Keynote Speaker: Dr Benjamin Walker (University College London)
Title: Intuition in applied mathematics
Abstract: Intuition can be a valuable tool for solving mathematical problems; more than once it has saved me from writing down the backwards heat equation, for instance. Unfortunately, intuition isn't always reliable and it can even be drastically wrong. In this talk, we'll explore some topics from research in microscale swimming where intuition can be misleading and incorrect, even in straightforward situations. Fortunately, we'll also see how mathematical tools can help us develop good intuition or improve our bad intuition. We'll then take a look at some classical examples from across mathematical modelling where gaining intuition can be quite challenging, and see how modern tools can help us overcome this. If you have a device like a laptop, tablet, or smartphone, bring it along and build your own intuition for complex mathematical systems using just your web browser and VisualPDE.com.
20-min Contributed Talks
Jan Kocka - UCL
Title: Diffusible metabolites lead to Turing patterns in microbial communities
Abstract: The stability and diversity of a microbial community is shaped by the metabolic interactions between its constituent species. However, these interactions are often mediated by diffusible metabolites, whose efficacy depends on the spatial organisation of the community. What determines this spatial structure remains broadly unknown. Here, we show that generic microbial communities can spontaneously self-organise into spatially-structured patterns from an initially well-mixed state. This instability is driven by a feedback between metabolite diffusion and microbial growth, and is suppressed in resource-rich environments. Taking advantage of an analogy with Turing pattern, we derive analytical bounds on the instability. The spatially structured state often reflects the underlying metabolic logic of the community, and we find that community functions like biomass production are altered compared to the well-mixed state. Overall, our results argue for the inevitability of spatial structure, and delineate how (spatial) structure emerges from (metabolic) function in microbial consortia.
Douglas Brown - Oxford
Title: Active Fluid Patterning in Inhomogeneous Environments
Abstract: Active stresses in biological cells and tissues drive many developmental processes. Increasing experimental evidence suggests that mechanical interactions with surrounding material can play a crucial role in guiding these processes. We introduce a minimal model of this scenario and investigate how pattern formation in an active material can be controlled by an inhomogeneous environment. We consider an active fluid in which a chemical species regulates local active stresses. We show that active stress patterns exhibit frictiotaxis, as observed in experiments, and systematically characterise how inhomogeneous external friction affects mechanochemical patterning instabilities. We find that hydrodynamic screening plays a crucial role in mediating the cross-talk between friction patterns and active fluid self-organization and identify a mechanochemical frustration mechanism that gives rise to pattern oscillations caused by inhomogeneous friction.
Gianmarco Spera - Oxford
Title: Pressure governs closing of density wake in concentrated thermal and active colloidal suspensions
Abstract: We investigate the density wake generated by an obstacle dragged through a dense assembly of thermal passive and active colloids. Combining experiments and numerical simulations, we show that pressure governs the near-field structure of the wake.
Julius Kiln - Oxford
Title: Resonances in Odd Viscoelastic Materials
Abstract: Odd viscoelasticity arises in parity-violating nonequilibrium materials, where it leads to unconventional mechanical responses and oscillatory relaxation even in overdamped systems. While many living and active chiral materials present promising candidates to exhibit odd viscoelasticity, there is currently no approach that allows for a rheological inference of the large number of elastic and viscous moduli that even a minimal isotropic odd viscoelastic material can depend on. Generalizing the century-old Papkovich-Neuber ansatz to active solids and fluids, our work introduces odd Papkovich-Neuber (OPN) solutions that enable us to study the boundary-driven response of odd materials in geometries that mimic common rheology methods. OPN solutions reveal three physically distinct resonances in general odd viscoelastic solids that are characteristic of the underlying material moduli and can all be interpreted within a single geometric framework. Underlying this unification is an equivalent description of overdamped odd viscoelastic materials in terms of damped harmonic oscillators. Resonances appear as the effective damping coefficient of these oscillators vanishes, which is facilitated by the activity that powers odd material properties.
