The Applied mathematics seminar is held regularly during termtime.
Monday 26 January 2026, 12:00-13:00
Arts, Lecture Room 2
In this talk, we propose mathematical models of microbial populations at both micro and macroscale levels. The sociobiological aspect reveals self-organisation, cell communication, and social evolution during the development of microbial colonies. We establish the biofilm spread rate in terms of model parameters and conditions under which microbial population oscillations (boom-and-bust) may occur. Bifurcation analysis and the interplay between Turing and Hopf instabilities are discussed. Numerical simulations demonstrating the existence of stable and oscillatory spatial patterns will be presented.
Monday 2 February 2026, 12:00-13:00
Arts, Lecture Room 2
Chemically active drops release a chemical solute, gradients in whose concentration cause interfacial flows which in turn drive the transport of the emitted solute. This non-linear coupling between solute distribution and fluid flow around the drop causes the drop to swim via an instability, if the system's Peclet number Pe--ratio of advective-to-diffusive solute transport--is larger than a finite threshold. In experiments, active drops generally have a density mismatch with the surrounding fluid, causing them to swim close to rigid surfaces. Motivated by this, we investigate here the propulsion of a viscous active drop parallel to a rigid wall, where it is confined by its own weight. We relax the prevalent modelling assumption of treating active drops as rigid particles, and consider a general propulsion mechanism: concentration gradients of the solute emitted by the drop result in diffusiophoretic interfacial flows in addition to Marangoni stresses, that cause the inertialess drop to translate. We show that, for the same confining force, a less viscous drop swims closer to the wall than a more viscous drop. This leads to stronger concentration gradients driving the drop's motion and hence faster swimming. We also investigate the influence of the relative strengths of diffusiophoretic and Marangoni flows--called the mobility ratio--and show that, for moderate values of Pe, the normalized swimming speed of the drop depends very weakly on its mobility ratio. In the process, we quantitatively justify the idea of studying the mathematically simpler problem of a rigid active particle to infer the motion of a fluid active drop.
Monday 9 February 2026, 12:00-13:00
Arts, Lecture Room 2
Single epithelial cell migration arises from the tight coupling of intracellular organization, cytoskeletal activity, viscous flow, and cell-scale deformation. This talk presents a unified variational framework that places these processes on a common energetic foundation.
The framework integrates three core components. First, endoplasmic reticulum (ER) remodeling is described using a diffuse-interface formulation that combines phase-field energetics, membrane curvature elasticity, and Cahn–Hilliard–Navier–Stokes coupling, capturing ER segregation, curvature-driven reorganization, and intracellular transport in the low-Reynolds-number regime. Second, cytoskeletal dynamics are incorporated through energetically consistent descriptions of actin turnover and microtubule reorganization, enabling polarity-biased and fluctuation-driven behavior. Third, cell shape and front–rear polarity are modeled using coupled diffuse-interface and Frank–Oseen-type energies, allowing active force generation and persistent migration to emerge naturally.
The framework is implemented using a new staggered numerical scheme for variational multiphysics systems. The approach is illustrated through a few representative examples: a single-cell migration model exhibiting spontaneous symmetry breaking and steady motion, and an image-calibrated simulation of curvature-guided ER transport initialized from fluorescence microscopy data.
Monday 16 February 2026, 12:00-13:00
Arts, Lecture Room 2
Everyone has seen the v-shaped Kelvin wake-pattern visible in the wake of a moving object on the surface of water. In this talk we show, using a simple mathematical argument, that by a judicious choice of a pressure distribution (modelling a boat), wave-free solutions are possible in the context of a model system; the forced Kadometsev-Petviashvili equation. Strikingly, we show that these solutions are stable, so they could potentially be visualised in a physical experiment. I will also briefly discuss some other of my research endeavours involving waves, bubbles, droplets and pendulums.
Monday 2 March 2026, 12:00-13:00
Arts, Lecture Room 2
TBA
Monday 9 March 2026, 12:00-13:00
Arts, Lecture Room 2
TBA
Monday 16 March 2026, 12:00-13:00
Arts, Lecture Room 2
This talk will introduce and connect three approaches to modelling opinion formation. Beginning with an agent-based model (ABM) with random pairwise interactions, we derive a system of coupled ordinary or stochastic differential equations (SDEs) by simultaneously rescaling time and the extent to which an agent updates their opinion after an interaction. We show how the precise form of these limiting equations connects to choices made in the ABM, in particular how introducing noise at various points in the ABM motivates different diffusion terms in the resulting SDE. Building on this system of SDEs, we then introduce age structure. Each individual ages continuously in time until a maximum age, at which point they die and re-enter the population at age zero with a new, randomly selected opinion. We study the corresponding mean-field limit, a non-linear non-local partial differential equation, showing the existence of steady states and new complex dynamics made possible by the continuous introduction of new individuals to the population.
Monday 23 March 2026, 12:00-13:00
Arts, Lecture Room 2
Abstract: TBA
Tuesday 28 October 2025, 12:00-12:50
Poynting, Lecture Theatre S06 (Small)
Many active systems are capable of forming intriguing patterns at scales significantly larger than the size of their individual constituents. Cyanobacteria are one of the most ancient and important phyla of organisms that has allowed the evolution of more complex life forms. Despite its importance, the role of motility on the pattern formation of their colonies is not understood. Here, we investigate the large-scale collective effects and rich dynamics of gliding filamentous cyanobacteria colonies, while still retaining information about the individual constituents' dynamics and their interactions. We investigate both the colony's transient and steady-state dynamics and find good agreement with experiments. We furthermore show that the Péclet number and aligning interaction strength govern the system's topological transition from an isotropic distribution to a state of large-scale reticulate patterns. Although the system is topologically non-trivial, the parallel and perpendicular pair correlation functions provide structural information about the colony, and thus can be used to extract information about the early stages of biofilm formation. Finally, we find that the effects of the filaments' length cannot be reduced to a system of interacting points. Our model proves to reproduce both cyanobacteria colonies and systems of biofilaments where curvature is transported by motility.
