Applied Mathematics Seminars Spring 2025
See below for information regarding the Applied Seminars in Spring 2025.
Seminars take place online on Tuesdays at 3.00pm on Zoom via the link https://ucl.zoom.us/j/99614222402. Many of the seminars will be ‘hybrid’ (i.e. in person +zoom). If you require any more information on the Applied seminars please contact Prof Jean-Marc Vanden-Broeck (e-mail: j.vanden-broeck AT ucl.ac.uk or tel: 020-7679-2835) or Prof Ilia Kamotski (e-mail: i.kamotski AT ucl.ac.uk or tel: 020-7679-3937).
Tuesday 14 January 2025 in Room G06, 21 Gordon Square
Speaker: Giulia Salussolia (Universidad Mayor, Chile)
Title: elastic or bent sheets in viscous flow
Abstract:
Understanding the dynamics of micro and nanometric plate-like particles in viscous flow is essential for several applications such as 2D nanomaterials fabrication, water contaminants control and biological modelling of microswimmers. This talk presents an approach to modelling plate-like particles - both flexible and rigid - in viscous flows. The approach involves designing a 2D slender body theory for plates and elastic sheets that simplifies the treatment of the fluid-structure interactions and accurately describes the flow and rheology of both passive and active plates/sheets. Derived from the boundary integral formulation of the incompressible Stokes equations, this theory reduces the surface integral over the particle boundary to a non-local line integral across the particle’s central line, excluding the edge effects and significantly reducing the computational cost. The 2D slender body theory for plates is then used to qualitatively explore the dynamics of deformable plate-like particles in shear flow, where the interplay between hydrodynamic stress and bending stiffness, along with initial configurations, governs their behaviour.
Tuesday 21 January 2025 in Room G06, 21 Gordon Square
Speaker: Bryn Davies (University of Warwick)
Title: Localisation in non-reciprocal wave systems
Abstract:
In this talk, we will explore the classical problem of defect-induced localisation in periodic media, extended to problems that are non-reciprocal. We will study a discrete system that is a variant of the Hatano-Nelson chain and show how on-site defects must be larger than some non-zero size to overcome the non-Hermitian skin effect and cause exponential localisation in the bulk. Further, we will show how defects in the coupling strength can lead to an exotic “scale-free” (linear) localisation phenomenon. In both cases, multi-scale perturbative analysis will be used to estimate the localisation. Finally, we will discuss ongoing work to realise the corresponding phenomena in continuous PDE models (with high-contrast coefficients).
Tuesday 28 January 2025 in Room G06, 21 Gordon Square
Speaker: Massimo Sorella (Imperial College)
Title: Spotaneous stochasticity for a 2d autonomous flow
Abstract:
In this talk, we present a 2d autonomous divergence free velocity field in $C^\alpha$ (for $\alpha<1$ arbitrary but fixed) for which solutions of the advection diffusion equation exhibit anomalous dissipation for some initial data. The proof relies on proving spontaneous stochasticity using a stochastic Lagrangian approach. This is a joint work with C. Johansson.
Tuesday 4 February 2025 in Room G06, 21 Gordon Square
Speaker: Karen Page (UCL)
Title: Mathematical modelling of diatom frustule morphogenesis
Abstract:
Diatoms are phytoplankton, microscopic single-celled organisms with species-specific shapes and intricately micropatterned silica frustules (glass-like shells). I will talk about their geometric beauty, why they are important, the evolution of their shapes, and mostly the morphogenesis of their frustules. It is thought that liquid-liquid phase separation of polyamines and other biomolecules creates a template around which silica precipitates. We have studied the resultant patterning, using nonideal reaction diffusion equations.
Tuesday 11 February 2025
NO SEMINAR
Tuesday 18 February 2025
NO SEMINAR - READING WEEK
Tuesday 25 February 2025 in Room G06, 21 Gordon Square
Speaker: Tobias Grafke (University of Warwick)
Title: extreme events in infinite dimensional systems via sharp large deviation estimates
Abstract:
Rare and extreme events are notoriously hard to handle in any complex stochastic system: They are simultaneously too rare to be reliably observable in experiments or numerics, but at the same time often too impactful to be ignored. Large deviation theory provides a classical way of dealing with events of extremely small probability, but generally only yields the exponential tail scaling of rare event probabilities. In this talk, I will discuss theory, and algorithms based upon it, that improve on this limitation, yielding sharp quantitative estimates of rare event probabilities from a single computation and without fitting parameters. Notably, these estimates require the computation of determinants of differential operators, which in relevant cases are not traceclass and require appropriate treatment. We demonstrate that the Carleman—Fredholm operator determinant is the correct choice. The applicability of this method to high-dimensional real-world systems, for example coming from fluid dynamics or molecular dynamics, are discussed.
Tuesday 4 March 2025 in Room G06, 21 Gordon Square
Speaker: Alex Doak (Bath University)
Title: New computations on rotational free-surface waves
Abstract:
Research of free-surface waves typically assumes irrotational flow. This is a good assumption in many cases, but there are settings where the base flow upon which free-surface waves propagate has shear, such as waves sheared by wind. Some authors have explored the problem of free-surface waves with constant vorticity, which can be treated using similar methodologies as used in potential flow. The problem of waves on an arbitrary vorticity is more challenging. A number of studies utilize the Dubreil-Jacotin transformation. This maps the flow onto a simple domain in which the free-surface is fixed, but the mapping does not allow for either overhanging streamlines or internal stagnation points (and hence critical layers), both known to be interesting features of waves with constant vorticity.
