BMC-BAMC 2025
BMC-BAMC 2025
We list minisymposia (MS) sessions with their draft timings. The sessions are as follows:
| Code | Session Title | Timing | Organizer(s) |
| MS01 (PCC/1.1-2) | Mathematical Insights in Neuroscience: From Theory to Reality | Day1PM | Kateryna Nechyporenko, Nicolas Verschueren van Rees (Exeter) |
| MS02 (PCC/1.1-2) | Hydrogel Dynamics | Day2PM | Tom Montenegro-Johnson, Ellen Jolley, Danny Booth (Warwick) |
| MS03 (PCC/1.1-2) | Inverse Problems and AI | Day2AM | Taysir Dyhoum (Manchester Metropolitan) |
| MS04 (PCC/1.5-6) | Mathematical Modelling of Radiation | Day1PM | Veronika Chronholm, Aaron Pim, Matt Evans, Daniel Hajnal (Bath) |
| MS05 (PCC/1.5-6) | Waves and metamaterials | Day2PM | Bryn Davies (Warwick), Gregory Chaplain (Exeter), Tristan Lawrie (Nottingham) |
| MS06 (PCC/2.1-2) | Modelling and quantifying pattern in living tissues | Day1PM | Giulia Celora (Oxford), Joshua Bull (Oxford) |
| MS07 (PCC/2.5-6) | At the interface between modelling, simulation and control of multi-fluid systems | Day1PM | Radu Cimpeanu, Susana Gomes (Warwick) |
| MS08 (FOR/EXP2) | Novel mathematical models and methods in ecology | Day1PM | Eduard Campillo-Funollet (Lancaster), James Van Yperen (Sussex) |
| MS09 (PCC/1.5-6) | Dynamics and asymptotics in biological media | Day2AM | Andrew Krause, Denis Patterson, Luci Mullen (Durham) |
| MS10 (PCC/1.1-2) | Dynamics on Complex Networks | Day3AM | Andrew Nugent (Warwick) |
| MS11 (PCC/1.1-2) | Multiscale modelling: Real world applications in solid and fluid mechanics | Day3PM | Laura Miller (Strathclyde), Raimondo Penta (Glasgow) |
| MS12 (FOR/SR7-8) | Mathematical models of plasticity | Day1PM | Ed Brambley, Tom Hudson (Warwick) |
| MS13 (PCC/2.1-2) | Mathematical modelling in cancer | Day2PM | Nicholas Harbour (Nottingham) |
| MS14 (PCC/1.5-6) | Oscillator Models in Biology | Day3AM | Daniel Galvis, Jake Ahern (Birmingham) |
| MS15 (PCC/2.1-2) | Mathematical and Computational Modelling of Heterogeneous and Multiscale Biological Tissues | Day3AM | Mariam Almudarra, Zita Borbala Fulop, Alejandro Roque-Piedra (Glasgow) |
| MS16 (NEW/BLU) | Queer, Equality, and Diversity | Day3PM | Lena Payne (Kent), Kat Phillips, Elliot Vincent (Warwick), Adam Onus (QMUL), Jenny Ward (Sussex), Luciano Rila (UCL) |
| MS17 (PCC/2.1-2) | Mathematics of Astrophysical Phenomena: Theory and Numerical | Day3PM | Manohar Kalluri, Velizar Kirkow (Exeter) |
| MS18 (PCC/2.1-2) | Autonomous dynamics and design principles of shape morphing materials | Day2AM | Jack Binysh (Amsterdam), Sami Al-Izzi (New South Wales), Anton Souslov (Cambridge) |
| MS19 (PCC/2.5-6) | Analytical Methods in Wave Phenomena | Day3PM | Elena Medvedeva, Andrey Korolkov (Manchester) |
| MS20 (PCC/2.5-6) | New Directions in Theoretical and Applied Inverse Problems | Day3AM | Bill Lionheart, Sean Holman (Manchester) |
| MS21 (PCC/2.5-6) | Spatial and temporal models of ecology and evolution | Day2PM | Thomas Tunstall, Wolfram Moebius (Exeter), Tim Rogers (Bath) |
| MS22 (PCC/2.5-6) | Computational Analysis of Neural Models | Day2AM | Huda Mahdi (Exeter) |
| MS23 (FOR/EXP2) | Biological Fluid Mechanics (Part 2): Microbiology | Day3AM | Mariia Dvoriashyna (Edinburgh), Jennifer Tweedy (Bath), Igor Chernyavsky (Manchester), Philip Pearce (UCL) |
| MS24 (FOR/EXP2) | Latest Advances in Mathematical Modelling of Neuroendocrinology and Beyond | Day2PM | Saeed Farjami (Exeter) |
| MS25 (FOR/EXP2) | Biological Fluid Mechanics (Part 1): Physiology | Day2AM | Mariia Dvoriashyna (Edinburgh), Jennifer Tweedy (Bath), Igor Chernyavsky (Manchester), Philip Pearce (UCL) |
| MS26 (FOR/SR7-8) | Nonlinear and stochastic dynamics in weather and climate science | Day2AM | Frank Kwasniok (Exeter) |
| MS27 (FOR/EXP2) | Prize winners from the 2025 IMA Lighthill Thwaites Prize | Day3PM | Alan Champneys (Bristol) |
MS01: 15:10-17:10, 23rd June 2025, Room PCC/1.1-2, presentation 15:10-15:30
Kateryna Nechyporenko (University of Exeter)
Title: Switching States: Heteroclinic Cycles as Organising Centres of Mean-Field Neuronal Dynamicsâ
Abstract: Neuronal networks often exhibit transitions between high and low activity regimes, known as up and down states. These states reflect large-scale, coordinated dynamics across populations of neurons, rather than the behaviour of individual cells. Such transitions are thought to be fundamental to how the brain processes information, filters sensory input, and consolidates memories, particularly during deep sleep and other low-arousal states. The precise mechanisms that control switching between different states are not fully understood and likely due to neuronal network properties. Here, we reveal an organising centre that governs these transitions, using a combination of bifurcation analysis and simulations of mean-field neuronal network models. Our analysis demonstrates that the dynamic structures we identify are general across established mean-field models of neural population activity, including the Wilson-Cowan, Tsodyks-Makram and Jansen-Rit frameworks, underscoring their universality. Our findings shed light on how this organising centre gives rise to distinct patterns of network activity, controlled by the dynamic balance between excitatory input and average connectivity (synaptic) strength that is a fundamental principle underpinning large-scale brain dynamics.
MS01: 15:10-17:10, 23rd June 2025, Room PCC/1.1-2, presentation 15:30-15:50
Oliver Cattell (University of Nottingham)
Title: Travelling fronts in a generalised neural field model that couples to the extracellular space
Abstract: Continuum models of cortical activity often take the form of integro-differential equations known as neural fields. These models are known to support travelling fronts, with front speed strongly dependent on the threshold of the firing rate activation function. However, these models ignore ion exchange with the extracellular space, which is known to play a role in several pathological behaviours. For example, in diseases such as migraine or epilepsy, large slow-moving waves in the extracellular ion concentrations known as spreading depression occur. The large concentration gradient induced by such a wave can force neurons into depolarisation block and prevent normal firing. To explore the role that the extracellular space has on the spatiotemporal patterns seen in cortex, we construct a simplified model of a scalar neural field with a Heaviside firing rate and threshold that is dependent upon ion concentration in the extracellular space. This is a proxy for changes in neuronal excitability driven by extracellular ionic concentrations. The transport of ions in the extracellular space is assumed to be via diffusion. In a single spatial dimension, we derive an expression for the front speed using an interface dynamics approach. We show how the front speed is modulated by the rate of diffusion. We also numerically investigate the propagation of fronts in two spatial dimensions and relate this to experimental data.
MS01: 15:10-17:10, 23rd June 2025, Room PCC/1.1-2, presentation 15:50-16:10
Matteo Martin (University of Padova, Department of Information Engineering)
Title: Folded singularities: Insights and predictions of subthreshold oscillations in single-cell intracellular recordings
Abstract: Experimental recordings from single neurons and astrocytes have revealed the presence of complex dynamics, including oscillations with varying amplitudes. However, due to their delicate nature and instrumental limitations, these small fluctuations are often regarded as noise. Despite this initial interpretation, whole-cell models and theories on folded singularities have provided new insights into the nature of these oscillations. In this presentation, we discuss the theory of folded singularities, its application to experimental data, and its potential for predicting single-cell behavior. To illustrate the first point, we present a case study where the folded singularity theory is used to model and explain mixed-mode oscillations observed in layer V cortical neurons. Specifically, we demonstrate how an increase in the intracellular cAMP concentration, which influences the M and HCN channel conductances, leads the system to produce subthreshold oscillations between action potentials. For the second objective, we present the analyses of a novel astrocyte model in which a folded node is detected, explaining the small fluctuations observed during the initial transient states when solved numerically. We also propose experimental protocols to verify predictions made at the single-cell level based on the detected folded singularity. In conclusion, these case studies showcase two applications of folded singularity theory, highlighting its role in interpreting small fluctuations observed both in vitro and in silico. Specifically, we emphasize how the analysis of folded singularities can provide valuable insights into the mechanisms underlying the generation of complex oscillations.
MS01: 15:10-17:10, 23rd June 2025, Room PCC/1.1-2, presentation 16:10-16:30
RamĂłn Nartallo-Kaluarachchi (University of Oxford)
Title: Nonequilibrium stochastic dynamics in the human brain
Abstract: Information processing takes the form of the complex patterns of neural activity that we study from the perspective of dynamical systems and network science. Recent work has found that human brain dynamics appear to operate in a stochastic nonequilibrium steady-state (NESS) leading to time-irreversible dynamics. Many studies focus on identifying differences in aggregate measures of nonequilibrium and there is not yet a causal characterisation of nonequilibrium neural dynamics. By abstracting the brain as a complex network, we investigate the structural origins of nonequilibrium dynamics in neural systems. First, we use random graphs and synthetic dynamics to investigate the relationship between network directedness and the entropu production rate (EPR) and find that nonequilibrium dynamics stem from network asymmetries. We present an autoregressive model to fit an Ornstein-Uhlenbeck process to neuroimaging data at task and at rest to confirm that the EPR is higher in task than rest and show that this is driven by a greater hierarchical asymmetry in the interactions. Next, we investigate how temporal irreversibility can be used to infer higher-order behaviours between brain regions. Using visibility graphs, we introduce the DiMViGI framework for measuring the irreversibility of higher-order interactions in neural recordings. We apply our framework to MEG recordings from a recognition task with six regions. Our work expands on a new paradigm for studying neural dynamics from the perspective of nonequilibrium stochastic processes, and demonstrates that such an approach can yield novel insights in the effective structure of functional interactions in the human brain.
MS01: 15:10-17:10, 23rd June 2025, Room PCC/1.1-2, presentation 16:30-16:50
Saeed Farjami (University of Exeter)
Title: Network Dynamics and Emergence of Synchronisation in A Population of KNDy Neurons
Abstract: The reproductive axis relies on the gonadotropin-releasing hormone (GnRH) pulse generator, driven by KNDy neurons in the hypothalamic arcuate nucleus. These neurons, co-expressing kisspeptin, neurokinin B (NKB), and dynorphin, generate pulsatile GnRH release. While the electrophysiological properties of single KNDy neurons are well-characterised, the network mechanisms underlying synchronisation and burst generation remain unclear. We refined our previously developed Hodgkin-Huxley-type model of a single KNDy neuron to better match experimental data, particularly the current-frequency response. Expanding on this, we built a computational model of a realistic KNDy neuron network incorporating both fast glutamate-mediated synaptic coupling and slower neuromodulatory interactions via NKB and dynorphin. This framework allows us to study how network structure and neuronal interactions drive emergent bursting and synchronisation. Our results highlight how glutamate, acting on a fast timescale, might be critical for initiating synchronisation, whereas slower NKB and dynorphin interactions regulate its maintenance and termination. We examine the impact of connectivity, functional heterogeneity, and neurotransmitter signalling on network activity. This is joint work with Krasimira Tsaneva-Atanasova and Margaritis Voliotis at University of Exeter.
MS02: 15:40-17:40, 24th June 2025, Room PCC/1.1-2, presentation 15:40-16:00
Matthew Butler (UCL)
Title: Dynamic swelling of a salty polymer
Abstract: By embedding salt particles within a soft elastomer, a previously neutral material can be made to swell significantly when submerged in water. The swelling is dynamic, resulting in order of magnitude increases in volume, before long-time deswelling back towards its original state. A mathematical model of the key physical processes captures the fundamental swelling behaviours, and agrees well with experimental measurements. Analysis of the governing equations highlights asymptotic regimes where different mechanisms are dominant at different times. This knowledge is used to extract important behaviours of the system, and optimise the experimental parameters for applications.
MS02: 15:40-17:40, 24th June 2025, Room PCC/1.1-2, presentation 16:00-16:20
Hangkai Wei (University of Oxford)
Title: Capillary entry pressure of a hydrogel packing
Abstract: The capillary entry pressure of a porous medium is defined as the minimum pressure required for a non-wetting fluid to start invading the porous medium by displacing the wetting fluid, typically beginning at the largest pore. In rigid porous media, this pressure is governed by the properties of the two fluids and the pore structure, as described by the YoungâLaplace equation. However, in soft porous media, the applied pressure can induce compression, reducing pore size and consequently increasing the capillary entry pressure. This mechanical-fluidic coupling challenges the conventional notion that capillary entry pressure is an intrinsic material property. In this study, we employ both experiments and modeling to investigate the capillary entry pressure during a forced-drainage process of a soft porous medium composed of a packing of hydrogel beads (~1 mm in diameter), where the hydrogel beads themselves exhibit nanoscale porosity (~10 nm). Our results demonstrate that (i) capillary entry pressure increases as the porous medium undergoes compression due to applied pressure and (ii) this increase persists even after fluid invasion has commenced, which our model fails to predict even when accounting for deformation-dependent pore closure. Further investigation rules out pore-size distribution as the primary factor and instead identifies the poro-viscoelastic creep behavior of hydrogelsâwhere the packing progressively compresses under sustained pressureâas the dominant mechanism governing this phenomenon.
MS02: 15:40-17:40, 24th June 2025, Room PCC/1.1-2, presentation 16:20-16:40
Matthew Hennessy (University of Bristol)
Title: Drying-induced bending of thin hydrogels
Abstract: The evaporation of fluid from the surface of a thin, pre-swollen hydrogel leads to out-of-plane bending. The bending moments originate from differences in the fluid concentration across the thickness of the gel, which give rise to differential deswelling. As the gradient of fluid concentration increases, so does the curvature of the gel. However, the concentration gradients eventually diminish and the gel relaxes back to its original shape, albeit with a smaller volume. Thus, the curvature of the gel increases from zero to a maximum and then decreases back to zero. By exploiting the slenderness of the gel, matched asymptotic expansions can be used to determine how the gel curvature evolves in time. The governing equations of 3D nonlinear poroelasticity reduce to a (2+1)D model consisting of a modified form of the 2D Foppl-von Karman equations that are coupled to a 1D diffusion equation. The diffusive flux depends on the mean curvature of the gel, capturing the chemo-mechanical coupling of the problem. The asymptotic results are compared with finite element simulations and experimental data from colloidal gels.
MS02: 15:40-17:40, 24th June 2025, Room PCC/1.1-2, presentation 16:40-17:00
Ellen Jolley (University of Warwick)
Title: Hydrogels as actuators for origami stents
Abstract: Origami-inspired design offers the potential for more compact and flexible stents (medical devices designed to hold open a vessel in the body). An origami stent can be folded into a very small and compact shape, allowing minimally-invasive insertion. Once in the body it expands, enabling it to adapt to complex vessel shapes, which reduces the risk of complications from the procedure. Responsive hydrogels have been proposed as a possible actuator: by designing hydrogel-based hinges, the swelling of the hydrogel as a result of changing physiological conditions could then trigger the unfolding of the stent. In this talk, we investigate the potential of various bending and folding mechanisms which use hydrogels as an actuator, by means of two approaches. Firstly, by conceptualizing the hydrogel as a network of beads connected by Hookean springs, the dynamics of swelling and deswelling can be captured as a change in the natural length of the springs. This allows us to build a numerical model of hydrogel swelling for complex geometries, meaning actuation designs can be tested quickly. Secondly, using a continuum poroelastic model of a hydrogel, we can analytically compute the force exerted by a hydrogel confined between surfaces.
MS02: 15:40-17:40, 24th June 2025, Room PCC/1.1-2, presentation 17:00-17:20
Daniel Booth (University of Warwick)
Title: Controllable microfluidics through active droplets and responsive hydrogels
Abstract: Precise, localised flow control in microfluidic devices remains a difficult challenge. In this talk, I demonstrate theoretically how active droplets might be harnessed to overcome this challenge. Active droplets are produced along the microchannel wall via stimulation of a responsive hydrogel, and the ensuing phoretic slip flows drive transport and mixing in the microfluidic device. I find optimal transport times for particles traversing the channel, and show that, by switching between two droplet configurations, chaotic mixing can be achieved in the microchannel.
MS03: 10:30-12:30, 24th June 2025, Room PCC/1.1-2, presentation 10:30-10:50
Sean Holman (University of Manchester)
Title: Learned prior approach to range and dose verification in proton therapy
Abstract: Proton therapy is a new and rapidly expanding technique for cancer treatment which exposes patients to a beam of protons to destroy tumours. This is similar to traditional radiotherapy, but has the advantage that energy deposited by the proton beam can be focussed. To ensure the beam is focussed at the correct point, treatment plans must be developed individually for each patient, usually based on high resolution CT scans. However, there is currently no accepted method to verify that the proton beam has actually delivered the dose as planned. One approach to tackle this problem is to measure prompt gamma ray and fast neutron emissions which occur during treatment. These data then lead to the inverse problem of determining the distributed source which gave rise to the measured emissions. This is a very low data emission tomography problem, and we attempt to apply a learned prior approach which is based on first using a trained neural net to approximate the source distribution. Our numerical experiments, based on synthetic data, show some improvement over traditional emission tomography techniques.
MS03: 10:30-12:30, 24th June 2025, Room PCC/1.1-2, presentation 10:50-11:10
Huda M Alshanbari (Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia)
Title: Application of machine learning algorithms in the domain of financial engineering
Abstract: Financial engineering is crucial for effectively combining finance with quantitative approaches. This study aims to forecast the performance of the Nasdaq stock market by considering numerous factors like wind, hydro, thermal, gas, and nuclear variables. To accomplish this, we utilize sophisticated predictive models, namely adaptive lasso (ALasso), elastic net (Enet), artificial neural network (ANN), convolutional neural network (CNN), and long short-term memory (LSTM). By using these advanced methods, our goal is to offer perceptive and precise predictions, which will enhance comprehension of the complex dynamics within the financial markets. The evidence suggests that the LSTM model has demonstrated superior accuracy in predicting changes in the Nasdaq stock market when compared to ALasso, Enet, ANN, and CNN. While ALasso, Enet, ANN, and CNN exhibit comparable RMSE and MAE values, their performance is slightly less competitive than that of the LSTM model. The marginal differences in RMSE (ALasso: 0.319, Enet: 0.317, ANN: 0.3, CNN: 0.32) and MAE (ALasso: 0.277, Enet: 0.276, ANN: 0.252, CNN: 0.278) emphasize the comparable effectiveness of various methods, but they somewhat drop below the LSTM model in terms of precision. The findings showed the significance of well-known and advanced ML techniques, particularly LSTM, for enhanced accuracy in financial market predictions.
MS03: 10:30-12:30, 24th June 2025, Room PCC/1.1-2, presentation 11:10-11:30
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.
MS03: 10:30-12:30, 24th June 2025, Room PCC/1.1-2, presentation 11:30-11:50
Nurjahan Sultana (Manchester Metropolitan University)
Title: Inverse Feature Attribution for Cross-Domain Skin Lesion Analysis: A Step Towards Explainable Adaptation
Abstract: Deep learning models for skin lesion classification often exhibit reduced performance when confronted with clinical photographs that differ substantially from the dermoscopic images used during training. Although domain adaptation techniques can mitigate this discrepancy, their interpretability in real-world clinical settings remains limited. In this study, we introduce a novel method, Inverse Feature Attribution (IFA), which identifies the minimal morphological or colour modifications required to reverse a modelâs predictionâthat is, to switch a lesionâs classification from benign to malignant or vice versa. We evaluate our approach using classifiers trained on multiple dermoscopic datasets (ISIC 2017, 2018, and 2020) while integrating morphological insights from the Derm7 resource. The models are then tested on diverse clinical datasets (PAD-UFES, and Fitzpatrick) to ascertain the critical feature shifts necessary for effective cross-domain adaptation. Preliminary findings reveal that, although domain adaptation methods can align overall feature distributions, the specific perturbations needed to âflipâ a lesionâs predicted class differ markedly between dermoscopic and clinical images, thus uncovering persistent gaps in feature alignment. By quantifying these counterfactual shifts, IFA provides a more transparent understanding of model biases and paves the way for the development of more interpretable and trustworthy AI solutions in the context of skin cancer detection.
MS04: 15:10-17:10, 23rd June 2025, Room PCC/1.5-6, presentation 15:10-15:30
Laura Hattam (IMI, University of Bath)
Title: A Bayesian inverse approach to proton therapy dose delivery verification
Abstract: A Bayesian inverse method is proposed that is used for proton beam therapy treatment verification in one-dimension. We simulate prompt-$\gamma$ particles emitted from a proton beam interacting with different tissue layers, which are then detected by sensors. A Bayesian framework is outlined to estimate the proton beamâs energy deposition profile within the tissue layers from the information obtained by the sensors. Both a uniform medium and a layered lung tumour are used to validate this method.
