therefore evaluate our modelâs performance on these tasks.
CT02: 15:10-17:10, 23rd June 2025, Room FOR/SR5, presentation 15:30-15:50
Igor Nesteruk (Isaac Newton Institute for Mathematical Sciences, University of Cambridge, UK)
Title: Should SARS-CoV-2 vaccinations be continued?
Abstract: The people, governments and researchers show much less interest in the COVID-19 pandemic. However, many questions still need to be answered: why the much less vaccinated African continent has accumulated 15 times less deaths per capita than Europe? or why in 2023 the global value of the case fatality risk is almost twice higher than in 2022? or should the vaccinations be continued. Despite of decrease in COVID-19 testing and reporting new infections, the numbers of new cases and deaths are still rather high in some countries [1, 2] and exceeded the endemic levels and seasonal flue mortality [3]. These facts make the development of new vaccines or the further use of existing ones very urgent. The averaged daily numbers of cases DCC and death DDC per million, case fatality risks DDC/DCC were calculated for 34 countries and regions to find trends versus vaccination levels [2, 4]. Possible linear and non-linear correlations with the averaged daily numbers of tests per thousand, median age of population A, and percentages of vaccinations and boosters were investigated [4]. DCC and DDC demonstrated strong increasing trends with the increase of A, [4]. This fact was also supported with the use of accumulated numbers of cases per capita [5]. Thus, the age is a pivot factor of visible (registered) part of the COVID-19 pandemic dynamics. Much younger Africa has registered less numbers of cases and death per capita due to many unregistered asymptomatic patients. With decreasing of testing level, the case fatality risk can increase drastically [4]. DCC and DDC values increase with increasing the percentages of fully vaccinated people and boosters, which definitely increase for greater A. After removing the influence of age, no correlations between vaccinations and DCC and DDC values were revealed [4]. Since CFR values always demonstrated decreasing trends with the increase of vaccination levels [2, 4], vaccinations and boosters can be recommended in order to reduce the severity of SARS-CoV-2 disease and probability of dying for infected individuals. Existing vaccines cannot reduce the number of new COVID-19 cases and deaths [1, 2, 4, 6]. Therefore, it is still necessary to avoid close contacts and crowded places, trace and isolate infected people, wear masks in transport and medical facilities, wash hands more often, etc. Recent epidemic waves can probably be controlled with the use of the immediate and sufficient increase of the number of tests [6]. 1. Nesteruk, I. (2024): Should we ignore SARS-CoV-2 disease? Epidemiology and Infection. 152:e57. doi:10.1017/S0950268824000487 2. Nesteruk, I. (2024): Should vaccinations against SARS-CoV-2 infection be continued? Preprint Research gate. November 6, 2024. DOI: 10.13140/RG.2.2.28947.90403 3. Nesteruk, I. (2023): Endemic characteristics of SARS-CoV-2 infection. Sci Rep 13, 14841. https://doi.org/10.1038/s41598-023-41841-8 4. Nesteruk, I. (2024): Trends of the COVID-19 dynamics in 2022 and 2023 vs. the population age, testing and vaccination levels. Front. Big Data 6:1355080. doi:10.3389/fdata.2023.1355080 5. Nesteruk, I., Keeling, M. (2023): Population age as a key factor in the COVID-19 pandemic dynamics. Preprint. Research Square. Posted November 30, 2023. https://doi.org/10.21203/rs.3.rs-3682693/v1 6. Nesteruk, I. (2024): Impact of vaccination and testing levels on the COVID-19 waves. J Allergy Infect Dis. 2024;5(1):44-55. https://probiologists.com/Uploads/Articles/11_638603156371379586.pdf
CT02: 15:10-17:10, 23rd June 2025, Room FOR/SR5, presentation 15:50-16:10
Luke Heirene (University of Oxford)
Title: Data Driven Mathematical Modelling Highlights the Impact of Bivalency on the Optimum Affinity for Monoclonal Antibody Therapies
Abstract: Monoclonal antibody (mAb)-based therapeutics are pivotal in treating diseases like cancer, with antibody-dependent cellular cytotoxicity (ADCC) being a key mechanism in which mAbs induce anti-tumour effects. In ADCC, mAbs bind to tumour antigens and Fc receptors on immune effector cells, forming trimeric complexes that trigger tumour cell killing. ADCC is influenced by mAb properties, Fc receptor interactions, and antigen characteristics, but the optimal conditions remain unclear. This study investigates how target antigen and mAb properties, particularly valency, modulate ADCC to identify parameters that maximize potency. We developed an ordinary differential equation (ODE) model to simulate mAb binding within the immune synapse and quantify trimeric complex formation. To link trimeric complex numbers to ADCC response, we validated the model using Bayesian inference on ADCC assay data. The results suggest lower-affinity mAbs enhance ADCC by increasing target cell-bound antibodies. Our validated model indicates a âsteric penaltyâ for bivalently target-bound versus monovalently bound antibodies. Due to constraints from dual antigen binding, these antibodies have limited mobility, reducing Fc receptor engagement. After validation, we explored how target expression, binding affinity, and valency affect ADCC potency as measured with EC50. Our key finding is that the optimal binding affinity for maximizing ADCC potency depends on valency. Monovalent antibodies are most potent at high affinity, while bivalent antibodies peak at lower affinities. Furthermore, the magnitude of this effect varies with target expression levels.
CT02: 15:10-17:10, 23rd June 2025, Room FOR/SR5, presentation 16:10-16:30
Alexis Farman (UCL)
Title: Enhancing immunotherapies: insights from the mathematical modelling of a microfluidic device
Abstract: A pivotal aspect of developing effective immunotherapies for solid tumours is the robust testing of product efficacy inside in vitro platforms. Collaborating with an experimental team that developed a novel microfluidic device at Childrenâs National Hospital (CNH), we developed a mathematical model to investigate immune cell migration and cytotoxicity within the device. Specifically, we study Chimeric Antigen Receptor (CAR) T-cell migration inside the channels, treating the cell as a moving boundary driven by a chemoattractant concentration gradient. The chemoattractant concentration is governed by two partial differential equations (PDEs) that incorporate key geometric elements of the device. We examine the motion of the cell as a function of its occlusion of the channel and find that certain cell shapes allow for multiple cells to travel inside the channel simultaneously. Additionally, we identify parameter regimes under which cells clog the channel, impairing their movement. All our findings are validated against experimental data provided by CNH. We integrate our model results into a broader model of the device, which also examines the cytotoxicity of CAR T-cells. This provides a tool for distinguishing experimental artefacts from genuine CAR T-cell behaviour. This collaboration enabled the team at Childrenâs National Hospital to refine experimental conditions and uncover mechanisms enhancing CAR T-cell efficacy. [1] D Irimia, G Charras, N Agrawal, T Mitchison, M Toner, Polar stimulation and constrained cell migration in microfluidic channels, Lab on a Chip 7 (12), 1783-1790
CT02: 15:10-17:10, 23rd June 2025, Room FOR/SR5, presentation 16:30-16:50
Freya Bull (University College London)
Title: Multi-scale modelling of blood rheology in sickle cell disease
Abstract: Sickle cell disease (SCD) is a haematological disorder, caused by a genetic mutation, in which mutant haemoglobin molecules can polymerise under low-oxygen conditions, altering the biophysical properties of the red blood cells. These cell-level differences then result in changes in the whole-blood rheology — and those rheological properties are in turn linked to the pathophysiology of SCD. Ongoing experimental work indicates that SCD blood exhibits increased frictional and viscous resistances to flow. Our work investigates the contribution of elevated red blood cell friction to the whole-blood rheology, utilising mathematical modelling and numerical simulation to develop descriptions of cell-cell interactions within blood flow.
CT03: 15:10-17:10, 23rd June 2025, Room FOR/SR6, presentation 15:10-15:30
Dimitrios Gourzoulidis (Imperial College London)
Title: Finite-Element Methods for Isothermal Fluctuating Hydrodynamics
Abstract: We propose a finite-element methodology for simulating isothermal fluctuatinghydrodynamics within a diffuse-interface framework. We analyse bothcontinuous and discontinuous Galerkin approaches for spatial discretisationalongside explicit and implicit temporal discretisation schemes. Byconstructing the fully discrete system, the correct covariance structure ispreserved up to numerical errors, while also addressing nonphysical spatialcorrelations. The methodology is validated against theoretical benchmarks,including the statistical properties of density and velocity fluctuations andthe interfacial wave spectrum at liquid-vapor interfaces. Finally, we discusshow the proposed framework can be extended to model increasingly complexapplications including two-phase processes, such as bubble nucleation.
CT03: 15:10-17:10, 23rd June 2025, Room FOR/SR6, presentation 15:30-15:50
Lewis Melvin (University of Manchester)
Title: Choking in Confined Hele-Shaw cells: Effect of Elastomer Geometry
Abstract: Fluid structure interactions (FSIs) have dramatically changed our understanding of many natural and industrial phenomena. In this talk, we will explore FSIs in a soft Hele-Shaw cell i.e., a thin fluid-filled plane formed between rigid plate and one side of a deformable block of elastomer, which is confined on all other sides by a rigid mould. The softness of the elastomer permits shape-morphing of the channel in response to fluid forcing. Beyond a critical flow rate, flow-induced deformation is sufficient for the elastomer to contact the opposite channel wall, which constricts the channel to the point that fluid flow through the channel is inhibited (âchoking the flowâ). In particular, we will focus on how elastomer geometry affects flow-induced choking by comparing the limits of deep and shallow elastomers.
CT03: 15:10-17:10, 23rd June 2025, Room FOR/SR6, presentation 15:50-16:10
Ferran Brosa Planella (University of Warwick)
Title: A Simple Model for Latent Thermal Energy Storage Systems with Encapsulated Phase-Change Material
Abstract: In 2022, heat accounted for nearly half of global final energy consumption and 38% of energy-related CO2 emissions. Decarbonizing heat production is essential to achieve current net-zero emissions goals. Thermal energy storage technologies can play a key role in decoupling supply and demand, but they remain underdeveloped for widespread commercial deployment. Latent Thermal Energy Storage (LTES) devices store energy as latent heat through the melting and solidification of phase-change materials (PCMs). These devices are promising due to their high energy density, but they often suffer from low power density caused by the low thermal conductivity of the PCM. To address this limitation, composite and encapsulated PCMs have been developed; however, these materials have yet to be commercialized at scale. Modelling can accelerate the development of these technologies, but many state-of-the-art models are overly complex and computationally expensive. This work presents a simplified, multiscale model for encapsulated LTES, derived using asymptotic methods. The proposed model matches the accuracy of state-of-the-art models while running 100 times faster. This advancement lays the groundwork for a new generation of fast, accurate LTES models that can support applications such as advanced real-time control algorithms and design optimisation.
CT03: 15:10-17:10, 23rd June 2025, Room FOR/SR6, presentation 16:10-16:30
Roman Cherniha (University of Nottingham, UK and National University of Kyiv-Mohyla Academy, Ukraine)
Title: A Mathematical Model for Fluid and Solute Transport in Poroelastic Materials
Abstract: Fluid and solute transport in poroelastic materials (biological tissue is a typical example) is studied. Mathematical modeling of such transport is a complicated problem because the specimen volume and its form (under special conditions) might change due to swelling or shrinking and the transport processes are nonlinearly linked. The tensorial character of the variables adds also substantial complication in investigation of the fluid and solute transport in poroelastic materials (PEM). Therefore, developing and solving adequate mathematical models is an important and still open problem. Using modern foundations of the poroelastic theory (see books by Loret B and Simoes FMF (2017), Coussy O. (2010), Taber LA (2004)) , a new model for PEM with the variable volume is developed in multidimensional case (the model in the 1D space case is presented in our recent paper published in Nonlinear Sci. Numer. Simulat. 132 (2024) 107905; https://doi.org/10.1016/j.cnsns.2024.107905 ). Governing equations of the model are constructed using the continuity equations, which reflect the well-known physical laws. The deformation vector is specified using the Terzaghi effective stress tensor. In the two-dimensional space case, the model is studied by analytical methods. The radially-symmetric case is studied in details. It is shown how correct boundary conditions in the case of PEM in the form of a ring and an annulus are constructed. As a result, boundary-value problems with a moving boundary describing the ring (annulus) deformation are constructed. The relevant nonlinear boundary-value problems are analytically solved in the stationary case. In particular, the analytical formulae for unknown deformations and an unknown radius of the annulus are derived. Illustrative plots for parameters, which are typical for the tumour tissue deformation, are presented as well. This is a joint work with J. Stachowska-Pietka and J. Waniewski (IBIB of PAS, Warsaw).
CT03: 15:10-17:10, 23rd June 2025, Room FOR/SR6, presentation 16:30-16:50
Edmund Chadwick (University of Salford)
Title: A novel Boundary Integral Method approach for solving the triple deck boundary layer equations
Abstract: Consider steady high Reynolds number uniform flow past a two-dimensional flat plate. A solution for this problem at the trailing edge of the flat plate is well-known by using matched asymptotic triple deck theory, resulting in a numerical discretisation of the inner deck for the lateral displacement function. From this, the flow in all the other asymptotic decks is obtained. In this presentation, instead we shall test an alternative approach given by the recent novel description for the Navier-Stokes velocity by a boundary integral distribution of fundamental solutions called NSlets. This integral description is approximated in the three decks, resulting in a boundary integral formulation in the inner deck discretretised by a boundary element formulation (with infinite boundary elements) to numerically determine the strength function which is shown to be the (negative) derivative of the lateral displacement function. From this, the fundamental solution is shown to approximate in the other asymptotic decks as well as the Goldstein near-wake to give the flow representation throughout. The two approaches are compared and contrasted, and importantly it is demonstrated that the novel boundary integral description is a valid alternative representation for this benchmark problem.
CT04: 15:10-17:10, 23rd June 2025, Room FOR/SR9, presentation 15:10-15:30
Abdullah Aldurayhim (Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia)
Title: Reaction Diffusion Systems for Living on Isolated Island
Abstract: This work investigates the distribution of population in isolated region, i.e. Easter Island, and the interaction between settlers and resources. The temporal differential system is first employed to model the hypothesis that misuse of resources in Easter Island can cause people extinction. The local analysis of this system is revised. Then, we extend the temporal system by adding more realistic diffusion terms, which presents the spatial distribution of the populations in the Island. The spatio-temporal system is analyzed in one and two spatial dimensions with diagonal diffusion matrix. Traveling wave solutions of the spatio-temporal system are found to appear in different profiles, namely, front, pulse and chaotic ones. The attained results reveal that the people misused the resources in Easter Island may cause extinction also in one spatial dimension. For two spatial dimensions, the driven instability is discussed to examine the existence of Turing patterns.
CT04: 15:10-17:10, 23rd June 2025, Room FOR/SR9, presentation 15:30-15:50
Hefin Lambley (University of Warwick)
Title: Autoencoders in function space
Abstract: High-resolution approximations of functional data arise frequently in data science, particularly in scientific computing and image processing. While discretisation (of differential equations) or pixellation (of images) makes problems finite dimensional, designing algorithms in function space first enables smooth operation between resolutions. We propose function-space versions of autoencodersâmachine-learning methods for dimension reduction and generative modellingâin both their deterministic (FAE) and variational (FVAE) forms. In infinite-dimensional function spaces, the probabilistic model underlying FVAE is not always well-defined: it requires a compatibility condition with the data distribution that is stringent in infinite dimensions. This condition is satisfied in certain cases, e.g., when the data arise from a stochastic differential equation, but not universally. In contrast, the FAE objective is well defined in many situations where FVAE fails, making it applicable in a much wider range of scenariosâparticularly those where a well-defined probabilistic model is challenging to establish. By formulating autoencoder objectives in function space, we enable training and evaluation on data discretised at arbitrary resolutions. This unlocks new applications in inpainting, superresolution, and generative modelling. We demonstrate this on scientific data sets, including data from fluid-flow simulations governed by the NavierâStokes equations, showing that FAE can inpaint unseen flows even when up to 95% of the data is missing. This is joint work (arXiv:2408.01362) with Justin Bunker and Mark Girolami (Cambridge), Andrew M. Stuart (Caltech) and T. J. Sullivan (Warwick).
CT04: 15:10-17:10, 23rd June 2025, Room FOR/SR9, presentation 15:50-16:10
Ethan Baker (University of Birmingham)
Title: White noise and Newtonian limits for the Generalised Relativistic Langevin Equation
Abstract: The generalised relativistic Langevin equation (GRLE) is an extension of the generalised Langevin equation (GLE) in which we consider the dynamics of a particle with relativistic kinetic energy. As with the GLE, given the memory kernel is a finite sum of exponentials, the process described by the GRLE has the Markov property. Using such a memory kernel, we prove the white noise and Newtonian limits for the GRLE. Namely, we show how both the relativistic underdamped Langevin equation and the GRE can be derived from the GRLE.
CT04: 15:10-17:10, 23rd June 2025, Room FOR/SR9, presentation 16:10-16:30
Kelvin Xie (University College London)
Title: A stochastic differential equation framework for gravity wave parameterisation with testing in an idealised setting
Abstract: Parameterisations of unresolved gravity waves used in general circulation models can be made more computationally efficient by introducing a stochastic component to the forcing. An additional advantage of introducing stochasticity is that intermittency associated with the scheme could be tuned to resemble the intermittency of observed gravity wave sources, and could therefore act to improve the physical fidelity of the scheme. Here, it is argued that using stochastic differential equations (SDEs) to drive the stochastic component provides a natural general framework to develop such schemes. The Holton-Lindzen-Plumb model of the quasi-biennial oscillation (QBO) is used to demonstrate the flexibility of the approach. The QBO generated in a (computationally expensive) deterministic broadband multiwave simulation is accurately reproduced using a number of quite different (cheap) stochastic schemes. The method of stochastic averaging is used to prove a matching result that shows that a wide class of such schemes, driven by different SDEs, can each reproduce the deterministic QBO provided that the characteristic timescale tau of the SDEs is sufficiently short. However each scheme has different intermittency properties, and as tau is increased their QBOs are shown to diverge, despite the time-averaged source spectrum in each case remaining unchanged. The SDE framework therefore provides great flexibility to tune a stochastic parameterisation to match observed intermittencies, meaning that future parameterisations can be developed that can account for non-steady gravity wave forcing in a physically consistent manner.
CT04: 15:10-17:10, 23rd June 2025, Room FOR/SR9, presentation 16:30-16:50
Hong Duong (University of Birmingham)
Title: Model reduction of complex systems
Abstract: Complex systems in nature and in applications (such as molecular systems, crowd dynamics, swarming, opinion formation, just to name a few) are often described by systems of stochastic differential equations (SDEs) and partial differential equations (PDEs). It is often analytically impossible or computationally prohibitively expensive to deal with the full models due to their high dimensionality (degrees of freedom, number of involved parameters, etc.). It is thus of great importance to approximate such large and complex systems by simpler and lower dimensional ones, while still preserving the essential information from the original model. This procedure is referred to as model reduction or coarse-graining in the literature. In this talk, I will present methods for qualitative and quantitative coarse-graining of several SDEs and PDEs, in the presence or absence of a scale-separation.
CT04: 15:10-17:10, 23rd June 2025, Room FOR/SR9, presentation 16:50-17:10
Gabor Kiss (Queen’s University Belfast)
Title: Controlling MackeyâGlass Chaos
Abstract: Time delays often lead to unexpected and chaotic behaviour in models of real-world systems. A classic example is the Mackey–Glass equation—a delay differential equation involving a single physical variable—originally proposed to describe blood cell production. In this talk, we explore simple but effective ways to control such chaos by introducing feedback mechanisms. Rather than stabilising a particular solution, our approach guides the entire system into a region where chaotic behaviour is no longer possible. These techniques are supported by both analytical results and simulations, and they have practical interpretations, such as modelling medical interventions or regulatory feedback. This is joint work with Gergely R\”ost (Bolyai Institute, University of Szeged, Hungary).