In this talk, we present a numerical method which allows for internal stagnation and overhanging streamlines, based off the formulation used by Wahlén & Weber (2023). Irrotational and constant vorticity waves are used as a test case, and solutions with arbitrary vorticity are presented. The talk finishes with a possible extension to stratified flows with a free-surface.
Tuesday 11 March 2025 in Room G06, 21 Gordon Square
Speaker: Bernhard Scheichl (TU Wien)
Title: On Stewartson’s collision problem on a sphere
Abstract:
This talk is about recent progress made on a long-standing fundamental problem in boundary layer theory and beyond. We consider the flow induced by a rigid sphere that spins around its diameter in an otherwise quiescent Newtonian fluid of uniform properties and filling an unbounded domain. Here we distinguish (roughly) between the unsteady flow due to start-up from rest, where the angular velocity increases to finally assume a constant value, and the, potentially attained, steady one. The associated Reynolds number (Re), as the only parameter at play, shall take on arbitrarily large values. We tackle this classical problem by solving the full Navier-Stokes equations using a finite-volume technique, which allows for reliable numerical predictions for values of Re exceeding 300,000 as well as by asymptotic analysis.
For comparison with previous results, three different starting conditions initiate the numerical computations: impulsively, ramp-type, staggered impulsively. The analytical description of the start-up phase in the first case is revisited and extended to finite-Re effects. One thereby finds that the flow meets both the axial and the equatorial symmetry automatically. An intriguing unsettled question concerns the equatorial collision and the associated ejection of a radial jet. Stewartson (1958) proposed a flow structure under the assumption of stationarity that shed light on the severe challenges arising when it comes to its self-consistent completion. The associated controversy about his and Smith & Duck’s (1977) conflicting structure, mostly regarding the presence and structure of the toroidal eddies, has gained attraction ever since. In contrast to claims made very recently, we demonstrate theoretically why the latter, resorting to free viscous—inviscid interaction, is to be favoured. However, we furthermore demonstrate that perfect stationarity cannot exist, which is also substantiated by the numerical results and the well-known equatorial break-up that terminates the solution of the problem governing the longitudinal boundary layer. First steps concerning its regularisation seem to resolve that discrepancy. In a nutshell, the present findings suggest a jet moving constantly into the fluid at rest while it produces vortices travelling back towards the equator. We believe that they finally provoke laminar-turbulent transition once the symmetries are relaxed. Finally, we give a brief account of how these results are modified if the sphere is axially squeezed or stretched. This is a topic of ongoing activities.
This research is carried out jointly by Bernhard Scheichl (TU Wien) and Christian Klettner and Frank T. Smith (both UCL).
Tuesday 18 March 2025 in room 413, 14-16 Taviton Street at 1pm
Speaker: Tom Montenegro-Johnson (Warwick)
Title: Responsive Hydrogels: Perspectives, Modelling, and Ongoing Efforts
Abstract:
Hydrogels are hydrophilic polymer scaffolds surrounded by adsorbed water. From a dry state, they are capable of swelling in volume by up to two orders of magnitude – becoming up to 99% water - whilst still remaining solid (if a little squishy).
Responsive hydrogels lose this affinity for water – sometimes quite profoundly – when an environmental stimulus, such as temperature or pH, transitions beyond a critical value. Conformational changes in the scaffold squeeze the water out, and the gel shrivels dramatically. This volume change is reversible (albeit non-reciprocal), allowing for cycles of activation and deactivation. As such, responsive hydrogels have important and exciting applications in microscale actuators.
This talk will describe some of the big open areas of hydrogel modelling, before detailing two (very) recent theoretical pieces of work on 1) thermoresponsive displacement pumps for microfluidic devices, and2) coupling pH-responsive gels to oscillating reactions to enable communication and synchronisation.
Please note, there will be no refreshments after the seminar this week.
Tuesday 25 March 2025, room Room G06, 21 Gordon Square
Speaker: Benjamin Walker (UCL)
Title: Multiscale methods and microswimmer models
Abstract:
Swimming on the microscale has long been the subject of intense research efforts, from experimental studies of bacteria, sperm, and algae through to varied theoretical questions of low-Reynolds-number fluid mechanics. The biological and biophysical settings that drive this ongoing research are often confoundingly complex, a fact that has driven the development and use of simple models of microswimmers. In this talk, we will showcase how we can often exploit separated scales present in these problems and models to reveal surprisingly simple emergent dynamics, including predictions of globally attracting, long-term behaviours. In doing so, we’ll also uncover a surprising cautionary tale that calls into question much of the intuition gained from commonplace models of microswimming. In particular, we’ll see that a wave-of-the-hands, which I have been guilty of before, can drastically and qualitatively change the dynamics that simple models predict, and we’ll see how such missteps can be addressed through systematic multiscale methods.