MS04: 15:10-17:10, 23rd June 2025, Room PCC/1.5-6, presentation 15:30-15:50
Veronika Chronholm (University of Bath)
Title: Simplified models for proton transport for treatment planning and uncertainty quantification
Abstract: Proton Beam Therapy (PBT) is a type of radiotherapy used for cancer treatment. Due to the sharply peaked dose-depth curve characteristic of protons, and the fact that protons stop at a finite depth inside the tissue, PBT is especially useful when treating tumours situated close to vital organs, which need to be spared from radiation damage. In terms of both treatment planning and uncertainty quantification, a physically accurate model for proton transport that is also quick to evaluate is needed. This talk will cover some possible models for proton radiation, as well as their application to clinically relevant problems.
MS04: 15:10-17:10, 23rd June 2025, Room PCC/1.5-6, presentation 15:50-16:10
Jere Koskela (Newcastle University)
Title: Jump diffusion models in proton beam therapy
Abstract: Proton beam radiotherapy is a key tool in precision cancer treatment, leveraging the physical interactions of protons with human tissue. Unlike photons, protons are absorbed after a predictable path length which allows more precise control over where their energy dose is delivered. Broadly speaking, state-of-the-art treatment planning tools come in two varieties: highly detailed but computationally expensive Monte Carlo algorithms which simulate every physical interaction between a proton and the surrounding tissue, or parametric curves fitted to measurement data, often in one dimension. I’ll describe a jump diffusion model which is intermediate between these two regimes. The diffusion coefficient absorbs many of the smaller nuclear interactions which greatly speeds up simulations. But the model retains three spatial dimensions and an explicit connection to the underlying physics, facilitating calibration and uncertainty quantification.
MS04: 15:10-17:10, 23rd June 2025, Room PCC/1.5-6, presentation 16:10-16:30
Emma Horton (University of Warwick)
Title: Moment asymptotics for neutron transport
Abstract: The neutron transport equation describes the flux of neutrons through an inhomogeneous fissile medium. It is well known that the solution can be represented as the average of a branching process, whose particles mimic that of neutrons undergoing fission. In recent years, this connection has been revisited in order to exploit recent developments in the theory of branching processes and inform more efficient Monte Carlo simulations. In this talk, we will discuss how this connection can be used to provide rigorous results on the asymptotic behaviour of the moments of the neutron population. Then, we propose a simple benchmark configuration where exact solutions are derived for these moments, which can be used for the verification of new functionalities of production Monte Carlo codes.
MS04: 15:10-17:10, 23rd June 2025, Room PCC/1.5-6, presentation 16:30-16:50
Matthew Evans (University of Bath)
Title: Cycle-Free Polytopal Mesh Sweeping
Abstract: In this talk, we discuss a form of permutative preconditioning that enables matrix-free methods for solving the (linear) Boltzmann Transport Equation (BTE), with applications in nuclear reactor simulations where efficient transport modelling is crucial for reactor physics and safety analysis. Mesh design plays a critical role in numerical methods, including discontinuous Galerkin (dG) finite element methods. Without careful handling, transport solvers can develop cyclic dependencies, leading to costly computational corrections. We present a novel property of bounded Voronoi tessellations and an accompanying algorithm that enables cycle-free, matrix-free dG discretisations of the BTE. This approach broadens the applicability of dG methods for transport problems on polytopal meshes, offering a robust, scalable, and parallel-friendly framework. We will explore this method in detail and demonstrate its effectiveness through computational experiments, showcasing both efficiency and adaptability to complex geometries.
MS04: 15:10-17:10, 23rd June 2025, Room PCC/1.5-6, presentation 16:50-17:10
Aaron Pim (University of Bath)
Title: An Uzawa Approach for Boundary Conditions in Kinetic equations.
Abstract: In this talk I will introduce a deep learning-based framework for weakly enforcing inflow boundary conditions in the numerical approximation of kinetic partial differential equations. Building on existing deep Ritz methods, I will propose the Deep Uzawa algorithm, which incorporates Lagrange multipliers to handle boundary conditions effectively. This modification requires only a minor computational adjustment but ensures enhanced convergence properties and provably accurate enforcement of boundary conditions, even for singularly perturbed problems.
MS05: 15:40-17:40, 24th June 2025, Room PCC/1.5-6, presentation 15:40-16:00
Alice Vanel (CNRS, Institut Fresnel)
Title: Modal approximations for plasmonic resonators
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MS05: 15:40-17:40, 24th June 2025, Room PCC/1.5-6, presentation 16:00-16:20
Tristan Lawrie (University of Nottingham)
Title: A Non-diffracting Angular Filter: Designing Wave Devices via Quantum Graph Theory.
Abstract: We conceptualise and numerically simulate a resonant metamaterial interface incorporating non-local, or beyond nearest neighbour, coupling that acts as a discrete angular filter. It can be designed to yield perfect transmission at customizable angles of incidence, without diffraction, allowing for tailored transmission in arbitrarily narrow wavenumber windows. The theory is developed in the setting of discrete, infinitely periodic quantum graphs and we realise it numerically as an acoustic meta-grating. The theory is then applied to continuous acoustic waveguides, first for the medium surrounding the interface and then for the interface itself, showing the efficacy of quantum graph theory in interface design.
MS05: 15:40-17:40, 24th June 2025, Room PCC/1.5-6, presentation 16:20-16:40
Levi Kaganowich (University of Salford)
Title: Rotating cylindrical acoustic invisibility cloak: solution using perturbation method
Abstract: Transformation Acoustics initiated a new paradigm of metamaterial designs in the mid-2000s. Using this approach, an invisibility cloak can be created, and this holds promise for stealth and noise reduction applications in aviation. However, adapting this design to meet the demands of realistic conditions has proven challenging. The work below focusses on the design of a stationary 2D cylindrical cloak and its performance whilst rotating, a result not yet reported in the literature. The study utilises linearised equations of motion with convective terms. A differential equation for acoustic pressure in an anisotropic rotating fluid is formulated assuming radial dependence of its effective density components and bulk modulus. For a slowly rotating cloak the corresponding solution and scattering coefficients for the acoustic incident plane wave are derived using a perturbation method and compared with a numerical solution. These scattering coefficients are used to evaluate the performance of the rotating cloak. Results show that rotation causes a reduction in cloaking performance with greater scattering observed for increasing rotational speeds, with a reasonable agreement (within 1.7%) between the methods within the range of applicability. The perturbation method used in this study provides a fast and computationally inexpensive approach to evaluating wave scattering from a rotating, radially graded anisotropic fluid region. The methodology and results presented lay a foundation for designing rotating acoustic cloaks, with potential applications in stealth technology and noise reduction in aviation.
MS05: 15:40-17:40, 24th June 2025, Room PCC/1.5-6, presentation 16:40-17:00
Robyn Edge (University of Exeter)
Title: Discrete EulerâBernoulli beam lattices with beyond nearest connections
Abstract: Endeavours to ascertain enhanced control over wave dynamics has driven a vast amount of research, propagating concepts such as dispersion engineering [1] and the development of highly unusual dispersive phenomena, due to the expanse of possible applications [2]. Of note is the ability to engineer regions with very low, or zero-group-velocity (ZGV) in dispersion curves, that have implications for enhanced energy harvesting devices and vibration control [3]. Combining these concepts with the recent interest surrounding discrete lattice systems with multiple degrees-of-freedom at the lattice sites [4], we look to manipulate and engineer dispersion relations for spatially non-local lattice systems. The analysis is founded using the simplistic yet powerful Euler-Bernoulli (EB) beam theory, with deformation pathways pertaining to both translational and rotational degrees-of-freedom at the lattice sites. Elastic wave propagation on discrete Euler-Bernoulli mass-beam lattices is characterised by the competition between coupled degrees-of-freedom at the mass-beam junctions. We influence the dynamics of this system by coupling junctions with beyond-nearest-neighbour spatial connections, affording freedom over the locality of dispersion extrema in reciprocal space, facilitating the emergence of interesting dispersion relations. A generalised dispersion relation for an infinite monatomic mass-beam chain, with any integer order combination of non-local spatial connections, is presented. It is demonstrated that competing power channels, between mass and rotational inertia, drive the position and existence of zero group velocity modes within the first Brillouin zone. [1] A. Kazemi, K. J. Deshmukh, F. Chen, Y. Liu, B. Deng, H. C. Fu, and P. Wang, Drawing dispersion curves: Band structure customization via nonlocal phononic crystals, Physical Review Letters 131, 176101 (2023). [2] R. Craster and S. Guenneau, Acoustic Metamaterials: Negative Refraction, Imaging, Lensing and Cloaking, edited by R. V. Craster and S. Guenneau, Vol. 166 (Springer Netherlands, 2013). [3] G. J. Chaplain, D. Pajer, J. M. D. Ponti, and R. V. Craster, Delineating rainbow reflection and trapping with applications for energy harvesting, New Journal of Physics 22, 10.1088/1367-2630/AB8CAE (2020).
MS05: 15:40-17:40, 24th June 2025, Room PCC/1.5-6, presentation 17:00-17:20
Matthaios Chouzouris (University of Edinburgh)
Title: Architecting Mechanisms of Damage in Topological Metamaterials.
Abstract: Architecting mechanisms of damage in mechanical metamaterials, by translating the target effective mechanical response to structural features of the lattice, poses a complex inversion problem. Of these metamaterials, Maxwell lattices, which are on the verge of mechanical stability, offer significant potential for advanced functionality. As a result of their robust topological and geometry-dependent properties that dominate the stress activation, simplified considerations may be used to more precisely design the damage evolution. Using continuum representations of these lattices we set up a framework that allows us to explicitly engineer the stress concentration around discontinuities. This in turn offers robust pathways to manipulate the mechanisms of damage and the fracture propagation.
MS05: 15:40-17:40, 24th June 2025, Room PCC/1.5-6, presentation 17:20-17:40
Katie Madine (University of Liverpool)
Title: Controlling flexural wave propagation and negative refraction using arrays of perpendicular gyroscopes
Abstract: This work demonstrates methods to control the propagation of elastic waves using periodic arrays of perpendicular gyroscopes on flexural plates. A perpendicular gyroscope is formed of two perpendicular beamsâwith the vertical beam attached upright at the base to the plateâand a gyroscope at the free end of the horizontal beam [1]. This design has similarities with the structure of a wind turbine, and for arrays, wind farms. The analytical model is studied alongside finite element simulations, in which boundary conditions are applied to simulate the presence of the spinners. The eigenmodes of individual gyroscopes are shown to produce dynamic chiral Chladni patterns in their attached plate. Arrays of perpendicular gyroscopes on plates are shown to support unusual phenomena, including negative refraction, unidirectional waves at chiral interfaces and other wave guiding effects. We investigate the control over the system afforded by altering parameters such as the rate of spin of the gyroscopes, the length of the beams and the orientation of the gyroscope axes. [1] Madine K. H. and Colquitt D. J. 2024. The perpendicular gyroscope: modal analysis of plate, beam and gyroscope multistructures. Phil. Trans. R. Soc. A.38220230358 http://doi.org/10.1098/rsta.2023.0358
MS06: 15:10-17:10, 23rd June 2025, Room PCC/2.1-2, presentation 15:10-15:30
Andrew Krause (Durham University)
Title: Exploring Complex Biological Dynamics through Interactive Simulations
Abstract: This talk will be a mix of “communicating” and “doing” science in different ways, aided by modern conceptual and computational tools. I will demonstrate the value of communication across disciplinary boundaries using real-time interactive simulations through VisualPDE.com. I will describe how past and ongoing work with developmental biologists, geographers, ecologists, and microbiologists can be enriched with these tools, and in particular how deep insights can be rapidly communicated without the need for vast disciplinary expertise. Among other examples, I will discuss the role of subcritical diffusion-driven instabilities in oncological and embryological settings, demonstrating the ease with which nuanced and technical theoretical ideas can be illustrated and explored in real-time. I will end by discussing fundamental limitations of phenomenological dynamical systems modelling in general, giving rise to the need for better frameworks to do science.
MS06: 15:10-17:10, 23rd June 2025, Room PCC/2.1-2, presentation 15:30-15:50
Amy Bowen (Francis Crick Institute)
Title: Robustness of pattern proportions during growth
Abstract: During embryonic development, a collection of undifferentiated cells undergoes cell fate specification to form a patterned tissue. This occurs through formation of a morphogen gradient, which then inputs into Gene Regulatory Networks (GRN) resulting in position-dependent differentiation. At the same time as patterning, the tissue is growing. Molecular noise and cellular heterogeneity affect both processes of patterning and growth, leading to variation in the overall size of the tissue and the sizes of constituent cell fate domains. Despite this, many biological systems exhibit pattern scaling: the pattern is consistently maintained proportionate to its size. Some developmental systems employ morphogen gradient scaling, where the gradient decay length scales with the tissue size, however, this is not observed in all developmental contexts: for example, in early development of the mammalian neural tube. We find a new mechanism for scaling independent of morphogen scaling whereby growth interacts the underlying properties of the GRN, namely, history-dependent system behaviour (hysteresis). We have set up a system that models morphogen and GRN dynamics in a growing tissue. We demonstrate scaling due to the interaction of the GRN and growth, without morphogen gradient scaling. This is the result of cells interpreting a dynamic signal and retaining âmemoryâ of their previous environment via hysteresis, a property encoded by the GRN. This result implies that the resultant pattern and scaling properties of a tissue is dependent on 2 critical timescales: the timescale of growth, and the timescale over which a GRN can process a signal.
MS06: 15:10-17:10, 23rd June 2025, Room PCC/2.1-2, presentation 15:50-16:10
Jack Jennings (Sheffield University)
Title: A computational study for the impact of clonal induction in the Drosophila pupal wing on domineering non-autonomy.
Abstract: ” The patterning of multicellular tissues relies on self-organisation, which emerges from dynamic, iterative interactions from the molecular to tissue scale. Molecular interactions, for instance through reaction-diffusion networks, result in symmetry breaking and cell polarisation. Short-range interactions between cells locally coordinate cell polarity and long-range biochemical and mechanical controls coordinate patterning across tissues. Thus, not only are interactions occurring on different length-scales, but also on different time-scales, and each level of organisation affects every other level. Consequently, understanding the biochemical and biophysical mechanisms underlying tissue self-organisation is a formidable challenge. To address this, we have extended the standard vertex model to obtain a qualitative understanding of self-organised patterning from junction to tissue scale (biochemical and mechanical feedbacks). As an example for tissue patterning we study the âcoreâ planar polarity pathway function in the developing wing of the fruit fly. Here we present our findings for the impact and range of clones on autonomous polarisation in the Drosophila wing alongside investigating the importance of mechano-sensitive E-cadherin in regulating tissue viscoelasticity and cell shape.”
MS06: 15:10-17:10, 23rd June 2025, Room PCC/2.1-2, presentation 16:10-16:30
Amy Milne (Swansea University)
Title: The role of environmentally mediated drug resistance in facilitating the spatial distribution of residual disease.
Abstract: The development of de novo resistance is a major disadvantage in molecularly targeted therapies and is an open field of research. While most of the current understanding of the emergence of resistance is focused on cell-intrinsic mechanisms, we know the microenvironment also plays a crucial role. We focus on interactions between cancer cells and cancer associated fibroblasts (CAFs) to understand the local crosstalk facilitating residual disease. We model these spatial dynamics with a hybrid-discrete-continuum model. The stress response caused by treatment with molecular inhibitors can trigger a signal for assistance to which CAFs respond. Introducing breaks in treatment allows the microenvironment to normalise as the stress response subsides. We investigate how fluctuating environmental conditions shape the local crosstalk and, ultimately, the resulting residual disease. We find that treatment response depends on the complex interactions between the cancer cells and CAFs, modulated by local concentrations of drug and signalling molecules. Our experimentally calibrated model determines environmental and treatment conditions that allow tumour eradication and those that enable survival. We find two very distinct mechanisms of resistance underpinning residual disease. Our work provides a better understanding of the mechanisms that drive the creation of localised residual disease, crucial to informing the development of more effective treatment protocols.
MS06: 15:10-17:10, 23rd June 2025, Room PCC/2.1-2, presentation 16:30-16:50
Nicholas Lai (University of Oxford)
Title: Mathematical Modelling of Tertiary Lymphoid Structures in Cancer
Abstract: Tertiary lymphoid structures (TLSs) are organised aggregates of immune cells that form at sites of inflammation in chronic diseases, such as cancer. It is hypothesised that, in cancer, TLSs act as local hubs for the generation and regulation of a tumour-specific immune response from within the tumour microenvironment (TME). TLSs initially form as well-mixed aggregates of T- and B-cells and mature into organised structures, consisting of an inner B-cell zone surrounded by an outer T-cell zone. The presence of TLSs correlates with positive patient outcomes in several cancer types, but the mechanisms governing their formation, maturation, and role in the antitumour response remain poorly understood. Motivated by analysis of spatial transcriptomics images of TLSs in colorectal cancer, we develop an agent-based model to investigate TLS formation, maturation, and function in cancer. We model T-cells and B-cells as discrete agents which are attracted to diffusible chemokines (CXCL13 and CCL19) produced by resident stromal cells in the TME. These interactions lead to the formation of a well-mixed lymphoid aggregate that later matures into distinct T- and B-cell zones due to the segregated expression of these chemokines. Our results identify key parameters governing TLS development and suggest conditions under which TLSs are able to control tumour growth. This framework provides a qualitative basis for understanding TLS dynamics and their potential role in cancer immunotherapy.
MS06: 15:10-17:10, 23rd June 2025, Room PCC/2.1-2, presentation 16:50-17:10
Iolo Jones (Durham University)
Title: Calculus, geometry, and PDEs on spatial data with diffusion geometry
Abstract: Calculus, geometry, and PDEs are ubiquitous in modelling spatial biological processes but have generally proved hard to apply directly to experimental data as spatial statistics. Diffusion geometry is a new framework for geometric data analysis that defines Riemannian geometry for data and probability spaces which allows us to use classical calculus and geometry methods directly on point clouds. In this talk, I will introduce new diffusion geometry methods for spatial data, such as the Hodge/Helmholtz decomposition of vector fields, and solving PDEs like the heat and wave equations.
MS07: 15:10-17:10, 23rd June 2025, Room PCC/2.5-6, presentation 15:10-15:30
Oscar Holroyd (University of Warwick)
Title: Feedback control of thin liquid films falling down inclined planes
Abstract: We outline methods to control a thin liquid film falling down an inclined plane towards an unstable flat solution by injecting or removing fluid from the base. The two-phase Navier-Stokes equations that govern the dynamics of a falling liquid film pose a challenging control problem: it is an infinite-dimensional, nonlinear system with complex boundary conditions, and we are limited to a finite-dimensional boundary control. By using a hierarchy of successively simplifying assumptions, we show that a linear quadratic regulator (LQR) control can be used to stabilize the otherwise unstable flat (or Nusselt) solution. We demonstrate that applying the LQR controls to the Navier-Stokes problem is successful well outside the parameter regime that the simplified models are designed for, and also in cases where observations of the system are restricted.
MS07: 15:10-17:10, 23rd June 2025, Room PCC/2.5-6, presentation 15:30-15:50
Alexander Wray (University of Strathclyde)
Title: Optimal control of multiphase flows
Abstract: Multiphase flows are ubiquitous in nature and industry, and controlling them has applications everywhere from carbon sequestration to medical diagnostics. As a consequence, control has seen an ever-increasing focus in the field of fluid dynamics. Unfortunately, inverse problems of this type are typically extremely computationally costly, and most existing studies have focussed on single phase flows which admit convenient bases on which to project suitable reduced dimensional models. Multi-phase studies have typically confined their focus to lubrication-type equations, which have limited applicability. Here the more complex problem of free-surface flow down an inclined plane is examined, simulated using the volume-of-fluid open-source solver Basilisk. Control is implemented via developing an extremely high-fidelity reduced order model using a projection method akin to the Method of Weighted Residuals, and using a Model Predictive Control loop to control the direct numerical simulation with judicious use of the model. Actuation is achieved via imposing a spatiotemporally-varying electric potential on an electrode parallel to the substrate. The model is investigated in detail, demonstrating a high degree of accuracy even into the short-wave regime. The control mechanism is shown to be applicable to both uniform and non-uniform target states, and the efficacy of the model predictive control loop is investigated across a wide variety of parameters.
MS07: 15:10-17:10, 23rd June 2025, Room PCC/2.5-6, presentation 15:50-16:10
Joshua Durrant (University of Limerick)
Title: Wrinkling in viscous fluids
Abstract: Thin sheets of viscous fluid will buckle under end-to-end compression. In the case of a floating viscous sheet, this buckling will take the form of wrinkles whose wavelength depends on parameters such as thickness, weight, and compressive force. We use perturbation analysis to derive a leading-order description of the sheet dynamics in the limit of a very thin sheet, and use linear stability analysis to investigate its wrinkling behaviour. Solving the problem numerically tells us more about the changes in fastest growing mode over time and the interesting jumps in tension that accompany them. We also solve the problem analytically with initial conditions of just two modes to gain insight into the problem and how the modes compete over time.