CT06: 10:30-12:30, 24th June 2025, Room FOR/SR4, presentation 10:30-10:50
Alexandra Hardy (The Open University)
Title: Kinetic theory of coupled binary-fluid surfactant systems
Abstract: We derive the hydrodynamic equations of coupled binary fluid and surfactant systems from microscopic forces and torques. At the microscopic level, the surfactant molecules are modelled as dumbbells, which can exert forces and torques on the fluid and the interface. By explicitly considering the molecular alignment, we introduce a new field variable, p, which represents the average orientation of surfactants. This, combined with the standard phase-field theory for binary fluids, yields the governing system of equations, which we solve both numerically and analytically. For the simulations, we employ a hybrid approach combining the finite difference method (FDM) and the spectral method. Regular perturbation theory is used for the equilibrium solutions, facilitated by assuming weak coupling between surfactant and fluid. Three investigations are presented, firstly we demonstrate excellent agreement between simulation and the analytical solutions for a planar water-oil interface. Second, we prove that our model accurately predicts the decrease in surface tension with increasing surfactant concentration, in line with experiments and related theories. Finally, we show that our model is capable of preventing surfactant-laden droplet coalescence due to the added polarization field p.
CT06: 10:30-12:30, 24th June 2025, Room FOR/SR4, presentation 11:10-11:30
Chris Pringle (Coventry University)
Title: Using periodic orbits to explain the onset of turbulence in tokamaks
Abstract: As with neutral fluids, plasmas can exhibit subcritical transitions to turbulence and do so in regimes relevant to tokomak fusion. In much of the plasma literature, this turbulence is described in terms of a stochastic collection of linear waves. We instead take ideas from classical shear flows to describe the dynamics in terms of underlying exact (periodic) solutions. For our case of tokomak plasmas, turbulence can be completely suppressed by introducing a background shear flow, whose amplitude is an important control parameter. As this parameter is decreased below a critical value, radially localised structures appear, becoming larger and more complex. We analyse both gyrokinetic simulations of plasma and a simpler fluid model. For the fluid model, we directly solve for a particular class of nonlinear solutions, relative periodic orbits, and determine their stability, thus explaining why these isolated structures appear in initial-value simulations. The increase of complexity as the flow shear is reduced is explained by a series of Hopf bifurcations of these nonlinear solutions, which we quantify via stability analysis. In gyrokinetic simulations, we are able to indirectly determine the underlying relative periodic orbits by imposing appropriate symmetry conditions.
CT06: 10:30-12:30, 24th June 2025, Room FOR/SR4, presentation 11:10-11:30
Samuel Johnson (University of Oxford)
Title: Mathematical Optimisation of Actin-Driven Protrusion Formation in Eukaryotic Chemotaxis
Abstract: In eukaryotic chemotaxis, cells extend and retract transient actin-driven protrusions at their membrane. These protrusions facilitate both the detection of external chemical gradients and directional movement via the formation of focal adhesions with the extracellular matrix. While extensive experimental work has characterised how protrusive activity varies with a range of environmental parameters, the mechanistic principles governing these relationships remain poorly understood. Here, we model the extension of actin-based protrusions in chemotaxis mathematically as an optimisation problem, wherein cells must balance the detection of external chemical gradients with the energetic cost of protrusion formation. The model highlights energetic efficiency in movement as a major predictor of phenotypic variation amongst motile cell populations, successfully reproducing experimentally observed but previously non-understood patterns of protrusive activity across a range of biological systems. Additionally, we leverage the model to generate novel predictions regarding cellular responses to environmental perturbations, providing testable hypotheses for future experimental work.
CT06: 10:30-12:30, 24th June 2025, Room FOR/SR4, presentation 11:30-11:50
Torin Fastnedge (University of Oxford)
Title: A homogenised model over branched channel filters
Abstract: Fibres from our clothes make up around 35% of all microplastics in our oceans, and it is estimated that each person in the UK produces on average 243g of microplastic fibres per year when washing their clothes in a standard washing machine. Conventional dead-end (mesh) filters clog relatively quickly. In collaboration with Beko plc, we consider a new method to increase the lifespan of such filters, coined ricochet separation. Ricochet separation inside a washing machine allows microfibre-free water to divert through branched channels at an angle to the flow, while microfibre particles ricochet back into the free-stream flow. The removal of clean water lowers the pressure drop over the dead-end filter, which follows the ricochet device, increasing the time before the filter needs to be cleaned. By using mathematical and homogenisation techniques, we find an analytic expression for the flow in this device, in various high-Reynolds-number regimes, so that we need not rely on computationally expensive numerical simulations. The results allow for strategies to optimise the operating regime of such filters in order to maximise their efficiency.
CT06: 10:30-12:30, 24th June 2025, Room FOR/SR4, presentation 11:50-12:10
Giulia Celora (University of Oxford)
Title: The electrochemical regulation and function of phase-separated condensates
Abstract: The cytoplasm is a highly crowded and heterogeneous environment. Recent evidence suggests that liquid-liquid phase separation (LLPS) plays a crucial role in the spontaneous spatial organization of biomolecules within membrane-less organelles â or biomolecular condensates. In this talk, I will discuss our recent theoretical progress in understanding the electrochemical regulation of biomolecular phase separation and the structural properties of biomolecular condensates. Interestingly, our findings reveal a complex feedback mechanism: while the electrochemical environment influences the formation of phase-separated coacervates, these coacervates, in turn, create microenvironments with distinct electrochemical properties from their surroundings. This interplay suggests biomolecular condensates could function both as sensors of the electrochemical properties of the cytoplasm, as well as an adaptive response to cope with its perturbations.
CT07: 10:30-12:30, 24th June 2025, Room FOR/SR5, presentation 10:30-10:50
Gabriel Nunez (The University of Manchester)
Title: Effective mass density for wave propagation in layered media: a study of the elastic/acoustic transition
Abstract: This work investigates the propagation of acoustic and elastic waves in layered materials, focusing on the effective mass density of the media in each regime and the transition between them. It is well-known that for elastic waves, the density of the effective media is isotropic, while for acoustics it is anisotropic. Usually, one can recover the equations of acoustics by taking the shear modulus to zero in those for elasticity. However, as the effective density does not explicitly depend on shear, the transition between the two regimes remains unclear. To determine such effective density, an inverse problem is solved. Specifically, the reflection and transmission coefficients of a system comprising two layers with different densities, placed between two half-spaces of identical, but unknown, anisotropic mass densities, are calculated. Since the objective is finding the effective properties of the layers, this unknown density is determined by imposing zero reflection and unit transmission coefficients, which is analogous to the dynamic self-consistent method. As expected, it is found that acoustic wave propagation is better modelled using an anisotropic effective density, while for elastodynamics, the effective medium remains isotropic. Most importantly, since the calculations are performed for any shear modulus, it is possible to explicitly understand and visualise the transition from isotropic elasticity to anisotropic acoustics by taking the no-shear limit. Therefore, this work provides a theoretical foundation for developing effective descriptions that incorporate anisotropic density and enable a smooth transition from elasticity to acoustics.
CT07: 10:30-12:30, 24th June 2025, Room FOR/SR5, presentation 10:50-11:10
Shresht Jain (University of Manchester)
Title: Soda forming: sequential ring buckling of uniaxially compressed beverage cans
Abstract: When uniaxially compressed empty cylinders buckle, they typically form periodic structures that break both axial and radial symmetry. By contrast, thin membranes develop undulations that break the symmetry along the axis of compression. We make a surprising observation that when a beverage can, mostly filled with a liquid, is compressed under uniaxial loading, the system buckles axisymmetrically. The resulting ring buckles are localised and appear sequentially, eventually filling the entire can surface. The final periodic pattern has a predictable wavelength that scales with the shell thickness and radius. We characterise the material properties of the cans experimentally in order to model their post-buckling behaviour. The results of our model, which is similar to the 1-D nonlinear Swift-Hohenberg equation, suggest that the sequential appearance of ring buckles occurs via homoclinic snaking. Our system provides a novel experimental demonstration of this mechanism, thereby linking nonlinear dynamics of localised patterns and mechanics of shell buckling
CT07: 10:30-12:30, 24th June 2025, Room FOR/SR5, presentation 11:10-11:30
Grace Curtis (University of Oxford)
Title: Bridging a gap: a heavy elastic beam on point supports.
Abstract: Flexible slender structures in contact with a rigid boundary and subject to a body force occur in a variety of industrial scenarios, including the flow-induced trapping of a fibre in a filter, or the catching of hair by a plughole. We study the deformation and slip-through of a heavy elastic beam suspended over two point supports under an increasing body force, as a microscale model for the filtration of a fibre. Using both asymptotic and numerical techniques, we investigate the behaviour of the beam under increasing force and the maximum force that can be supported before the beam slips and falls between the supports, and the dependency of this maximum force on the support separation. In particular, we show analytically the existence of a critical support separation below which the beam can withstand an infinite force, and the resulting hanging-catenary-type solution. We then generalize the model to explore how frictional forces impact the deformation and load-bearing capacity of the beam.
CT07: 10:30-12:30, 24th June 2025, Room FOR/SR5, presentation 11:30-11:50
Hao Ye (University of Manchester)
Title: Elastic fibres in shear flows can maintain steady orientations
Abstract: Solid particles in low-Reynolds-number shear flow generally follow complex trajectories known as Jeffery orbits. It is, however, possible to construct rigid particles that adopt a constant orientation relative to the flow, typically while drifting across streamlines. A recent study by Roggeveen & Stone [1] analysed the existence and stability of such orientations for âboomerangâ-shaped rigid fibres formed by two straight arms of different lengths. They found that such fibres adopt steady orientations for a certain range of geometries, characterised by the aspect ratio, đ, of the two arms and the angle, α, between them. We extend the analysis to the case of elastic fibres that deform in response to the shear flow’s traction. We model the latter by slender body theory, coupled to a large-amplitude, geometrically nonlinear beam model. We find that steady orientations exist for a wide range of the fluid-structure interaction (FSI) parameter â, which consists of fibre resistance, shear rate, and bending stiffness. As â approaches zero, these solutions match those for rigid fibres. We also identify families of additional steady configurations that only exist for elastic fibres and are thus generally disconnected from the solutions of [1]. We assess the stability of these steady configurations and thus identify the parameter regime within which the elastic fibres approach a constant shape and orientation while translating relative to the shear flow. Outside this regime, fibres follow Jeffrey-orbit-like time-periodic motions, undergoing increasing deformations as â increases. 1. Roggeveen and Stone, Journal of Fluid Mechanics 939, A23-1-22 (2022)
CT07: 10:30-12:30, 24th June 2025, Room FOR/SR5, presentation 11:50-12:10
Jack Wildman (University of Liverpool)
Title: Modelling Multiphysics Metasurfaces
Abstract: We will discuss the mathematical modelling of multiphysical metasurfaces â structured interfaces capable of producing metamaterial effects at the intersection of disparate physical systems. Building upon the existing work [1], we will consider a thin elastic plate, patterned by resonant elements and submerged in an acoustic fluid. The dispersive properties of this system are studied both numerically and with finite element modelling, with critical comparisons made between the two methods. We construct a general mathematical framework, capable of describing the behaviour of resonant interfaces, which couple different physical systems. Several interesting effects will be demonstrated, including the mode conversion between flexural waves in the plate and acoustic waves in the fluid and the manipulation of subsonic interfacial waves. [1] E. A. Skelton, R. V. Craster, A. Colombi, and D. J. Colquitt. The multi-physics metawedge: graded arrays on fluid-loaded elastic plates and the mechanical analogues of rainbow trapping and mode conversion. New Journal of Physics, 20(5):053017, May 2018.
CT07: 10:30-12:30, 24th June 2025, Room FOR/SR5, presentation 12:10-12:30
John Chapman (Keele University)
Title: Rays, multipoles, and caustics
Abstract: It is shown that the familiar three-dimensional multipole in acoustics (`Hankel function times associated Legendre function’) has a ray structure of greater interest than might be supposed, and this structure makes possible a new theory of near-field scattering. The key idea is that in constructing ray fields one must include subsonic rays as being just as important as ordinary rays, even though the governing wave equation contains just a single parameter, `the speed of sound’.
CT08: 10:30-12:30, 24th June 2025, Room FOR/SR6, presentation 10:30-10:50
Max Dew (University of Liverpool)
Title: Natural death rate drives star graphs from amplifiers to suppressors of natural selection
Abstract: Evolutionary graph theory (EGT) considers evolutionary dynamics in a structured population that is represented by a graph. Fixation probability is the likelihood of a single mutation taking over the resident population. It has been found that graph structure impacts the fixation probability, with certain graphs acting as amplifiers or suppressors of selection. However, the type of update rule used in the model can impact this result. For example, the star graph is an amplifier for birth-death with fitness on birth (Bd) dynamics and is a suppressor for death-birth with fitness on birth (dB) dynamics. Typically, EGT has focused on discrete-time models, which can be hard to link with realistic population dynamics. Recently, these discrete-time models have been generalized to a continuous-time Markov-process model based on eco-evolutionary dynamics, where the results for dB and Bd dynamics can be recreated by suppressing ecological dynamics. This work shows that within this continuous-time framework, there exists a continuous transition from Bd to dB results. Using the star graph as an example, we prove that the transition from Bd to dB depends on the magnitude of the natural death rate. By increasing the natural death rate of individuals, population structures that typically amplify selection under Bd dynamics can be driven to suppress fixation. Exploring the fundamental drivers behind this qualitative shift will provide further insights into whether population structures will amplify or suppress selection under realistic population dynamics.
CT08: 10:30-12:30, 24th June 2025, Room FOR/SR6, presentation 10:50-11:10
Antonio Malpica-Morales (Imperial College London)
Title: Fluctuating Dynamical Density Functional Theory for Financial Assets
Abstract: Financial markets are complex, multi-scale systems that exhibit emergent price phenomena, including varying trends, volatility clustering, and bubble formation. We formulate a first-principles derivation of the time evolution of the probability density of asset prices. Markets are represented by N agents, with each agent employing the geometric Brownian motion to estimate the asset price. Drawing inspiration from classical fluids, where multi-scale interactions amongst interacting agents/particles are encapsulated by the Fluctuating Dynamical Density Functional Theory (FDDFT), we reduce the high-dimensional agent-based model to a single tractable equation for the stochastic evolution of the price probability density. This FDDFT-based approach captures how agent interactions and random market fluctuations jointly shape the asset-price behaviour. Our bottom-up derivation can offer new insights into price dynamics, encompassing both price fluctuations and the collective phenomena that can lead to extreme market events.
CT08: 10:30-12:30, 24th June 2025, Room FOR/SR6, presentation 11:10-11:30
Jonathan Ward (University of Leeds)
Title: Mean-field approximations of Markov chain dynamics on networks
Abstract: Many real-world phenomena can be modelled as dynamical processes on networks, with COVID19 being a prominent example: the disease spread from infected to susceptible people that came into contact. Many such dynamical processes on networks can be represented by Markov chains, but it is necessary to use approximations to analyse them mathematically. Mean-field approximations that neglect structural features of the network are widely used, but their derivation is based on probabilistic reasoning, so it is difficult to characterise the error introduced. In this talk I will describe how a method called “approximate lumping” can be used to derive mean-field approximations of dynamical processes on networks directly from their Markov chain descriptions. This provides a common framework from which various forms of standard mean-field approximation can be derived. It also sheds light on the sources of approximation error, although quantifying these errors remains an open problem.
CT08: 10:30-12:30, 24th June 2025, Room FOR/SR6, presentation 11:30-11:50
Toby Kay (Imperial College London)
Title: Generalized Fluctuating Dynamic Density Functional Theory: Derivation and Applications
Abstract: Classical density functional theory (c-DFT) is a powerful tool for studying the equilibrium density distribution of complex many-body systems, bridging the microscopic and macroscopic descriptions of fluids through a variational principle that minimises the systemâs free energy. For dynamic settings, dynamic DFT (DDFT) extends this framework to capture the time evolution of the density profile. However, DDFT is often insufficient for systems far from equilibrium where fluctuations become significant, necessitating a stochastic extension: fluctuating DDFT (FDDFT). Here we derive a generalized FDDFT from first principles starting from the microscopic Hamiltonian dynamics using coarse-graining techniques, including Zwanzigâs projection operator method and the principle of maximum entropy. The resulting FDDFT applies to arbitrary observable fields, where the dynamics are driven by a thermodynamic force expressed in terms of an entropy functional. The dynamics consist of reversible, dissipative, and stochastic contributions, each directly linked to the underlying microscopic dynamics via the Liouville operator, Green-Kubo relations, and the fluctuation-dissipation theorem. To showcase the effectiveness and utility of our framework, we apply it to two prototypical fluid systems: colloidal and viscous fluids. In the latter case, we rigorously recover the Landau-Lifshitz fluctuating Navier-Stokes equations, providing fundamental derivation of this well-known phenomenological model.
CT08: 10:30-12:30, 24th June 2025, Room FOR/SR6, presentation 11:50-12:10
Christopher Howls (University of Southampton)
Title: Things that go bump near the line: the smoothing of the Higher Order Stokes Phenomenon:
Abstract: For over a century, the Stokes phenomenon had been perceived as a discontinuous change in the asymptotic representation of a function. Berry then demonstrated it is possible to smooth this discontinuity in broad classes of problems with the prefactor for the exponentially small contribution switching on/off taking a universal error function form. Later it was shown that the concept of a higher-order Stokes phenomenon was fundamentally needed to explain asymptotic results in common situations. In such cases the exponentially small terms underpinning a Stokes phenomenon may change, depending on the variation of problem parameters. Until now, the higher-order Stokes phenomenon had also been treated as a discontinuous event. This talk will show that the higher-order Stokes phenomenon is, in fact, also smooth and occurs universally, but now with a prefactor that takes the form of a *new* special function, based on a Gaussian convolution of an error function. We provide multiple examples spanning special functions to PDE solutions which give rise to a ghost-like smooth contribution, present in the vicinity of a Stokes line, but which takes the form of a bump that rapidly but smoothly tends to zero on either side. In such cases there is no net Stokes phenomenon across the line, but its lurking spectral presence is nevertheless felt.
CT09: 10:30-12:30, 24th June 2025, Room FOR/SR9, presentation 10:30-10:50
Said Elahjel (University of Exeter)
Title: Codimension two bifurcations of fast-slow system.
Abstract: Abstract For fast-slow systems with one fast and one slow variable, there is a good understanding of generic codimension one bifurcations by examining ways that persistence conditions can be violated. In particular, the work of Nyman et al. (Nonlinearity, 2020) shows that codimension one bifurcations of critical manifolds are possible bifurcations under a notion of global singular equivalence. They show that in addition, a change in the slow subsystem can lead to a bifurcation in several possible ways. One can use this approach to define conditions that classify all generic codimension one degeneracies. In this work, I generalize this approach to understand generic codimension two bifurcations of a fast-slow system with one fast and one slow variable.
CT09: 10:30-12:30, 24th June 2025, Room FOR/SR9, presentation 10:50-11:10
Oleg Kirillov (Northumbria University)
Title: Local stability analysis of spiral Poiseuille flow with radial temperature gradient
Abstract: Geometrical optics stability analysis has proven effective in deriving analytical instability criteria for 3D flows in ideal hydrodynamics and magnetohydrodynamics, for both compressible and incompressible fluids. This method models perturbations as high-frequency wavelets evolving along fluid trajectories. Detecting local instabilities reduces to solving ODEs for the wave vector and wavelet amplitude, with coefficients derived from the background flow. While viscosity and diffusivity were traditionally seen as stabilizing, recent extensions of this framework reveal their destabilizing potential in visco-diffusive and multi-diffusive flows. Encouraged by these findings, this talk examines the visco-thermodiffusive McIntyre instability of spiral Poiseuille flow with a radial temperature gradient (SPFRT) using the generalized geometrical optics approach. SPFRT combines circular Couette flow and annular Poiseuille flow driven by an axial pressure gradient, while the temperature gradient induces centrifugal buoyancy. Neglecting vertical Archimedean buoyancy simplifies the derivation of analytical thresholds for both oscillatory and monotonic McIntyre instability. A key advancement in this study lies in the relationship between parametric optimization and the construction of envelopes of curve families. This enables the derivation of universal stability criteria by computing the envelopes of neutral stability curves, parameterized by the axial (or azimuthal) wavenumber. Treating the equations for neutral stability as polynomials in the wavenumber, we identify their discriminant set, which includes the equation for the envelope and provides explicit instability criteria. These new analytical criteria apply across a wide range of Prandtl numbers, extending beyond the reach of numerical methods in many critical physical and industrial applications.