Demosthenes Georgiou - Imperial
Title: Persistence, resetting, and first-passage times of an active Ornstein–Uhlenbeck particle
Abstract: We study the first-passage time statistics of an active Ornstein–Uhlenbeck particle on a finite one-dimensional interval with an absorbing boundary at one end and a reflecting boundary at the other, subject to stochastic resetting. In the weak-activity regime, we develop a perturbative solution of the Fokker–Planck equation and use a renewal framework to obtain analytical expressions for the first-passage-time distribution and its low-order moments. In the absence of resetting, activity can either increase or decrease the mean first-passage time, depending on the relation between the persistence time and the diffusive time to absorption. When resetting is introduced, we determine both the onset of beneficial resetting and the finite range of resetting rates for which resetting lowers the mean first-passage time of the active system. We further show that the resetting transition depends on the velocity resetting protocol. Finally, by comparing the active particle with resetting to the passive Brownian particle without resetting, we construct a phase diagram that identifies the regions of parameter space in which activity and resetting together reduce the mean first-passage time.
5-min Flash Talks
Yuxin Jia - Imperial
Title: Conformational Trapping and Transport of Active Polymers in Compliant Media
Abstract: We study the transport of a single flexible active polymer in a two-dimensional crowded environment with different obstacle conditions. These include no obstacles, static rigid obstacles, and elastically tethered obstacles with different stiffness. Using overdamped Langevin simulations, we show that mean squared displacement alone does not fully resolve the underlying dynamics. We therefore introduce two survival observables based on radius of gyration and vorticity. These measure geometric compactness and rotational coherence separately. This allows us to classify the polymer dynamics into localised, transient, and diffusive regimes. We find that obstacles have two competing effects. They promote polymer collapse, but they also disrupt stable spiral formation. As obstacle stiffness increases, the transient regime expands and the localised regime shifts to higher activity. These results show that obstacle compliance is a key control parameter for conformational trapping and long-time transport in crowded active systems.
Sara Drummond-Curtis - UCL
Title: Multi-timescale dynamics of microswimmers
Abstract: Microswimmers typically undergo rapid motion to propel themselves through fluid. When considering the long-time swimmer dynamics of interest, the effect of the rapid motion is often assumed to average out without significantly affecting the trajectories. However, recent work has shown that this is not always the case. In this talk, we consider how the interaction between rapid propulsive motion and environmental factors influences swimmer trajectories. Touching upon examples of boundaries and external flows, we exploit the separation of timescales through a systematic multiscale analysis to derive effective equations for the long-time dynamics. As a result of our analysis, qualitatively different predictions emerge, highlighting the role of fast-time motion on the long-time swimmer dynamics as they navigate their environment.
Hsiang-Yun Tseng - Cambridge
Title: Mechanical effects on competition between two-species biofilms
Abstract: While the advancing fronts of expanding bacterial colonies are often successfully modeled as homogeneous continuum fluids, real biofilms are complex active mixtures of phenotypically diverse individuals. A prominent example is the coexistence of large, slow-growing, matrix-producing cells and small, fast-dividing, motile flagellated cells. In this work, we explore how disparities between the two species—specifically geometry and growth rate—shape the competitive landscape at the expanding colony front. By performing agent-based simulations and developing a phenomenological continuum model, we aim to characterize the mechanical properties of the boundaries separating these distinct domains formed by the two species and uncover the conditions required for stable coexistence during spatial expansion.
Ross Monaghan - Imperial
Title: Complete wetting of active Brownian particle
Abstract: In equilibrium systems, one can control the height of a film wetting a surface by tuning the chemical potential of the liquid; at gas-liquid coexistence the surface height diverges in a transition known as a complete wetting transition. We explore a non equilibrium system consisting of active Brownian particles accumulating at a hard-wall. We introduce a particle reservoir with fixed density to act as a source of active particles. By tuning the particle density of this reservoir, we demonstrate how one can induce a complete wetting transition for the active particles accumulating at the wall.