MS07: 15:10-17:10, 23rd June 2025, Room PCC/2.5-6, presentation 16:10-16:30
Madeleine Moore (Loughborough)
Title: Making a deposit: the competition between advection, diffusion and adsorption in evaporating sessile droplets
Abstract: The evaporation of liquid droplets has received significant research interest due to its fundamental significance in a variety of industrial and engineering applications such as inkjet printing, microscale and colloidal patterning, DNA microarray technologies and the manufacture of Q/OLEDs. One of the key reasons for this is the familiar âcoffee-ringâ effect that refers to the ringlike stain left behind after a solute-laden droplet evaporates on a surface and its potential use in depositing specific patterns. While deceptively simple, there is a wealth of complexity in the problem, primarily embedded in the â potentially coupled â aspects of evaporation, the associated liquid flow and particle transport. These difficulties have limited the vast majority of existing models to only treating the simplest possible cases of asymptotically-flat, circular droplets evaporating in isolation. This has dramatically limited their applicability in real-world contexts, in which these simplifications are generally broken. In this talk, we will discuss recent advances that attempt to broaden the existing theory with an eye on the ultimate goal of dynamically controlling the process to suit a specific application.
MS07: 15:10-17:10, 23rd June 2025, Room PCC/2.5-6, presentation 16:30-16:50
Marc Pradas (The Open University)
Title: Exploiting bifurcations to control droplet snaps on smooth patterned surfaces
Abstract: The shape and stability of a droplet in contact with a solid surface are influenced by the surfaceâs chemical composition, topography, and, crucially, the dropletâs size. As its size changesâtypically through evaporation or condensationâdroplets on smooth patterned surfaces can undergo sudden changes in shape and position. These abrupt transitions, known as snaps, are induced by the surface pattern and arise from fold and pitchfork bifurcations, which respectively drive symmetric and asymmetric motions. However, determining which type of snap is likely to occur remains an open fundamental question, with implications for the rational design of surfaces to control droplet behaviour. Here, we combine theoretical analysis with diffuse-interface simulations to investigate the dynamics of droplet snaps and their dependence on the systemâs physical properties. Our results reveal that asymmetric patterns induce imperfect pitchfork bifurcations, which can be exploited to direct droplet motion. Additionally, we show that the likelihood of symmetric or asymmetric snaps depends on the separation between fold and pitchfork bifurcation points and how this separation evolves as droplets grow or shrink. These findings can inform strategies for controlling droplets using smooth surface patterns and have broader relevance in systems where competing bifurcations dictate stability, such as snap-through instabilities in elastic media.
MS07: 15:10-17:10, 23rd June 2025, Room PCC/2.5-6, presentation 16:50-17:10
Demetrios Papageorgiou (Imperial College London)
Title: Using light-actuated photosurfactant Marangoni phenomena for liquid mixing and sculpting
Abstract: Photosurfactants are soluble surface active agents that can change conformation under illumination of different frequencies. When exposed to visible light they conform to the trans state, while illumination by shorter wavelength UV light transforms trans surfactants to the cis state by bending their hydrocarbon tails. The process is reversible. We introduce mathematical models that describe the two surfactant species, their exchange kinetics in the bulk due to light switching, their adsorption/desorption from interfaces (e.g. air-water), and the exchange between them at the interface. In general, this leads to nonlinear coupled systems for the flow, surfactant concentrations (bulk and interfacial) and nonlinear interfacial deflections, to produce a challenging and rich mathematical problem. We use the models to study the fundamental problem of harnessing non-uniform light gradients to induce mixing and interfacial non-uniformities in horizontal liquid layers covering a solid substrate. This is carried out asymptotically for small spatially varying light gradients superimposed onto a background uniform illumination. We obtain analytical solutions and use them to reproduce experimental observations of light-actuated particle trapping by a local light pulse. Furthermore, we present light profiles that generically induce Marangoni flows with vortical structures, and use our analytical framework to show that inverse problems can be posed and solved to determine the required light gradients that can produce pre-determined interfacial amplitudes to achieve controlled sculpting.
MS08: 15:10-17:10, 23rd June 2025, Room FOR/EXP2, presentation 15:10-15:30
Matt Dopson (Newcastle University)
Title: Understanding the cyclic populations of the short-tailed field vole in the UK using long term experimental data
Abstract: The short-tailed field vole (microtus agrestis) is the most abundant mammal in the UK, with populations reaching up to 80 million individuals. However, voles experience huge fluctuations in population numbers with up to a tenfold change over the course of regular 3.5 year cycles. Previous research has aimed to understand the mechanics behind these oscillations, but most of this work focuses on tundra regions. The ongoing Glen Finglas grazing experiment spans over 20 years, focusing on how managing grazing pressures affects various groups of species – including voles – in the more temperate upland acid grasslands of Scotland. Here, I will first present new data analysis on the Glen Finglas experiment, in particular the relationship between voles and the vegetation they use as a food source and shelter. I will then show how this data can be used to create and fit a mathematical model, capturing the vole’s complex life history and interactions. Understanding these small animals is important as they are a key prey species for many predators and can also cause massive damage to plants and tree saplings. This mathematical model furthers our understanding of vole dynamics in temperate regions.
MS08: 15:10-17:10, 23rd June 2025, Room FOR/EXP2, presentation 15:30-15:50
Axa-Maria Laaperi (Newcastle University)
Title: Fires of the future: Modelling and inference of wildfire spread dynamics.
Abstract: Wildfires disrupt ecosystems, with much evidence to show that climate change is exacerbating vulnerability in regions poorly adapted to such disturbances. These events are driven by complex, multi-scale interactions where small perturbations in environmental factors can trigger large-scale shifts, complicating prediction efforts. We propose a coupled convection-reaction-diffusion system for modelling wildfire spread dynamics. This system integrates spatial and temporal variability to identify thresholds for spread and identify impacts of abrupt environmental changes on burnt areas and rates of propagation. Bayesian inference and Monte Carlo methods are employed for parameter estimation and uncertainty quantification, ensuring robust model validation against unseen data. We do this by incorporating environmental, meteorological, and historical fire data from the Global Wildfire Information System and the Department for Environment, Food and Rural Affairs (UK). Recent wildfire events around the globe highlight the need for insights into environmental vulnerability, property loss, and infrastructure risk. By enabling near-real-time simulations, this model aims to provide a computational tool for emergency response, long-term management strategies, and assessments of climate change-induced outlier weather patterns influencing fire behaviour. This work highlights the potential of mathematical modelling to advance understanding and management of critical ecological disturbances.
MS08: 15:10-17:10, 23rd June 2025, Room FOR/EXP2, presentation 15:50-16:10
Lena Payne (University of Kent)
Title: How scent based movement affects herd size
Abstract: Animals deposit scent marks whenever they move, be it by pheromones, scat or some other biological indicator. Animals of the same species can use this to either move towards/follow one another to work together or move apart if they believe the area to be resource deprived. Similarly other animals decision making will be affected by these markers – particularly if they prey upon, or are preyed upon by the marking species. I am building a model to see how these markings effect how herds form and interact with their environment.
MS08: 15:10-17:10, 23rd June 2025, Room FOR/EXP2, presentation 16:10-16:30
Zak Sattar (University of Edinburgh)
Title: The Impact of a Cut-off on Front Propagation in a Predator-Prey Reaction-Diffusion System
Abstract: In 1983, Dunbar proved the existence of travelling wave solutions to a Lotka-Volterra predator-prey reaction-diffusion system where only the predator diffuses. Here, we investigate the effect of a cut-off in the predator population for low population densities on the wave propagation dynamics of the system. We give a proof for the existence of travelling wave solutions in the presence of a cutoff, and we show that these solutions are not necessarily monotone. Moreover, we determine the correction to the âcriticalâ travelling wave propagation speed that is due to the cut-off. Finally, we discuss how our approach can be generalised to other related reaction-diffusion systems, such as to a classic fox-rabies epidemiological model. Our analysis is based on a combination of geometric singular perturbation theory and the desingularisation technique known as blow-up.
MS08: 15:10-17:10, 23rd June 2025, Room FOR/EXP2, presentation 16:30-16:50
Daniel Bearup (University of Leicester)
Title: Effects of hierarchical habitat structure on metapopulation dynamics
Abstract: Models for metapopulation dynamics have typically assumed that the underlying landscape is fundamentally isotropic. That is to say: (1) any variation in habitat quality is essentially random; (2) it is possible to move between two points via any other point. These characteristics clearly do not apply to river habitats. Here, habitat quality depends, at least in part, on how far a stretch of river is from the riverâs source. Furthermore, movement between two tributaries will typically be via a larger water course to which both are connected. In this talk, I will outline a modelling framework for metapopulation dynamics in a landscape with a regular dendritic structure, such as might be used to model a river network or other hierarchically structured habitats. I will characterise how population spread within this structure differs from that seen within an isotropic landscape. Finally, I will discuss how a generalised reaction-diffusion framework could be developed to describe population spread in habitats with these features.
MS09: 10:30-12:30, 24th June 2025, Room PCC/1.5-6, presentation 10:30-10:50
Molly Brennan (University College London(UCL))
Title: Spatial Instabilities as a Resilience Mechanism in Cancer Immunotherapy
Abstract: Tumour progression and treatment is an area of extensive cross-disciplinary research, with mathematical and computational modelling gaining traction in recent decades as a method of informing and optimising treatment strategies. Modelling choices can have drastic effects on the insights obtained, so the models we use should retain the key features and behaviours of the system they are emulating. In this work we show the importance of spatial structure to tumour resilience in a classical immunotherapy model with effector cells and IL-2 compounds. Using linear stability analysis, numerical continuation, and direct simulations, we see the formation of spatially structured tumour-cell populations that persist far into treatment regimes where corresponding homogeneous systems would predict a cancer-free state. This persistence extends across a wide range of treatment regimes, including across dosing strengths, and in time-dependent and spatially-incorporated treatments, highlighting the importance of spatial structure when using mathematical models to guide treatment in an innately spatiotemporal problem.
MS09: 10:30-12:30, 24th June 2025, Room PCC/1.5-6, presentation 10:50-11:10
Carles Falco (University of Oxford)
Title: Modelling adhesion-based phenomena in collective cell migration
Abstract: This talk explores mathematical models of cell-cell adhesion and their application to collective cell migration. We present a local continuum model of cell-cell adhesion, derived from a nonlocal aggregation-diffusion framework in the limit of short-range interactions. This model, which takes the form of thin-film type equations, captures the cell sorting patterns observed experimentally and provides explicit stationary solutions linked to the differential adhesion hypothesis. We then show global existence established under sharp conditions for the local aggregation-diffusion model. Finally, we use an agent-based model to study collective orbiting in epithelial spheroids, where the interplay between cell-cell adhesion, cell-matrix adhesion, and interface geometry, governs transitions from coordinated rotation to arrested motion.
MS09: 10:30-12:30, 24th June 2025, Room PCC/1.5-6, presentation 11:10-11:30
Thomas Jun Jewell (University of Oxford)
Title: Chase, Run, and Spin: Nonlocal Models of Interacting Species
Abstract: From shivers of sharks chasing schools of fish, to pigment cells pursuing each other on zebrafish skin, to leader and follower cells in the neural crest of an embryo, chase-and-run interactions can drive spatial structure and collective migration across biological systems. These interactions are often long-ranged (nonlocal): sharks can spot prey from afar, and pigment cells can extend pseudopodia towards neighbouring cells. We explore these dynamics using nonlocal advection-diffusion models, based on integro-partial differential equations, with two interacting species: chasers and runners. These models exhibit a rich range of behaviour, including stationary patterns, travelling holes, aggregates of chasers pursuing aggregates of runners, and other complex spatio-temporal dynamics. We show how chase-and-run interactions and differential self-interaction act as competing forces to determine whether the system can self-organise and whether patterns are stationary or oscillatory in time. Additionally, we explore the effects of chiral (angular) movement, which is often exhibited by cells and also used by prey animals to evade predators. We show how chirality can promote stationary pattern formation in chase-and-run systems. All of these dynamics are studied across two classes of nonlocal advection-diffusion model, âdirect sensingâ and âgradient sensingâ, which differ in their underlying assumptions but consistently produce similar qualitative behaviour, suggesting some robustness in our findings.
MS09: 10:30-12:30, 24th June 2025, Room PCC/1.5-6, presentation 11:30-11:50
Lucinda Mullen (Durham University)
Title: Spatio-temporal oscillations in the KellerâSegel model of chemotaxis with logistic growth
Abstract: Nonlinear reaction-cross-diffusion models, such as the KellerâSegel model of chemotaxis, have been proposed to describe spatial and spatiotemporal pattern formation observed in nature. Example applications include pigmentation on snake skin, and intricate patterns of bacteria, slime moulds, and other microorganisms. While useful to understand pattern formation in such systems, linear stability analysis of spatially homogeneous states can fail to capture the emergent dynamics of solutions to this system. In this talk, we discuss spatio-temporal oscillations, and even chaotic solutions, which emerge in these systems despite the absence of Hopf or wave bifurcations which would indicate oscillatory behaviours. We use multiple scales asymptotics to develop a quintic weakly nonlinear theory that predicts the structure of solutions to such systems near Turing bifurcations, and in particular near the codimension-2 point where the bifurcation changes from supercritical to subcritical. Focusing for concreteness on a KellerâSegel model with logistic growth of the cell density, we numerically show that solutions are generically oscillatory, and provide evidence that they are likely chaotic. Motivated by this behaviour, we also consider the theory of competing modes with slowly varying amplitudes to help explain the emergence of oscillations, motivated by similar approaches in fluid dynamics on subharmonic instabilities. We conjecture that these instabilities are distinct from other routes of spatiotemporal oscillation observed in reaction-transport systems, but that they may play important roles in understanding complex and chaotic motions observed in some systems.
MS09: 10:30-12:30, 24th June 2025, Room PCC/1.5-6, presentation 11:50-12:10
Rachel Nicks (University of Nottingham)
Title: Insights into oscillatory neural dynamics using a phase-amplitude framework
Abstract: Model reduction techniques can provide useful insight into the dynamics behaviour of high dimensional oscillatory systems such as networks of neurons or neural field models. In this talk we will discuss the recently introduced phase-isostable framework which extends the classical technique of phase reduction to include a notion of a distance from limit cycle. This allows for representation of off cycle trajectories, the description of a greater variety of dynamics and greater accuracy in capturing the behaviour of the full model. We will highlight how this framework can be utilised to reveal bifurcations of phase-locked states in discrete networks and how this can be extended to networks with conduction delays and networks where the node oscillations are induced by delays. If time allows, we will also see how the framework can be applied to continuum neural field models to investigate instabilities of oscillatory phase waves to more exotic patterned states, including chimeras.
MS09: 10:30-12:30, 24th June 2025, Room PCC/1.5-6, presentation 12:10-12:30
Benjamin Walker (University College London)
Title: Multi-timescale motility of microswimmers in background flows
Abstract: Despite their small size, microswimmers can have big impacts. Ranging from biofuel-related algae to disease-causing parasites, these swimmers exhibit a range of complex behaviours, many driven by interactions with fluid flow and surface interactions. In this talk, we will examine the role that the finest details of their swimming (e.g. the precise stroke that they use) play in generating their long-time, large-scale behaviours, focussing on the impacts of background flows. We’ll employ multi-timescale asymptotics (often seen in the context of oscillators) to systematically identify the important aspects of their swimming. As a result, we highlight a surprisingly simple dynamics that emerges from the complex interplay between swimmer and flow, as well as a means for reciprocal swimmers (who ordinarily make no progress on their own) to exploit background flows to achieve net propulsion.
MS10: 10:30-12:30, 25th June 2025, Room PCC/1.1-2, presentation 10:30-10:50
Susana Gomes (University of Warwick)
Title: On evolving network models and their influence on opinion formation
Abstract: In this talk, I will present a model for continuous-time opinion dynamics on an evolving network. In this model, individual’s opinions evolve continuously in time according to a Hegselmann-Krause model, but where the interaction between agents is mediated by a network. This network evolves in time through a system of ordinary differential equations for the edge weights. We interpret each edge weight as the strength of the relationship between a pair of individuals, with edges increasing in weight if pairs continually listen to each otherâs opinions and decreasing if not. We investigate the impact of various edge dynamics at different timescales on the opinion dynamics itself, both analytically and numerically. We will see that the dynamic edge weights can have a significant impact on the opinion formation process since they may result in consensus formation but can also reinforce polarisation. Overall, the proposed modelling approach allows us to quantify and investigate how the network and opinion dynamics influence each other and ultimately allows us to design control methodologies that steer the population to desired states.
MS10: 10:30-12:30, 25th June 2025, Room PCC/1.1-2, presentation 10:50-11:10
Emily Claughton (University of Nottingham)
Title: Dynamics of vowel mergers on networks
Abstract: Language pronunciation changes over time. An example of pronunciation change is the âvowel mergerâ, where the frequencies that are produced when two vowel sounds are spoken gradually become identical. For instance, some speakers do not distinguish between ‘cot’ and ‘caught’. We explore the dynamics of a network of speakers in which some speakers â referred to as mutators â have already undergone a vowel merger, while all others speakers maintain distinct frequencies for the two vowels. Two speakers interact by first producing vowels from speaker-specific frequency distributions, and then updating these distributions depending on the input they receive, i.e. the vowel frequencies produced by their interlocutor. We first show through agent-based simulations how the position of mutators in the network and their number affects vowel mergers. To understand this behaviour, we derive an exact ODE for the mean production frequencies of each speaker, which holds for any network topology and network size. A spectral analysis of the ODE reveals that mutators introduce modes of convergence between the two vowels that depend on their position in the network. Crucially, our analysis shows that while the degree of a mutator is the dominant determinant of the speed of convergence, the actual value depends on node properties beyond nearest neighbours.
MS10: 10:30-12:30, 25th June 2025, Room PCC/1.1-2, presentation 11:10-11:30
David OSullivan (University of Limerick)
Title: Modeling diffusion in networks with communities: A multitype branching process approach
Abstract: The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools to analyze diffusion processes on networks with communities are needed. In this paper, we develop theoretical tools using multitype branching processes to model and analyze diffusion processes, following a simple contagion mechanism, across a broad class of networks with community structure. We show how, by using limited information about the networkâthe degree distribution within and between communitiesâwe can calculate standard statistical characteristics of propagation dynamics, such as the extinction probability, hazard function, and cascade size distribution. These properties can be estimated not only for the entire network but also for each community separately. Furthermore, we estimate the probability of spread crossing from one community to another where it is not currently spreading. We demonstrate the accuracy of our framework by applying it to two specific examples: the stochastic block model and a log-normal network with community structure. We show how the initial seeding location affects the observed cascade size distribution on a heavy-tailed network and that our framework accurately captures this effect.
MS10: 10:30-12:30, 25th June 2025, Room PCC/1.1-2, presentation 11:30-11:50
Luisa Estrada (University of Warwick)
Title: On the limits of PAC learning of networks from opinion dynamics
Abstract: Agents in social networks with threshold-based dynamics change opinions when influenced by sufficiently many peers. Existing literature typically assumes that the network structure and dynamics are fully known, which is often unrealistic. In this work, we ask how to learn a network structure from samples of the agents’ synchronous opinion updates. Firstly, if the opinion dynamics follow a threshold rule where a fixed number of influencers prevent opinion change (e.g., unanimity and quasi-unanimity), we give an efficient PAC learning algorithm provided that the number of influencers per agent is bounded. Secondly, under standard computational complexity assumptions, we prove that if the opinion of agents follows the majority of their influencers, then there is no efficient PAC learning algorithm. We propose a polynomial-time heuristic that successfully learns consistent networks in over 97% of our simulations on random graphs, with no failures for some specified conditions on the numbers of agents and opinion diffusion examples.
MS10: 10:30-12:30, 25th June 2025, Room PCC/1.1-2, presentation 11:50-12:10
Benedict Russell (University of Warwick)
Title: Policy Gradient Dynamics of Cooperation-Promoting Partner Selection
Abstract: Social Dilemmas are a great challenge for self-interested autonomous agents, as they must set aside the immediate reward of selfish behaviour for cooperation to emerge. Mechanisms such as partner selection have been proposed to overcome this challenge, with promising results obtained through agent-based simulation. However, we lack an understanding of the robustness of such results and the theoretical basis for when and why certain rules promote cooperation remains limited. In this paper, we provide a theoretical framework to analyse softmax policy gradient and network dynamics in multi-agent systems with different partner selection rules, integrating evolutionary game theory, Markov chains, and dynamical systems. Known to promote cooperation in social dilemmas, we derive a model for the Out-for-Tat partner selection rule and compare it with random matching as a control mechanism. We investigate parameter regimes under which cooperation emerges or fails to materialise. Our analysis, backed by simulations, reveals how these selection rules can promote or hinder cooperative behaviour and offer insights into their robustness.
MS10: 10:30-12:30, 25th June 2025, Room PCC/1.1-2, presentation 12:10-12:30
Tim Rogers (University of Bath)
Title: Origins of Instability in Symmetric Networked Dynamical Systems
Abstract: Robustness to perturbation is a key topic in the study of complex systems occurring across a wide variety of applications from ecology to economics. In this talk I will explore the eigenspectrum of the Jacobian matrices associated to a general class of networked dynamical systems. I will show that stability is always determined by a spectral outlier, but with pronounced differences to the corresponding eigenvector in different regimes. Depending on model details, instability may originate in nodes of anomalously low or high degree, or may occur everywhere in the network at once. Importantly, the dependence on extremal degrees results in considerable finite-size effects with different scaling depending on the ensemble degree distribution. Our results have potentially useful applications to network monitoring to predict or prevent catastrophic failures.