CT09: 10:30-12:30, 24th June 2025, Room FOR/SR9, presentation 11:10-11:30
Sam Harris (University College London)
Title: Flowers, bees and vortices: applications of a two-domain AAA-least squares algorithm
Abstract: Over the past seven years, the adaptive Antoulas-Anderson (AAA) algorithm for complex, rational approximation and so-called `lightning least-squaresâ methods for solving Laplace problems in simply connected domains have been developed by Trefethen, Costa and their colleagues. These methods were then combined into a single `AAA-least squares algorithmâ, which computes the rational approximation of a harmonic function in seconds on a standard laptop. In this talk, a new extension to the algorithm developed for solving general, inhomogeneous two-domain interface problems is presented, and its efficacy demonstrated in two examples. First, a problem in sensory electrostatics is considered. Arthropods such as bees, spiders and hoverflies are positively charged, causing nearby flowers to polarise in their presence. The two-domain AAA-least squares algorithm is used to model the electric field in this scenario, showing that flowers produce electric field perturbations detectable to nearby arthropods and differentiated by the morphology and material properties of the flower. Second, a scenario in vortex dynamics is studied, where a simply connected domain of fluid in rotational flow, known as a vortex patch, is surrounded by fluid in irrotational flow. Vortex patch equilibria are sought â solutions where the shape of the vortex patch is invariant over time in a rotating or translating frame. In this problem, the two-domain AAA-least squares algorithm can be used to reproduce known analytical and numerical vortex patch equilibria. It is speculated that this method could be used to find further equilibrium solutions, such as scenarios involving configurations of vortex patches, sheets and point vortices.
CT09: 10:30-12:30, 24th June 2025, Room FOR/SR9, presentation 11:30-11:50
Phil Trinh (University of Bath)
Title: The mystery of the low-surface tension limit of the Taylor bubble
Abstract: In this talk, I revive a thirty-year old mystery about the zero surface-tension limit of the Taylor bubble (a 2D or 3D bubble rising in a Hele-Shaw channel under the combined influence of gravity and surface tension). It is known that a selection mechanism exists, permitting the existence of a countable infinite number of bubble solutions. However, from the 1980s, there has been a debate about the behaviour of such bubble solutions as the surface tension parameter tends to zero. Recent numerical and asymptotic work has identified additional crucial features, but the thirty-year old problem remains challenging and largely open.
CT09: 10:30-12:30, 24th June 2025, Room FOR/SR9, presentation 11:50-12:10
Jenny Allcock (The Open University)
Title: Droplet motion on chemically heterogeneous fibres
Abstract: Fluid droplets can move spontaneously on substrates, due to geometry or surface properties. Modelling this motion is an area of research that has become popular over the past decades, with most work considering small droplets on flat planes, whether smooth, topologically rough, or with periodic variations. We consider the dynamics of a small three-dimensional droplet of viscous liquid surrounding a cylindrical fibre that has been treated chemically to have a wetting pattern along its length. We assume slip at the liquid-solid interface and small contact angles at both the advancing and receding contact lines. The Stokes flow equations are simplified by expressing the height of the liquid-air interface as a quasistatic expansion, and asymptotic matching is used to equate the slopes of the interface of the bulk of the droplet and the regions near the contact lines. The result is a system of first order ordinary differential equations, which describe the location of the contact lines. Analytical work shows that the dropletâs curvature around the fibre works to offset the curvature in the axial direction, resulting in lower overall droplet velocity than for a similar droplet on a Cartesian plane. We consider various sinusoidal wetting patterns and compare numerical solutions of these with the results in existing literature for such a droplet, and extend our investigations to the situation where the fibre has a smooth wetting gradient.
CT09: 10:30-12:30, 24th June 2025, Room FOR/SR9, presentation 12:10-12:30
Michael Grinfeld (University of Strathclyde)
Title: Admissibility criteria and wild solutions in gas dynamics
Abstract: Recent work using convex integration techniques has uncovered a wealth of new weak solutions of equations of fluid dynamics. These results raise the question of how one deals with radical non-uniqueness of solutions of Cauchy problems. In the context of the Riemann problem for isentropic compressible Euler equations, we show that a version of the least action principle allows us to pick a unique solution. This is joint work with H. Gimperlein (U. Innsbruck), R. J. Knops (Heriot-Watt U.), and M. Slemrod (U. Wisconsin, Madison and Weizmann Institute of Science, Rehovoth).
CT10: 15:40-17:40, 24th June 2025, Room FOR/SR4, presentation 15:40-16:00
Parna Mandal (University of Leeds)
Title: Exploring the Impact of Human Mobility on Cholera Transmission Dynamics
Abstract: Cholera transmission is highly influenced by human mobility, environmental contamination, and sanitation practices. Traditional epidemiological models often assume homogeneous mixing of populations, overlooking structured movement patterns that shape disease dynamics. This study presents an agent-based model (ABM) integrating a SEIRS epidemiological framework with the density-augmented Exploration and Preferential Return (d-EPR) mobility model to simulate cholera spread. The d-EPR model captures real-world movement patterns by balancing habitual return behaviour with exploration of new locations. Our results demonstrate that structured mobility significantly alters disease dynamics. The d-EPR model sustains localised outbreaks by concentrating infections in frequently visited high-risk hubs, whereas random movement leads to rapid but transient epidemics. In structured mobility scenarios, repeated exposure within high-density areas prolongs the outbreak duration, forming persistent transmission hotspots that mirror real-world cholera spread in urban settings. These findings highlight the need for intervention strategies that account for movement behaviours, such as targeting sanitation improvements and vaccination efforts at frequently visited locations. By comparing disease transmission under structured versus random mobility, this study underscores the critical role of human movement in epidemic persistence. Our findings contribute to spatial epidemiology and inform public health policies by advocating for mobility-aware cholera mitigation strategies. Future research should incorporate empirical mobility data to enhance model realism and improve intervention planning in high-risk regions.
CT10: 15:40-17:40, 24th June 2025, Room FOR/SR4, presentation 16:00-16:20
Kamil Drynda (University of Nottingham)
Title: Modelling SUMOylation in Plants
Abstract: As the climate warms the environment changes, as do the stresses plants experience. The SUMO (Small Ubiquitin-like Modifier) pathway is a key process that mediates plant responses to stress. As part of an interdisciplinary project, we are developing mathematical models to understand how SUMO transduces environmental signals into specific physiological responses. The model incorporates key processes in the SUMO cycle, which involves SUMO proteins performing post-translational modifications on a Target protein. We used the mathematical models composed of systems of non-linear differential equations to simulate observed changes in SUMO-cycle components after salt, drought and flagellin stress in different root tissues (integrating new experimental data generated as part of the SUMOcode project, www.sumocode.org
CT10: 15:40-17:40, 24th June 2025, Room FOR/SR4, presentation 16:20-16:40
Shenghao Zhang (University of Manchester)
Title: Flow and deformation of deflated capsules in confined domains
Abstract: The motion and deformation of deflated elastic capsules in confined flows underpins the dynamics of soft particle suspensions in biological systems, particularly red blood cell (RBC) transport in the micro-circulation. We investigate the motion of a deflated capsule with a neo-Hookean shear-softening membrane as it flows through a circular tube. Our study is motivated by experiments (Chen et al., Soft Matter, vol. 19, 2023, pp 5249-5261), in which a suspension of synthetic microcapsules capable of flowing and deforming like RBCs is used to investigate micro-haemodynamics. To model three-dimensional fluid-structure interactions, we use the BioFM package (T. KrĂŒger et al., Springer, 2017) which couples the lattice Boltzmann method for fluid motion with the immersed boundary method for membrane deformation. Under confinement, the capsule undergoes significant shape alterations due to compressive effects from the channel walls. The confinement in the transverse direction leads to buckling and membrane folding, a phenomenon observed in both experiments and simulations. A key parameter governing the deformation dynamics is the capillary number (Ca), which represents the ratio of viscous forces to elastic forces within the membrane. By varying Ca, we analyse how this balance influences deformation patterns and quantify the additional pressure drop caused by the capsuleâs presence. Moreover, at sufficiently large pressure gradients, the viscous drag surpasses the membrane’s tension limit, causing the capsule tip to experience a rapid, finite-time blow-up of strain. Building on these insights, we demonstrate how the Lattice Boltzmann approach captures the interplay of shear-thinning and deflation to determine the capsuleâs rheology.
CT10: 15:40-17:40, 24th June 2025, Room FOR/SR4, presentation 16:40-17:00
Charlotte Taylor Barca (University of Manchester)
Title: Modelling cell state dynamics in melanoma
Abstract: Melanoma cells can transition between cell states, contributing to therapy resistance and immune evasion. These state changes involve dynamic and reversible shifts in gene expression, making it essential to understand the underlying regulatory mechanisms for developing effective therapies. We present a mathematical model of a minimal gene regulatory network comprising key transcription factors associated with melanoma cell states. Using deterministic temporal and spatio-temporal differential equation models, we analyse gene expression dynamics and classify stable states in a biologically meaningful way. We exploit an approximation, based on cooperative binding of transcription factors, in which the models are piecewise smooth. At the population level, we use a naĂŻve model of intercellular communication to explore how cells within a tumour can exhibit coordinated behaviour through travelling waves of gene expression. Additionally, we propose a method for deriving a condition that determines the final state of a population of communicating cells. This model provides a framework for better understanding some of the mechanisms driving gene expression dynamics and to inform and validate experimental hypotheses.
CT10: 15:40-17:40, 24th June 2025, Room FOR/SR4, presentation 17:00-17:20
Torkel Loman (University of Oxford)
Title: Mixed positive and negative feedback loops drive diverse single-cell gene expression dynamics
Abstract: Genetic circuits with only a few components can generate complex gene regulatory dynamics. Here, we combine stochastic modelling and single-cell time-lapse microscopy to reveal the possible behaviours generated by a key gene circuit motif: the mixed positive/negative feedback loop. Our minimal stochastic model of this motif reveals ten distinct classes of behaviours, including stochastic pulsing, oscillations, and bistability. Using an automatic classifier we map these behaviours across parameter space, showing how the behaviours are influenced by a few important biological parameters (such as the strength of the positive and negative feedbacks). Experimental validation in two different mixed feedback circuits in the bacterium B. subtilis (ÏB and ÏV), confirms our model’s predictive power. Guided by our simulations, we are able to transition between dynamic behaviours by modulating in vivo parameters. Together, these results demonstrate how mixed feedback loops generate diverse single-cell behaviours, improving our understanding of this common biological network motif and informing our efforts to engineer them for synthetic biology applications.
CT11: 15:40-17:40, 24th June 2025, Room FOR/SR5, presentation 15:40-16:00
Attiq Iqbal (University of Limerick)
Title: Homogenization-based modelling of drug release from porous tablets
Abstract: Porous tablets are a common form of medication, used to deliver painkillers, antihistamines, and other drugs. Their microstructure consists of soluble drug particles and soluble or insoluble filler, surrounded by voids. The structure of a tablet is designed to dissolve in the stomach, releasing the microstructural active drug at a controlled rate. Understanding and predicting this release process is crucial for optimizing drug formulations. In this talk, I will present an asymptotic homogenization approach for modelling chemical release from porous materials like tablets, particularly those that dissolve as the chemical is released. This method reduces computational costs by deriving models that operate independently at two distinct scales: (a) a global homogenized model capturing average behaviour across the entire porous tablet, and (b) a representative microscale model focusing on a single microstructural particle. At the microscale, a set of three-dimensional unit cell problems are solved, each containing a spherical microparticle within a cell, to determine an effective diffusion coefficient with respect to the microparticleâs size. This coefficient is then utilized at the macroscale to predict the drug kinetics of a spherically symmetric tablet, providing results such as the internal drug concentration, the fraction of solid drug remaining, and the cumulative mass released through the tablet’s outer surface. Additionally, as microparticles near the boundary dissolve, the overall size of the tablet reduces, requiring a moving boundary framework at the macroscale. To account for this, an additional differential equation is derived to track the evolution of the tablet boundary over time.
CT11: 15:40-17:40, 24th June 2025, Room FOR/SR5, presentation 16:00-16:20
Bethany Clarke (Imperial College London)
Title: Structural Anisotropy Stabilises Asymmetric Beating in Instability Driven Filaments
Abstract: Cilia and flagella are microscopic, hair-like appendages, which drive fluid flow at the microscale. They line the epithelial cells in parts of the body, for instance transporting mucus in the airways, or circulating cerebrospinal fluid in the brain. Some cells and microorganisms have cilia or flagella on their surface, which they use to propel themselves through flows. Cilia exhibit asymmetric beating patterns that break time-reversal symmetry needed to facilitate fluid transport at the cellular level. The intrinsic anisotropies in ciliary structure can promote preferential beating directions, further influencing their dynamics. In this talk, by modelling a single cilium as a slender filament using the follower force model, whereby the filament is driven by a compressive force at its tip, we explore how intrinsic curvature and direction-dependent bending moduli impact filament dynamics. We perform numerical simulations and bifurcation analysis on the resulting dynamics, utilising a Jacobian-Free Newton-Krylov method to track time-periodic and steady state solutions, and linear stability analysis to analyse their stability. Our results show that while intrinsic curvature can induce asymmetric beating patterns when filament motion is restricted to a plane, this beating is unstable to out of plane perturbations. Furthermore, we find that a 3D whirling state, seen for isotropic filament dynamics, can be suppressed when sufficient asymmetry or anisotropy are introduced. Finally, for bending moduli ratios as low as 2, we demonstrate that combining structural anisotropy with intrinsic curvature can stabilise asymmetric beating patterns, highlighting the crucial role of anisotropy in ciliary dynamics.
CT11: 15:40-17:40, 24th June 2025, Room FOR/SR5, presentation 16:20-16:40
Eleonora Agostinelli (University of Oxford)
Title: Using Asymptotic Methods to Link Discrete and Continuous Structured Mathematical Models of Early Atherosclerosis
Abstract: Atherosclerosis is a chronic inflammatory disease characterised by lipid accumulation within arterial walls and driven by macrophage interactions with extracellular material, particularly lipid. In this work, we use mathematical modelling to investigate the dynamics of the macrophages in early atherosclerosis. We develop a discrete, lipid-structured mathematical model that accounts for cell proliferation and crowding, and also extracellular material uptake and offloading. With this model we are able to describe the dynamics of key biophysical quantities in the plaque, in particular the total number of macrophages and the total amount of intracellular material contained within the macrophages. Moreover, we rigorously derive a continuum approximation of the discrete model using the method of discrete multiple scales and asymptotic analysis techniques. In this way, we systematically derive a partial differential equation that accurately describes the distribution of macrophage content at leading order. We take advantage of the continuum form to analyse the mathematical system and understand its biological implications, such as the effects of proliferation and crowding on plaque composition. We also investigate the important spatio-temporal regions that appear degenerate but can be understood via boundary layer analysis.
CT11: 15:40-17:40, 24th June 2025, Room FOR/SR5, presentation 16:40-17:00
Sofie Verhees (Heriot-Watt University)
Title: Coupling cell signalling and mechanics: a mathematical model of RhoA-driven mechanotransduction
Abstract: Communication and interactions between cells happen mostly through intercellular signalling processes. These signalling pathways are important in all physiological activities of the cell, such as cell movement, immune response, and tissue development. In many of these signalling pathways, the chemical processes and mechanics of the cell work together. How exactly these two phenomena communicate is not well known. To better understand this process, we introduce a model of the RhoA signalling pathway with a two-way coupling between the signalling processes and cell mechanics. A common way to model the chemical processes of cell signalling pathways are reaction-diffusion equations, which include the diffusion of signalling molecules and membrane receptors, and the reactions between the molecules and receptors. This is coupled to the mechanical properties, governed by the equations of linear elasticity, such that the mechanics of the extracellular matrix influences the interaction between the signalling molecules and the results of the signalling pathways affect the deformation of the cell. Simulations results are produced using a numerical method based on bulk-surface finite elements and exhibit novel findings such as the effect of cell shape on the dynamics, a threshold-like response to changes in substrate stiffness, and the emergence of mechanical homeostasis, where the cell deformation is robust under larger changes in substrate stiffness as in agreement with experiments.
CT11: 15:40-17:40, 24th June 2025, Room FOR/SR5, presentation 17:00-17:20
Mariam Almudarra (University of Glasgow)
Title: Non-local Effects and Inelastic Distortions in Avascular Tumour Growth
Abstract: This work examines the dynamics of avascular tumour growth, focusing on the inelastic distortions that arise from growth and are introduced through a multiplicative decomposition of the deformation gradient tensor. Building on [1], we derive a governing law for the evolution of growth-induced inelastic distortions by linking generalised forces with kinematic descriptors associated with the growth tensor. Based on the dissipation inequality, this formulation reveals the interactions between inelastic distortions and the source and sink terms in the mass balance equations, highlighting the interplay between mechanical stresses and chemical interactions. A key aspect of this study is the non-local behaviour of chemicals (in time and/or space), which we identify as a significant factor in the growth process [2]. To represent the non-local properties of these chemicals, assumed to be generated by the tumourâs complex and multi-scale microenvironment, we introduce integro-differential operators with power-law-type kernels, a formulation naturally connected to fractional calculus. We then investigate how the anomalous behaviour of these chemicals affects key variables governing the systemâs evolution and offer new perspectives on the challenges of modelling growth processes in heterogeneous biological systems. References: [1] Grillo, A. and Di Stefano, S. (2023). Mathematics and Mechanics of Complex Systems, 11(1), 57-86. DOI:10.2140/memocs.2023.11.57. [2] Almudarra MM, Ramirez-Torres A (2025) Examining avascular tumour growth dynamics: A variable-order non-local modelling perspective. Mathematics and Mechanics of Solids, 30(2):501-526. doi:10.1177/10812865241230269
CT11: 15:40-17:40, 24th June 2025, Room FOR/SR5, presentation 17:20-17:40
Alexander Houston (University of Glasgow)
Title: Spontaneous Oscillations in Heterogeneous Active Nematics
Abstract: The framework of active nematics may be used to model many living systems, including cell layers and bacteria [1]. The study of active nematics has focused on uniform activity, but real biological systems are not homogeneous, rather they have population variance or are composed of different species. It has been recently demonstrated that the structure of activity in a material can be controlled through modulating light intensity [2]. This provides motivation to understand the effects of activity patterning, both to gain insight into the in vivo behaviour of living systems and to enable desired dynamics to be engineered in active matter. A central feature of active nematics is that, when confined, they exhibit a transition to a flowing state, provided their activity exceeds a critical value [3]. In this context we show that activity variation allows control of the structure of the flowing state and, most strikingly, can lead to oscillatory dynamics. We show analytically that the behaviour of the confined active nematic can be mapped onto a dynamical system, the coefficients of which are determined by the activity variation, and confirm these results numerically. We find that an activity gradient can induce oscillations, and in this case determine how the properties of the system influence the oscillation frequency. [1] A. Doostmohammadi et al. Nat. Commun., 2018, 9, 3246. [2] R. Zhang et al. Nat. Mater., 2021, 20, 875-882. [3] R. Voituriez et al. EPL, 2005, 70, 404.
CT12: 15:40-17:40, 24th June 2025, Room FOR/SR6, presentation 15:40-16:00
Benjamin Cookman (University of Manchester)
Title: Numerical Investigation of Darrieus-Landau Instability Models in Premixed Flames
Abstract: The Michelson-Sivashinsky (MS) equation is widely used to model the non-linear flame development of the Darrieus-Landau instability. This is a successful model primarily for its analytical âcoalescent polesâ solutions which provide close qualitative match to planar stability, dynamical flame development and the cusped structure of steady wrinkled flames. Less often is quantitative analysis performed therein. By contrast, the Markstein model for flame propagation can be thought of as a precursor to the MS equation before extra assumptions have been made, and relates deviations in flame speed to the structure of the flame and its surrounding gasdynamics. By performing direct numerical simulations (DNS) of the combustion equations, we obviate the need for flame models at the expense of larger computations. Under idealised conditions these combustion equations are equivalent to the simplified equations from the relevant asymptotic studies, with the advantage that flame structure is inherently resolved. In this work DNS under these idealised conditions is compared to the MS equation model and Markstein model. We find that both the MS equation and Markstein models provide the qualitative match that is expected, but that these models have significant quantitative drawbacks. In particular, Markstein numbers are calculated by evaluating relevant flame quantities on two progress variable contours, one representing the flame structure, and another representing upstream gasdynamics. The flame quantities conform closely to a Markstein model, but Markstein numbers differ significantly from the values expected by classical asymptotic theory.