Monday 3 November 2025, 12:00-12:50
Poynting, Lecture Theatre S06 (Small)
Understanding and preventing bacterial infections requires insight into how microorganisms move and interact within realistic, structured environments such as biofilms or tissues. From a modelling perspective, these systems can be studied across multiple scales — from continuum PDEs approaches and agent-based models to single-cell descriptions. In this talk, we focus on this latter class of single-cell models, and study the coupling between individual motile bacteria and their environment.
We first examine how suspended particles influence the swimming of flagellated bacteria, combining analytical and semi-analytical results to explain the experimentally observed speed increase in suspensions. We then turn to microorganisms for which motility relies on elasto-hydrodynamic instabilities and such minimal models cannot capture key features of their motility. We present elasto-hydrodynamic simulations for the swimming of the oral pathogen Selenomonas sputigena and the gliding motion of filamentous cyanobacteria.
Monday 17 November 2025, 12:00-12:50
Poynting, Lecture Theatre S06 (Small)
Cytoplasmic streaming, the persistent flow of fluid inside a cell, induces intracellular transport, which plays a key role in fundamental biological processes. In this talk, we will discuss two types of cytoplasmic flows inside living cells.
First, we consider naturally occurring cytoplasmic flows during cell division. 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. Through a combination of numerical and analytical modelling, we reveal a hydrodynamic mechanism for stable spindle positioning beneath the cortical cap.
In the second half of the talk, we examine artificial cytoplasmic streaming. Recent experiments in cell biology have probed the impact of artificially induced intracellular flows in the spatiotemporal organisation of cells. In these experiments, mild heating via focused infrared light from a laser induces long-range, thermoviscous flow of the cytoplasm inside a living cell, a method popularised in cell biology as FLUCS (focused-light-induced cytoplasmic streaming). We present an analytical, theoretical model describing the fluid flow induced by the laser. Our quantitative findings show excellent agreement with recent experimental results and will enable the design of new controlled experiments to establish the physiological role of physical transport processes inside cells.
Monday 24 November 2025, 12:00-12:50
Poynting, Lecture Theatre S06 (Small)
Flooding is one of the most critical climate-related risks in the foreseeable future, and scientifically robust models are vital for assessing scenarios of flood risk. However, the hydrological models on which many important decisions currently rest are known to be uncertain. Hundreds of models are proposed in the literature, most having roots in research from the 1970s and onwards---and yet only a handful are applied in practice. While many models are tested through empirical inter-comparison studies, many questions involving the fundamental mathematical makeup of the models remains limited. In a recent skills survey of the hydrology professional community, less than 3% of respondents reported highest academic qualifications in mathematics: this is a sector that would benefit from many of the rigorous views, tools, and techniques that we possess and apply in our approach to science.
In this seminar talk, I was speak, informally, about my interesting year working with JBA Trust, a leading industry-based charity whose aim is to improve societal resilience to environmental risks, as part of the ICMS Mathematics for Humanity programme. I will talk about the interesting mathematical challenges that exist within the sector, and role that mathematicians can play in collaborating with hydrologists. I will discuss the interplay of conceptual vs. physics-based models of flooding, and the role of asymptotics in establishing decisions about model differentiation and comparison.
Monday 1 December 2025, 12:00-12:50
Poynting, Lecture Theatre S06 (Small)
In biomedical applications, there are many interactions between cells and their direct environment, for instance, in wound healing, the skin cells are attracted to migrate towards the wound by cytokines secreted by the immune cells.
For the sake of computational efficiency, in mathematical modelling and for theoretical purposes, the Dirac Delta distributions are often utilized as a replacement for cells or vesicles, since the size of cells or vesicles is much smaller than the size of the surrounding tissues. Here, we consider the scenario that the cell or the vesicle releases the diffusive compounds to the immediate environment, which is modelled by the diffusion equation but with two approaches, distinguishing by whether considering the intracellular environment as part of computational domain or not. Both homogeneous and spatially-inhomogeneous flux density over the cell boundary are studied. In particular, for the spatially-inhomogeneous flux density, we proposed a multi-Dirac approach to capture the inhomogeneity of the flux over the cell boundary.
Monday 8 December 2025, 12:00-12:50
Poynting, Lecture Theatre S06 (Small)
Wave-driven propulsion (WDP) is a little-known type of locomotion in which a floating body generates surface waves to push itself forwards. Some animals have evolved to use WDP when moving on the water surface, such as water striders and water snakes. Meanwhile, WDP technologies have the potential to revolutionise engineering applications, such as reduced fuel consumption in shipping and low-energy water robots that can clean up oil spills.
In this seminar I will explore a simple model for WDP based on the wave equation, showing how to derive the optimum forcing using variational calculus as well as via numerical optimisation. I will also explore a more realistic model based on coupling the equations of motion of a floating raft to a quasi-potential flow model of the fluid, showing good comparison with experimental data. Finally, I will discuss some of the key open challenges in the area and the road ahead for the future.
References