MS11: 15:40-17:40, 25th June 2025, Room PCC/1.1-2, presentation 15:40-16:20
Mohit Dalwadi (University of Oxford)
Title: Losing symmetry and causing chaos: Emergent 3D dynamics of rapidly yawing microswimmers
Abstract: I investigate how the rapid yawing motion of 3D microswimmers affects their emergent dynamics in viscous shear flow. This can be considered an active version of the classic fluid mechanics result of Jefferyâs orbits for inert spheroids, first explored in the 1920s. Using a technical multiple scales (asymptotic) analysis for systems, I show that the rapid yawing generates non-axisymmetric emergent effects, hydrodynamically equivalent to a passive particle with two orthogonal planes of symmetry. Moreover, I show that this effective asymmetry can cause chaotic behaviour in the emergent dynamics. This is in stark contrast to the emergent dynamics generated by (constant) rapid rotation, a different type of short-scale motion, which only generates non-chaotic emergent dynamics.
MS11: 15:40-17:40, 25th June 2025, Room PCC/1.1-2, presentation 16:20-16:40
Prabakaran Rajamanickam (University of Strathclyde)
Title: Homogenised free energies for nano-doped cholesteric systems
Abstract: Colloidal nanoparticles, like quantum dots and gold nanoparticles, offer exciting possibilities for manipulating the optical and mechanical properties of liquid crystals when dispersed within them. This study investigates the impact of such nanoparticles on confined cholesteric systems using a homogenized Landau-de Gennes framework. We reveal the emergence of biaxial liquid crystal phases in spatially homogeneous systems, even when the colloidal particles themselves are uniaxial. Additionally, we explore the rich landscape of metastable states and their transitions in inhomogeneous systems, extending previous work that did not incorporate nanoparticles.
MS11: 15:40-17:40, 25th June 2025, Room PCC/1.1-2, presentation 16:40-17:00
Zita Borbala Fulop (University of Glasgow)
Title: Multiscale Analysis of Electrically Stimulated Vascularised Tumours: A Patient-Specific Theoretical and Computational Approach
Abstract: Electroporation-based therapies such as electrochemotherapy (ECT) hold great promise for improving cancer treatments. While highly effective for superficial tumours, its application for deep-seated malignancies is challenged by complex microstructural properties, and current models often lack a multiscale theoretical framework to capture those phenomena. Here, we develop and solve a novel system of coupled partial differential equations of Darcy-Laplace type obtained by applying the asymptotic homogenisation technique. We study the tumour response stimulated by an electric field, deriving effective macroscale equations for pressure, velocity, and electric potential while incorporating both hydraulic and electric microscale tissue heterogeneities. Our coupled multiscale approach bridges the gap between the tumour microstructure and macroscale dynamics, offering a more comprehensive understanding of how tumour size, morphology, and hydraulic-electrical interactions influence interstitial flow. Using patient-specific data, we further investigate how the shape of the microscale cell inclusion affects the macroscale domain, specifically the pressure profile and electric field distribution. We present a parametric analysis of the hydraulic conductivity tensor and macroscale numerical simulation results for pressure and velocity fields, highlighting the role of the electric field in modulating fluid flow. Our findings provide meaningful insights toward advancing ECT protocols.
MS11: 15:40-17:40, 25th June 2025, Room PCC/1.1-2, presentation 17:00-17:20
Hannah-May D’Ambrosio (University of Glasgow)
Title: The effect of capillary forces on lubricated viscous gravity currents
Abstract: Gravity-driven flow is ubiquitous in nature, industry, and biology, from the large scales of geophysical applications such as the flow of lava and ice sheets, to the small scales of industrial and medical applications, including coating processes and nasal drug delivery. The majority of previous theoretical studies of single-layer and two-layer viscous gravity currents assume a dominant balance of viscous and gravitational forces, which frequently admit similarity solutions. Whilst these models provide various insights into the flow and are applicable in the bulk, key assumptions are expected to break down near the front of the viscous gravity currents. One of these involves capillary forces, which are typically neglected in the bulk, but become important near the front where free surface gradients are large. In this talk, we explore a reduced-order model that incorporates gravitational, viscous, and capillary forces to describe the evolution of a thin film of lubricated viscous fluid near its front. We determine predictions for the free surface and the flow within the gravity current and show that, perhaps as expected, capillary forces act to reduce spreading, and hence the extent of the current, relative to the predictions of models which ignore this effect. We compare our findings against direct numerical simulations of the full problem obtained using a phase field method.
MS11: 15:40-17:40, 25th June 2025, Room PCC/1.1-2, presentation 17:20-17:40
Alejandro Roque Piedra (University of Glasgow)
Title: Chemoelectrical Dynamics in Neural Tissue.
Abstract: This research aims to develop a mathematical model to describe the chemoelectrical dynamics of nervous tissue derived from the mass balance principle, the principle of virtual work, and the entropy imbalance in a mixture of ionic species. In this formulation, the flux corresponding to the ions is used as the kinematic descriptor to account for the diffusive motion of the various species [1]. Furthermore, as usually done when studying the nervous tissue, we enforce the electroneutrality constraint which introduces a Lagrange multiplier describing the interactions between ions. This approach addresses the fact that the traditional NernstâPlanck equation does not directly account for ionic interactions, while the electroneutrality requires these interactions [2]. The resulting governing equations are imposed on a biphasic domain that simulates the intracellular and extracellular spaces of nervous tissue. At the interface between the two media (the cellular membrane), an electric current density consistent with the HodgkinâHuxley model is considered. Finally, a benchmark problem is solved using the weak formulation in COMSOL. (with Ariel RamĂrez-Torres, Alfio Grillo) References: [1] Fried E, Sellers S (2000). Microforces and the theory of solute transport. [2] Sarkar S, Aquino W (2011). Electroneutrality and ionic interactions in the modeling of mass transport in dilute electrochemical systems.
MS12: 15:10-17:10, 23rd June 2025, Room FOR/SR7-8, presentation 15:10-15:30
Ed Brambley (University of Warwick)
Title: An Overview of Mathematical Modelling in Metal Forming
Abstract: Metal forming covers a collection of industrial processes for deforming metal into the right shape. Examples include rolling blocks of metal to form thin sheets, and stamping sheets of metal to form car door panels. Mathematically, the governing equations are those of continuum mechanics, but are complicated by the constitutive laws needed to model the combination of elasticity, plasticity, and large deformations. Most “modelling” currently used in industry is brute force Finite Element “modelling”, and does not take advantage of small parameters, steady states, or stability analysis. There is huge potential for the use of the techniques of applied mathematics in creating new models of various processes of importance to industry, for example for use in online control and optimization, or even for validating Finite Element simulations. This is a call to arms for mathematical modellers everywhere: your metal forming industries need you!
MS12: 15:10-17:10, 23rd June 2025, Room FOR/SR7-8, presentation 15:30-15:50
Mozhdeh Erfanian (University of Warwick)
Title: Mathematical modelling of wire flat-rolling
Abstract: Flat wires are manufactured through the rolling technique, where a wire with a circular cross-section is cold rolled between a pair of cylindrical rolls. Since the wire can both elongate and widen, achieving a final product that closely matches the desired specifications requires accurate prediction of the lateral spread. A mathematical model for wire rolling is presented, focusing on predicting the lateral spread. The wire is assumed to be a rigid perfectly plastic material, and the 3D state of deformation is simplified to plane-stress deformation with the assumption of small thickness and width compared to the length of the roll gap (effectively a thin-wire large-roller assumption). This provides, for the first time, a model of lateral spread without any fitting parameters, which can serve as a reliable tool for validating FE results or guiding process design.
MS12: 15:10-17:10, 23rd June 2025, Room FOR/SR7-8, presentation 15:50-16:10
Steve Fitzgerald (University of Leeds)
Title: Nonlinear response of crystal dislocations: a stochastic PDE approach
Abstract: Under most circumstances, dislocations are driven through their crystal by a combination of applied stress and thermal fluctuations. Their average velocity, as a function of stress and temperature, is a crucial ingredient of discrete and continuum models of dislocation dynamics and plasticity at the mesoscale. This velocity has been experimentally shown [1,2] to be an extraordinarily nonlinear function of stress: up to the fortieth (40th) power at low temperatures. In this talk I will use a path integral approach to determine the average velocity from the stochastic PDE governing the dislocation motion, and explain how this enormous nonlinearity arises (spoiler: itâs not really a power law at all). The resulting formulae are in good agreement with atomistic simulations [2], and consistent with the original observations. The underlying model (an elastic string driven through a periodic potential) may also be applied to other systems, such as Josephson junctions in superconductors. [1] Turner, A. & Vreeland, T. Acta Met.18, 1225â1235 (1970) [2] Altshuler, T. & Christian, J. Phil. Trans. Roy. Soc. London A 261, 253â287 (1967) [3] Gilbert, M., Queyreau, S. & Marian, J. Phys. Rev. B 84, 174103 (2011)
MS12: 15:10-17:10, 23rd June 2025, Room FOR/SR7-8, presentation 16:10-16:30
Eva Zaat (Warwick Mathematics Institute, University of Warwick)
Title: Three-point bending of sheet metal
Abstract: The three-point bending test evaluates a metal sheet’s response to bending. The ability to accurately predict the behaviour of material in this experiment is sought-after by mechanical engineers, as it would provide a link between experimental results and the material’s properties. We endeavour to gain a comprehensive understanding of the underlying principles governing the deformation and failure of materials during this test by constructing a mathematical model of three-point bending. We will discuss the experimental setup, the challenges encountered in obtaining consistent results and the analysis of the data collected. The key factors that were identified as influencing the outcomes at various length-scales include the direction of the grains in the material, the hardening of the material and the friction between the sheet and the punch of the testing equipment. We therefore explore hardening and friction laws to formulate an accurate mathematical description of the experiment. Additionally, we would like to address some of the challenges posed by non-linearities in the underlaying governing equations, using asymptotic analysis and numerical simulations to provide insights into the influence of these factors. In the long term, this model would be validated against further experimental data and could be adapted to other experimental scenarios.
MS12: 15:10-17:10, 23rd June 2025, Room FOR/SR7-8, presentation 16:30-16:50
Doireann O’Kiely (MACSI, University of Limerick)
Title: Modelling wrinkles in metal sheets
Abstract: Wrinkles occur in a plethora of everyday situations and technological applications, across skin, balloons, flexible electronics and metal forming processes. In many situations these wrinkles can be described using elasticity models, but when wrinkles form in metal sheets, plastic deformation is highly likely. In this talk I will outline some recent work to model wrinkling beyond the elasticity threshold.
MS12: 15:10-17:10, 23rd June 2025, Room FOR/SR7-8, presentation 16:50-17:10
Maciej Buze (Lancaster University)
Title: Upscaling a model of anti-plane near-crack-tip plasticity
Abstract: Near-crack-tip plasticity arises from the rearrangement of atoms near a crack tip in response to stress accumulation. This process is primarily mediated by topological defects known as dislocations, which serve as carriers of plastic deformation. Such deformations can play a crucial role in shielding materials from further crack propagation, making their rigorous mathematical modelling essential for understanding structural integrity in engineering applications. In this talk, I will present recent and ongoing work on a mathematically rigorous bottom-up approach to modelling near-crack-tip plasticity. Starting from an anti-plane atomistic bond-energy formulation, we establish a rigorous atomistic-to-continuum limit, where the limiting continuum energy aligns with known linearised elasticity models for Mode III crack and screw dislocations interaction. A key novelty of our approach lies in simultaneously accounting for both cracks and dislocations while considering a joint limit in which the lattice spacing tends to zero and the number of dislocations goes to infinity.
MS13: 15:40-17:40, 24th June 2025, Room PCC/2.1-2, presentation 15:40-16:00
Nicholas Harbour (University of Nottingham)
Title: Mathematical modelling of differentiation therapy for glioma stem cells
Abstract: Glioblastoma (GBM) is the most aggressive and most common primary brain tumour in adults and is uniformly fatal, with a poor median survival time of 15. Standard of care for GBM consist of radiotherapy either alone or following surgical resection, despite this, radio-resistance almost always occurs making recurrence inevitable. Failure of the current standard of care has been partly attributed to a special sub-population, the glioma stem cells (GSCs), which initiate and drive tumour growth. Treatment cannot be successful unless all GSCs are eliminated. However, GSCs are known to be highly resistant to radiotherapy, and complete surgical removal is impossible in GBM. Therefore, new treatments that specifically target GSCs could have a potentially large benefit. BMP4 has been shown to induce differentiation of GSCs towards a less malignant, astrocytic-like (ALCs) lineage reversing the GSC state and reducing radio-resistance. We develop a data driven mechanistic mathematical model that accounts for the GSCs, tumour cells (TCs) and ALCs as well as their response to both radiotherapy and BMP4 induced differentiation therapy. We parameterise our model based on data collected from twelve GSC cell lines, that underwent various BMP4 and radiotherapy treatments. Through virtual clinical trials we determine an optimal dosing strategy for BMP4 in combination with radiotherapy. We identify several key parameters that impact the efficacy of BMP4 therapy including radiosensitivity and proliferation rate. These parameters can be used to strategically select candidates for real clinical trials that will likely have the largest benefit.
MS13: 15:40-17:40, 24th June 2025, Room PCC/2.1-2, presentation 16:00-16:20
Kit Gallagher (University of Oxford / Moffitt Cancer Center)
Title: Deriving Optimal Treatment Timing for Adaptive Therapy: Matching the Model to the Tumour Dynamics
Abstract: Adaptive therapy (AT) protocols have been introduced to combat drug-resistance in cancer, and are characterised by breaks in maximum tolerated dose treatment (the current standard of care in most clinical settings). These breaks are scheduled to maintain tolerably high levels of tumor burden, employing competitive suppression of treatment-resistant sub-populations by treatment-sensitive sub-populations. AT has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate-resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma, with initial clinical results suggesting that it can offer significant extensions in the time to progression over the standard of care. However, these clinical protocols may be sub-optimal, as they fail to account for variation in tumor dynamics between patients, and result in significant heterogeneity in patient outcomes. Mathematical modelling and analysis have been proposed to optimise adaptive protocols, but they do not account for clinical restrictions, most notably the discrete time intervals between the clinical appointments where a patient’s tumor burden is measured and their treatment schedule is re-evaluated. We present a general framework for deriving optimal treatment protocols which account for these discrete time intervals, and derive optimal schedules for a number of models to avoid model-specific personalisation. We identify a trade-off between the frequency of patient monitoring and the time to progression attainable, and propose an AT protocol based on a single treatment threshold. We show that this threshold is highly patient-specific, motivating the personalisation of AT schedules. Finally, we identify a subset of patients with qualitatively different dynamics that instead require a novel AT protocol based on a threshold that changes over the course of treatment.
MS13: 15:40-17:40, 24th June 2025, Room PCC/2.1-2, presentation 16:20-16:40
Hugh Selway-Clarke (UCL)
Title: In silico testing of hypotheses for the effect of smoking on somatic evolution in the healthy human lung
Abstract: Recent single-cell genomic analysis of healthy lung tissue (Yoshida et al, Nature 2020) has shown remarkable intra-tissue heterogeneity in the degree of effect smoking has on mutational burden, as well as an expansion of less-mutated basal cell sub-populations after smoking cessation. These two findings suggest potential mechanisms for somatic evolution in the healthy lung, which forms the backdrop for lung cancer formation. Here, we use computational modelling, based on a model of lung homeostasis previously verified by lineage tracing (Teixeira et al, eLife 2013), to assess the ability of these hypotheses to reproduce observations. Applying machine learning methodology via a set of biologically motivated metrics to simulations of basal lung cell populations over the course of patients’ lifetimes, we find preliminary evidence for a protected sub-population of basal cells in the lung which are less affected by smoking. The simulations suggest that this protected sub-population, in combination with immune targeting of highly mutated cells being dampened during smoking, can best reproduce the unexpected dynamics seen in the data. With further testing and validation in epidemiological datasets, this mechanistic understanding will streamline future research into the early detection and prevention of lung cancer.
MS13: 15:40-17:40, 24th June 2025, Room PCC/2.1-2, presentation 16:40-17:00
Nikolaos Sfakianakis (University of St Andrews)
Title: The Mathematical Hallmarks of Cancer: Past, Present, and Future
Abstract: Cancer is a complex disease governed by a set of distinct biological capabilities, collectively known as the Hallmarks of Cancer. These hallmarks include sustaining proliferative signalling, evading growth suppressors, resisting cell death, enabling replicative immortality, inducing angiogenesis, and activating invasion and metastasis. More recently, additional hallmarks have been identified, such as avoiding immune destruction, deregulating cellular energetics, and promoting genome instability. Since its inception over 50 years ago, Mathematical Oncology has played a critical role in studying these hallmarks through a variety of mathematical frameworks, including differential equations, agent-based models, and stochastic processes. These approaches have been instrumental in quantifying tumour growth, metastasis, treatment responses, and therapeutic resistance, contributing to a deeper understanding of cancer biology and informing clinical strategies. This lecture will examine key developments in the mathematical study of cancer hallmarks, tracing their evolution from early conceptual models to their integration into modern cancer research and clinical applications. We will explore how mathematical models provide insights into tumour dynamics, cancer cell interactions with the microenvironment, and the emergence of resistance. A particular focus will be given to modelling tumour progression, invasion, metastasis, and treatment efficacy. Finally, we will discuss recent advances in Mathematical Oncology and the key challenges that lie ahead. This will include emerging research directions, novel modelling techniques, and the integration of Artificial Intelligence and Virtual Reality into mathematical frameworks. We will also examine the ongoing challenges in translating mathematical predictions into clinical practice, ultimately aiming to contribute to improved patient outcomes and the advancement of personalized medicine.
MS13: 15:40-17:40, 24th June 2025, Room PCC/2.1-2, presentation 17:00-17:20
Vedang Narain (University of Oxford)
Title: Modelling the effect of vascular architecture on the outcome of cancer therapies
Abstract: Tumour angiogenesis generates structurally and spatially abnormal blood vessels. Consequentially, poor blood perfusion and increased hypoxia impair a tumour’s response to therapies. Strategies to normalise vasculature have yielded mixed results, limiting their clinical deployment. In this work, we used mathematical and computational models to determine the influence of a tumourâs vascular architecture on its treatment response. We first identified vascular features correlated with enhanced perfusion following radiotherapy in human tumour xenografts (Köry et al., 2024). We found that immature vascular networks exhibited the largest increases in perfusion after irradiation. We also found that blood rerouting following radiotherapy-induced pruning could transiently increase perfusion, underscoring the potential of a single dose to induce a window of normalisation in which successive doses could be more effective. To formalise the link between perfusion and oxygenation, we evaluated and refined mathematical rules governing haematocrit distributions using microfluidic network data. We used these rules to simulate oxygen transport in synthetic vascular networks and evaluated architectural metrics on their ability to predict hypoxia. Our investigation found that network connectivity was a robust characteristic for inferring tumour oxygenation and, as a result, the oxygen-modulated response to radiotherapy. We also demonstrated that biophysical factors could induce a normalisation window. Finally, we developed a computational pipeline to analyse and simulate real-world vascular networks from microscopy images of murine tumours. Using this pipeline, we found evidence to support our inferences from synthetic networks. With further experimental validation, our findings could inform new translational research to enhance a tumour’s sensitivity to therapies.
MS13: 15:40-17:40, 24th June 2025, Room PCC/2.1-2, presentation 17:20-17:40
Meritxell Brunet Guasch (The University of Edinburgh)
Title: Quantifying the evolution of metastatic potential across cancer tissues
Abstract: Cancers of different origins exhibit remarkable variation in the incidence of metastatic disease, yet the underlying causes of this heterogeneity remain largely unexplored. In particular, the evolution of traits that enable metastasis seeding is poorly understood. Here, we integrate multi-region tumor biopsies from paired primary and metastatic samples across different cancer types (n=32 colorectal, n=17 breast and n=15 pancreatic cancers) and SEER epidemiological data with a mathematical model of metastasis evolution. The model parameters include the rate at which the primary tissue evolves metastatic ability, and the rate at which metastatically-able cells disseminate to form metastases, which are learned from the data via Approximate Bayesian Computation (ABC). Our findings reveal differences across both primary tissues and metastases organs. In colorectal cancers, only a fraction of cancers will seed metastasis to the lymph nodes, but those that do acquire this ability early in tumor progression. In both colorectal and breast cancer, distant metastases are seeded by one or only few metastatically competent clones, suggesting the evolution of a âspecialâ trait necessary for metastasis. A similar pattern is observed in breast adenocarcinoma. Conversely, in pancreatic adenocarcinomaâa far more aggressive diseaseâmost primary tumor regions are capable of distant metastasis, indicating an inherent metastatic proclivity of the founder cell. This study provides a unifying framework for understanding the evolution of metastasis, which may guide future, more systematic investigations into the potential molecular drivers of metastatic progression.
MS14: 10:30-12:30, 25th June 2025, Room PCC/1.5-6, presentation 10:30-10:50
Daniel Galvis (University of Birmingham)
Title: Phase synchronisation of a coupled Stuart-Landau oscillator chain with endpoint heterogeneity
Abstract: Cell-intrinsic heterogeneities and their impact on collective dynamics are key to understanding how pancreatic beta-cell networks coordinate insulin secretion. For example, subpopulations of highly-excitable beta cells may act as pulse generators, pacemakers, or hubs, playing a crucial role in governing network-wide responses. Evidence suggests a non-uniform spatial organisation of these cells, and our previous models explored how this non-uniformity impacts on network-wide activation thresholds and phase synchronisation. Another modelling study recently proposed that similarity in intrinsic properties may better predict pairwise synchronisation over direct coupling in beta-cell networks. Moreover, they found evidence for increased coupling strength and increased cell-intrinsic excitability along the shortest paths between synchronised nodes. Motivated by this, we developed a model of coupled Stuart-Landau oscillators where two intrinsically-active endpoint nodes are indirectly coupled through a chain of interior nodes. We examined how coupling strength and excitability of these interior nodes impacts on the activation and phase synchronisation of the endpoint nodes. Through simulation and numerical continuation, we characterised the existence and stability of several phase-locked solutions. Specifically, we focussed on two key solution typesâthe âchevronâ and âanti-phase chevronâ solutionsâwhere endpoint nodes are either in phase or antiphase, respectively. We further identified a consistent structure in the stability exchanges of these solution types, featuring a bistable region and a loop-shaped branch of unstable, asymmetric solutions. Our findings highlight that chains with distributed heterogeneities can support multiple phase-locked solutions, offering insights relevant to various real-world networks.