CT12: 15:40-17:40, 24th June 2025, Room FOR/SR6, presentation 16:00-16:20
Will Simpkins (University of Bristol)
Title: How Imperfections Trigger Asymmetric Snap-Through in Arches
Abstract: Recent research on the snap-through buckling of elastic structures has undergone a paradigm shift, transitioning from the classic “buckliphobic” approach of determining buckling loads to avoid catastrophic failure to a “buckliphilic” approach of using shape transitions to enable novel modes of functionality. While static buckling loads and linearly stable configurations are well-documented for the former, the dynamic behaviour critical to the latter remains underexplored. In this work, we consider a compressible bi-stable circular arch under a central load, which can induce asymmetric snap-through due to a pitchfork bifurcation. From simulations, we find that this snap-through is preceded by an extended period of pre-snap-through oscillations. We carry out a multiple-scales analysis of the system to describe both these oscillations and the snap-through which follows them. From this, we have found that imperfections play a critical role in driving the growth of the critical snap-through mode through their non-linear interactions with the oscillatory modes. Our asymptotic analysis allows us to fully characterise the underlying bifurcation and the snap-through time of the system under arbitrary imperfections. These results provide new insights into the dynamic nature of snap-through instabilities and highlight potential engineering applications for thin curved structures.
CT12: 15:40-17:40, 24th June 2025, Room FOR/SR6, presentation 16:20-16:40
Minerva Schuler (University of Warwick)
Title: A mathematical model for rocking bioreactors using feedback control
Abstract: Cultivated meat, also known as cell-based or artificial meat, is an alternative protein source created from animal cells grown outside of their natural environment. Cells are initially grown on a very small scale in so-called seed trains. Once a sufficiently large number of cells with the desired properties have formed, they are then transferred to larger vessels known as bioreactors for proliferation (growth and multiplication). This stage, combining multi-phase fluid mechanics with advection-diffusion processes, is the focus of my research and this talk. The most common bioreactors are stirred bioreactors, where the media is agitated by stirring with propellers. Previous research has suggested that this type of reactor may create high shear stresses, which have a particularly noticeable impact for the production of cultivated meats, as mammalian cells are particularly shear sensitive. To mediate these issues, an alternative reactor design is the rocking-wave bioreactor. Here, the whole reactor, a small 5-10L bag half-filled with liquid, is gently rocked back and forth, generating waves and vortical structures in the flow which induce mixing and oxygen transfer at the surface, allowing cells to proliferate while reducing shear. I will present our mathematical model and dedicated direct numerical simulation (DNS) framework of rocking bioreactors, which is then used to develop a feedback control strategy to optimise mixing while maintaining a target value for the shear stress, aiding cell growth.
CT12: 15:40-17:40, 24th June 2025, Room FOR/SR6, presentation 16:40-17:00
Ardiansyah Fauzi (Northumbria University)
Title: Mathematical Modeling and Data Assimilation for the 2022 Ireland Meteotsunami
Abstract: Meteotsunamis are long-period sea surface oscillations induced by atmospheric disturbances, often modeled using the nonlinear shallow water equations (NSWE). Their generation involves resonant interactions such as Proudman and Greenspan resonance, leading to wave amplification. While extensively studied in regions like the Mediterranean and the Great Lakes, meteotsunamis in the Celtic Sea remain poorly understood due to limited offshore observations. This study focuses on numerical modeling and offshore monitoring strategies for meteotsunamis using data assimilation (DA) techniques. We employ NSWE with atmospheric forcing to simulate meteotsunami dynamics and assess the impact of offshore monitoring networks. A key aspect of this research is the proposed deployment of offshore bottom pressure gauges (OBPGs) at strategic locations, where meteotsunamis are most likely to develop. These sensors provide sea-level data that can be assimilated into numerical models using ensemble-based DA methods to improve wavefield reconstruction and model accuracy. We apply this framework to the 2022 Ireland meteotsunami, using recorded air-pressure anomalies from automatic weather stations (AWSs) and tide gauge data to reconstruct the event and evaluate the role of resonance mechanisms in wave amplification. Additionally, we demonstrate how a densely deployed OBPG network combined with DA techniques can significantly enhance the accuracy of meteotsunami modeling and monitoring in the Celtic Sea. Our findings provide a mathematical framework for integrating offshore observations and data assimilation, improving our understanding of meteotsunami dynamics in underexplored regions.
CT12: 15:40-17:40, 24th June 2025, Room FOR/SR6, presentation 17:00-17:20
Abhishek Ghosh (University of Glasgow)
Title: Efficient Modelling Framework for Liquid Crystal Displays: A Fast and Accurate Two-Dimensional Approach
Abstract: We introduce a modelling framework for Liquid Crystal Displays that enables rapid simulation of large pixelated display areas. This dynamic model accounts for the director orientationâexpressed either as a director angle or in Q-tensor formâand the electric potential, incorporating elastic, weak anchoring, dielectric, and flexoelectric effects. By approximating the dependence of the director and electric potential on the coordinate perpendicular to the display substrates, the inherently three-dimensional system is effectively reduced to a two-dimensional model. This reduction preserves the ability to accurately capture pixel edge effects and fringe fields. Computational simulations using COMSOL Multiphysics validate this two-dimensional approximation against a full three-dimensional model, demonstrating that the simplified approach accurately predicts director reorientation under applied fields. The two-dimensional model, being over 50 times faster than its three-dimensional counterpart, enhances the understanding of non-periodic pixel activation patterns and serves as an efficient tool for optimizing electro-optical performance. As an example, a 324-pixel system (with pixel electrodes of 5 microns and an inter-electrode gap of 0.5 microns) was simulated for 5 seconds of modelled time, completing within just 30 minutes of computational time.
CT12: 15:40-17:40, 24th June 2025, Room FOR/SR6, presentation 17:20-17:40
Robert Garvey (University of Limerick)
Title: Hydrodynamics and drug dissolution in USP4.
Abstract: The dissolution of solid spherical particles is a canonical problem found in many applications. Of particular interest is the dissolution of drug particles in the pharmaceutical industry. In-vitro dissolution testing is crucial in investigating drug quality, stability, and regulatory compliance. The United States Pharmacopoeia set guidelines for testing dissolution and outlines seven main testing apparatus. One such widely utilised apparatus is the flow through device, USP4. The USP4 apparatus comprises of three main components: a reservoir containing the dissolution medium; a pump responsible for controlling the flow rate of the fluid; and a flow-through cell where the drug sample is situated as dissolution occurs. The solvent fluid is ordinarily pumped in a semi-sinusoidal manner or at a constant flow rate. This flow rate impacts dissolution characteristics. Mathematical modelling may be utilised to understand the complex interaction between the hydrodynamics and the dissolution process within the USP4 system. We investigate existing models; such models are solved numerically. We use non-dimensionalisation and asymptotic methods to derive analytical asymptotic solutions to these existing model equations. Our analytics are compared with numerical results and found to give good agreement; such analytical solutions are particularly valuable due to the time-consuming nature of solving these equations numerically, owing directly to the presence of the Basset history integral force. This Basset history integral may be interpreted as a fractional derivative. Existing models are unable to accurately capture all experimental data. We discuss recent developments on the modelling of hydrodynamics and dissolution and outline potential improvements.
CT13: 15:40-17:40, 24th June 2025, Room FOR/SR9, presentation 15:40-16:00
Hamid Naderi Yeganeh (UCL)
Title: On Proving Global Stability of the Positive Equilibrium of the Planar Ricker Model for a Range of Parameters
Abstract: A conjecture about the planar Ricker map (x, y) â (x e^(râxâαy), y e^(sâyâÎČx)) states that if the interior fixed point exists and is locally asymptotic stable, then it’s globally asymptotic stable too. In 2023, Baigent et al. used a Lyapunov function to prove that if 0<r,sâ€2 and=”” 0<α,ÎČ,=”” then=”” every=”” orbit=”” of=”” the=”” planar=”” ricker=”” map=”” converges=”” to=”” a=”” fixed=”” point.=”” in=”” this=”” talk,=”” we=”” present=”” method=”” which=”” applies=”” that=”” lyapunov=”” function=”” solve=”” conjecture=”” for=”” range=”” parameters.=””
CT13: 15:40-17:40, 24th June 2025, Room FOR/SR9, presentation 16:00-16:20
Oscar de Wit (University of Cambridge)
Title: Nonlinear instability and overdamped limit for a PDE model for ants
Abstract: We model a collective of ants as a stochastic interacting particle system and derive a rigorous mean-field limit PDE, which is a non-local nonlinear parabolic PDE. We show the existence of a global attractor and explicit criteria in terms of the model parameters for nonlinear instability. That is, we rigorously show the existence of non-trivial dynamics for non-gradient nonlinear active matter models. We also show how the model relates to a Keller-Segel model with a discontinuous drift, in the overdamped limit for the interaction strength. We show explicit asymptotic approximations of the PDE solutions and show further numerical results for the overdamped limit, giving insight into how non-gradient active matter systems relate to gradient active matter.
CT13: 15:40-17:40, 24th June 2025, Room FOR/SR9, presentation 16:20-16:40
Edgardo Villar-SepĂșlveda (University of Bristol)
Title: Homoclinic snaking & localised patterns beyond all asymptotic orders
Abstract: The concept of criticality of a Turing bifurcation in reaction-diffusion systems has been widely studied. The computation of the cubic coefficient of the amplitude equations for a Turing bifurcation can be found anywhere. When that coefficient is negative, then the bifurcation is said to be supercritical, and the pattern that turns up after the Turing bifurcation becomes stable. On the other hand, if that coefficient is positive, then the bifurcation is said to be subcritical, so the Turing pattern becomes unstable (i.e., invisible, when integrating the system). I will talk about what happens at exponentially small scales close to codimension-two Turing bifurcation points in which the cubic coefficient becomes zero. Specifically, we will see that there are generic conditions under which one can ensure the existence of a Maxwell point in which the homogeneous steady state of the system has the same minimal energy as a large amplitude pattern that is not predicted by the third-order amplitude equations. The existence of such a point allows the system to not have a preference for the large-amplitude pattern or the homogeneous steady state, implying (generically) the existence of a connection between these two states, which gives rise to the existence of localized solutions. We will explore the extension of the region under which these kinds of patterns exist close to the codimension-two Turing bifurcation point.
CT13: 15:40-17:40, 24th June 2025, Room FOR/SR9, presentation 16:40-17:00
Hong Tang (University of Bristol)
Title: Bifurcation Analysis of Multiple Limit Cycles in Boundary Equilibrium Bifurcations (BEBs) in Hybrid Systems
Abstract: A boundary equilibrium bifurcation (BEB) in a hybrid dynamical system occurs when a regular equilibrium collides with a switching surface in phase space. This causes a transition to a pseudo-equilibrium embedded within the switching surface, but limit cycles (LCs) and other invariant sets can also be created and the nature of these is not well understood for systems with more than two dimensions. This work treats two codimension-two scenarios in hybrid systems of any number of dimensions, where the number of small-amplitude limit cycles bifurcating from a BEB changes. The first scenario involves a limit cycle (LC) with a Floquet multiplier 1 and for nearby parameter values the BEB creates a pair of limit cycles. The second scenario involves a limit cycle with a Floquet multiplier â1 and for nearby parameter values the BEB creates a period-doubled solution. Both scenarios are unfolded in a general setting, showing that typical two-parameter bifurcation diagrams have a curve of saddle-node or period-doubling bifurcations emanating transversally from a curve of BEBs at the codimension-two point. The results are illustrated with three-dimensional examples and an eight-dimensional airfoil model. Detailed computational results show excellent agreement to the unfolding theory and reveal further interesting dynamical features that remain to be explored. Similar conclusions are also believed to apply to some non-smooth climate models.
CT13: 15:40-17:40, 24th June 2025, Room FOR/SR9, presentation 17:00-17:20
Andrei Sontag (University College London)
Title: Pathways for overturning consensus in human collective decision-making
Abstract: Political decisions are the epitome of how many aspects of our lives are determined by collective decision-making. However, active participation in collective decision-making is often highly variable, with many individuals temporarily abstaining from voting in the face of uncertainty. Whilst memory and noise have been found to aid consensus formation, the role of neutrality in collective decision-making is not well understood, and the level of individual behavioural complexity required for the emergence of group consensus is not well-characterised. In this talk, I will show that symmetric autonomous systems with neutral intermediate states, such as voters of a two-party system who can abstain, present only two possible dynamical pathways for consensus switching. I will also show how experiments with human participants helped us verify our predictions. The typical pathway observed in our experimental data corresponds to an increase in the number of abstentions as the system transitions from one state of consensus to the other, suggesting that they play a critical role in facilitating consensus change by reducing the effective population size, making it more susceptible to fluctuations, as opposed to what has been previously believed. Our findings provide a parsimonious explanation of consensus formation and change, giving insight into distributed decision-making protocols in animal and human collectives and suggesting efficient solutions to automated collective decision-making problems.
CT14: 15:40-17:40, 24th June 2025, Room FOR/SR10, presentation 15:40-16:00
Ory Schnitzer (Imperial College London)
Title: Bistability and singularity in the onset of drop Quincke rotation
Abstract: The Quincke effect refers to the spontaneous rotation of insulating particles in an electric fieldâa symmetry-breaking phenomenon that arises beyond a critical field strength, with the axis of rotation perpendicular to the field but otherwise unconstrained. It has long been known that drops also exhibit Quincke rotation, with electrohydrodynamic flows driven by electrical shear stresses at the interface raising the critical field for onset. However, the hysteretic onset of this instability, observed for sufficiently low-viscosity drops, has remained theoretically elusive. In particular, simulations have struggled in this regime owing to the apparent formation of charge-density ‘shocks’ engendered by surface convection. I will present a recent theoretical investigation of a simplified two-dimensional model involving a circular (non-deformable) drop in an electric field, spanning arbitrary viscosity ratios and field strengths. This analysis reveals how bistability and singularity emerge together in the onset of drop Quincke rotation. Furthermore, our study uncovers novel charge-density singularity structures universally supported by the leaky-dielectric equations, with broad implications for electrohydrodynamic modelling. This is joint work with Gunnar G. Peng (UCL). Some aspects of this research were also conducted in collaboration with Rodolfo BrandĂŁo (Bristol) and Ehud Yariv (Technion).
CT14: 15:40-17:40, 24th June 2025, Room FOR/SR10, presentation 16:00-16:20
Aleena Urooj (Aston University)
Title: Instabilities induced by an Initially Piecewise Linear Viscosity Profile with a Discontinuity
Abstract: In this study we investigate a viscous instability in which a fluid containing a species, which affects the viscosity of the fluid, is injected into a two dimensional porous medium. The initial concentration of the species is not linearly increasing except for an isolated discontinuity where the concentration increases. Using the quasi-steady state approximation the stability of the system can be reduced to a coupled system of ODEs. As the species diffuses the instantaneous growth rates evolve in time. The stability of the system is obtained numerically. Although the discontinuity initially destabilises the system, eventually, after a finite amount of time, the system becomes stable. Numerical simulations were performed to validate the predictions made by the linear stability analysis.
CT14: 15:40-17:40, 24th June 2025, Room FOR/SR10, presentation 16:20-16:40
Michael Armstrong (Northumbria)
Title: Kinetic Theory and Thermodynamics of Confined Soliton Gas
Abstract: We investigate the dynamics of soliton gas of the focusing nonlinear Schršodinger (fNLS) equation with a moving boundary condition, which models the effect of a âpistonâ on the gas. Using the method of images for the two-soliton solution, we extend the kinetic description of fNLS soliton gas derived in [1] to incorporate the boundary condition. As an illustrative case, we analyse the interaction of a uniform gas composed of nearly identical solitons and compare the analytical predictions with direct simulations of the fNLS equation. Finally, we discuss the relevance of these findings to the physically relevant dynamics of soliton gas governed by the Gross-Pitaevskii equation with a moving external potential. [1] G. El and A. Tovbis, Phys. Rev. E 101, 052207 (2020).
CT14: 15:40-17:40, 24th June 2025, Room FOR/SR10, presentation 16:40-17:00
Henry Thomas (University of Plymouth)
Title: Heat transfer around a circular cylinder forced by Foppl vortices
Abstract: Viscous flow past a cylinder can be approximated via discrete vortices in potential flow. In this presentation we shall show how this approximation is useful in exploring heat transfer from a cylinder both theoretically and numerically. In steady, uniform flow, distinct regimes corresponding to various values of the Reynolds number (Re) are now well documented and described. Low Reynolds numbers (Re < 4) are characterised by stable and attached flow; moderate Reynolds numbers (4 < Re < 40) exhibit a pair of attached, symmetric vortices, which begin a process of cyclic shedding for 40 < Re. We employ Fopplâs solution as a powerful tool in exploring heat transfer about a cylinder in an analytic framework. In order to make a meaningful comparison to the viscous, physical system, the parameters of this solution can be related to the Reynolds number. This relationship is especially pertinent to heat transfer, as neglecting free convection, the Nusselt number is simply a function of the Reynolds and the Prandtl number. To determine the temperature field, the convection-diffusion equation associated to the analytic velocity field is solved numerically. We observe a dramatic change in the local heat transfer rate as we move around the circumference of the circular cylinder. At the front stagnation point there is a large exchange of heat, whereas at the rear, the vortices confine the temperature in the wake region. With an increase in the vortex strength, a minimum of the local heat transfer rate can be observed at the separation point.
CT14: 15:40-17:40, 24th June 2025, Room FOR/SR10, presentation 17:00-17:20
Joseph Pollard (University of New South Wales)
Title: Defect Dynamics in Cholesteric Liquid Crystals: Insights from Contact Topology
Abstract: Cholesteric liquid crystals are comprised of chiral molecules, leading to a macroscopic ‘twisting’ of the material with a consistent sense of handedness. The requirement of maintaining a consistent sense of handedness imposes strong constraints on the structure and dynamics of the material’s defects, its ‘disclination lines’. We show that the standard framework for thinking about the forces on defects in achiral nematics, in terms of the Peach–Koehler force, may fail to correctly predict the motion of the disclination lines when applied to cholesterics. By modelling the material as a contact structure, we are able to use techniques from the field of contact topology to give a topological classification of their disclination lines, to directly calculate the effective elastic forces acting on them using the Gray stability theorem, and ultimately to explain their dynamical behaviour. The predictions of this theory are shown to agree with the results of numerical simulations.
CT15: 10:30-12:30, 25th June 2025, Room FOR/SR4, presentation 10:30-10:50
Gregory Holba (The Open University)
Title: A novel perspective on cerebrospinal fluid flow in perivascular spaces
Abstract: Cerebrospinal fluid (CSF) bathes the brain and flows within and around it, delivering nutrients and carrying away waste. Without effective waste clearance, neurodegenerative conditions can develop, such as Alzheimerâs and Parkinsonâs diseases, which affect over 50 million people worldwide. Given the increasing prevalence of such conditions, understanding the causes of these diseases is becoming imperative. The flow of CSF is of particular interest within the perivascular spaces (PVS) of the brain. These are thought to be the entry and exit points of the glymphatic system, the brainâs waste clearance system. Where blood arteries penetrate the brain, they are surrounded by PVS, which act as annular conduits for CSF flow into the brain matter. Given that CSF flow is known to be strongly influenced by the cardiac cycle, a common approach to modelling CSF flow in the PVS has been to analyse the flow driven by the motion of blood vessel walls, assumed to exhibit a sinusoidal motion. A wide range of flow rates have been predicted, often thought to be too small in themselves to account for effective waste clearance. We propose a more complex pumping mechanism that drives CSF flow in the PVS. We consider a combination of an elastic peristaltic blood vessel wall motion and brain pulsation that induces oscillations of the outer walls of the PVS. We use lubrication theory to derive the equations of motion and to investigate the effects of the additional driver on the pressure and flow rate of the CSF in the PVS.