MS14: 10:30-12:30, 25th June 2025, Room PCC/1.5-6, presentation 10:50-11:10
Emmanuel Molefi (Newcastle University)
Title: Multimodal Modeling of Ultradian Rhythms Using the Hankel Alternative View of Koopman (HAVOK) Analysis
Abstract: Ultradian rhythms â quasi-rhythmic fluctuations in behaviour and physiology with periods shorter than 24 hours â are observed across various organisms, including humans. Despite their role in key biological processes such as sleep architecture and hormone regulation, their underlying mechanisms remain poorly understood. Here, we model ultradian dynamics using the Hankel alternative view of Koopman (HAVOK) framework â a data-driven technique for dynamical systems modelling based on early concepts from Takensâ embedding theorem and Koopman operator theory. This analysis provides a mechanism whereby dynamics of a nonlinear system can be captured by a linear model with intermittent forcing. Accordingly, enabling us to examine the types of linear dynamics that would be generated by a simple/regular oscillator versus more complex dynamics captured as intermittent forcing. Our findings demonstrate intermittently forced linear systems as a useful framework for understanding ultradian rhythms and their regulation. This has important implications for understanding ultradian variation in health and disease; importantly, for navigating disabling conditions such as epilepsy, depression, and schizophrenia.
MS14: 10:30-12:30, 25th June 2025, Room PCC/1.5-6, presentation 11:10-11:30
Melvyn Tyloo (University of Exeter)
Title: Resilience of synchronized networks to time-scale separation
Abstract: Coupled biological oscillators might evolve on different timescales because of their intrinsic dynamics or due to damages to some of the components. In this talk, we will evaluate how the response of synchronized oscillators is affected when a subset of them evolves on a different timescale. We will discuss network structures that are essentially insensitive to timescale separation and present scenarios where the response is significantly altered.
MS14: 10:30-12:30, 25th June 2025, Room PCC/1.5-6, presentation 11:30-11:50
Stanislaw Biber (University of Surrey)
Title: Mechanisms for Entrainment in Deep Brain Stimulation Treatment for Parkinsonâs Disease
Abstract: Deep brain stimulation (DBS) is used in Parkinsonâs Disease to alleviate symptoms and improve quality of life. First implemented more than 60 years ago, now more than 25,000 devices are implanted annually. In DBS, electric leads are implanted in, for example, the subthalamic nucleus (STN) of the brain. Typically, electric stimulation is applied 24 /7 with pulses of a fixed width, amplitude and frequency. State-of-the-art devices are estimated to alleviate symptoms 60% of the time. Mechanisms by which DBS works are largely unknown, limiting the ability to further improve symptom control. Recent work has made at least three important steps. First, on medication some patients exhibit a peak in the electrocortical activity in a narrow gamma band (~60-90 Hz). Second, in the presence of stimulation the gamma band peak is enhanced and shifts to half the stimulation frequency. Third, a mechanistic mathematical model that explains the shift in terms of entrainment has been developed. However, open questions remain as to the robustness of the approach. Here we present our analysis of mathematical models for DBS, with the focus on entrainment mechanisms. Our long-term goal is to inform the future design of closed-loop DBS devices that adapt to patient need in real time.
MS14: 10:30-12:30, 25th June 2025, Room PCC/1.5-6, presentation 11:50-12:10
Hardik Poptani (University of Liverpool)
Title: Spatio-Temporal Patterns Forming in FitzHugh-Nagumo Model
Abstract: In 1952, Hodgkin and Huxley have introduced a model describing the initiation and propagation of action potentials in neurons using nonlinear differential equations. Taking inspiration, FitzHugh (1961) has simplified the Hodgkin-Huxley model into two variable model with cubic nonlinearity describing properties of excitation and propagation of sodium and potassium ions in neurons. FitzHugh-Nagumo equations have been popularised as a prototype reaction-diffusion system which can also reproduce such phenomena as travelling waves in nerve fibre or formation of Turing Patterns in reaction-diffusion systems. Turing Patterns are periodic stationary patterns emerging in reaction-diffusion systems which were first reported by Alan Turing in his seminal paper published in (1952). Keller and Segel (1971) have shown that similar patterns can also emerge in reaction-diffusion-advection systems. In many such cases to analyse the amplitude of Turing Patterns, Fourier Series have been used. However, such analysis methods such as weak nonlinear analysis has been used to analyse which involves using a critical parameter and small timescale expansions around the parameter to form an amplitude equation as they do not involve convergence unlike Fourier Series. In addition, a requirement for deriving amplitude equations involves expansions up to third order which can be described by cubic nonlinearity, which appears in the FitzHugh-Nagumo equations. For this presentation, we will be talking about the spatio-temporal patterns observed in FitzHugh Nagumo model along with using Fourier analysis and Weak Nonlinear Analysis to compute and compare the amplitude of the Turing Patterns without diffusion and with a model involving advection.
MS14: 10:30-12:30, 25th June 2025, Room PCC/1.5-6, presentation 12:10-12:30
Jake Ahern (University of Birmingham)
Title: Modelling seizure cycles and anti-seizure medication timing
Abstract: This talk explores the interplay between rhythmic brain excitability and the pharmaceutical control of epileptiform discharges (ED) using a combination of mathematical modeling and analysis of EEG data. Seizures and other ED are commonly modulated by oscillations ranging from a day (circadian) to multiple days (multidien) and years. Despite robust evidence for ED cycles, little is known about how anti-seizure medications (ASM) interact with these cycles. This study utilizes a mathematical description of seizure initiation to investigate how the temporal pattern of ASM doses impacts seizure frequency. A modified subcritical Hopf bifurcation model simulates seizure dynamics across a dynamic brain network, incorporating periodic fluctuations in excitability to generate seizure cycles. Using 24-hour EEG recordings, the aperiodic component of the signal is analyzed to investigate brain excitability and its relationship with ED. Simulations examine the impact of rhythmic excitability on seizure patterns and identify the optimal timing for ASM administration. These findings provide insights into the phase-dependent effects of ASM dosing and the potential role of excitability rhythms in seizure modulation.
MS15: 10:30-12:30, 25th June 2025, Room PCC/2.1-2, presentation 10:30-11:10
Laura Miller (University of Strathclyde)
Title: Homogenized modelling of the electro-mechanical behaviour of a vascularised poroelastic composite representing the myocardium
Abstract: We propose a novel model for a vascularised poroelastic composite representing the myocardium which incorporates both mechanical deformations and electrical conductivity. Our structure comprises a vascularised poroelastic extracellular matrix with embedded elastic inclusions (representing the myocytes) and we consider the electrical conductance between these two solid compartments. There is a distinct length scale separation between the scale where we can visibly see the connected fluid compartment separated from the poroelastic matrix and the elastic myocyte and the overall size of the heart muscle. We therefore apply the asymptotic homogenisation technique to derive the new model. The effective governing equations that we obtain describe the behaviour of the myocardium in terms of the zero-th order stresses, current densities, relative fluidâsolid velocities, pressures, electric potentials and elastic displacements. It effectively accounts for the fluid filling in the pores of the poroelastic matrix, flow in the vessels, the transport of fluid between the vessels and the matrix, and the elastic deformation and electrical conductance between the poroelastic matrix and the myocyte. This work paves the way towards a myocardium model that incorporates multiscale deformations and electrical conductivity whilst also considering the effects of the vascularisation and indeed the impact on mechanotransduction.
MS15: 10:30-12:30, 25th June 2025, Room PCC/2.1-2, presentation 11:10-11:30
David Morselli (University College London)
Title: Modelling T-cell migration in the tumour microenvironment
Abstract: The success of antitumour immunotherapy is based on the ability of immune cells to migrate in the stroma and establish contact with the tumour cells. Previous experimental studies demonstrated the influence of collagen fibres’ orientations on the migration of resident T cells, showing that aligned fibres may prevent immune cells from entering tumour islets. However, the exact mechanisms governing the migration are still poorly understood. We present here a stochastic agent-based model for T-cell migration in the microenvironment of tumours. The model includes the alternate forward and backward movements of immune cells on collagen fibres. We apply our framework to model T-cell migration in human tumours, using collagen fibres’ configurations obtained from human tissue slices. Different collagen configurations appear to be associated with different treatment outcomes. Comparison of the model with experimental data allows us to understand which mechanisms affect migration the most and gain insight into T-cell infiltration of tumours. These insights could suggest therapeutic strategies to improve immune infiltration in the context of immunotherapy.
MS15: 10:30-12:30, 25th June 2025, Room PCC/2.1-2, presentation 11:30-11:50
Sarah Donaldson (University of Glasgow)
Title: A Physiologically Accurate Active Strain Model for Left Ventricular Contraction
Abstract: Modelling the mechanical properties of the myocardium such as the passive and active responses is an essential component of mathematical cardiac models. Passive myocardium is considered to be anisotropic and hyperelastic, and its contractile function is usually modelled by an active stress approach, where the total stress is obtained by adding the passive and active stress tensors together. Another method to model myocardial contraction is the active strain approach, where the deformation gradient is multiplicatively decomposed into passive and active components, overcoming issues of mathematical convexity arising from the active stress approach. Furthermore, the active strain approach depends on local distortions that relate to the microstructure of myofilaments, by signifying the sequential order between active distortion and elastic stretch. In this work, a new active strain model is introduced, that is physiologically accurate with parameters that could be calibrated from measured data. By further incorporating a limiting function on the elastic stretch that a living myocyte can experience, the new active strain model can accommodate different levels of active contraction. An existing left ventricular model is then used to simulate realistic left ventricular pump function, which is implemented with an immersed boundary method with finite element extension. We compare the new active strain model with the active stress approach using the same left ventricular model. Results suggest that the new active strain model can simulate left ventricular dynamics as effectively as the active stress model, with subtle differences in fibre stress, despite the two models being fundamentally different.
MS15: 10:30-12:30, 25th June 2025, Room PCC/2.1-2, presentation 11:50-12:10
Andrea Pastore (Politecnico di Torino)
Title: An approach to growth mechanics based on the analytical mechanics of nonholonomic systems
Abstract: A novel framework bridging the Analytical Mechanics of nonholonomic systems [1] with the biomechanics of volumetric growth in biological tissues [2] is presented. To establish this connection, some key results of nonholonomic mechanics are adapted to the continuum framework of biomechanics [3,4,5]. In this presentation we introduce the so-called “growth tensor” [6] as the primary descriptor of the mediumâs structural kinematics, and, by considering the mass source as a phenomenologically assigned quantity, we reformulate the mass balance law as a nonholonomic constraint that dictates the evolution of the growth tensor. With this foundation, we develop a theoretical framework for growth mechanics based on a Lagrangian formulation that systematically incorporates the nonholonomic constraint on the growth tensor [5]. Despite its non-integrable nature, this constraint is handled within a variational setting by extending a previously developed approach that refines Kozlovâs “Vakonomic dynamics,” ensuring its compatibility with established mechanical models [7,8]. References: [1] Neimark, J., Fufaev, N.A.: Dynamics of Nonholonomic Systems. AMS, 1972. [2] Epstein, M., Maugin, G.A.: Int. J. Plasticity 16(7-8) 951-978 (2000). [3] Grillo, A., Di Stefano, S., Math. Mech. Solids 28(10) 2215-2241 (2023). [4] Grillo, A., Di Stefano, S.: Math. Mech. Solids 29(1) 62-70 (2024). [5] Grillo, A., Pastore, A. & Di Stefano, S.: J. Elast. 157, 3 (2025). [6] DiCarlo, A., Quiligotti, S.: Mech. Res. Commun. 29(6) 449-456 (2002). [7] Llibre, J., RamĂrez, R., Sadovskaia, N.: Nonlinear Dynamics, 78 2219-2247 (2014). [8] Pastore, A., Giammarini, A., Grillo, A.: Acta Mechanica, 235 2341-2379 (2024).
MS15: 10:30-12:30, 25th June 2025, Room PCC/2.1-2, presentation 12:10-12:30
Mohammed Alwady (University of Glasgow)
Title: Homogenised balance equations of passive liquid crystals flow in quasi-rigid porous media
Abstract: In this paper, we derive a new mathematical model for the macroscopic behaviour of a quasi-rigid porous matrix interacting with an incompressible passive uniaxial nematic liquid crystal via the asymptotic homogenization technique. We assume that the typical distance between the channels (microscale) is significantly smaller than the average size of a whole domain (macroscale). This technique exploits the sharp length scale separation, characterised by a small parameter É to derive the quasi-static governing equations for the new macroscale model by upscaling the fluidâstructure interaction problem between the solid phase and the fluid phase. The resulting system of partial differential equations, which governs the fluid flow, incorporates the microscale interactions in the coefficients of the model, which are to be computed by solving classical periodic cell problems. The final homogenized model provides a novel constitutive relationship for the nematic liquid crystal flow with the alignment of the director field and the microstructural configuration of the porous matrix that leads to a viscoelastic constitutive behaviour at the macroscale. As a result, we can establish from this complex anisotropic flow pattern at the macroscale another pattern that purely describes the fluid dynamics of the system when we can neglect the role of the solid stresses in the bulk. This work can, from a perspective, help understand the macroscale behaviour of passive nematic liquid crystals in quasi- rigid porous structures, and it is relevant to a wide range of applications in the various fields of engineering and science. This includes modelling and analysing biological fluid transport, cellular motility, and biomechanical interactions. These results have immediate applications in tissue engineering, drug delivery, and the investigation of cellular dynamics in complex environments.
MS16: 15:40-17:40, 25th June 2025, Room NEW/BLU, presentation 15:40-16:00
Daniel Ratliff (Northumbria University)
Title: What is the Queer Experience in UK Mathematics?
Abstract: The historical image of a stereotypical mathematician (an older cis white man, perhaps with unkempt hair) is being increasingly challenged and is beginning to change. Modern mathematics is constantly working towards being a diverse environment, and whilst efforts have often focused on visible characteristics (like race and gender) there remains a challenge to support less visible ones like neurodiversity and queerness. This often comes from a difficultly in assessing the barriers and experiences of these groups, which can be as hidden as the identities affected by them, so as a queer mathematician myself I got to asking â what is the queer experience in mathematics? What are the barriers queer mathematicians face in modern mathematics? This talk follows my journey into trying to find an answer to these questions. Finding no direct survey or literature for UK mathematics, Iâll start by talking about a comprehensive one in adjacent STEM subjects and what it tells us might be some of the challenges queer mathematicians might face. This leads nicely onto what members of the community have been doing recently to help overcome these challenges, including establishing the Queer Equality and Diversity (QED) network over the last year. Throughout, Iâll frame this journey with my own experiences over the past year and highlight the wonderful, supportive community Iâve found along the way.
MS16: 15:40-17:40, 25th June 2025, Room NEW/BLU, presentation 16:00-16:20
Tacey O’Neil (The Open University)
Title: Hiding out in analysis
Abstract: I will talk about both my research interests in analysis and geometric measure theory along with my experiences of coming out as transgender in my fifties. There may be selfies.
MS16: 15:40-17:40, 25th June 2025, Room NEW/BLU, presentation 16:20-16:40
Tyler Kelly (Queen Mary University of London)
Title: Queer Liberation and Joy in Mathematics
Abstract: Mathematics is done best when one can free oneself to think deeply in mathematics. Queer and trans people and identities are recently often under political and personal attack globally and locally. A lack of safety affects one’s ability to think deeply. We will talk about what it means to create environments and space to enable queer and trans people to do their best mathematics.
MS16: 15:40-17:40, 25th June 2025, Room NEW/BLU, presentation 16:40-17:00
Lena Payne (University of Kent)
Title: Queer Experiences in Academia
Abstract: I will be talking about personal experiences of being Queer in academia, and the specific barriers and issues faced in academia. I will also discuss how the queer community, and wider academia community can hope to combat this and support one another.
MS16: 15:40-17:40, 25th June 2025, Room NEW/BLU, presentation 17:00-17:20
Kat Phillips (University of Warwick)
Title: Queerly Engaging Discussions (Panel Session)
Abstract: To conclude our minisymposium, this panel session will bring together our invited speakers for an open discussion on the experiences, challenges, and opportunities facing LGBTQ+ mathematicians today. We will faciliate a space to reflect on the key themes raised throughout the talks, including visibility, inclusion, and the intersections of personal and mathematical identity. This session aims to build connections among attendees, celebrate the contributions of LGBTQ+ mathematicians, and inspire collective action toward a more equitable mathematical community. Whether you are an early-career mathematician, a seasoned academic, or an ally looking to learn, we invite you to join us in this important conversation.
MS17: 15:40-17:40, 25th June 2025, Room PCC/2.1-2, presentation 15:40-16:00
Mitchell Berger (U. of Exeter)
Title: Measures of topological structure within subregions of space
Abstract: Suppose we have a collection of curves inside (or outside a bounding surface. How do we describe their geometric and topological complexity? Here we give as an example a simulation of a magnetic field inside a cube, in a model of a magnetic cloud. Separatrix layers can be found which separate different coherent magnetic structures. These structures have mutual windings and self-twist and writhe. Measures such as winding, twist, and writhe will be shown to depend on the shape of the bounding surface, including the distribution of curvature via the Gauss-Bonnet theorem.
MS17: 15:40-17:40, 25th June 2025, Room PCC/2.1-2, presentation 16:00-16:20
Anthony Yeates (Durham University)
Title: Meaningful definition of magnetic helicity in spherical shells
Abstract: It is well known that the magnetic helicity integral of magnetohydrodynamics is non-unique if the magnetic field passes through the domain boundary. In particular, it depends on the choice of vector potential. In some sense, any choice is equally meaningful, because all are invariant under ideal deformations vanishing on the boundary. However, we propose that some choices are more physically meaningful than others, if one wishes to measure topological complexity of the magnetic field. For the particular case of a spherical shell domain â motivated by the Sunâs atmosphere â I will outline how several desirable properties point to a particular choice of vector potential.
MS17: 15:40-17:40, 25th June 2025, Room PCC/2.1-2, presentation 16:20-17:00
Rekha Jain (University of Sheffield)
Title: Analytical studies of Sun’s inertial modes
Abstract: In this talk, I will present an analytical model that unifies many of the solar inertial waves as a single family of mixed inertial modes. Here, mixed modes refer to the prograde- and retrograde-propagating members of this family. This model explains many of the inertial modes that have been recently identified either by numerical eigenmode solvers or observed on the Sun. I will also discuss some other properties of the mixed modes in the context of the model.
MS17: 15:40-17:40, 25th June 2025, Room PCC/2.1-2, presentation 17:00-17:20
Chen Wang (Beijing Normal University at Zhuhai)
Title: Zonostrophic instability and its stochasticity
Abstract: Zonostrophic instability refers to the phenomenon that weak zonal mean flow grows exponentially in a random field of waves and can explain the formation of strong zonal flows that are ubiquitous on planet atmosphere. In previous studies of zonostrophic instability, it was often assumed that although the waves are stochastic, the mean flow evolves deterministically, following an ergodic assumption that the zonal mean is equivalent to the ensemble mean. In this study, we will demonstrate that this assumption does not hold well for general conditions, and the mean flow can be considerably stochastic. We will further evaluate the impact of mean-flow stochasticity on the zonostrophic instability, and demonstrate that it results in an underestimation of the growth rate. An improved dispersion relation is derived based on the impact of mean-flow stochasticity.
MS17: 15:40-17:40, 25th June 2025, Room PCC/2.1-2, presentation 17:20-17:40
Jack Reid (University of St Andrews)
Title: How important are far-side observations of the Sun for global non-potential models of the solar corona?
Abstract: Numerical magnetofrictional simulations are valuable tools for studying the solar coronal magnetic field and making predictions useful for forecasting space weather. Such models rely upon magnetograph observations of the emergence of new magnetic flux on the Sun, but, to date, the necessary observations have only be available from Earth. Consequently, these models can incorporate new magnetic flux only within a limited range of longitudes visible from Earth. Therefore, it is instructive to assess how far this limitation impairs the accuracy of such models. In order to do so, two global coronal simulations are performed, incorporating emergent flux, in one case, simply as observed with Earth-bound magnetographs and, in the other, also including emergence on the far side of the Sun inferred from STEREO. When incorporating flux on the far side of the Sun, simulations report significantly higher total magnetic flux, energy, currents, and, which is geomagnetically influential, open magnetic flux. Structures on the eastern limb, which are rotating onto the solar disc and into view from Earth, differ widely between the two simulations, but converge considerably before reaching the western limb. How much more accurate the open v. closed magnetic field structure and non-potentiality of the magnetic field are when including flux on the far side of the Sun is demonstrated. In light of these improvements with far-side flux emergence, the importance of having full, 4Ï-steradian observational coverage of the Sun is underlined.
MS18: 10:30-12:30, 24th June 2025, Room PCC/2.1-2, presentation 10:30-11:10
Dominic Vella (University of Oxford)
Title: Some surprises in the nonlinear dynamics of snap-through
Abstract: Elastic snap-through is a striking phenomenon in which a system, such as an arch or a shell, rapidly transitions from one state to another. Typically the transition occurs as a saddle-node bifurcation but I will show that some natural scenarios have a more intricate bifurcation structure. This structure has consequences for when and how snap-through occurs. In particular, the bifurcation structure can lead to premature snap-through but also allows for control of whether snap-through occurs symmetrically or asymmetrically.