CT15: 10:30-12:30, 25th June 2025, Room FOR/SR4, presentation 10:50-11:10
Reuben O’Dea (University of Nottingham)
Title: Flow and transport in the human placenta
Abstract: The placenta is a fundamental organ for human reproduction, facilitating fetal growth via the exchange of oxygen, nutrients and waste products between mother and fetus, by means of a dense network of fetal villi bathed in maternal blood flowing through the intervillous space (IVS). However, the influence of placental structure on maternal haemodynamics in the IVS and associated transport and delivery of oxygen and nutrients to the developing fetus is not well-understood. The majority of macroscale studies of IVS transport adopt geometrically-simplified representations of parts of the placenta for analytic tractability or computational expediency, thereby prohibiting a clear understanding of how the complex placental structure impacts flow and transport phenomena and how this translates to whole-organ function. We seek to address this through a comprehensive computational study of IVS flow and solute transport within physiologically-relevant geometries defined via recent ex-vivo physiological, micro-CT and MRI data. We exploit these results both to reveal how the flow transport and oxygen uptake are strongly influenced by the interior structure of the placenta, and to demonstrate how such insight can be used to construct and validate some reduced model descriptions. Lastly, I will describe how this work is being used within an interdisciplinary study combining approaches from mathematics, machine learning, placental physiology, MRI and engineering to identify markers of stillbirth risk.
CT15: 10:30-12:30, 25th June 2025, Room FOR/SR4, presentation 11:10-11:30
Devi Prasad Panigrahi (University College London)
Title: Intermittent attractions lead to emergent material properties in migrating cell aggregates
Abstract: Cells migrate in response to gradients in extra-cellular chemical signals in a process known as chemotaxis. Recent experiments on the model microorganism Dictyostelium discoideum have shown that dense aggregates of cells collectively undergoing chemotaxis exhibit emergent fluid-like properties such as viscosity and surface tension. In this work, we use simulations to explain how active interactions between cells give rise to these emergent phenomena. We propose an agent-based model for intermittent cell-cell attachments and show that it gives rise to emergent fluid-like behavior for an aggregate of cells. We generalize this model to include cell-surface attachments, and show that surface-associated aggregates display properties similar to a liquid droplet resting on a surface. Furthermore, we study the situation where cells self-generate and respond to a chemical gradient by consuming an externally supplied chemo-attractant. Our simulations reveal how individual cells move inside the swarm as the cells move as a collective. Finally, we predict some of the key cellular processes that are responsible for this collective behavior, and provide hypotheses to be tested in future experimental studies.
CT15: 10:30-12:30, 25th June 2025, Room FOR/SR4, presentation 11:30-11:50
Mark Lynch (University of Warwick)
Title: Modelling the Role of Altruism in Epidemics
Abstract: Quarantining of infected individuals strongly mitigates the spread of most diseases. It is widely believed that quarantining requires coercion, such as non-pharmaceutical interventions implemented by governments. However, people are likely to be at least weakly altruistic and so may protecting others by self-quarantining when infected. Little is known about the effect of altruism on behaviour during epidemics. Here, we show that even extremely weakly altruistic populations can be expected to quarantine in a self-organised way to such an extent as to strongly suppress the spread of an infectious disease. In a game theoretic extension of a simple compartmental SIR model, we assume that well-informed, rational individuals seek to minimise both their own costs, coming from infection and social distancing, as well as the corresponding costs borne by the population. The population costs are accounted for by the individuals according to the strength of their altruism, a measure of the number of population members that an individual treats as equivalent to themselves. We find that infected individuals can spontaneously suppress the disease by social distancing and that this occurs down to a remarkably low level of altruism. This outcome remains rational, even in the presence of a moderate level of asymptomatic cases and/or completely selfish individuals. Our hope is that these results could help to bootstrap such altruistic behaviour by revealing its broad rationality.
CT15: 10:30-12:30, 25th June 2025, Room FOR/SR4, presentation 11:50-12:10
Tarek Acila (University of Warwick)
Title: Mathematical Modelling of Inverse Blebbing
Abstract: The hostile environment in which biological cells live constantly exposes them to external forces. Because of their elastic membranes, they use their mechanical and chemical characteristics to alter their shapes to maintain their functionality. Cells use a biophysical mechanism called shape change to offset applied pressures. Cells can change their shape to counteract any applied forces. In this talk, we focus on a specific type of shape change known as Inverse Blebbing. We start with a biological introduction and then slowly make our way to the mathematical set-up of this problem. We derive a continuum mathematical PDE model that describes inverse blebbing using techniques from differential geometry and continuum mechanics. Then, we showcase some numerical results produced from the model and their biological relevance. Lastly, we finish off with possible extensions and generalisations.
CT15: 10:30-12:30, 25th June 2025, Room FOR/SR4, presentation 12:10-12:30
Cara Neal (University College London)
Title: Continuum modelling of blood clogging in vascular networks
Abstract: This formation of clogs in particle suspensions can have catastrophic consequences in biological systems, such as the flow of stiffened red blood cells in conditions like sickle cell disease (SCD). In particular, clogging can result in painful vaso-occlusive crises, the leading cause of hospitalisations among SCD patients. Predicting the locations of clogs and how they propagate across complex vascular networks is therefore of significant importance. Building on recent work that investigates clogging in a single constricted channel [1], we present a two-phase continuum model consisting of a suspended particle phase and Darcy seepage flow to examine the onset of clogging in branching vascular networks with varying channel geometries. By applying appropriate conditions for mass conservation and modelling the solid flux distribution at junctions, we explore the variation in particle volume fraction across the network. We demonstrate the geometric conditions under which vascular networks experience clogging and how these blockages propagate through the network. Additionally, we show how the diversion of solid flux away from clogs can lead to intermittent clogging in other regions of the branching structure. [1] Herale et al. 2025. Emergent clogging of continuum particle suspensions in constricted channels. arXiv preprint arXiv:2502.02396.
CT16: 10:30-12:30, 25th June 2025, Room FOR/SR5, presentation 10:30-10:50
Michael Rennick (University of Edinburgh)
Title: Fluid Simulations of N Immiscible Components
Abstract: Interactions between multiple immiscible fluid components occur frequently in natural and industrial processes. For instance, the dynamics of injected CO2 with water and oil is critical for enhanced oil recovery, and the generation of emulsion droplets consisting of oils and other fluids has applications in the medical, cosmetic and food industries. Additionally, lubricant coating on surfaces, exploited by pitcher plants, can help to repel liquid droplets and exhibits self-healing properties. Despite the prevalence of these multicomponent systems, models that can accurately capture the dynamics of an arbitrary number of immiscible fluids remain lacking. A critical bottleneck is the problem of reduction consistency, whereby a N component system must reproduce the N-1 component system when one fluid is absent. In our work, we develop a fully reduction consistent numerical scheme capable of simulating fluid systems with no limitations on the number of components. Enabled by these new developments, we demonstrate how the classic four colour theorem can explain key physics in phase separation processes. Finally, we investigate key applications including three component droplet emulsion generation and patterned lubricated surfaces.
CT16: 10:30-12:30, 25th June 2025, Room FOR/SR5, presentation 10:50-11:10
Freddie Jensen (University of Warwick)
Title: Observations from modelling nonlinear acoustics in brass instruments
Abstract: We discuss interesting features of a model presented at last year’s BAMC, which combines weak nonlinearity and complex geometry in duct acoustics without flow, with applications to sound in brass instruments. Topics discussed here include curvature-induced plane-wave tunnelling, a method of quantifying the speed of sound around bends, an ambiguity around forward/backward decomposition, and a new test case in the study of nodes and turning points.
CT16: 10:30-12:30, 25th June 2025, Room FOR/SR5, presentation 11:10-11:30
Negin Nazari (University of Limerick)
Title: Mathematical modelling of solvent infiltration into a porous granule
Abstract: Understanding drug release from pharmaceutical granules is vital to the development of targeted release profiles. In this talk, in the context of a recent model describing diffusion and solubility-limited drug dissolution and release from a porous spherical granule composed of drug and excipient [1], we consider the possible importance of liquid solvent infiltration. For this, we use the Darcy-Buckingham law to pose time-dependent one-dimensional model equations for two-phase flow in an unsaturated porous medium; these can be reduced to a single partial differential equation for the saturation function, which describes locally the volume fraction of available pore space that is occupied by solvent. Neglecting the air viscosity leads the well-known Richards equation; using a combination of analytical and numerical techniques, we find that solvent infiltrates exponentially quickly. If air viscosity is not neglected, we find that that the solvent infiltrates algebraically slowly. As a consequence, using the Richards equation will dramatically underestimate the time taken to fill a porous granule. In addition, the results are compared with those obtained with a simple model which is similar to the classical Washburn equation for capillary flow in a bundle of parallel cylindrical tubes. Finally, the significance of our findings are discussed as regards extending this model to include drug release. References: [1] Moroney, K. M. & Vynnycky, M., Mathematical modelling of drug release from a porous granule, Appl. Math. Mod. 100 (2021) 432-452.
CT16: 10:30-12:30, 25th June 2025, Room FOR/SR5, presentation 11:30-11:50
Yaojue Xiong (University of Bristol)
Title: Poroelastic phase-field modelling of fracture during the drying of colloidal suspensions
Abstract: Crack formation in drying colloidal suspensions plays a crucial role in applications such as medical diagnostics, inkjet printing, and nanofabrication. During drying, the solute particles accumulate at the evaporating surface, leading to a phase transformation into a deformable porous solid. We model the unidirectional drying of a colloidal suspension using linear poroelasticity, incorporating a decomposition of the strain tensor into elastic and drying-induced volumetric components. The poroelastic model is integrated into a phase-field fracture theory, employing a spectral decomposition of the elastic strains into tensile and compressive components, which is an essential feature in capturing fracture patterns observed from experiments. Furthermore, we discuss the impact of the intrinsic crack length scale and boundary conditions on the crack patterns and propose a scaling analysis to derive a semi-analytical expression for the crack spacing in terms of physical variables.
CT16: 10:30-12:30, 25th June 2025, Room FOR/SR5, presentation 11:50-12:10
Alan Champneys (University of Bristol)
Title: Mathematical Modelling for Sustainable Development
Abstract: Listening to the student voice, they want to know how to use their maths to make the world a better place. So we launched a 4th-year module on Mathematical Modelling for Sustainable Development. This caused me to realised that sustainable development (in the broadest possible UN sense) is not just about charity, data, disaster prediction, politics and guilt. It is not a zero sum game. As such, mathematicians need to get involved to help us understand trade-offs and scenario predictions. Equally though, as mathematicians we need to climb down from our ivory towers and adapt our thinking. It has led me to ask questions like: “what is a mathematical model?”, agreeing with George Box that all models are wrong but some are useful, “what does useful mean?”, “how to optimally use mathematical modelling as part of the scientific method in socio-economic situations?” and “how to ethically communicate to stakeholders the conclusions of a mathematical model, and also its caveats?”. I don’t know the answers, but I want to share my journey, covering brief examples in energy and healthcare.
CT16: 10:30-12:30, 25th June 2025, Room FOR/SR5, presentation 12:10-12:30
Kevin Moroney (University of Limerick)
Title: Formation of crystal polymorphs: modelling the impact of gravity
Abstract: An individual compound may have different crystalline forms (polymorphs) having vastly different physicochemical properties. This is of vital importance in the pharmaceutical industry, where only a single polymorph of a particular drug may have the desired therapeutic effect. Some recent scientific and commercial interest has focused on harnessing gravity to control polymorphic formation by performing crystallisation in microgravity in low Earth orbit. In this talk, a recently published approach to model the impact of gravity on the polymorphism for a specific type of crystallisation called antisolvent crystallisation is presented. Population-balance equations are developed to describe the particle size distributions of two polymorphs in a crystalliser over time for different initial supersaturation levels, antisolvent fractions and gravity levels. Descriptions of nucleation and gravity-impacted crystal growth are included. The model consists of two first-order non-linear hyperbolic equations for the polymorph particle size distributions, and an ordinary differential equation for solute concentration in the solvent. The crystal growth rate is assumed to be limited by mass transfer to the crystal surface as determined by solute diffusion and density-driven convection. The equations are nondimensionalised and analysed qualitatively using the method of characteristics which is used to inform the numerical solution method. The model is applied to the crystallisation of L-histidine, an essential amino acid with two polymorphs whose formation has been reported to be influenced by gravity. The impact of gravity on the evolution of these polymorphs over time is considered by varying the gravitational force from microgravity to hypergravity conditions.
CT17: 10:30-12:30, 25th June 2025, Room FOR/SR6, presentation 10:30-10:50
Michael Nguyen (University College London (UCL))
Title: A minimal two-basin model with Rossby waves in the Arctic Ocean
Abstract: The Arctic Oceanâs dynamics are fundamentally different to midlatitude oceans, where large-scale circulation is primarily governed by the Sverdrup balance. Circulation in the Arctic is instead driven by wind forcing and basin topography, but predicting their evolution in a changing climate remains an open challenge. We present a minimal two-basin model that incorporates these factors to explore simplified Arctic flows. We analytically find Rossby waves by solving the linearised, rigid-lid Shallow-water equation using complex variables and apply Fourier mode-matching to link the two basins together. These are compared with fully nonlinear numerical simulations, offering insight into how Arctic circulation responds to changing conditions.
CT17: 10:30-12:30, 25th June 2025, Room FOR/SR6, presentation 10:50-11:10
Sebastian Dooley (University of Warwick)
Title: Data-driven equation discovery for liquid film flows
Abstract: Partial differential equation (PDE) discovery is an exciting alternative to standard first principles-based methodologies regularly used in mathematical modelling, particularly in regimes outside the reach of traditional approaches. This talk explores PDE discovery methods, with their application to liquid film flows as central motivation, drawing on synthetic data and direct numerical simulation results where appropriate. To begin with, we focus our attention on the recovery of linear equations and nonlinear test cases that are commonly used to validate equation discovery frameworks. This is before looking to what we believe to be a novel application of equation discovery: a highly nonlinear, single equation thin-film model. We then discuss challenges for other established thin film equations, highlighting important derivation aspects to build analytical understanding that enhances the data-driven process. Finally, we steer the developed framework towards new regimes of interest, such as thick liquid film flows, in which classical physical understanding is well complemented by the present approach.
CT17: 10:30-12:30, 25th June 2025, Room FOR/SR6, presentation 11:10-11:30
Nick Ryan (University of Oxford)
Title: Surface-tension-driven buckling of a thin viscous sheet
Abstract: In the manufacture of thin glass sheets, e.g., for smartphone and tablet screens, buckling can cause ripples to become set into the final product, making it unusable. We present a simplified model problem that attempts to capture how this spontaneous buckling â driven by local compressive stress â can occur. We model a thin disc of viscous fluid retracting under surface tension and consider how initial sinuous and varicose perturbations affect the shape evolution. We use asymptotic methods to simplify the problem, where the small parameter is the inverse aspect ratio of the sheet. To resolve the behaviour at the highly curved edge of the sheet, we use the finite element method (FEM) to solve a modified 2D Stokes-flow problem in this boundary layer to obtain a similarity solution. We use this solution to apply an effective boundary condition at the edge of the sheet, allowing us to calculate an asymptotic solution for how the initial perturbations to the sheet evolve as the sheet retracts. We compare our asymptotic solution to the solution calculated via direct numerical simulation (using FEM) and find that there can be (potentially large) transient buckling of the sheet centre-surface. Furthermore, we examine how the choice of initial perturbations can determine which buckling modes are dominant, and we explain how this depends on the stresses in the disc.
CT17: 10:30-12:30, 25th June 2025, Room FOR/SR6, presentation 11:30-11:50
Eric Hester (University of Bath)
Title: Towards optimal complexity solvers for multiphase systems: A Cahn-Hilliard case study
Abstract: How can we efficiently solve the Cahn-Hilliard equation? It is the archetypal multiphase problem, demonstrating all the complexities of these systems: 1. It naturally develops intricate geometries and order Δ boundary layers. 2. The regions evolve dynamically through nonlinear coupled bulk-boundary physics. 3. Realistic scenarios involve extreme separation of time and length scales as Δ tends to 0. We first implement a spectral method in the Dedalus framework. Using orthogonal Jacobi polynomials with careful choice of weighted inner product and test functions allows efficient implementation of standard PDE operators using sparse banded matrices and fast Fourier transforms. This parallelisable approach achieves optimal scaling for initial times. But realistic regimes develop narrow spatial scales that this approach struggles to resolve as Δ approaches 0. Optimal performance demands deeper understanding of this asymptotic limit. This calls for some classic applied mathematics! We begin with elegant signed-distance boundary-layer coordinates. A matched asymptotic expansion reveals the leading order tanh solution. Shifting into tanh coordinates then diagonalises our linear operators using yet more Jacobi polynomials, allowing formal solutions to arbitrary order. We thereby reproduce the familiar Mullins-Sekerka/Stefan problem at leading order before calculating higher order corrections. We finally use this knowledge to build fast spectral element solvers with Δ-independent performance, showing how we unlock better scaling as we incorporate more of our asymptotic tools and estimates into the solver design.
CT17: 10:30-12:30, 25th June 2025, Room FOR/SR6, presentation 11:50-12:10
Emiliano Renzi (Northumbria University)
Title: Mathematical modelling of tsunami magnetic anomalies
Abstract: This study presents a mathematical model of magnetic anomalies induced by tsunamis, arising from time-dependent seabed deformation in an otherwise still ocean. The seabed deformation is characterised as a slender fault, with its lateral extent far exceeding its longitudinal scale. Employing a perturbative method with multiple time scales alongside a Greenâs function approach, we examine how the wave field and its associated magnetic anomaly evolve across transoceanic distances. Our analysis reveals that lateral propagation in two horizontal dimensions reduces the period of both the surface wave and the induced magnetic signal, in contrast to one-dimensional scenarios. As the wave propagates, its front bends and stretches, altering the magnetic signal. Notably, the magnetic anomaly gradually separates from the leading tsunami wave, advancing ahead by a distance proportional to the fault’s longitudinal scale. We further derive an asymptotic formula describing the behaviour of the long leading wave that precedes the dispersive group over vast ocean distances. This result holds promise for enhancing rapid tsunami risk assessment and informs the development of magnetic field-based early warning systems. Overall, this research advances the understanding of tsunami-induced magnetic anomalies and offers insights for improving future hazard detection strategies.
CT17: 10:30-12:30, 25th June 2025, Room FOR/SR6, presentation 12:10-12:30
Ellen Luckins (University of Warwick)
Title: Multiscale modelling of latent heat storage devices
Abstract: One developing technology for the green energy transition is heat energy storage. The idea is to capture and store heat that would otherwise be wasted, which can then be released and used (eg: to heat buildings) at a later time. In latent heat storage, the heat is stored and released by the change of phase (freezing or melting) of a material with a high latent heat of fusion. A challenge in developing these latent heat storage devices (LHSD) is that the phase-change material (PCM) is often a poor thermal conductor, limiting the speed at which the device can be charged and discharged. One solution is to have a mesh of copper wires through the PCM, which conducts heat much faster through the device. We use homogenisation analysis (the method of multiple scales) to derive reduced models for the LHSD in two distinct parameter regimes: (1) where the copper and PCM can be modelled as a composite material and a sharp freezing front moves through the device, and (2) where the heat conduction through the copper dominates and freezing occurs simultaneously throughout the device, in which case our homogenised model describes the evolution of the mushy mixture of solid and liquid. Although sharp-interface models (type 1) are typically assumed in the engineering literature, we demonstrate that the best device performance occurs in the mush parameter regime and so models of type 2 should be used instead.
CT18: 10:30-12:30, 25th June 2025, Room FOR/SR9, presentation 10:30-10:50
Wenbin Chen (University of Bristol)
Title: Wave Models in the Classical Painlevé Problem
Abstract: The so-called PainlevĂ© paradox, which shows the inconsistency and indeterminacy in rigid body models, is demonstrated by PainlevĂ©âs example. In this work, we try to resolve the problem by taking into account extra physics. In particular, we incorporate wave propagation and damping into the model. A new nonsmooth dynamical system is developed and the conditions for switching between different modes of motion are determined. The model is then compared with the compliant contact model and analysed in the case in which the paradox can occur. between different modes of motion are determined. The model is then compared with the compliant contact model and analysed in the case in which the paradox can occur.