MS18: 10:30-12:30, 24th June 2025, Room PCC/2.1-2, presentation 11:10-11:30
Stephane Poulain (University of Oslo)
Title: Hovering of active fluid-lubricated foil
Abstract: Recent experiments show that a vibrating elastic foil can hover near a solid surface while supporting substantial weight, effectively acting as a contactless suction cup. To explain this phenomenon, we develop a theoretical framework that describes the underlying physical mechanisms. Using lubrication theory, we quantify how the foilâs elastic deformations couple with the viscous fluid flow in the intervening gap. Our analysis explains how the soft foil rectifies the reversible forcing, breaking time-reversal symmetry. In the presence of gravity, a simple scaling law predicts the equilibrium hovering height and the maximum weight the foil can sustain before detaching from the surface. Numerical simulations validate our predictions and align with experiments. Beyond fundamental insights, our findings offer design principles for soft robotics and contactless grippers.
MS18: 10:30-12:30, 24th June 2025, Room PCC/2.1-2, presentation 11:30-11:50
Nico Schramma (University of Amsterdam)
Title: Light-controlled chloroplast morphodynamics in single-celled algae
Abstract: The ability of photosynthetic organisms to convert light into biochemically available energy is the basis for most life on earth. At the same time, too much light can be detrimental for an organisms survival. Plants and algae have to constantly cope with fluctuating light in their environment. Besides biochemical and developmental mechanisms, they have evolved the ability to re-arrange their intracellular structure by collectively moving their chloroplasts – light harvesting organelles – within their cell-body to adaptively tune the overall light absorption. We uncover that the bioluminescent dinoflagellate Pyrocystis lunula, native to dim light conditions 100m deep into the ocean, can rearrange its intracellular structure efficiently by rapidly contracting a topologically complex network of chloroplasts that spans throughout the cell. By exploiting buckling of the network strands it exhibits mechanical deformation similar to that of meta-materials, resulting in efficient compaction within the cell wall confinement. Ultimately, we show using dynamic light stimulation, that the cellâs response follows rules similar to temporal low-pass filtering – an elegant adaptation process at a single-cell level toward environmental fluctuations. Besides the physiological and ecological relevance, the light-morphodynamics of the chloroplast network represents a well-controlled active matter system, manifesting a biological metamaterial.
MS18: 10:30-12:30, 24th June 2025, Room PCC/2.1-2, presentation 11:50-12:10
Alexander Boggon (University of Exeter)
Title: Shape dynamics of a morphing cilium
Abstract: Cilia are long, slender cellular appendages consisting of a highly conserved three-dimensional structure and driven by thousands of molecular motors distributed along their length. Eukaryotic microorganisms generate varied dynamic shape sequences with these structures to drive a range of motile behaviours. Yet, typical methods overlook the complexity in the dynamics by considering a single, typically large, spatiotemporal scale. Here we conduct a multi-scale analysis of the cilium driven dynamics in the marine alga Pterosperma. Low-resolution behavioural tracking reveals three motility macrostates resulting from distinct ciliary actuation. However, implementing a novel mathematical framework based on shape decomposition of ciliary waveforms extracted from high resolution recordings, we find that the beat pattern is being continuously modulated and is capable of undergoing rapid shape changes unobservable at reduced resolution. We can then map the entire spectrum of ciliary shape dynamics performed by a living organism uncovering striking structure in the dynamics including a novel dispersion relation that constrains the cilium shape space. Having uncovered remarkable complexity in the ciliary shape dynamics produced we look to explore the fundamental design principles underlying ciliary function. We develop a macroscopic robophysical model with actuation along its length which relies purely on mechanical coupling to organise the shape dynamics. We discuss how such an engineered system can be leveraged to develop our intuition for the functional role of structural components within the cilium and how this leads to diverse beat patterns.
MS18: 10:30-12:30, 24th June 2025, Room PCC/2.1-2, presentation 12:10-12:30
Clement Moreau (CNRS, LS2N, Nantes Université)
Title: The $N$-link model for slender rods in a viscous fluid: well-posedness and convergence to classical elastohydrodynamics equations
Abstract: In this talk, I will present a recent result on convergence and well-posedness of equations modelling a coarse-grained flexible slender fiber immersed in a viscous fluid. Modeling and simulating flexible filaments in a viscous fluid is a prominent issue in many problems related to microbiology. The elastohydrodynamics equations governing the motion of a continuum, flexible, inextensible fiber are a nonlinear, fourth-order parabolic system of partial differential equations, which is known to be challenging to analyse and simulate and, in turn, warrants the use of coarse-grained, simplified counterparts. A popular choice among other models available is the so-called “$N$-link model”, which relies on a mechanical discretization of a continuum filament into rigid links with elastic joints. Despite being widely used for simulation and tested to numerically converge for large $N$, a formal proof of convergence of this model towards the PDE model was lacking, and giving sense to this convergence is not trivial because the $N$-link equations do not straightforwardly correspond to a classical approximation of the underlying PDE. Hence, in this presentation, after describing both models, I will establish the existence and uniqueness of solutions for the $N$-link model and prove the convergence of these solutions towards the solutions to classical elastohydrodynamics PDEs. The proofs rely mainly on energy dissipation in the system, as well as compactness arguments. This work was conducted in collaboration with François Alouges, Aline Lefevbre-Lepot and Jessie Levillain
MS19: 15:40-17:40, 25th June 2025, Room PCC/2.5-6, presentation 15:40-16:20
Michael Nieves (Keele University)
Title: Edge resonance in discrete elastic waveguides
Abstract: We discuss the problem of edge resonance for Lamb waves in a semi-infinite discrete elastic strip, represented by a triangular lattice. In analogy with the reflection problem in the corresponding continuum, for real frequencies the edge resonance phenomenon for the lattice strip is characterised by localised vibrations at its free edge. We verify the existence of a complex edge resonance frequency for the lattice, associated with a mode of the homogenous problem without incident wave. Importantly, when the number of rows in the strip of fixed width is large, we show the latticeâs edge resonance frequency approximates corresponding frequency in the analogous continuum problem for the effective strip. Interestingly, con- vergence to the complex edge resonance frequency is monotonic only with respect to its real part, while its imaginary part exhibits a minimum absolute value for a lattice strip with 65 rows in the transverse direction. All analytical results are accompanied by numerical simulations that illustrate the methods adopted in studying the reflection problem and their effectiveness when benchmarked against independent calculations based on the finite element method. This talk is based on joint work with Dr Giorgio Carta, Prof. Michele Brun and Prof. Vincent Pagneux.
MS19: 15:40-17:40, 25th June 2025, Room PCC/2.5-6, presentation 16:20-16:40
Paulo Piva (University of Sheffield)
Title: From Frequency to Time: Interpreting Reflections in Layered Acoustic Medium via Formal Power Series
Abstract: Sensing the acoustic properties of layered media using localised ultrasound pulses is a standard technique in non-destructive testing. A key experimental observation is that each echo of an incident pulse can be approximated as a reflection from a specific set of interfaces within the medium. This suggests that the solutions of the Helmholtz equationâthe Fourier transform of the wave equationâencode the full sequence of echoes for any wave with a small compact support in time, at all fixed spatial points. In this talk, we explore how this connection can be made precise using formal power series expansions of reflection and transmission coefficients for single or multiple acoustic layers. Each term in the series corresponds to a product of successive reflection and transmission coefficients of acoustic half-spaces, providing a mathematical framework to interpret frequency-domain data as time-domain reflections and transmissions. Moreover, our calculations reveal the limitations of this interpretation, identifying cases where the reconstruction of echoes from frequency-domain information breaks down or becomes less accurate.
MS19: 15:40-17:40, 25th June 2025, Room PCC/2.5-6, presentation 16:40-17:00
Valentin Kunz (Ohio State University)
Title: Linking one and two dimensional complex analysis in diffraction theory
Abstract: Classical complex analysis (involving a single complex variable) is a powerful tool in applied mathematics. We are interested in the mathematical theory of wave diffraction, where some problems seem out of reach of classical complex analysis methods in the sense, that these methods do not yield closed-form analytical solutions to the corresponding boundary value problem (where the wave-fields’ dynamics are governed by the Helmholtz equation). In this talk, we shall outline how the theory of several complex variables (SCV) yields some new insights on the mathematical structure of such diffraction phenomena, and how it ‘links back’ to classical complex analysis, thus enabling us to re-use classical methods within the SCV framework.
MS19: 15:40-17:40, 25th June 2025, Room PCC/2.5-6, presentation 17:00-17:20
Charlotte Charlton (The University of Manchester)
Title: The influence of multiple scattering on the giant monopole resonance
Abstract: By exploiting resonance phenomena, metamaterials are designed to control elastic waves for tailored physical behaviour such as cloaking and wave attenuation. A useful resonance that is physically realisable is the giant monopole resonance, which occurs when a compressional wave strikes a cavity in a rubber-like medium. In this talk, we look at the interaction effects on the resonance when a small number of voids are present in a soft elastic medium. In particular, we show that the additional voids provide more freedom to tune the resonance compared with a single void of equivalent volume.
MS19: 15:40-17:40, 25th June 2025, Room PCC/2.5-6, presentation 17:20-17:40
Matthew Nethercote (University of Cambridge)
Title: Aeroacoustics of Dynamic Stall
Abstract: Aerodynamic noise from aircraft and wind turbines is known to be one of the most intrusive types of noise pollution and has been a major source of controversy for populations living or working nearby airports and wind farms. While aerofoils are designed to achieve maximum aerodynamic performance by operating at high angles of attack (AoA), they are also more susceptible to flow separation and stall due to changes in the flow conditions (e.g. gusts, wind shear, wake interaction) which can lead to a drastic reduction in performance and a significant increase in noise. Dynamic stall is also a complex phenomenon triggered by rapid changes in the aerofoil’s AoA which turbine blades are highly prone to, and the produced noise is an important issue for the development of next-generation electric propulsion and energy production. We will be considering the attached flow/weak stall situation which occurs at low AoA. We are building upon some very recent work where Goldsteinâs formulation of Rapid Distortion Theory has been used in symmetric shear flow problems with a small Mach number. For our purposes, we consider the case where this shear flow is slightly asymmetric and is disturbed by a vortex sheet within a boundary layer of the aerofoil. These problems were solved using the scalar Wiener-Hopf technique and after deforming to steepest descent contours, the far-field is composed of three parts: steepest descent, critical boundary layer and wake modal contributions. The effects of the boundary layer profile on acoustic directivity will be provided.
MS20: 10:30-12:30, 25th June 2025, Room PCC/2.5-6, presentation 10:30-11:10
Zakhar Shumaylov (University of Cambridge)
Title: Convergent Data-Driven Regularisation in Inverse Problems
Abstract: In the last decade, processing of imaging data has undergone a paradigm shift from knowledge driven approaches, deriving imaging models from first principles, to purely data driven approaches, instead deriving models from data. Most inverse problems of interest are ill-posed and require appropriate mathematical treatment for recovering meaningful solutions and while purely data-driven learning have been able to achieve remarkable empirical success for image reconstruction, they often lack rigorous reconstruction guarantees. In this talk I will discuss image reconstruction methods that operate at the interface of these paradigms and feature both a knowledge driven (mathematical modelling) and a data driven (machine learning) component. A particular emphasis will be made on learned methods with mathematically rigorous reconstruction guarantees, and their theoretical properties will be discussed.
MS20: 10:30-12:30, 25th June 2025, Room PCC/2.5-6, presentation 11:10-11:50
Bill Lionheart (University of Manchester)
Title: Symmetries and Polarization Tensors for Electromagnetic Detection
Abstract: In many inverse problems we want to detect, locate or classify objects. In the context of electromagnetic detection of objects in the eddy current regime polarization tensors can be used to represent the effect of an object on the field. We have a particular interest in the detection of land mines and unexploded ordnance, as well as weapons detection. We show how the symmetries of the object can be understood inter terms of harmonic polynomials invariant under groups. We also show how the real and imaginary parts of the rank 2-tensor can be used for classification and discuss the measurement of how the eigenvectors differ. While machine learning is a powerful tool for classification, novel algebra and geometry also arises in these problems. This is joint work with Paul Ledger and James Elgy.
MS20: 10:30-12:30, 25th June 2025, Room PCC/2.5-6, presentation 11:50-12:30
Pablo Arratia (University of Bath)
Title: Enhancing Dynamic CT Image Reconstruction with Neural Fields and Optical Flow
Abstract: In this talk, we investigate image reconstruction for dynamic Computed Tomography. The motion of the target with respect to the measurement acquisition rate leads to highly resolved in time but highly undersampled in space measurements. Such problems pose a major challenge: not accounting for the dynamics of the process leads to a poor reconstruction with non-realistic motion. Variational approaches that penalize time evolution have been proposed to relate subsequent frames and improve image quality based on classical grid-based discretizations. Neural fields have emerged as a novel way to parameterize the quantity of interest using a neural network with a low-dimensional input, benefiting from being lightweight, continuous, and biased towards smooth representations. The latter property has been exploited when solving dynamic inverse problems with neural fields by minimizing a data-fidelity term only. We investigate and show the benefits of introducing explicit motion regularizers for dynamic inverse problems based on partial differential equations, namely, the optical flow equation, for the optimization of neural fields. We compare it against its unregularized counterpart and show the improvements in the reconstruction. We also compare neural fields against a grid-based solver and show that the former outperforms the latter in terms of PSNR in this task.
MS21: 15:40-17:40, 24th June 2025, Room PCC/2.5-6, presentation 15:40-16:00
George Constable (University of York)
Title: Cell fusion and the evolution of sex: Sex and the sexes from a model of cell fusion and stress
Abstract: While the precise mechanisms that select for sexual reproduction are often hotly contested, it is widely understood that they are reliant on the structure of environmental changes over space and time. Here we use adaptive dynamics to show how binary cell fusion, the first step involved in sexual reproduction in most eukaryotes, can be selected for as a stress response in temporally switching stochastic environments [1]. This behaviour qualitatively recapitulates the reproductive behaviour in many unicellular eukaryotes. Should organisms be unable to mount an environment-dependent response, we demonstrate how switching-induced fixed points (bet hedging strategies) can emerge. Extending the model, we are able to qualitatively capture observed patterns of geographical parthenogenesis, whereby spatial regions emerge in which females abandon sexual reproduction in response to challenging environmental conditions [2]. [1] Liu, Xiaoyuan, Jonathan W. Pitchford, and George WA Constable. “Cell size and selection for stress-induced cell fusion in unicellular eukaryotes.” PLOS Comp. Bio. (2025) [2] Liu, Xiaoyuan, Jon W. Pitchford, and George WA Constable. “Parthenogenesis, sexual conflict, and selection on fertilization rates in switching environments” Under Review (2024)
MS21: 15:40-17:40, 24th June 2025, Room PCC/2.5-6, presentation 16:00-16:20
Beth Stokes (University of Bath)
Title: Should I stay, or should I go: Sex ratio response drives a diverse range (anti-)correlated intra-species behaviours
Abstract: The decision of an individual or group to leave its current environment may be influenced by various factors. These include external or inter-species factors such as the presence of predators or food availability, and also intra-species dynamics like mate searching or the strength of social ties within a group. Understanding the consequences of these behaviours on the population level dynamics is non-trivial. In this work, we explore a stochastic model describing the movement of males and females of a species between localised patches, in which the movement rates are dependent on the sex ratio within the patch. By deriving a system of stochastic differential equations governing the fluctuations in these patches we can model a diverse range of intra-species behaviours driven solely by an individual’s response to local sex ratio. We subsequently uncover and explore how various individual behaviours can give rise to large scale (anti-)correlated movements between the sexes.
MS21: 15:40-17:40, 24th June 2025, Room PCC/2.5-6, presentation 16:20-16:40
Joao Luiz de Oliveira Madeira (University of Bath)
Title: Can deleterious mutations surf deterministic population waves? – Functional law of large numbers for a spatial model of Muller’s ratchet
Abstract: In this work, we study the deterministic scaling limit of a model introduced by Foutel-Rodier and Etheridge in 2020 to study the impact of cooperation and competition on the fitness of an expanding asexual population whose individual birth and death rates depend on the local population density. The interacting particle system can be mathematically described as particles performing symmetric random walks that undergo a birth-death process with rates that depend on the local number of particles. Phenomenologically, each particle represents a chromosome, and we keep track of two features of each particle: its spatial location and its number of deleterious mutations. After each birth event, with some positive probability, the daughter particle can acquire an additional mutation which will give it a lower reproduction rate than its parent. We show that under an appropriate scaling, the process converges weakly to an infinite interdependent system of partial differential equations, proving a conjecture of Foutel-Rodier and Etheridge. For the case where the reaction term satisfies a Fisher-KPP condition, we prove a conjecture of Foutel-Rodier and Etheridge regarding the spreading speed of the population into an empty habitat. We also prove some further results regarding the asymptotic behaviour of the system of PDEs in the monostable case, and use this to control the evolution of proportions of mutations in the interacting particle system. This is a joint work with Marcel Ortgiese and Sarah Penington.
MS21: 15:40-17:40, 24th June 2025, Room PCC/2.5-6, presentation 16:40-17:00
Alexander Sadykov (Exeter University)
Title: Nonequilibrium models of population dynamics can reveal the causes of the demographic transition
Abstract: Traditional studies in population dynamics have largely centred on equilibrium states or, more recently, on transient dynamics [1]. Rooted in Malthusâs seminal work [2], it was long assumed that exponential growth must eventually confront resource limitations, leading to an equilibrium (i.e. a balance between birth and death rates) [3]. However, numerous natural and experimental systems display prolonged nonequilibrium behaviour. For instance, bacterial colonies thriving in nutrientârich media [4], controlled rodent populations [7], the rapid early growth of invasive species [5], and the extended demographic transition observed in human populations [6] all challenge classical equilibrium assumptions. We introduce a nonequilibrium framework in which total resources are allowed to expand in proportion to population size, while resource distribution among individuals evolves toward greater equity by natural selection. Our six-phase model of population transition captures the dynamic interplay between resource accumulation and resource redistribution inequality. This approach may shed light on the fundamental causes underlying demographic transitions and offers a versatile mathematical framework with potential applications in ecology and socio-economic planning. References: [1] Gotelli, N.J. (2008). A Primer of Ecology. Sinauer Associates. [2] Malthus, T.R. (1798). An Essay on the Principle of Population. [3] Rosenzweig, M.L. & MacArthur, R.H. (1963). Graphical Representation of PredatorâPrey Interactions. [4] Monod, J. (1949). The Growth of Bacterial Cultures. Annual Review of Microbiology. [5] Sakai, A.K., et al. (2001). The Population Biology of Invasive Species. Annual Review of Ecology and Systematics. [6] Lee, R. (2003). The Demographic Transition: Three Centuries of Fundamental Change. Population and Development Review.
MS21: 15:40-17:40, 24th June 2025, Room PCC/2.5-6, presentation 17:00-17:20
Matthew Asker (University of Leeds)
Title: Time-fluctuating metapopulations: fixation and extinction
Abstract: Microbial populations evolve within spatially structured and dynamically changing environments, a reality often overlooked by classical modelling approaches. From microbial infections spreading across host organs to environmental pollutants altering ecological niches, understanding the effects of and interplay between spatial structure and environmental change is essential for developing insights into the evolutionary dynamics of microbial communities. Here, we present a comprehensive analysis of a two-species metapopulation model, incorporating selection bias, to investigate how microbial species evolve while competing under stochastic population bottlenecks of varying strength. Our analytical framework provides insights into the long-lived behaviour of the system: will we see total extinction of all species, or will a species take over and remain, and how long does this take? We find distinct deviations from the predictions of the so-called âcirculation theoremâ for graphs which are circulations when environmental fluctuations are considered. We address the problem of eliminating an unwanted (advantageous) mutant in the population, and how best to do so while minimising the risk of total extinction. By combining analytical and computational methodologies, we uncover the rich dynamics underlying microbial population evolution in spatially structured and dynamically changing environments.
MS21: 15:40-17:40, 24th June 2025, Room PCC/2.5-6, presentation 17:20-17:40
Mainul Haque (University of Nottingham)
Title: A detailed analysis of a predator-prey model’s spatial and temporal dynamics with Allee and transmissible disease in species.
Abstract: This paper introduces a mathematical model utilising ordinary differential equations (ODEs) to simulate population dynamics influenced by the Allee and transmissible diseases in species. The model is expanded to incorporate the spatial aspects of ecological interactions by transforming the ODE system into a partial differential equation (PDE) system using reaction-diffusion equations. The study reveals that the Allee effect in the non-spatial model can have both stabilising and destabilising influences, including single and two-parameter bifurcations and chaos, on food chain dynamics, depending on the context and the strength of the impact at each trophic level. The research considers the two-dimensional spatial movement of species to enhance the understanding of food chain dynamics. Analytical conditions for Turing and non-Turing instability are derived, and numerical results support these findings. The study identifies several patterns resembling the labyrinthine formations typically anticipated in ecological models and investigates unexpected “Leaser Slime” patterns found in fungi and algae in aquatic environments. In ecological research, slime moulds are crucial for nutrient cycling and soil health as they decompose organic material. This investigation highlights their role as an intermediary life form, bridging the gap between simpler microorganisms and more complex organisms like fungi, plants, and animals, thereby challenging traditional views on species boundaries.
MS22: 10:30-12:30, 24th June 2025, Room PCC/2.5-6, presentation 10:30-10:50
Jonathan Crofts (Nottingham Trent University)
Title: An isogeometric collocation method for neural fields on curved geometries
Abstract: The aim of this study is to develop a new numerical algorithm for simulating neural fields on curved geometries, and eventually patient-specific cortical geometries, using Computer-Aided Design (CAD) techniques. We present a CAD-integrated analysis approach, referred to as isogeometric collocation, for solving neural field equations on surfaces that closely resemble cortical geometries typically derived from neuroimaging data. Our methodology involves solving partial integro-differential equations directly using isogeometric collocation techniques, combined with efficient numerical procedures such as heat methods for determining geodesic distances between neural units. To demonstrate the effectiveness of our approach, we initially investigate localised activity patterns in a two-dimensional neural field equation posed on a torus, with the eventual goal of extending the analysis to human brain geometries derived directly from neuroimaging point cloud data. This approach provides a powerful tool to investigate the impact of cortical geometry on neural activity, from the formation of localised patterns like traveling waves, to the study of pathological neural dynamics.
MS22: 10:30-12:30, 24th June 2025, Room PCC/2.5-6, presentation 10:50-11:10
Stephen Coombes (University of Nottingham)
Title: Revisiting the Haken Lighthouse Model: Bridging Spiking and Non-Spiking Neural Networks
Abstract: Simple spiking neural network models, such as those built from interacting integrate-and-fire (IF) units, exhibit rich emergent behaviours but remain notoriously difficult to analyse, particularly in terms of their pattern-forming properties. In contrast, rate-based models and coupled phase oscillators offer greater mathematical tractability but fail to capture the full dynamical complexity of spiking networks. To bridge these modelling paradigms, Hermann Hakenâthe pioneer of synergeticsâintroduced the Lighthouse model, a framework that provides insights into synchronisation, travelling waves, and pattern formation in neural systems. In this work, I revisit the Lighthouse model and develop new mathematical results that deepen our understanding of self-organisation in spiking neural networks. Specifically, I derive the linear stability conditions for phase-locked spiking states in Lighthouse networks structured on graphs with realistic synaptic interactions (alpha-function synapses) and axonal conduction delays. Furthermore, I demonstrate that in the limit of slow synaptic dynamics, the Lighthouse model reduces to a Wilson-Cowan-type rate-based model, thus establishing a formal connection between spiking and rate-based approaches. Extending this analysis to a spatially continuous (non-local) setting, I develop a variant of Turing instability analysis to explore emergent patterns. Finally, I show how localized bump solutionsâwhich are difficult to construct in IF networksâarise naturally in the Lighthouse model and analyse their stability against wandering states. These results reinforce the Lighthouse model as a valuable tool for studying structured neural interactions and self-organisation, further advancing the synergetic perspective on neural dynamics.
MS22: 10:30-12:30, 24th June 2025, Room PCC/2.5-6, presentation 11:10-11:30
Angelica Pozzi (University of Nottingham)
Title: A Thalamo-Cortical Model to Advance Treatments of Tourette Syndrome
Abstract: Tourette Syndrome (TS) is a common neurological disorder characterised by motor and vocal tics, affecting approximately 1 in 100 children in the UK. Although it is more prevalent among children, many adults continue to experience significant symptoms. Touretteâs is associated with thalamo-cortical circuit dysfunction, but a precise mechanistic explanation is lacking. Recent studies have shown that non-invasive median nerve stimulation (MNS) can help reduce tics, highlighting the need for a deeper exploration of the brain circuits involved to improve the design of healthcare treatments utilising wearable devices. Here, we develop a mathematical model of the thalamo-cortical loop in the context of TS. We couple a neural mass model of the cortex, capturing the interplay between excitatory and inhibitory populations, with a mean-field model of the thalamus, incorporating interactions between reticular and thalamo-cortical cells (expressing so-called rebound currents). We first analyse these subsystems independently using bifurcation theory before coupling them. Neuroimaging data (MEG/EEG) inform model parameters to replicate power spectrograms observed in both healthy individuals and TS patients undergoing MNS. To gain a deeper understanding of such responses, we determine the Arnolâd tongue structure of the network model in response to periodic forcing via a numerical calculation of the largest Lyapunov exponent. This is complemented with an analytical study of the tongue borders using tools from coupled oscillator theory. Our findings provide a foundation for in-silico testing of neurostimulation protocols to optimise treatment strategies for TS.
MS22: 10:30-12:30, 24th June 2025, Room PCC/2.5-6, presentation 11:30-11:50
Huda Mahdi (University of Exeter)
Title: Alpha-Delta Transitions in Cortical Rhythms as grazing bifurcations
Abstract: The Jansen-Rit model of a cortical column in the cerebral cortex has been used to model large-scale brain activity as well as event-related potentials. It couples a pyramidal cell population with two interneuron populations, of which one is fast and excitatory and the other is slow and inhibitory. Using this model we investigate the mechanism of transition between alpha oscillations (associated with wakefulness in the frequency band from 8 to13 Hz) and delta oscillations (associated with sleep, below 4 Hz). For realistic parameter values, the non-linear coupling functions between populations have the form of discontinuous, threshold-like responses that approximate all-or-nothing switches. This structure allows us to interpret the system as a perturbation of a piecewise-smooth Filippov system with sharp transitions between distinct dynamical regimes. In the limit we can identify the boundary between alpha and delta oscillations as a discontinuity-induced grazing bifurcation of the periodic orbits corresponding to alpha oscillations. At the grazing the minimum of the pyramidal-cell output reaches the threshold for switching off the excitatory interneuron population, leading to a collapse in the excitatory feedback, giving a simple neurological mechanism for a phenomenon previously described as a “false bifurcation” (Forrester et al., 2020).
MS23: 10:30-12:30, 25th June 2025, Room FOR/EXP2, presentation 10:30-10:50
Weida Liao (University of Cambridge)
Title: Hydrodynamic mechanism for stable spindle positioning in meiosis II oocytes
Abstract: Cytoplasmic streaming, the persistent flow of fluid inside a cell, induces intracellular transport, which plays a key role in fundamental biological processes. In meiosis II mouse oocytes (developing egg cells) awaiting fertilisation, the spindle, which is the protein structure responsible for dividing genetic material in a cell, must maintain its position near the cell cortex (the thin actin network bound to the cell membrane) for many hours. However, the cytoplasmic streaming that accompanies this stable positioning would intuitively appear to destabilise the spindle position. Here, through a combination of numerical and analytical modelling, we reveal a hydrodynamic mechanism for stable spindle positioning beneath the cortical cap. We show that this stability depends critically on the spindle size and the active driving from the cortex, and demonstrate that stable spindle positioning can result purely from a hydrodynamic suction force exerted on the spindle by the cytoplasmic flow. Our findings show that local fluid dynamic forces can be sufficient to stabilise the spindle, explaining robustness against perturbations not only perpendicular but also parallel to the cortex. Our results shed light on the importance of cytoplasmic streaming in mammalian meiosis. Reference: W. Liao and E. Lauga, PRX Life, 2, 043003, 2024
MS23: 10:30-12:30, 25th June 2025, Room FOR/EXP2, presentation 10:50-11:10
James Cass (University of Exeter)
Title: Efficient computational modelling of excavate flagellates
Abstract: Flagellates, single-celled eukaryotes characterized by their distinctive arrangement of motile appendages, provide key insights into the morphology and ecology of the Last Eukaryotic Common Ancestor (LECA). Currently considered the closest living relatives of LECA, excavates are a group of flagellates exhibiting diverse morphological featuresâincluding variations in flagellar number and body shapeâthat strongly influence their ecological behaviours such as swimming and prey capture. To study this diversity of morphology and behaviour in silico requires general methods that efficiently solve the Stokes equations with complex time-dependent boundary conditions while implementing interactions with active prey particles. We present a fast computational library implemented in the compiled language Julia, based on the boundary-element regularised stokeslet method. Using 3D microswimmer and fluid flow visualisations coupled with simplified morphological models derived from representative excavate taxa, we explore the hydrodynamic consequences of differing flagellar arrangements and body shapes, and interactions with a surface. These findings will ultimately inform a broader comparative framework integrating high-speed microscopy observations and genomic data, providing new functional ecological perspectives critical to reconstructing LECA’s biology.
MS23: 10:30-12:30, 25th June 2025, Room FOR/EXP2, presentation 11:10-11:30
Tom Montenegro-Johnson (University of Warwick)
Title: I don’t think you’re ready: surfing jelly
Abstract: Self-oscillating gels are chemically-responsive hydrogels coupled to an oscillating chemical reaction of a background solute. The gels respond to the oscillating solute concentration field by periodically swelling and deswelling: expelling their adsorbed water as they transition to a hydrophobic state, and reswelling once they return to a hydrophilic state. This hydrophilic-phobic transition occurs when the local solute concentration passes through a critical value. Self oscillating gels have been used to make surface crawlers, but here we show that a very simple system – comprising two oscillating gel spheres linked by a rigid rod, can also swim in the inertialess Stokes regime – albeit rather slowly. Herein, we derive analytical results for the swimming velocity of these “dumbgel” swimmers, and upon placing them in a solute bath, identify two modes of behaviour upon encountering propagating reaction-diffusion waves: Bobbing and Surfing. Though somewhat slower than flagellated swimmers, the relative simplicity of the system, with no hinges or moving components, lends itself well to large scale production.
MS23: 10:30-12:30, 25th June 2025, Room FOR/EXP2, presentation 11:30-11:50
Edwina Yeo (UCL)
Title: Active LĂ©vĂȘque boundary layers: bacterial adhesion in shear flow
Abstract: The mitigation of bacterial adhesion to surfaces and subsequent biofilm formation is a key challenge in healthcare and manufacturing processes. To accurately predict biofilm formation you must determine how changes to bacteria behaviours and dynamics alter their ability to adhere to surfaces. In this work we examine the flow of a dilute suspension of motile bacteria over a flat absorbing surface. We determine how bacteria shape and motility alter adhesion, developing reduced models for the density of the bacteria near the boundary inspired by the classical LĂ©vĂȘque boundary layer problem. We use our reduced model to demonstrate that bacterial motility leads to enhanced dispersion and therefore increased adhesion of bacteria to surfaces, with spherical bacteria showing slightly more adhesion compared to elongated bacteria. We derive fundamental scalings for how the adhesion rate depends on both the distance from the source of the bacteria and the individual motility parameters of the bacteria, validating these scalings using numerical simulations of individual bacteria.
MS23: 10:30-12:30, 25th June 2025, Room FOR/EXP2, presentation 11:50-12:10
Henry Andralojc (University of Bristol)
Title: Dynamics of Wound Closure in Living Nematic Epithelia
Abstract: Successful healing of wounds is essential for any organism wishing to survive external damage. Our understanding of the relevant biochemistry to healing has mostly been provided through the study of biological models including mice, chicks and, more recently, fruit flies; Drosophila. Fruit flies are not humans, however many of the processes relevant to healing are conserved between species. The hope is that understanding healing in Drosophila will generate insight into mammalian healing, ultimately leading to the development of practices that can aid clinicians and patients. Less well understood is the role of forces in the tissue â which one would reasonably expect to play a leading role; forces are required to close a hole in any material, biological or not! Therefore, in this talk, I will present a fluid-mechanical model for the flow of epithelial tissue surrounding a âwoundâ free-boundary â i.e. a model for re-epithelialisation. Inspired by recent experiments observing wound-healing in the wing epithelium of Drosophila pupae, we model the tissue as an active nematic fluid and solve the free-surface problem of a closing hole. By including additional active stresses arising from variations in the nematic alignment, we also target the role of activity in the bulk. Our model indicates that contractile active stresses accelerate wound closure, whereas extensile stresses delay it. This suggests the efficacy of healing may be improved by the generation of contractile stresses local to the wound, and hints at the actual mechanical-response to wounding in Drosophila.
MS23: 10:30-12:30, 25th June 2025, Room FOR/EXP2, presentation 12:10-12:30
Zahra Valei (University of Edinburgh)
Title: Enhanced Diffusivity of Passive Polymers in Active Nematic Flows
Abstract: The interplay between active and passive components is a defining feature of biomaterials, where continuous energy conversion by active elements drives the system out of equilibrium, influencing dynamics of passive components. Prior studies examined polymeric inclusions in ensembles of self-propelled particles [1] or athermal baths [2] but overlooked hydrodynamic effects of active fluids and active turbulence. Here, we present the first study of a flexible polymer in active turbulence, revealing how polymeric degrees of freedom interact with turbulent flows to shape polymer dynamics. We employ a hybrid simulation approach combining Multi-Particle Collision Dynamics [3] and Molecular Dynamics [4]. Our results show that passive polymers in active nematic turbulence exhibit a thousand-fold diffusivity increase, driven by short-time polymer advection in active flows with finite correlation times. This phenomenon is governed by a set of key dimensionless numbers: Peclet and Weissenberg numbers, intrinsically linked via Eriksen number, which characterizes the ratio of fundamental length scales. We demonstrate that the interplay between these dimensionless numbers fully dictates polymer diffusivity. These findings highlight how biological systems may exploit activity to tune polymer properties, influencing their dynamics and function. Future studies should incorporate macromolecular properties, introducing further length scales, to better mimic biological complexity and deepen insights into self-organization in active materials. References [1] Harder et al. (2014). Physical Review E, 90. [2] Vandebroek et al. (2015). Physical Review E, 92. [3] Kozhukhov & Shendruk (2022). Science Advances, 8. [4] Slater et al. (2009). Electrophoresis, 30.
MS24: 15:40-17:40, 24th June 2025, Room FOR/EXP2, presentation 15:40-16:00
Belinda Lombard (University of Birmingham)
Title: Data-Driven Mathematical Modelling of the HPA Axis and Hormonal Rhythms in Humans
Abstract: The hypothalamic-pituitary-adrenal (HPA) axis is the endocrine system controlling dynamic responses to stressors. Mathematical modelling and experiments in rodents have shown that negative feedback loops underpin rhythmic activity within this axis, but a human equivalent model is lacking. This talk outlines a data-driven approach to calibrate a model of hormonal rhythms in the human HPA axis. The model is written in terms of Delay Differential Equations (DDEs) and predicts the conditions that lead to pulsatile secretion of cortisol and ACTH hormones with ultradian (<24 hrs) periodicity. Oscillatory solutions arise via a Hopf bifurcation, physiologically determined by a balance between the hypothalamic circadian drive and feedback loop delay. The model was calibrated using data consisting of cortisol and ACTH plasma hormone profiles measured every 20 minutes over 24 hrs in 10 healthy individuals. Wavelet analysis revealed unique patterns in hormonal rhythms across individuals, including variability quantification. Model fitting yielded specific parameter values for each participant and estimated cohort distributions. Bifurcation analysis determined the conditions needed to sustain ultradian rhythmicity, and the sensitivity of the oscillatory solution to parameter variability. Coupling a model of sleep regulation will help explore the interactions between stressors and sleep disruptions, offering insights into how circadian rhythms affect neuroendocrine regulation in humans.
MS24: 15:40-17:40, 24th June 2025, Room FOR/EXP2, presentation 16:00-16:20
Wolf Byttner (University of Exeter)
Title: Ion channel distributions underlying sex differences in corticotroph cell excitability
Abstract: Pituitary corticotroph cells are important players in our response to stress. They regulate the release of cortisol from the adrenals by releasing Adrenocorticotropic Hormone (ACTH) in response to hypothalamic signals. These cells are electrically active, like neurones, and the pattern of electrical activity determines ACTH release. Duncan et al. (2023) observed that female mice had more âA-typeâ corticotroph cells, which exhibit sharp action potentials. Male mice, instead, had more âB-typeâ corticotrophs, with wider spikes. A-type corticotrophs are less easily stimulated to produce bursts of action potentials than B-type corticotrophs. Since bursts release more ACTH than single action potentials, the differences between A-type and B-type excitability may be linked to gender differences in the regulation of the stress response. Here, we study the differences between A-type and B-type excitability in corticotrophs. We adapt a computational corticotroph cell model from Fletcher et al. (2017) to reproduce A-type and B-type excitability and ask what differentiates the two types. Parameters of this models include the ionic conductances regulating excitability. We first generate a database of models, from which we extract the parameter sets that produce clear A-type and B-type excitability. We then use machine learning tools to understand the combinations of parameters that are important for determining excitability type. Preliminary results suggest that increasing the conductance of voltage-dependent Ca2+ channels and K+ channels switches cell from type B to type A excitability. This prediction is testable in the lab, using the dynamic clamp technique to add virtual ionic conductance models to real corticotroph cells.
MS24: 15:40-17:40, 24th June 2025, Room FOR/EXP2, presentation 16:20-16:40
John Terry (University of Birmingham & Neuronostics Ltd.)
Title: Circadian variability in interictal epileptiform discharges: The role of sleep and neuroendocrine axes
Abstract: Background: Classically, seizures are assumed to occur at random. However, recent research has uncovered underlying rhythms both in seizures and in key signatures of epilepsyâso-called interictal epileptiform dischargesâwith timescales that vary from hours and days through to months. Many people with epilepsy identify precipitants of their seizures, the most common of which include stress, sleep deprivation and fatigue. Methods: To quantify the impact of a possible role of physiological mechanisms on the occurrence of interictal epileptiform discharges, 24-hour EEG recordings from a cohort of 107 people with idiopathic generalized epilepsy were analysed using a mathematical model that incorporated the time-varying effect of the hypothalamic-pituitary-adrenal (HPA)-axis and sleep staging on the level of excitability in brain regions. Results: Two subgroups with distinct distributions of epileptiform discharges were found: one with highest incidence during sleep and the other during day-time. By calibrating the forcing term of the mathematical model using independently collected human cortisol (the primary stress-responsive hormone characterised by circadian and ultradian patterns of secretion) data and sleep-staged EEG from healthy human participants it was shown that either the dynamics of cortisol or sleep stage transition, or a combination of both, could explain most of the observed distributions of epileptiform discharges. Conclusions: These findings provide conceptual evidence for the existence of underlying physiological drivers of rhythms of epileptiform discharges. These findings should motivate future research to explore these mechanisms in carefully designed experiments using both animal models and people with epilepsy. This is a joint work in collaboration with Isabella Marinelli (University of Birmingham), Jamie J. Walker (University of Exeter), Udaya Seneviratne (Monash University), Wendyl DâSouza (University of Melbourne), Mark J. Cook (University of Melbourne), Clare Anderson (University of Birmingham), Andrew P. Bagshaw (University of Birmingham), Stafford L. Lightman (University of Bristol) and Wessel Woldman (University of Birmingham & Neuronostics Ltd).
MS24: 15:40-17:40, 24th June 2025, Room FOR/EXP2, presentation 16:40-17:00
Duncan MacGregor (University of Edinburgh)
Title: Heterogeneous population spiking dynamics and secretory signal processing in vasopressin neurons
Abstract: Hormone secreting vasopressin neurons of the brainâs hypothalamus form part of the homeostatic brain/body systems that maintain osmotic pressure (salt/water balance). In response to synaptic input signals encoding osmotic pressure and changes in plasma volume, they generate spikes (action potentials) which trigger their secretory terminals in the posterior pituitary gland. The thousands of neuronsâ secretory signals sum together to generate a blood plasma vasopressin signal that acts at the kidneys to control water loss. These neurons are distinctive for their phasic patterned spiking, consisting of long bursts and silences lasting tens of seconds. However, they are also highly heterogeneous in their activity levels and patterning, and this heterogeneity changes dynamically both with acute and chronic stimulation. In normal conditions, many are slow firing or only show simple patterned continuous spiking. After prolonged osmotic stimulation many more shift into the phasic patterning. Here we use a coupled spiking and secretion model fitted to multiple in vivo recordings of these neurons in varied physiological states to investigate what combination of activity-dependent changes to their intrinsic properties and input signals might explain these changes in patterning. We then use the coupled models as a heterogeneous population to simulate the summed plasma signal and predict how the dynamic patterning properties relate to functional signal processing.
MS25: 10:30-12:30, 24th June 2025, Room FOR/EXP2, presentation 10:30-10:50
Jennifer Tweedy (University of Bath)
Title: Drug delivery for age-related macular degeneration using the unconventional outflow of the eye
Abstract: Nearly 3% of people in the UK are living with some degree of sight loss; one of the commonest causes is age-related macular degeneration (AMD), affecting 2.4% of people over 50 years. Several retinal conditions, including AMD, are treated with drugs delivered via injection into the vitreous chamber. We develop a new model of an alternative delivery method using eyedrops. Aqueous humour is a fluid produced within the eye at an approximately constant rate, and it leaves by two routes: the so-called conventional and unconventional outflows. The conventional outflow drains into specialised channels leading to the venous system. The unconventional outflow bypasses these drains and seeps backward through the tissues in the eye, interacting with the blood vessels therein, and being gradually forced out of the eye through the sclera (white) by the intraocular pressure. The tissues involved are modelled as porous media, while osmotic pressure differences between blood and fluid in the surrounding tissue are captured by accounting for albumin transport. There is also a narrow gap between the tissues, where Stokes flow is used, which could also open in response to changes in the intraocular pressure. We add drug transport to this model. The model is greatly simplified by assuming all tissues are thin. Results indicate that the drug concentration drops off rapidly towards the posterior (the intended delivery site); however, drugs typically used to treat AMD are effective even in tiny concentrations, suggesting this method of delivery has potential.