CT18: 10:30-12:30, 25th June 2025, Room FOR/SR9, presentation 10:50-11:10
Andrey Korolkov (University of Manchester)
Title: Embedding formula for lattice problems: WienerâHopf perspective
Abstract: In boundary value problems, one key advantage of analytical solutions over numerical ones is that the dependence on parameters is explicit. This explicit dependence is particularly useful for optimizing regimes and addressing inverse problems. Here, we explore an intermediate method known as embedding, where complete analytical solutions are not derived, yet it is still possible to obtain some analytical dependence of the solution on specific parameters. A systematic approach to deriving embedding formulas for plane wave diffraction problems was outlined by Craster in 2003. The steps involve: identifying an operator H that âannihilatesâ the incident plane wave, creates singularities near the edges of the scatterer, preserves boundary conditions, and also commutes with the Laplace operator; introducing the auxiliary oversingular solutions; studying the combination of the modified field H(u) and the auxiliary solutions with some unknown coefficients. It is then shown, through uniqueness arguments, that the solution to the plane diffraction problem can be expressed in terms of these auxiliary solutions. In this work, we propose an alternative approach. Simply put, we argue that every em- bedding formula is rooted in a matrix WienerâHopf equation, and the embedding formula is essentially the canonical solution to this matrix WienerâHopf problem. We demonstrate the effectiveness of this approach by revisiting well-known problems, such as the problem of diffraction by a strip, and the problem of diffraction by a wedge. Additionally, we derive new embedding formulas for wave problems on lattices.
CT18: 10:30-12:30, 25th June 2025, Room FOR/SR9, presentation 11:10-11:30
Jisui Huang (University of Liverpool)
Title: Optimal-Transport-Based Superpixel Clustering for Image Segmentation
Abstract: We propose an unsupervised image segmentation method with optimal transport as the region metric. 1. We define a selective segmentation functional of superpixels. The final segmentation can be represented as a union of superpixels by optimising the energy. 2. We use the Wasserstein metric to measure the distance between two sets of superpixels, which can overcome global inhomogeneity and noise. 3. We design a fast region merging strategy to minimise our functional, showing a significant computational advantage. 4. Experiments demonstrate that our model can outperform some state-of-the-art models while keeping a reasonable computational overhead.
CT18: 10:30-12:30, 25th June 2025, Room FOR/SR9, presentation 11:30-11:50
Hamid Alemi Ardakani (University of Exeter)
Title: A fourth-order potential enstrophy conserving C-bracket scheme for nonlinear shallow-water sloshing
Abstract: The second-order mass-, energy-, and potential-enstrophy-conserving discretisation introduced by Arakawa & Lamb (1981) for the shallow-water equations with periodic boundary conditions, and extended by Salmon (2004) in the context of Hamiltonian Poisson-bracket discretisation, is further extended to a fourth-order discretisation in the potential-vorticity dependent component of the Poisson-bracket, for the problem of nonlinear shallow-water sloshing over a corrugated bottom surface in a rectangular rigid basin, with non-symmetric porous side walls and coupled no-flow and non-periodic influx-efflux boundary conditions, undergoing a prescribed coupled surge-sway motion. Adaptation to a finite domain with non-periodic inflow-outflow boundary conditions requires a new approach to the boundary conditions at porous solid boundaries in the context of the fourth-order discretisation on the Arakawa C grid. The scheme is implemented, shown to preserve the total mass, energy, and potential enstrophy over long-time integration. This higher-order C-bracket sloshing integrator provides a robust, stable, fast and precise building block for long-time computational modelling of floating ocean wave energy extractors with flexible components.
CT18: 10:30-12:30, 25th June 2025, Room FOR/SR9, presentation 11:50-12:10
Elena Medvedeva (The University of Manchester)
Title: Diffraction by a Transversal Screen in a Square Lattice Waveguide
Abstract: The Wiener-Hopf method is a powerful tool in complex analysis used to solve partial differential equations in various fields, in particular for acoustics and elasticity. In this talk, we explore its application to a discrete analogue of a well-known wave diffraction problem: the scattering of a waveguide mode by a transversal Dirichlet strip, formulated on a square lattice. This leads to a 4Ă4 Wiener-Hopf system, which simplifies to a 2Ă2 system in the symmetric case. As is well known, matrix Wiener-Hopf equations do not generally have a constructive solution; however, there are established approaches for particular problems and formulations. In particular, in the continuous case of the discussed problem, a direct matrix factorisation in the form of Khrapkov-Daniele can be obtained in a special case, while the pole removal technique can be applied in the general situation. We will discuss how classical Wiener-Hopf techniques extend to the discrete setting, compare analytical approaches â such as direct matrix Wiener-Hopf factorisation and the pole removal technique â as well as numerical methods based on the discrete lattice Greenâs function, and examine wave transmission and reflection in the discrete waveguide with a transversal screen. These results help connect discrete and continuous approaches in wave diffraction theory and provide insights into their applications in mathematical physics and wave phenomena.
CT18: 10:30-12:30, 25th June 2025, Room FOR/SR9, presentation 12:10-12:30
Paul Mannix (Imperial College London)
Title: Constructing PDFs of spatially dependent fields using finite elements
Abstract: A probability density function (PDF) of a spatially dependent field provides a means of calculating arbitrary moments of the field or, equivalently, the proportion of a spatial domain that is mapped to a given set of values. When calculating the PDF of continuous fields, rather than collections of discrete data points, traditional methods do not make use of all of the available information. To address this issue, we describe a function space approach to estimating the PDF which better exploits the functional representation of fields returned by spectral methods. By applying the method to an example of turbulent mixing, simulated using a pseudo-spectral method, we numerically demonstrate the efficacy of the proposed approach and explain how the resulting PDFs are traditionally used to reveal information about the energetics behind stratified turbulence and mixing.
CT19: 15:40-17:40, 25th June 2025, Room FOR/SR4, presentation 15:40-16:00
Matthew Shirley (University of Oxford)
Title: Modelling the Manufacture of Optical Fibres with Complicated Designs
Abstract: Fibre optic cables have emerged as a critical technology underpinning modern communication networks and sensing technologies. This growth has caused many specialised designs for particular applications to emerge, with design features such as non-axisymmetric cross-sections, complicated internal structures, and regions of glass doped with rare-earth metals, all with the aim of altering the optical properties of the fibre. Manufacture of these specialised optical fibres relies on careful control of the flow of molten glass to ensure the final product matches the intended design. This is complicated by the presence of dopants in the glass which will alter its physical properties. Previously, mathematical models have been developed to describe the manufacture of optical fibres made of pure silica, modelling the molten glass as a thread of Newtonian fluid undergoing extensional flow. However, a focus on analytical solutions has restricted their application to simpler designs. In this talk, we will extend the existing mathematical models to account for the presence of doped glass through a discontinuous spatially-varying viscosity. We will show how asymptotic analysis can reduce the solution of the full three-dimensional model to a two-dimensional problem for the evolution of the cross-section. We will describe the software we have developed to solve this resulting 2D problem for arbitrarily shaped fibres, with any distribution of doped glass, demonstrating its application to a variety of designs. We will conclude by showing how the model can be used to optimise the final shape of the fibre by varying the initial shape and draw speed.
CT19: 15:40-17:40, 25th June 2025, Room FOR/SR4, presentation 16:00-16:20
Matheus de Carvalho Loures (University of sheffield)
Title: Elastostatic tomography of roller bearings
Abstract: Wind turbines have become a crucial component of renewable energy systems, with their adoption steadily increasing worldwide in recent years. As their usage expands, ensuring their efficiency and structural integrity is essential. Vibration-based monitoring techniques play a significant role in assessing turbine performance and detecting potential defects early. Given this importance, exploring elasticity-based methods can enhance the amount and quality of information obtained from sensor data. In this presentation, we introduce an approach that leverages the method of fundamental solutions to address the inverse problem of static load identification. Essentially, this technique can be viewed as a form of elastic tomography, allowing us to evaluate the structural condition of wind turbines more effectively. By applying this methodology, we aim to improve monitoring strategies, contributing to the reliability and longevity of wind energy infrastructure.
CT19: 15:40-17:40, 25th June 2025, Room FOR/SR4, presentation 16:20-16:40
Samuel Palama (University of Nottingham)
Title: Modelling sound radiation of structures under light-fluid assumption at high frequencies using DEA
Abstract: Predicting the vibroacoustic behaviour of structures in contact with water and at high frequencies can be a complex task due to the fluid-structure interaction. Computation time increases with frequency and the complexity of the structure. Being able to predict the sound radiated by a naval vehicle in contact with water could help in improving passengersâ comfort as well as the impact on the marine fauna. In order to do so, we use a prediction method called Dynamical Energy Analysis (DEA), so far employed mainly to assess the vibrational energy levels in the structure itself. DEA is a phase-space based ray-tracing method determining energy densities in terms of the ray densities in a structure and can be applied on FEM-meshes. Here, as a first step, we expand the DEA methodology to take into account radiation into a light fluid (i.e. relative to the structure â typically air). While the structure-borne results are based on ray-tracing, we employ the so called Wigner transform to reconstruct information necessary to predict the sound radiation into the fluid. We will demonstrate the new technique using some simple model systems.
CT19: 15:40-17:40, 25th June 2025, Room FOR/SR4, presentation 16:40-17:00
Alessio Kandiah (University of Liverpool)
Title: Dispersion and localisation of gravity-induced waves in a chiral elastic strip
Abstract: We present an analytical description of a chiral elastic lattice strip, of variable gyricity, subjected to gravity, with either Dirichlet or Neumann boundary conditions on the upper and lower boundaries. We focus on asymmetric waveforms and show that in such waveguides, elastic chiral vortex waves can occur. It is shown that the dispersion of chiral elastic waves can be controlled by changing the properties of the spinners and the gravitational effects. The dynamics of the discrete lattice strip, subjected to gyroscopic forces and gravity, can be used as an approximation of inertia-gravity guided waves through the equatorial channel on a rotating sphere. This talk is based on the results of the paper [1]. [1] A. Kandiah, I. S. Jones, N. V. Movchan and A. B. Movchan. Coupled dynamics of chiral waves and gyroscopic systems with applications to atmospheric phenomena. ArXiv Preprint ArXiv:2502.09666, 2025. https://doi.org/10.48550/arXiv.2502.09666
CT19: 15:40-17:40, 25th June 2025, Room FOR/SR4, presentation 17:00-17:20
James Christian (University of Salford)
Title: Counterpropagating waves in discrete nonlinear equations: instability spectra & spontaneous patterns
Abstract: (joint with Henry J. Anderson, University of Salford) Models such as the discrete nonlinear Schrödinger (dNLS) and Ablowitz-Ladik (AL) equations play fundamental roles in theoretical physics and applied mathematics. They often govern the discrete diffraction of waves travelling through periodic structures in the presence of cubic nonlinearity. The origin of the dNLS equation is firmly rooted in the physically local response of the host medium. On a more abstract level, its AL generalization acquires desirable properties (e.g., exact integrability) that appear through imposing nonlocal nonlinear coupling between nearest-neighbour channels. Previous research on the dNLS and AL equations has considered their connections in the context of spontaneous pattern formation with ring-cavity feedback. Our presentation here will address counterpropagating waves. The counterpropagation scenario is a type of problem distinct, both physically and mathematically, from the ring cavity. It is of the (1+2) class [rather than (1+1)] and the boundary conditions are more subtle. The simplest case involves equal-intensity plane-wave pump fields; we are primarily concerned with searching for the condition under which a static spatial modulation of finite amplitude (i.e., a Turing pattern) may develop on top of such weakly-perturbed background waves. A derivation of the threshold instability spectra will be given, which requires the exponentiation of a 4×4 system matrix (in comparison with the simpler 2×2 ring-cavity case). Such spectra, obtained by deploying linear analysis, quantify the dominant transverse length-scale characterizing emergent patterns. The long-wavelength asymptotics will also be explored, restoring the continuum limit of the two discrete models. To conclude, our predictions from linearization are tested against numerics.
CT20: 15:40-17:40, 25th June 2025, Room FOR/SR5, presentation 15:40-16:00
Nathan Schofield (University of Oxford)
Title: Mechanistic modelling of cluster formation in metastatic melanoma
Abstract: Melanoma is a type of skin cancer that becomes much more lethal when it spreads or metastasises to other tissues. During tumour initiation, melanoma cells form clusters within the primary tumour which promote metastasis. In the absence of biological tools to visualise cluster formation at primary tumour sites, we develop a series of mathematical models to generate mechanistic insight into their formation. We use a coagulation-fragmentation-proliferation framework to describe cluster growth dynamics, incorporating different functional forms for cell proliferation and cluster splitting. We fit the models to experimental data, using a Bayesian framework to perform parameter inference and information criteria to perform model selection. For this work we utilise in vitro data for two distinct melanoma cell phenotypes, one more proliferative and the other more invasive, with data available for both monoculture experiments, which give rise to homogeneous clusters, and co-culture experiments which result in heterogeneous clusters. We provide a quantitative evaluation of the differences between phenotypes, and predict that the invasive phenotype more quickly forms large clusters through an increase in the coagulation rate. We also evaluate how well different modelling assumptions fit the data to increase our understanding of the mechanisms driving metastasis.
CT20: 15:40-17:40, 25th June 2025, Room FOR/SR5, presentation 16:00-16:20
Elliott Hughes (University of Oxford)
Title: Assessing the performance of PDE models for collective cellular behaviour
Abstract: Mechanistic mathematical models of biological systems aim to capture the essential underlying biology. Model parameters can be estimated by calibrating the model outputs with experimental data and the resulting parametrised models can then be used to predict system dynamics in novel situations. However, if the mathematical models do not accurately capture the underlying biology, the models may have poor predictive power. In this talk we analyse the performance of a suite of partial differential equation models for collective cell behaviour. By comparing model outputs against data sets from colony growth experiments which are distinguished by their initial colony shape, we first demonstrate that parameter estimates from standard reaction-diffusion models are sensitive to the initial colony conditions, resulting in poor predictive power. Subsequently, we compare the performance of these models with alternative fluid-based models that aim to more accurately capture the behaviour of the cellular colony at its boundary.
CT20: 15:40-17:40, 25th June 2025, Room FOR/SR5, presentation 16:20-16:40
Peter Kissack (University of Birmingham)
Title: Assessing the Impact of Anti-Seizure Treatments in Network Models of the Brain
Abstract: Epilepsy is a common neurological condition characterised by recurrent seizures, the genesis of which has been associated with the interplay between local dynamics and network structures within the brain. By measuring correlations between signals from electroencephalography data, we can derive macro-scale networks representing the brain’s functional connectivity. Using techniques from graph theory and dynamical systems, we can quantify aspects of the topology of these networks and model the propagation of seizure activity associated to given network structures. In two recent studies, we have investigated the link between features of brain network topology (i.e. trophic coherence) and long-term changes and robustness, using synthetic dynamic network models and clinical data from people with idiopathic generalised epilepsies. In both projects, we found preliminary evidence of how dynamic network models enables us to quantify the impact of ASMs on seizure-risk.
CT20: 15:40-17:40, 25th June 2025, Room FOR/SR5, presentation 16:40-17:00
Claudia Miranda (University College London (UCL))
Title: Minimal kinetic modelling unravels heterogeneity and variability in sickle cell disease
Abstract: Sickle-cell disease (SCD) is a genetic blood disorder with symptoms induced by the polymerisation of sickle haemoglobin (HbS) inside red blood cells (RBCs). In low oxygen concentrations, HbS polymer chains form, pushing and damaging the cellular membrane of RBCs. This makes RBCs acquire abnormal shapes and become stiffer and stickier. In turn, blood viscosity effectively increases, and with it, the likelihood of developing a blood clot. SCD can cause various complications, including severe pain, organ damage, and anaemia. Despite decades of intensive research, significant gaps remain in our understanding of SCD. Amongst others, there is neither a universal biomarker nor a specific therapeutic window. Moreover, cell-resolved measurements of HbS polymerisation in whole cell populations are only recently starting to be made. These experiments reveal that SCD saturation distributions at intermediate oxygen tensions are bimodal, suggesting the existence of two subpopulations of RBCs in SCD patients â one with a significant amount of polymer, and the other with fewer polymers present. However, it is not clear how these distributions arise mechanistically due to the large number of variables involved in the models presented to this date. In this work, we present a minimal model of polymerisation in SCD with analytical solutions that contain the key physics explaining the heterogeneity seen in the saturation distributions. The model can also describe how likely the RBCs are to sickle within a relevant timescale. This is an initial step towards exploring the validity of critical HbS concentration and saturation as biomarkers for SCD.
CT20: 15:40-17:40, 25th June 2025, Room FOR/SR5, presentation 17:00-17:20
Henry Kerr (University of Exeter)
Title: Travelling Waves Through Spiking Neuronal Networks with Voltage-gated Ion Channels
Abstract: Travelling waves of firing activity are a well-attested and robust mode of interaction across neural populations. From a mathematical perspective, travelling waves are an analytically tractable behaviour even on large networks of individually-modelled neurons. Here, we examine the existence and stability of multi-spike travelling waves in networks of leaky integrate-and-fire neurons with local adaptation such as that mediated by voltage-gated ion channels. This allows us to study the relationship between the neuronâs internal dynamics as modulated by the ion channels and the network-wide dynamics represented by the travelling wave. We observe that the ion channel plays a conditional self-excitatory role, promoting and stabilising faster waves until the solution branch is lost due to the emergence of additional firing events. In certain parameter ranges we observe the disconnection of solution branches, opening gaps in the range of possible wave speeds. We present this work upon one-dimensional networks with an eye towards extension into higher dimensions.
CT20: 15:40-17:40, 25th June 2025, Room FOR/SR5, presentation 17:20-17:40
Mariia Dvoriashyna (School of Mathematics, University of Edinburgh)
Title: Transport of All-trans retinoic acid in myopigenesis
Abstract: The prevalence of myopia (short-sightedness) is rising rapidly, posing significant long-term implications for ocular health. Consequently, there’s a need to better understand myopigenic signalling pathways. All-trans retinoic acid (atRA) plays a role in this signalling, yet its transport within ocular tissues remains unclear. This study aims to better understand atRA transport in the eye. We developed a mathematical model for atRA transport in the posterior ocular tissuesâchoroid (the vascular layer adjacent to the outer retina) and sclera (the outermost layer of the eye)âof mice and humans. The model includes atRA synthesis by cells in the choriocapillaris (a capillary layer in the choroid), degradation by scleral cells, and binding to the carrier protein serum albumin (SA). atRA and SA are transported via diffusion and convection, requiring consideration of various fluid flows in the eye. We considered both control mice and an experimental scenario where animals were fed atRA, which increases atRA levels in the bloodstream. We conducted a global sensitivity analysis to quantify the role of uncertain model parameters. The model predicts that atRA synthesised in the choriocapillaris effectively permeates the sclera in both species at biologically relevant levels. Feeding conditions significantly increase atRA levels in the choroid and sclera. Our findings underscore the important role of atRA in retinoscleral myopigenic signalling.
CT21: 15:40-17:40, 25th June 2025, Room FOR/SR6, presentation 15:40-16:00
Andrea Giudici (University of Oxford)
Title: A reduced-order mechanical model of a pouch-cell lithium-ion battery across scales
Abstract: In a lithium-ion battery, the intercalation of lithium ions into active particles causes a variety of mechanical effects across scales. At the microscale, it causes the micrometre-sized active particles in the electrodes to expand; at the mesoscale, this expansion leads to isotropic swelling of the electrode material; and at the macroscale, it results in thickness changes and stresses that cascade back to smaller scales. Modelling the mechanics of batteries is challenging due to their inhomogeneous composition and complex layered structure. However, it is also essential for understanding how mechanical effects influence electrochemistry, degradation, and overall performance. By exploiting the slender geometry and the large contrast in elastic moduli among battery components, we employ asymptotic techniques to analytically describe the meso- and macro-scale deformation and stress states in a pouch cell battery. This stress state can be linked back to the micro-scale, allowing us to quantify the effects of the mechanics on the electrochemistry of a lithium-ion battery.