MS25: 10:30-12:30, 24th June 2025, Room FOR/EXP2, presentation 10:50-11:10
Nikhil Desai (University of Cambridge)
Title: A model for mucociliary clearance in the human maxillary sinus
Abstract: The maxillary sinuses are a pair of hollow spaces within the human skull, located on either side of the nose, near the check region. They are lined with an epithelium that contains mucus-producing cells and tiny active appendages called cilia. The cilia beat constantly to sweep the continuously secreted mucus out of the sinus into the nasal cavity, thus maintaining a clean mucus layer within the sinuses. This process is called mucociliary clearance, and it is essential for the health and defence of the nasal environment. Disruption in mucus clearance can lead to diseases such as chronic rhinosinusitis, which mainly affects the maxillary sinuses. We present here a continuum mathematical model, which includes the essential bio-physical features of mucociliary clearance inside the human maxillary sinus. We study the flow of a thin fluid film inside a fluid-producing cavity lined with an active surface: fluid is continuously produced by a wall-normal flux in the cavity and then is swept out, against gravity, due to an effective tangential flow induced by the cilia. We show that a steady layer of mucus develops over the cavity surface only when the rate of ciliary clearance exceeds a threshold, which itself depends on the rate of mucus production. We use a scaling analysis, which highlights the competition between gravitational retention and cilia-driven drainage of mucus, to explain our computational results. We discuss the biological relevance of our findings, noting that measurements of mucus production and clearance rates in healthy sinuses fall within our predicted regime of steady-state mucus layer development.
MS25: 10:30-12:30, 24th June 2025, Room FOR/EXP2, presentation 11:10-11:30
Bindi Brook (University of Nottingham)
Title: Airway remodelling in asthma
Abstract: Inflammation, airway hyper-responsiveness (which causes constriction of the airways at lower trigger levels than in normal subject) and airway remodelling (long term structural changes of the airway wall) are key features of asthma. While this is well-established, it is not clear how they are linked or whether they are causes or symptoms of the disease. In this talk I will describe a theoretical morphoelastic model of asthmatic airways, developed in parallel with an experimental study, that accounts for mechanochemical drivers of airway remodelling with some illustrative results. I will discuss the effect of remodelling on the mechanical properties of the airways and consequent changes in how the lung is ventilated. Finally I will describe insights into how homoeostasis is maintained in healthy airways and therefore what perturbations might drive the airway into a diseased state.
MS25: 10:30-12:30, 24th June 2025, Room FOR/EXP2, presentation 11:30-11:50
Igor Chernyavsky (University of Manchester)
Title: Untangling the geometry and function of the umbilical cord in humans and other species
Abstract: The umbilical cord is a crucial lifeline between the mother and her developing fetus. Despite being part of a transient organ, it has a lifelong impact on fetal health. Intriguingly, the umbilical cord also exhibits high evolutionary diversity across placental mammals, while the impact of its unique coiled structure on human pregnancy pathologies, such as fetal growth restriction, has been a long-standing controversy in the literature. However, the cordâs role in oxygen supply and thermal regulation has remained relatively unexplored. This study investigates how the cordâs structure modulates solute and heat exchange in humans and other species. Firstly, informed by multimodal imaging, we develop mathematical models to characterise solute transport within and between helical umbilical vessels. Our combined analytical and numerical approaches reduce complexity and offer direct insights into the dominant geometrical determinants of solute and heat exchange. Secondly, we systematically analyse possible vascular configurations and demonstrate that the anatomical structure in normal cords tends to minimise diffusive exchange coupling, with direct implications for thermal regulation of the fetus. Finally, we test the hypothesis that the cordâs helicity has the capacity to amplify the oxygenation of the metabolically active cord tissue, which is motivated by a complete lack of vasa vasorum in human umbilical cords. This is a joint work with Tianran Wan, Davis Laundon, Shier Nee Saw, Nicholas Cheng, Hwee Kuan Lee, Edward D. Johnstone, Rohan M. Lewis and Oliver E. Jensen. The authors acknowledge partial support by A*STAR, EPSRC, BBSRC and Wellcome Leap.
MS25: 10:30-12:30, 24th June 2025, Room FOR/EXP2, presentation 11:50-12:10
Alannah Neff (University of Edinburgh)
Title: A model of solute transport in the cranial subarachnoid space
Abstract: Cerebrospinal fluid (CSF) is a clear Newtonian fluid surrounding the brain and spinal cord in the subarachnoid space (SAS). CSF pulsates during the cardiac cycle due to changes in brain volume: during systole, increased brain volume displaces CSF into the spinal SAS; during diastole, brain volume decreases and the CSF flow reverses. CSF motion is hypothesised to play a vital role in nutrient transport and the clearance of harmful substances, including toxins and toxic proteins. CSF is also a potential pathway for drug delivery via intrathecal administration. This work aims to understand solute transport in CSF for applications in metabolic waste clearance and drug delivery. In this study we develop a simplified model of CSF flow and solute transport in cranial SAS, represented as a two-dimensional domain with oscillating lower boundary. We use small aspect ratio đ of the domain and apply lubrication theory to obtain an analytical solution for the fluid flow at the leading order in đ (oscillatory flow) and the steady component of the first order flow. The solute transport is modelled with an advection-diffusion equation, and we derive the long time-scale transport equation, which we solve numerically. We examine solute transport in two scenarios: (i) drug entry via the spinal canal, estimating delivery time to the brain, and (ii) clearance of toxic proteins from perivascular pathways, assessing SAS efficiency. This approach allows us to understand the fundamental mechanisms of solute transport in the CSF and provides a framework for investigating more realistic domain geometries and displacements.
MS25: 10:30-12:30, 24th June 2025, Room FOR/EXP2, presentation 12:10-12:30
Matthew Ghosh (University of Oxford)
Title: Modelling the deformation and solute-induced degradation of poroelastic materials
Abstract: Poroelastic materials, consisting of a deformable solid skeleton with fluid flowing within the pore space, can weaken when interacting with chemical species, such as enzymes or salts. One example of such a material is a hydrogel, which has a wealth of biomedical applications in urology; for example, as a stent in the ureter or as a spacer to separate tissues in the radiotherapy of the prostate. These materials degrade via the scission of polymer cross-links, reducing their overall stiffness. To gain fundamental insights into these complex systems, we build on the framework developed by MacMinn et al. for a poroelastic material in a channel and use the finite element method and analytical techniques to understand the time-varying and steady-state mechanics of the system. Our framework couples large-deformation poroelasticity with an advection-diffusion equation for the solute; furthermore, we introduce a decay equation for the material stiffness, whose rate of decay depends on the solute concentration. We analyse a system of finite length driven by an imposed fluid flux and a fixed solid stress at a moving boundary and examine the effect of weakening the poroelastic material. We assume that the timescales for weakening and solute diffusion are longer than those for poroelastic deformation and advection and exploit this separation of timescales to undertake an asymptotic reduction of the model. To conclude, we impose a cyclic fluid flux at the left boundary and investigate how these oscillations, fast on the timescales of weakening and solute diffusion, affect the systemâs long-term behaviour.
MS26: 10:30-12:30, 24th June 2025, Room FOR/SR7-8, presentation 10:30-10:50
Frank Kwasniok (University of Exeter)
Title: Data-driven deterministic and stochastic subgrid-scale parameterization for atmosphere and ocean models: a pattern-based approach
Abstract: Data-driven machine-learning-type deterministic and stochastic subgrid modelling schemes for atmosphere and ocean models are discussed. A pattern-based approach is taken where pairs of patterns in the space of resolved variables (or functions of these) and in the space of the subgrid forcing are identified and linked in a predictive manner. On top of this deterministic part of the subgrid scheme the subgrid patterns may be forced stochastically with a fitted vector-autoregressive process. Both the deterministic and the stochastic scheme can be constrained by physically motivated conservation laws, such as momentum conservation or (kinetic) energy conservation but enstrophy dissipation. The method can also be extended by combining it with a clustering algorithm to arrive at a set of local subgrid models. The schemes are machine-learning-style, but not based on deep learning. Unlike black-box approaches such as neural networks, the present methodology still allows to understand and interpret the subgrid model. The subgrid modelling schemes are explored in the multiscale Lorenz 1996 system and then implemented in a spectral quasi-geostrophic three-level atmospheric model with realistic mean state and variability.
MS26: 10:30-12:30, 24th June 2025, Room FOR/SR7-8, presentation 10:50-11:10
Igor Shevchenko (National Oceanography Centre)
Title: On energy-aware hybrid models for ocean modelling
Abstract: In this talk we discuss deterministic and stochastic energy-aware hybrid models that enable simulations of Geophysical Fluid Dynamics (GFD) models at low resolutions without compromising on the quality of the flow dynamics compared with high-resolution runs. The proposed hybrid models bridge the data-driven and physics-driven modelling paradigms by combining regional stability and classical GFD models at low resolution that cannot reproduce high-resolution reference flow features which are, however, resolved. Hybrid models use an energy-aware correction of advection velocity and extra forcing compensating for the drift of the low-resolution model away from the reference phase space. The main advantages of hybrid models are that they allow for physics-driven flow recombination within the reference energy band, reproduce resolved reference flow features, and produce more accurate ensemble forecasts than their classical GFD counterparts. Hybrid models offer appealing benefits and flexibility to the modelling and forecasting communities, as they are computationally inexpensive and can use both numerically-computed flows and observations from different sources. All these suggest that the hybrid approach has the potential to exploit low-resolution models for long-term weather forecasts and climate projections thus offering a new cost effective way of GFD modelling.
MS26: 10:30-12:30, 24th June 2025, Room FOR/SR7-8, presentation 11:10-11:30
Tobias Grafke (Warwick Mathematics Institute)
Title: Transition path sampling for noise induced tipping
Abstract: Tipping points and transitions in metastable systems are a notoriously hard problem in complex system science and climate science. Noise induced tipping, where stochasticity pushes the system over an activation barrier into a novel long-lived state, fall into the purview of transition path sampling. Examples include the North Atlantic Meridional Circulation (AMOC), transporting warm water to northern Europe, which is suspected to in a metastable regime, where freshwater hosing can tip the system to a new steady state where the AMOC is switched off. In practice, we are often interested in drawing from the ensemble of transition paths to investigate typical tipping trajectories and their physical properties, for example in order to learn climatological mechanisms of the tipping point. In this talk, I will present a novel numerical scheme for sampling the transition path ensemble, particularly suited for the presence of multiple coexisting tipping mechanisms, by combining pathspace Markov chain Monte Carlo with metadynamics.
MS26: 10:30-12:30, 24th June 2025, Room FOR/SR7-8, presentation 11:30-11:50
Peter Ashwin (University of Exeter)
Title: The quest for robust early warnings of bifurcations in noisy systems
Abstract: We highlight how nonlinear behaviour (both of forcing in time, and of the system) can affect the skill of early warning signals (EWS) when using measures based on critical slowing down (CSD), due to the breakdown of extrapolation. We highlight how this can occur in a forced chain of nonlinear dynamical systems where an upstream system crossing a tipping point can shorten the timescale of valid extrapolation for a warning of downstream tipping. Indeed, downstream tipping points can have a warning on a time horizon comparable with the timescale of the upstream tipping process rather than the timescale of the forcing.
MS26: 10:30-12:30, 24th June 2025, Room FOR/SR7-8, presentation 11:50-12:10
David Stainforth (London School of Economics and Political Science)
Title: On the use of reduced-order models to guide the design of Earth System Model ensembles
Abstract: Complicated computer models of the earthâs climate system – so called Earth System Models (ESMs) – are central to many areas of climate science and their outputs are widely used to support assessments of the expected impacts of climate change. Their projections of future climate are typically based on scenarios for future greenhouse gas emissions. Beyond uncertainty regarding the most appropriate scenario, however, there are several additional sources of uncertainty. These include intrinsic uncertainty related to initial condition sensitivity in a complex nonlinear system, substantial uncertainty regarding the most informative starting state for the model, and sensitivity of the model response to its structure or the assumed value of model parameters. These are referred to as micro-initial-condition uncertainty, macro-initial-condition uncertainty, and model uncertainty [1]. How best to explore these different sources of uncertainty is important for a wide range of climate change studies. The computational cost of running these high-dimensional models provides significant constraints on how many simulations can be run. However, reduced-order models with some of the essential characteristics of the climate system, can be used to study the uncertainty exploration process itself, and thereby guide the design of ESM ensembles. Here I will present recent explorations of initial-condition [2] and model uncertainty[in prep] in climate-style projections with a low-dimensional chaotic model. I will argue that these results imply the need for larger ensembles of ESMs, designed to focus on uncertainty quantification. [1] Stainforth et al., Phil Trans Roy Soc., 2007. [2] De-Melo-Virissimo and Stainforth, Chaos, 2024.
MS26: 10:30-12:30, 24th June 2025, Room FOR/SR7-8, presentation 12:10-12:30
Henry Addison (University of Bristol)
Title: Generative Machine Learning Emulation of Precipitation from km-scale Regional Climate Simulations
Abstract: Dynamical downscaling of climate simulations to local scales is valuable for understanding climate change impacts and planning adaptation measures, but is very computationally expensive. We present CPMGEM (Convection-Permitting Model Generative EMulator) [1]: a novel application of a generative machine learning model, a diffusion model, that skilfully emulates precipitation simulations by a regional convection-permitting model. This achieves similar results at daily timescales to dynamical downscaling at a fraction of the computational cost. This emulator enables stochastic generation of high-resolution (8.8km) daily-mean precipitation samples, fine enough for use in applications such as flood modelling, conditioned on coarse (60km) weather states from a general circulation model (GCM). We trained the emulator to produce output over England and Wales, using Met Office simulations from the United Kingdom Climate Projections (UKCP) Local product, covering 1980-2080. It produces predictions that have realistic spatial structure and that have a similar frequency distribution as the CPM. Potential applications include producing high-resolution precipitation predictions for large-ensemble climate simulations and across different GCMs and scenarios to better sample uncertainty. I will also discuss the calibration of the spread of precipitation samples and the emulatorâs skill in reproducing changes in seasonal mean, extremes and distribution of daily intensities predicted by the CPM over the 21st century. I may also cover initial results from an extension to jointly emulate multiple variables. [1] Addison, H., Kendon, E. J., Ravuri, S., Aitchison, L. and Watson, P.A.G., 2024. Machine learning emulation of precipitation from km-scale regional climate simulations using a diffusion model. arXiv preprint https://arxiv.org/abs/2407.14158
MS27: 15:40-17:40, 25th June 2025, Room FOR/EXP2, presentation 15:40-16:00
Molly Brennan (University College London(UCL))
Title: From membrane channels to bacterial colonies: An asymptotic upscaling of transport through the bacterial membrane
Abstract: Membranes regulate transport in a wide variety of applications, from industrial filtration and synthetic fabrics to biological cells and tissues. In bacteria, membrane channels control sensing and communication, and enable cells to filter antibiotics and resist treatment. In this talk we systematically upscale the transport across a bacterial membrane, deriving effective boundary conditions that explicitly account for the microscale channel structure, combining multiscale methodologies including asymptotic homogenisation and boundary layer theory. This allows us to treat the bacterial membrane as an effective interface, over which a significant concentration difference can be sustained. The effective conditions we derive preserve information about the microscale structure while reducing computational complexity, providing insight into how microscale properties affect membrane permeability and metabolite transport over much larger lengthscales. Incorporating these conditions into an additional population-level upscaling we see how membrane microstructure affects colony behaviour. More broadly, because we consider a generic membrane geometry and our results hold for general (outer) problems away from the interface, the results we derive have a wide scope of applications beyond bacterial membranes. For example, in modelling water vapour and heat loss through fabrics.
MS27: 15:40-17:40, 25th June 2025, Room FOR/EXP2, presentation 16:00-16:20
Anna Curran (Imperial College London)
Title: A theoretical study of the regularisation of stagnant caps of surfactant
Abstract: Surfactants are molecules which lower the surface tension at an interface between two fluids, and their existence, even in trace amounts, is largely unavoidable. Their effect on a flow, desirable or not, is relevant in a wide range of biological, industrial, and engineering applications. When present in a convergent flow they are swept to a point on the interface, reducing the surface tension there and producing Marangoni forces acting in the direction opposite to the flow. In the worst case scenario a âstagnant capâ of surfactant forms, acting as a no-slip surface and effectively immobilising the interface. This critical case then typically hinders the oncoming flow. We present a detailed analytical study, based on complex variable methods, which examines the remobilising effects of both surface diffusion and solubility on the structure of steady stagnant caps of surfactant on both liquid-liquid and liquid-air interfaces. Both insoluble and soluble surfactants in a viscous fluid can be considered using this approach. Explicit steady equilibrium solutions for the flow and surfactant concentration in each case are constructed in terms of logarithmic derivatives of special functions. The singularity structure of the solution is analysed using techniques from both exponential asymptotics and Liouville-Green theory, providing mathematical insight into the parameter regimes controlling the regularisation of the stagnant cap.
MS27: 15:40-17:40, 25th June 2025, Room FOR/EXP2, presentation 16:20-16:40
Zoe Godard (University of Oxford)
Title: Cyclic loading of non-linear heterogeneous poroelastic material
Abstract: Many poroelastic materials are subject to cyclic loads or deformation throughout their lifetime, ranging from biological systems, such as tendon and cartilage, to geological systems, such as a seabed beneath waves. Heterogeneity is common in these materials and significantly affects their response to periodic loading and deformation. We characterise the behaviour of a soft porous material in response to a uniaxial cyclic load or displacement, and explore how this response is affected by continuous heterogeneity in the stiffness or permeability. We present a one-dimensional non-linear poroelastic model, assuming Darcy flow through the pores of the solid skeleton which we assume has Neo-Hookean elasticity, and impose a local decrease in the stiffness or permeability. We apply either a uniaxial cyclic stress or a uniaxial cyclic displacement at one boundary, and no flux at the other boundary. We show that the response of the system to an applied load is qualitatively distinct from the response to an applied displacement and is less affected by heterogeneous permeability than heterogeneous stiffness. By exploring a range of frequencies, magnitudes and locations of heterogeneity, we characterise the effect of heterogeneity on net absolute strain and flux. This simple model provides a foundation for understanding how heterogeneity affects the poroelastic response to cyclic loading and deformation, which can be used to inform and build more complex, higher-dimensional models.
MS27: 15:40-17:40, 25th June 2025, Room FOR/EXP2, presentation 16:40-17:00
Peter Lewin-Jones (University of Warwick)
Title: Collision of liquid drops: bounce or merge?
Abstract: Collisions and impacts of drops are critical to numerous processes, including raindrop formation, inkjet printing, food manufacturing and spray cooling. For drop-drop collisions, increasing the relative speed leads to multiple transitions: from merging to bouncing and then back to merging – transitions which were recently discovered to be sensitive to the drops’ radii as well as the ambient gas pressure. To provide new insight into the physical mechanisms involved and as an important predictive tool, we have developed a novel, open-source computational model for both drop-drop collisions, using the finite element package oomph-lib. This uses a lubrication framework for the gas film and incorporates fully, for the first time, the crucial micro- and nano-scale influences of gas kinetic effects and disjoining pressure. Our simulations show strong agreement with experiments for the transitions between merging and bouncing, but can also go beyond these regimes to make new experimentally-verifiable predictions. We will show how our model enables us to explore the parameter space and discover the regimes of contact (that are inaccessible to experiments). Finally, we will overview the impact of drops onto liquid baths, where for a fixed impact speed, the collision outcome can go from merging to bouncing to merging and back to bouncing with increasing bath depth. Our lubrication equation must be modified to capture the curvature of the trapped gas film, and our resulting simulations are the first to successfully predict the transitions between bouncing and merging in drop-bath impacts.
MS27: 15:40-17:40, 25th June 2025, Room FOR/EXP2, presentation 17:00-17:20
Andrew Nugent (University of Warwick)
Title: Steering opinion dynamics through control of social networks
Abstract: We propose a model for continuous time opinion dynamics on an evolving network. Contrary to many existing models, in which the network evolves by discretely adding or removing edges, we instead consider a model for opinion formation which is coupled to a network evolving through a system of ordinary differential equations for the edge weights. We focus on controlling a population towards consensus in this setting, where controls are applied to the edge weight dynamics only, rather than directly affecting individualsâ opinions. This approach has two major challenges: ensuring that the population does not break into polarised opinion clusters and that the target opinion remains accessible. In this talk I will present results on the existence of controls and discuss methods for finding effective and optimal controls.
MS27: 15:40-17:40, 25th June 2025, Room FOR/EXP2, presentation 17:20-17:40
Joseph Webber (University of Warwick)
Title: Getting stressed about frozen gels
Abstract: When exposed to temperatures below freezing, we are all familiar with the damage that can occur to porous materials as ice forms – be this in the formation and growth of potholes in tarmac or the altogether disappointing experience that are frozen strawberries. It’s commonly believed that the expansion of water as it freezes drives the buildup of stresses in the pore matrix, but for years it has been known that these stresses are far too small, and that actually a process called ‘cryosuction’, where the formation of ice draws water from the pores to rapidly grow even bigger chunks of pure ice, is the main driving factor behind this damage. Hydrogels – squishy, elastic, yet porous materials – provide the ideal media to understand the interplay between ice growth, elastic deformation and interstitial fluid flows when freezing is instigated, providing for the first time a complete mathematical model for the origin of shear and normal stresses driving this damage to deformable porous media. Owing to the small pore size, ice cannot form within the nanometre-scale gaps in a gel, but instead grows at a cooled boundary, sucking water through the gel and drying it out, until eventually a steady state of stressed, deswollen, gel adjacent to pure ice is formed. Understanding how the deswollen gel that is left behind is sheared and squeezed gives key insights into a number of problems, including the cryopreservation of human organs for transplant.