CT21: 15:40-17:40, 25th June 2025, Room FOR/SR6, presentation 16:00-16:20
Marc Suñé Simon (University of Oxford)
Title: Solving the Biharmonic problem in the tension-induced giant folding of an elastic sheet
Abstract: Tension applied to elastic sheets leads to out-of-plane deformation. When this tension is localised it induces giant folding: a small in-plane tensile deformation induces a very large angle between the edge of the sheet and the horizontal. In this talk I will focus on the methods to solve the Biharmonic equation for the Airy stress function of a planar sheet under tension. The results are then applied to determine scaling of the folding angle as a function of applied strain.
CT21: 15:40-17:40, 25th June 2025, Room FOR/SR6, presentation 16:20-16:40
Rodolfo Brandao Macena Lira (University of Bristol)
Title: Sedimentation of Elastic Filaments
Abstract: Experiments have shown that a straight elastic filament bends as it settles under gravity in a viscous fluid. Previous theoretical studies have argued that the observed bending is due to nonlocal hydrodynamic interactions between different parts of the filament. In this talk, we propose an alternative mechanism that does not rely on nonlocal effects. We employ a simpler, local model based on the Resistive Force Theory, where hydrodynamic forces depend on the local orientation and velocity along the filament. We focus on steady states, in which case our model involves a single dimensionless compliance parameter, η. Irrespective of η, the model predicts two trivial solutions, corresponding to perfectly horizontal and vertical filaments. However, for η above a critical value, a new branch of solutions emerges, corresponding to filaments exhibiting non-trivial shapes. The theoretical shapes are in good agreement with those observed in experiments. To gain further insight into our predictions, we consider the limit of flexible filaments (large η) and derive closed-form asymptotic formulae for the filament shape and settling speed.
CT21: 15:40-17:40, 25th June 2025, Room FOR/SR6, presentation 16:40-17:00
Elliot James Badcock (Imperial College London)
Title: Application of the One-Way Navier-Stokes equations to real world flows
Abstract: # Advancements in One-Way Navier-Stokes Methods for Complex Flow Stability Analysis The One-Way Navier-Stokes (OWNS) equations have emerged as a powerful tool for analyzing stability in slowly varying shear flows. These equations provide an efficient spatial marching approximation to the fully elliptic disturbance equations, with the critical advantage of resolving all one-way phenomenaâa significant improvement over the parabolised stability equations (PSE), which fail to capture small-scale disturbance phenomena and non-modal effects. Despite their effectiveness, OWNS implementations face a persistent challenge: the placement of recursion parameters that drive the parabolisation process. These flow-dependent parameters require increasingly precise calibration as spatial step size decreases. This difficulty becomes particularly acute when studying transonic boundary layer flows, where recursion parameters differ significantly between subsonic and supersonic regimes and must change continuously through the transition region. Our research makes two significant contributions to address these limitations. First, we have extended the application of OWNS beyond the canonical cases found in existing literature to non-canonical flows representative of real-world applicationsâspecifically boundary layers over true three-dimensional geometries. Second, we have developed a novel computational approach that permits significantly larger step sizes while maintaining accurate resolution of all disturbance phenomena. These advancements substantially improve the practical utility of OWNS methods by reducing computational costs and expanding their applicability to complex flow configurations. The ability to maintain accuracy with larger spatial steps represents a considerable breakthrough that enables more efficient stability analysis of aerodynamic flows in industrial applications.
CT21: 15:40-17:40, 25th June 2025, Room FOR/SR6, presentation 17:00-17:20
Matthew King (University College London)
Title: Implementation of boundary conditions along arbitrary boundaries in pseudo-spectral time domain solvers.
Abstract: We explore the implementation of Dirichlet and Neumann boundary conditions along boundaries or arbitrary shape in the first-order acoustic-wave equations within a spatio-temporal domain. While our approach is demonstrated in this context, it is more broadly applicable problems that may be solved using pseudo-spectral time domain solvers, making use of the fast Fourier transform (FFT) for accurate computation of spatial derivatives and allowing for correction terms to numerical dispersion. In these problems, typically used are boundaries that mimic free-space, such as by a perfectly matched layer, or are defined on rectangular grids and utilize sine and cosine transforms over the FFT. The method we propose allows the boundary to take any shape without introducing staircasing effects from interpreting the boundary shape along the computational grid. While the proposed method presents similarities to immersed boundary methods, we utilize properties of the pseudo-spectral time domain solver and the band-limited interpolant to ensure a solution that is supported by the discrete wavenumbers of the computational grid.
CT22: 15:40-17:40, 25th June 2025, Room FOR/SR9, presentation 15:40-16:00
Lawrence Ma (University of Bath)
Title: Modelling Arctic Sea Ice Extent Using a 1D Energy Balance Model with Parameter Optimisation
Abstract: The Arctic sea ice extent has been declining at an accelerating rate in recent years. This work analyses sea ice extent data from the National Snow and Ice Data Center (NSIDC), performing a preliminary statistical analysis and data fitting to characterise trends. Building on this, we apply the Nelder-Mead optimisation method to tune parameters within a one-dimensional energy balance model (EBM) to produce simulation results that more closely align with observed data. Results indicate that parameter optimisation can enhance model alignment with real data, though limitations remain due to inherent model assumptions. We discuss potential strategies to address these limitations in future work.
CT22: 15:40-17:40, 25th June 2025, Room FOR/SR9, presentation 16:00-16:20
Alex Ratcliffe (University of Southampton)
Title: Exact WKB Analysis of Quasinormal Modes
Abstract: Understanding how black holes interact with matter is vital to our understanding of gravity. Einsteinâs equations govern these interactions but are intractable in many cases. Progress can be made if we consider the matter as a perturbation to the black hole spacetime, then if certain symmetries exist, the perturbation can be described by quasinormal modes. Mathematically, if a small parameter exists in the problem, solving for these modes and their corresponding frequencies amounts to solving a boundary value problem (BVP) where one of the points is inside a boundary layer. Asymptotic methods are efficient at performing this boundary matching but to fully understand analytic properties we need access to all exponential orders which will dominate the frequencies when the small parameter increases. We can achieve this via the so-called Exact WKB method, which determines exact quantization conditions that solve our BVP to any perturbative or exponential order. In this talk I will demonstrate this method, devolved in collaboration with Ines Aniceto, for a simplified toy example which still retains the flavour of physically relevant black hole problems and other BVPs related to biconfluent Heun equations.
CT22: 15:40-17:40, 25th June 2025, Room FOR/SR9, presentation 16:20-16:40
Spyridon Garouniatis (University of Warwick)
Title: Large Deviations for Slow/fast systems driven by a quadratic Gaussian process
Abstract: We consider a system where the effective dynamics involve increments given by a rapidly fluctuating Gaussian process. Such systems describe various physical models that introduce quadratic non-linearity and time scale separation. Our interest lies in studying rare events in the evolution of the slow process in the regime of fast fluctuations of the driving Gaussian process. The rate function governing these rare events is expressed through an asymptotic expansion of a Fredholm determinant associated with an integral operator whose kernel has multiple jump discontinuities. Our results become explicit when the driving Gaussian process is an Ornstein-Uhlenbeck process.
CT22: 15:40-17:40, 25th June 2025, Room FOR/SR9, presentation 16:40-17:00
Samuel Brevitt (Queen Mary University of London)
Title: Multiplicity of quasi-stationary distributions in an open random dynamical system
Abstract: Consider two maps on the unit interval – one uniformly expanding, and one contracting. Iteratively, we flip a coin, and apply one map or the other. Depending on the bias of the coin, $p$, the resultant dynamics may be chaotic, contractive, or – when $p=1/2$ – weakly chaotic. In this talk we investigate the dynamics of this random map in the presence of a hole in the phase space. What we reveal is a rich phase diagram with transitions between different types of dynamics under variation of the bias $p$ and the hole size $Δ$. We show that the system hosts a continuum of infinitely many quasi-stationary distributions (QSDs), each corresponding to its own escape rate. The stability of these QSDs is investigated, demonstrating that they determine the asymptotic dynamics of this open random dynamical system.
CT22: 15:40-17:40, 25th June 2025, Room FOR/SR9, presentation 17:00-17:20
Harbir Lamba (George Mason University, Fairfax, VA, USA)
Title: Reducible cascading networks with applications
Abstract: If every node in a network has an input-output response within the class of generalized Prandtl-Ishlinskii (PI) operators, then remarkable simplifications are possible. For arbitrary network sizes and topologies (under mild additional conditions) the aggregate response of the network to an exogenous input can be rigorously reduced to that of a single (more complicated) PI node. This is true even if cascades can occur within the network and the output of the network feeds back into the input. This new PI node is completely determined by the aggregate response function of the network to a monotonic input. This function can then be used to replicate the aggregate response of the network to arbitrary continuous inputs with minimal computational effort. I shall give two examples. In the first the network represents traders who are using strategies based upon both the market price and the opinions of their network neighbours. The input to the network is the price which is in turn affected by the net buy/sell trader responses. In the second the network is an economy with the input being the inflation rate. The output of each node represents the inflation expectations of a particular sector and is based upon both the actual inflation rate and the expectations of neighbouring sectors. The aggregate inflation expectations then feed back into the actual inflation rate.
CT22: 15:40-17:40, 25th June 2025, Room FOR/SR9, presentation 17:20-17:40
Tjeerd olde Scheper (Oxford Brookes University)
Title: Towards a Proof of Rate Control of Chaos
Abstract: Rate Control of Chaos (RCC) is a control method that stabilises nonlinear dynamic systems into steady state or periodic orbits. It has been used to control toy examples of forced nonlinear oscillators and physical combustion engines, but its theoretical principles are not yet fully understood. Indeed, current applications are based upon heuristics and experimentation. RCC is also employed to create controlled scale-free nonlinear systems and as a mechanism for nonlinear representation spaces in machine learning. Developing an understanding of the mathematics that underpin RCC, therefore, promises to improve and fine-tune existing applications. The method works â in a practical sense â by adapting several terms of a system through a control function. Hence, the control becomes an integral part of the dynamic system. In particular, the control function is present globally and adapts as necessary; allowing for control of (non-)exponential contraction or expansion within an attractor. The control function itself introduces various control parameters, each of which appear to adapt the topology of the system, and numerical simulation has demonstrated various controlled phenomena with appropriate parameter choices. In this talk, RCC and some of its applications will be reviewed before discussing the current understanding of the ongoing work towards building an understanding of the underlying mathematical aspects of RCC, as well as some indications for exciting possible avenues for further research.
CT23: 15:40-17:40, 25th June 2025, Room FOR/SR10, presentation 15:40-16:00
Supawit Petpradittha (University of Manchester)
Title: The propagation of topological defects in cellular monolayers.
Abstract: Within epithelial monolayers, T1 transitions are the main mechanism for cellular neighbour exchange, a fundamental process in tissue development and tissue plasticity. Moreover, under external loading such as shear displacement, the propagation of T1 transitions is intimately linked to the motion of topological defects across a monolayer. Although there have been studies on how cellular tissue responds to external loads where T1 transitions are allowed to occur, the relationship between loading and defect motion remains poorly understood. In this work, using the 2D vertex model, we explore how topological defects due to T1 transitions move in monolayers under external loads, finding that they can propagate along the boundary or the lattice directions of an initially periodic hexagonal monolayer depending on the direction of the loads imposed. Furthermore, in periodic hexagonal lattice monolayers of two rows, defects propagate with constant speed or get trapped, depending on constitutive parameters. Our simulations and low-order models characterise the motion of topological defects in monolayers and may help us address interactions between topological defects in more realistic disordered materials.
CT23: 15:40-17:40, 25th June 2025, Room FOR/SR10, presentation 16:00-16:20
Sara Drummond-Curtis (UCL)
Title: A quadrupole model for multi-timescale microswimmers near a boundary
Abstract: Although the presence of boundaries can significantly affect microswimmer trajectories, simple swimmer models typically assume the swimmer is in the far field and neglect near-field effects for convenience. In this talk, we show the importance of modelling the hydrodynamics near the boundary for rapidly deforming microswimmers. By incorporating a higher order singularity into our model, we can better see the impact of the boundary as the swimmer approaches it. We also account for the effect of the rapid deformation of the swimmers by exploiting the separated timescales with multiscale analysis, which extends our parameter space and causes different dynamics to emerge. Together, we use these changes in our model to show qualitatively different behaviour in a large proportion of the parameter space when compared to the dynamics predicted by the simple swimmer models.
CT23: 15:40-17:40, 25th June 2025, Room FOR/SR10, presentation 16:20-16:40
Anushka Herale (University College London)
Title: A minimal continuum model of clogging in spatio-temporally varying channels
Abstract: Particle suspensions in confined geometries exhibit rich dynamics, including flowing, jamming, and clogging. It has been observed that jamming and clogging in particular are promoted by variations in channel geometry or fluid material properties – such variations are often present in industrial systems (e.g. local confinements) and biological systems (e.g. stiffening of red blood cells in deoxygenated conditions in sickle cell disease). The aim of this talk is to shed light on the macroscopic dynamics of particulate suspensions in these conditions. To this end, we present a continuum two-phase model of particle suspensions based on granular rheology that accounts for spatio-temporally varying material properties or channel geometries. The model comprises a continuous particle phase which advects with flow and has material properties dependent on the particle volume fraction, and a suspending fluid which flows through the particle phase obeying Darcyâs law. We solve the system using a finite-volume method and simulate the evolution of an initially uniform particle density. We find that varying material properties and varying geometry can induce heterogeneity in particle volume fraction. We are able to show the emergence of high and low particle density regions in volume-driven flows. These results clarify how spatial variation in material and channel properties can contribute to clogging of particle suspensions.
CT23: 15:40-17:40, 25th June 2025, Room FOR/SR10, presentation 16:40-17:00
Gareth Jenkins (UCL)
Title: A model for the evidence dynamics of forensic trace materials
Abstract: Microscopic particles of contraband materials can be deposited onto surfaces via fingerprints, and these trace evidence samples can then be analysed to infer key details of suspected criminal activities. A forensic reconstruction such as this will be more robust if we can develop an understanding of how these materials behave. We are working towards a model which can replicate the transfer patterns found in experimental data of crystalline explosive particles. We use a coarse-grained model for the crystalline particles, approximating them as aggregates of elastic spheres with breakable bonds. In this talk we cover the methodology of this model, and discuss insights made about transfer patterns.
CT23: 15:40-17:40, 25th June 2025, Room FOR/SR10, presentation 17:00-17:20
Norberto Lucero Azuara (Queen Mary University of London)
Title: Constructing two dimensional stochastic processes in a comoving frame
Abstract: How do living organisms navigate their environment? While random walk models, provide a foundation for understanding biological movement, they fall short in capturing the active control exerted by living organisms. This study explores stochastic processes in two dimensions, defined in the Cartesian frame and how they transform into the comoving frame, which better represents the organismâs perspective. By examining probability distributions, autocorrelations, and dynamical equations, we uncover key features of these processes in the comoving frame. For the example of the Ornstein-Uhlenbeck process we propose two simple equations in the comoving frame that replicate the stochastic behavior observed in the Cartesian frame, offering new insights into modeling active biological movement.
CT23: 15:40-17:40, 25th June 2025, Room FOR/SR10, presentation 17:20-17:40
Naratip Santitissadeekorn (University of Surrey)
Title: Influence network reconstruction from discrete time-series of count data modelled by multidimensional Hawkes processes
Abstract: Identifying key influencers from time series data without a known prior network structure is a challenging problem in various applications, from crime analysis to social media. While much work has focused on event-based time series (timestamp) data, fewer methods address count data, where event counts are recorded in fixed intervals. We develop network inference methods for both batched and sequential count data. Here the strong network connection represents the key influences among the nodes. We introduce an ensemble-based algorithm, rooted in the expectation-maximization (EM) framework, and demonstrate its utility to identify node dynamics and connections through a discrete-time Cox or Hawkes process. For the linear multidimensional Hawkes model, we employ a minimization-majorization (MM) approach, allowing for parallelized inference of networks. For sequential inference, we use a second-order approximation of the Bayesian inference problem. Under certain assumptions, a rank-1 update for the covariance matrix reduces computational costs. We validate our methods on synthetic data and real-world datasets, including email communications within European academic communities. Our approach effectively reconstructs underlying networks, accounting for both excitation and diffusion influences. This work advances network reconstruction from count data in real-world scenarios.
CT24: 10:30-11:30, 26th June 2025, Room PCC/1.1-2, presentation 10:30-10:50
Georgia Lupton (University of Liverpool)
Title: Boundary representations of anisotropic power diagrams
Abstract: Typically, when finding the boundaries of an anisotropic power diagram, methods evaluate the points on the boundary of each cell which give a discretised version of the boundaries. Deriving analytical boundaries can be challenging. A recently introduced method for computing the analytical boundary of 2D anisotropic power diagrams has a time complexity of $O(n^4)$, where $n$ represents the number of cells. While this approach successfully determines the boundaries, its high computational cost makes it inefficient for large cell counts. Therefore, in my talk, I will discuss a new algorithm which implements a sweep circle to reduce the time taken for a large number of cells. I will also show how this approach is adaptable for other tessellations and metrics.
CT24: 10:30-11:30, 26th June 2025, Room PCC/1.1-2, presentation 10:50-11:10
Kawa Manmi (University of Warwick)
Title: Simplified Models for Understanding Battery SEI Layer Growth
Abstract: The solid electrolyte interphase (SEI) is a crucial protective layer that forms primarily on the negative electrode of lithium-ion batteries during early cycling, particularly in the manufacturing formation and aging process. This layer continues to grow slowly throughout the battery’s life as a major degradation mechanism. The properties of the SEI fundamentally impact battery performance, including irreversible capacity loss, rate capability, cycling stability, and safety. Due to the layer’s inherent complexity – with its heterogeneous composition, spatiotemporal evolution, and multiple length scales – both experimental investigation and mathematical modelling of SEI formation and growth remain challenging. Zero-dimensional models have emerged as a computationally efficient approach to capture the essential physics while reducing this complexity. This talk will first compare common zero-dimensional SEI growth models in the context of both formation and normal cycling conditions. The second part will introduce our ongoing work with collaborators at WIAS Berlin on developing new mathematical frameworks based on non-equilibrium thermodynamics to better describe SEI evolution. This work aims to bridge the gap between simplified zero-dimensional models and the underlying physical processes governing SEI formation and growth.
CT24: 10:30-11:30, 26th June 2025, Room PCC/1.1-2, presentation 11:10-11:30
Aigerim Saken (University of Liverpool)
Title: Anisotropic Power Diagrams for Modelling Polycrystalline Structures and Beyond
Abstract: Polycrystalline materials, including metals, alloys, ceramics, and rocks, consist of a network of crystalline grains whose geometry strongly influences their physical, chemical, and mechanical properties. Accurately analyzing, visualizing, and simulating these grain structures is essential for understanding and optimizing material behavior. While classical Voronoi diagrams have long been used to model such networks, they often impose overly simplistic assumptions. Recent advances have demonstrated that Generalized Balanced Power Diagrams (GBPDs) provide significantly more accurate representations, particularly in anisotropic settings where grains exhibit direction-dependent properties. This talk will introduce the GBPD framework, discuss its advantages over traditional models, and showcase its application to large-scale 3D polycrystal datasets. Beyond materials science, GBPDs also offer promising applications in image segmentation, where accurate partitioning of spatial data is crucial. By leveraging anisotropic properties, they provide a flexible tool for various computational geometry problems. I will present our latest computational results, highlight key challenges, and discuss future directions for using anisotropic power diagrams in both material modeling and image processing.
CT26: 10:30-11:30, 26th June 2025, Room PCC/2.1-2, presentation 10:30-10:50
Keren Tapper (University of Edinburgh)
Title: A Multiscale Model for a Split Area Fishery with Periodic Fishing Efficiency
Abstract: The traditional fisheries of the Haenyeo Divers in the Jeju region of Korea are seeing a reduction in fishing output due to competition between fishing and tourism. We consider an ODE model for the total benefit to the Haenyeo community which assumes that the fishery is spread into two separate areas for these two competing activities. Under the additional assumption that migration between the two areas is fast, the model equations are singularly perturbed and can be analysed via an application of the dynamical systems-based geometric singular perturbation theory. This approach allows us to reduce the long-term dynamics of the model solutions to the dynamics on a globally attracting slow manifold. Finally, we extend the model by introducing seasonality of the fishing efficiency, modelled via a piecewise periodic function. By applying the desingularisation technique, known as “blow-up”, we regularise and analyse the transition between the two parts of the seasonality dynamics.
CT26: 10:30-11:30, 26th June 2025, Room PCC/2.1-2, presentation 10:50-11:10
Jared Carpenter (University of East Anglia)
Title: The stability of nanobubbles in plant xylem
Abstract: Plants transport water, nutrients and signalling molecules via their vascular system. To successfully carry out this transport, plants must overcome several physical challenges. For instance, the transportation of water from the root to the shoot is driven by transpiration and occurs in the xylem. This process operates under absolute negative pressure, which is a metastable state and can induce nanobubble (bubbles between 50 and 200nm in diameter) formation. These nanobubbles can be detrimental to the plant because they have the potential to form an embolism in the plant xylem. Plants therefore need to balance these physically dangerous conditions with their needs for water, nutrient acquisition and signalling. How plants meet these conflicting demands is currently unknown. I will present current ideas and approaches for addressing this fascinating problem. One hypothesis is that plants utilise polar lipids (surfactants) on the nanobubble surface to induce a variable surface tension which helps to break down the bubble. However, the conditions for this break-up are unknown. We model the xylem as a Stokes flow containing the nanobubble, introduce surfactants and apply linear stability theory to the governing system of partial differential equations to examine the stability of the bubble by perturbing its radius. We then determine under what conditions the bubble will remain in a stable state or will become unstable and break up. This analysis sheds light on the process by which plants can avoid the harmful situation of embolism formation in the xylem.
CT26: 10:30-11:30, 26th June 2025, Room PCC/2.1-2, presentation 11:10-11:30
Galane Luo (University of Birmingham)
Title: Mechanics of the plant cell wall and twisting morphologies
Abstract: The cell wall is a complex material comprising a pectin ground matrix reinforced by cellulose microfibrils which dynamically reorient during wall deformation. The wallâs plastic, anisotropic deformation under constant turgor pressure amounts to growth of the cell. Understanding the mechanical underpinnings of wall extension, and hence plant growth, is important for food security and sustainable development. By combining the theories of transversely isotropic fluids, pressure-driven viscous sheets, and dynamic fibre-reorientation, a modelling framework has been developed to explain the growth mechanisms of slender plant organs. This talk will showcase the modelling framework and the latest theoretical advances with experimental backing, including a generalised Lockhart equation that accounts for helical organisations of cellulose, leading to an explanation of twisting morphologies. Various industries are interested in understanding and controlling twisting morphologies in plants; for example, spiral grain in forestry, and twisting mutants in agriculture.
CT27: 10:30-11:30, 26th June 2025, Room PCC/2.5-6, presentation 10:30-10:50
Harry Stuart (University of Oxford)
Title: Models for subglacial floodwave dynamics in the event of supraglacial lake drainages
Abstract: Due to warming climates, meltwater lakes are forming on the surface of Greenland at higher altitudes. These lakes may drain to the bedrock where they then propagate horizontally resulting in hydraulic jacking of the ice sheet. This causes surface uplift and can result in a short term increase of ice sliding speeds. It is not well understood how such events affect the larger scale annual evolution of the subglacial drainage system. Models to capture this behaviour are presented by making use of the theory of hydrofracture. First, a radial axisymmetric model is formed that demonstrates expected early time behaviour for a lake drainage in a largely flat environment. Then symmetry is broken for a planar scenario in which the ensuing floodwave propagates down-glacier. Results of the model are presented and compared to observations of GPS stations placed near draining lakes. Results are also compared to observations from remote sensing of ice surface velocities to characterise the propagation velocity of floodwaves beneath the ice.
CT27: 10:30-11:30, 26th June 2025, Room PCC/2.5-6, presentation 10:50-11:10
Chenyang Ren (University of Manchester)
Title: Dynamics of evaporating, interconnected droplets
Abstract: We report on the dynamics of a pair of droplets, connected together by a microchannel and undergoing constant contact radius evaporation. We see that for droplets of equal contact radii, unidirectional flow can arise from differences in droplet geometry and results in larger droplet feeding the smaller droplet as they evaporate out. However, for droplets of unequal contact radii, the shape of the droplet pair can invert, during the evaporation process, causing a reversal in the flow direction during the evaporation process. A stability analysis shows that the dropletsâ transportation on a short-time scale is underpinned by a supercritical pitchfork bifurcation. However, over a long time-scale, the loss of volume to evaporation allows the system to step through a series of states, corresponding to quasi-steady solutions of the droplet geometry on a short-time scale. If the symmetry of the contact radii is broken, the supercritical pitchfork bifurcation unfolds. Thus, we show that the droplet shape inversion and the associated flow reversal can be understood as a jump from the disconnected to connected branch of the bifurcation. This work establishes symmetry breaking as a mechanism to induce evaporation-driven flow reversal in connected droplets.
CT27: 10:30-11:30, 26th June 2025, Room PCC/2.5-6, presentation 11:10-11:30
Christian Vaquero-Stainer (Okinawa Institute of Science and Technology)
Title: Marangoni bursting of a non-volatile droplet on a liquid interface
Abstract: The surface-tension driven spreading of an immiscible liquid on the surface of another is a ubiquitous phenomenon in nature. It is a well-studied problem, and yet several key phenomenon remain open questions. When a droplet of liquid is deposited onto the surface of another immiscible liquid, the droplet will either spread (or contract) transiently to form a stable liquid lens, or it will continuously spread over time. This is determined by the spreading parameter S; for S>0, the liquid will continuously spread, since the combined surface and interfacial tensions of the deposited liquid cannot balance the surface tension of the underlying fluid. If the deposited liquid also acts as a surfactant, there are additional dynamics introduced owing to the Marangoni stress induced by concentration-dependent surface-tension. Recent studies have focussed on the spreading and stability of the spreading surfactant. It has been observed that for volatile liquids, the âMarangoni burstingâ phenomenon can occur (Keiser et al. 2017, Jaberi 2023), whereby the spreading surfactant breaks up into chains of daughter droplets due to thickness-dependent evaporation which alters the Marangoni stress. In this study, we examine the spreading dynamics of a non-volatile surfactant through a combination of experiments, theoretical analysis and direct numerical simulation. We explore the spreading rates in such a scenario, and elucidate the underlying mechanisms behind the droplet breakup driven only by viscous and capillary forces in the absence of evaporation.
CT28: 10:30-11:30, 26th June 2025, Room FOR/EXP2, presentation 10:30-10:50
Zoe Leibowitz (Imperial College London)
Title: Automatic Generation of Matrix-Free Routines for PDE Solvers with Devito via PETSc
Abstract: Traditional numerical solvers are often optimized for specific hardware architectures, making their adaptation to new computing environments challenging. The rapid evolution of hardware increases the complexity of rewriting and re-optimizing these solvers. By combining domain-specific languages (DSLs) with automated code generation, the level of abstraction is raised, enabling the generation of high-performance code across diverse hardware architectures. Moreover, providing users with a high-level problem specification facilitates the development of complex PDE solvers in a form closer to continuous mathematics, reducing code complexity and maximizing reuse. Devito, a DSL and compiler for finite-difference solvers, has been extended to integrate iterative solver functionality through an interface with the Portable Extensible Toolkit for Scientific Computing (PETSc), enabling the generation of solvers for various computational fluid dynamics (CFD) problems. As an industry-standard framework, Devito automates the generation of highly optimized explicit finite-difference kernels and stencil computations and has been extensively used in large-scale seismic inversion and medical imaging applications. The new developments introduce automatic generation of matrix-free routines in Devito, allowing interaction with PETScâs extensive suite of existing solvers. Key enhancements include support for iterative solvers, implicit time-stepping, coupled solvers, and matrix-free preconditioning. These features are fully integrated into Devitoâs symbolic API while maintaining compatibility with staggered grids, subdomains, and custom stencils. This work expands Devitoâs capabilities, enabling it to address a broader range of high-performance computing challenges, including incompressible flow problems in CFD. The new framework is demonstrated through benchmark simulations, including the backward-facing step and flow around a cylinder.
CT28: 10:30-11:30, 26th June 2025, Room FOR/EXP2, presentation 10:50-11:10
Jens Persson (Mid Sweden University, Sweden)
Title: Two-scale convergence, periodic unfolding and amplified sequences
Abstract: We trace two-scale convergence and periodic unfolding back to the more general concept of general two-scale convergence governed by a two-scale operator. Furthermore, we regard sequences bounded in Sobolev spaces and their gradients in the context of both two-scale convergence and periodic unfolding. This leads us to a comparison between very weak two-scale convergence and periodic unfolding in the setting of sequences amplified by the scale parameter, a situation that occurs, e.g., in the homogenization of problems involving both spatial and temporal micro-oscillations. Such approaches may provide alternative ways to characterize the nature of micro-oscillations.
CT28: 10:30-11:30, 26th June 2025, Room FOR/EXP2, presentation 11:10-11:30
Cameron Hall (University of Bristol)
Title: Clustering approaches for power grid networks
Abstract: In a wide variety of applications, valuable insights into data can be gained by identifying clusters of datapoints that are “close” to each other under some metric. In the specific context of power system stability modelling, it is useful to identify sets of generators that are “coherent” with each other, in the sense that they respond similarly when the power grid is disturbed. Unfortunately, there is no single (coherent?) definition of coherency in the power systems literature that can be used efficiently and without ambiguity to construct sets of coherent generators. In this talk, I will discuss how ideas from unsupervised learning (particularly clustering methods) can be applied to the problem of defining coherency and identifying sets of coherent generators in power grid networks. In particular, I will discuss the possibility of using realisation (based on Schoenberg, Young, and Householder’s work on distance matrices from the 1930s) as a useful tool for analysing datasets where the distances between datapoints can be determined but there is no physically-meaningful space in which the data are embedded.
CT29: 10:30-11:30, 26th June 2025, Room FOR/SR7-8, presentation 10:30-10:50
Ruibo Kou (Department of Mathematics, University of Warwick)
Title: The Stochastic Casimir Effect
Abstract: We model the one-dimensional âclassicalâ vacuum by a system of annihilating Brownian motions on R with pairwise immigration. A pair of reflecting or absorbing walls placed in such a vacuum at separation L experiences an attractive force which decays exponentially with L. This phenomenon can be regarded as a purely classical Casimir effect for a system of interacting Brownian motions.
CT29: 10:30-11:30, 26th June 2025, Room FOR/SR7-8, presentation 10:50-11:10
Charlie Cameron (University of Bath)
Title: Spatially adaptive hybrid model
Abstract: This paper introduces a novel hybrid modelling approach for one-dimensional, one-species reaction-diffusion systems, combining stochastic and deterministic methods to optimise simulations of reaction diffusion systems. This model aims to develop a framework to simulate complex systems in which stochasticity is important to capture, however is unfeasible when the particle count is high. The model automatically adapts to concentration levels across the domain, using the Stochastic Simulation Algorithm (SSA) in regions where particle counts are low, while switching to computationally efficient partial differential equations (PDEs) in areas with higher concentrations. Moment-closure method is employed to provide an equivalence framework between the stochastic reaction network and a corresponding PDE. Our regime conversion method eliminates the need for a user-defined interface between high- and low-concentrations. This automatic adaptability is particularly valuable, enabling the model to be applied to a variety of systems without manual spatial adjustments. We focus on a single species, demonstrating the efficiency and reliability of our methods on systems ranging from one-dimensional diffusion to the Fisher-KPP equation. Our approach offers an efficient, flexible, and scalable framework for simulating reaction-diffusion dynamics in reaction-diffusion, overcoming the limitations of traditional hybrid models.
CT29: 10:30-11:30, 26th June 2025, Room FOR/SR7-8, presentation 11:10-11:30
Gianluca Audone (Politecnico di Torino)
Title: Variably Scaled Kernels: Adaptive Strategies for Complex Data Modeling
Abstract: Variably Scaled Kernels (VSKs) have shown considerable promise within Gaussian Process (GP) regression frameworks, offering enhanced flexibility by adapting to local data characteristics. Unlike traditional stationary kernel approaches, the effectiveness of VSK methods critically depends on the choice of an appropriate scaling function, which modulates kernel behavior to reflect spatially varying smoothness and discontinuities. This work investigates the application of VSKs in GP regression, emphasizing the crucial role played by scaling functions. While the potential of scaling functions to mirror the behavior of target phenomena and improve approximation accuracy has been suggested, rigorous theoretical justification within GP contexts remains under-explored. Addressing this gap, we propose adopting a data-driven strategy, leveraging neural networks to learn optimal scaling functions directly from observational data. Initial results indicate that such learned scaling functions closely align with underlying data patterns, significantly enhancing interpolation accuracy and modeling performance compared to traditional stationary kernels. The preliminary outcomes presented here support the viability of this adaptive, data-driven approach for scaling function selection, suggesting substantial improvements in Gaussian Process regression capabilities and highlighting avenues for future theoretical and practical exploration.
CT30: 10:30-11:30, 26th June 2025, Room FOR/SR4, presentation 10:30-10:50
Bernhard Scheichl (Institute of Fluid Mechanics and Heat Transfer, TU Wien (Vienna, Austria))
Title: Stewartson’s collision problem on a sphere and on spheroids
Abstract: We consider the flow induced by a rigid sphere and, in an extension of our study, oblate/prolate spheroids spinning about their axes of rotational symmetry in an otherwise quiescent Newtonian fluid of uniform properties that fills an unbounded domain. Here we distinguish between the unsteady flow due to (impulsive) start-up from rest and the (asymptotically attained) steady one. The associated Reynolds number (Re), as the only parameter at play, shall take on arbitrarily large values. We tackle this classical problem by solving the full Navier-Stokes equations numerically using a finite-volume technique as well as by rigorous asymptotic analysis. The most intriguing and still controversially debated questions concern the existence of a steady state for all values of Re and here specifically of two symmetric toroidal vortices astride the equatorial plane, engendered by the colliding longitudinal wall jets that emanate from the poles. Stewartson (1958) proposed a structure of stationary collision, but its self-consistent completion faces severe challenges. In contrast to claims made very recently, we demonstrate theoretically why Smith & Duck’s (1977) conflicting alternative structure, resorting to free viscous-inviscid interaction, is to be favoured. However, we furthermore show the inexistence of a perfectly stationary flow. This is also substantiated by our detection of an upper bound of Re for stationarity, the equatorial finite-time break-up that terminates the solution of the wall layer problem and the first steps of its regularisation, revealing a permanently unsteady radially ejected jet. This research is jointly with Christian Klettner and Frank T. Smith (both UCL).
CT30: 10:30-11:30, 26th June 2025, Room FOR/SR4, presentation 10:50-11:10
Azza Algatheem (University of Bisha)
Title: Interaction Between Two Rigid Hydrophobic Spheres Oscillating in an Infinite BrinkmanâStokes Fluid
Abstract: This study investigates the dynamics of two oscillating rigid spheres moving through an infinite porous medium saturated with Stokes fluid flow, addressing the problem of how fluid properties, permeability, frequency, and slip length influence the system The objective is to model the interactions between the spheres, which differ in size and velocity as they move along the axis connecting their centers while applying slip boundary conditions to their surfaces. We derive the governing field equations using a semi-analytical method and solve the resulting system of equations numerically through a collocation technique. Our novel quantitative results include insights into the drag force coefficients for both in-phase and out-of-phase oscillations of each hydrophobic sphere, considering parameters such as diameter ratio, permeability, frequency, velocity ratios, slip lengths, and the distances between the spheres. Notably, when the spheres are sufficiently far apart the normalized drag force coefficients behave as if each sphere is moving independently. Additionally, we present streamlines that illustrate the interactions between the spheres across a range of parameters, highlighting the novelty of our findings.
CT30: 10:30-11:30, 26th June 2025, Room FOR/SR4, presentation 11:10-11:30
Anand Oza (New Jersey Institute of Technology)
Title: Waves and interaction modes of capillary surfers
Abstract: We present the results of a combined experimental and theoretical investigation into “capillary surfers,” which are millimetric objects that self-propel while floating at the interface of a vibrating fluid bath. Recent experiments showed that surfer pairs may lock into one of seven bound states, and that larger collectives of surfers self-organize into coherent flocking states. Our theoretical model for the surfers’ positional and orientational dynamics approximates a surfer as a pair of vertically oscillating point sources of weakly viscous gravity-capillary waves. We derive an analytical solution for the associated interfacial deformation and thus the hydrodynamic force exerted by one surfer on another. Our model recovers the bound states found in experiments and exhibits good quantitative agreement with experimental data. Generally, our work shows that self-propelling objects coupled by interfacial flows constitute a promising platform for studying active matter systems in which both inertial and viscous effects are relevant.
CT31: 10:30-11:30, 26th June 2025, Room FOR/SR5, presentation 10:30-10:50
Taysir Dyhoum (Manchester Metropolitan University)
Title: Comparing the Effectiveness of Using I and C Spatial Statistics as Tools to Assess Heterogeneity for Gastric and Rectal Cancer Biomedical Images
Abstract: Histopathologists frequently obtain biopsies, which yield imaging data. The images are evaluated to produce several diagnostic summaries, such as the proportion of the tumor. They are also analyzed by superimposing a standard grid of points, which are then classified. Histopathologists can use this classification to estimate the proportion of tumors and other statistical measures and likelihoods. For the first time, this work investigates the heterogeneity of (rectum and stomach cancer) images by applying two spatial clustering measures to the classified points and determining the most appropriate spatial autocorrelation statistical tool. We examine the effectiveness of Moranâs I statistical measurement on a large sample set and conclude that it is the best instrument for assessing heterogeneity/clustering in several directions. We are researching the link between cluster orientation and lumen surface, an important pathogenic feature.
CT31: 10:30-11:30, 26th June 2025, Room FOR/SR5, presentation 10:50-11:10
Bethel Agozie (University of Glasgow)
Title: Blood Flow in a Vessel with Rapid Change in Stiffness
Abstract: Blood flow in veins and arteries is strongly dependent on the non-linear mechanical properties of the vessels. In particular, rapid changes in the mechanical properties of vessels can result in resonant-like behaviour, leading to complicated wave solutions. Motivated by applications to retinal haemorrhage, we consider blood flow in an elastic vessel with a sudden jump in stiffness. Theoretical flow solutions have been previously investigated for this situation, but only in a limited range of the parameter space, which is not suitable for many practical applications. In this talk, we discuss a methodology for exploring the parameter space further, allowing us to reach regions of the parameter space suitable for applications. We describe the nature of the resonant solutions that arise due to the jump in stiffness and discuss how these solutions behave across the parameter space as a function of the elastic properties of the vessel.
CT31: 10:30-11:30, 26th June 2025, Room FOR/SR5, presentation 11:10-11:30
Joshua Bull (University of Oxford)
Title: The good, the bad, and the vasculature: spatial models of tumour-macrophage-vessel interactions
Abstract: Interactions between a growing tumour and the surrounding microenvironment can determine disease progression and treatment efficacy. Key to this is the interplay between the tumour and the immune system, as well as structural elements such as the extracellular matrix and blood vessels. While the immune system should provide a defence against disease, in cancer it can be hijacked to aid tumour growth instead of eliminating cancerous cells. Here, we focus on how tumours reprogram macrophages, a key immune cell type, to help individual tumour cells migrate towards nearby blood vessels and escape into the vasculature. Just as macrophages may be either beneficial or detrimental to tumour cells depending on their phenotype, the surrounding vasculature can either help or hinder the tumour. Blood vessels act as a source of anti-tumour immune cells, which are recruited from the vasculature, but also as a source of oxygen and nutrients that encourage tumour growth. Finally, in the presence of a sufficiently high density of perivascular macrophages or tumour cells, local pressure accumulation around a blood vessel can cause it to become occluded, preventing it acting as a source of either oxygen or immune cell extravasation. In this talk, we consider two spatially resolved models of this system: a complex ABM, and a simpler surrogate model consisting of a system of ODEs. We discuss the relative merits of the two models, and use them to explore how the spatial interplay between macrophages, vessels, and tumour growth influences tumour progression and simulated treatments.