Applied Mathematics Seminars Autumn 2025
See below for information regarding the Applied Seminars in Autumn 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 ), Prof Ted Johnson (e-mail: e.johnson AT ucl.ac.uk) or Edwina Yeo (edwina.yeo.14 AT ucl.ac.uk).
Please consider suggesting possible speakers.
Applied Seminar Suggestion Form
Tuesday 14 October 2025 in Maths Room 706
Speaker: Cecilie Andersen (Smith Institute, mathematical consultant)
Title: Exponential asymptotics for the Saffman-Taylor problem in a wedge
Abstract:
Saffman Taylor viscous fingering is a classic problem in potential flow theory and exponential asymptotics. In this problem an inviscid fluid is injected into a Hele Shaw channel displacing a viscous fluid and in the steady state a single finger occupies some proportion of the width of the channel. As surface tension approaches zero a countably infinite set of permissible fingers will select a unique zero surface tension solution. Exponential asymptotics have proved essential in deriving this selection mechanism. In this talk I discuss a generalisation of the Saffman Taylor problem to a wedge geometry. This is motivated by desires to understand the more physically relevant Saffman Taylor instability in a circular geometry with injection of the inviscid fluid outwards from a central source. The wedge geometry already shows much greater complexity than the classic problem in a channel. In particular, the bifurcation diagram changes qualitatively and now the countably infinite set of permissible fingers all disappear in pairs before the zero surface tension limit can be reached. Notably, we are still able to capture this behaviour with exponential asymptotics techniques and I will present the key ideas from this analysis.
Tuesday 21 October 2025 in Maths Room 706
Speaker: Timo Betcke (UCL)
Title: Rust – A new paradigm for Scientific Computing
Abstract:
Rust is a modern low-level programming language in direct competition to C++. Although its first stable version was only released in 2015 it has already found widespread adoption in industry, with core components of both Android and the Windows Operating System being transitioned to Rust. Key benefits for Rust include a modern memory safety model that finds most memory bugs already at compile time and a traits-based type system which allows a high degree of flexibility in designing complex data structures. But is Rust ready for Scientific Computing applications? Over the last two years my group has developed a number of Rust libraries for HPC. In this talk we focus on RLST, the Rust Linear Solver Toolbox, a comprehensive dense and sparse linear algebra library developed by our group in Rust. We discuss how the Rust type system can be used to reimagine the capabilities and flexibility of a modern linear algebra library and we present a number of implementational details from n-dimensional dense arrays to working with operators over abstract function spaces in RLST.
Tuesday 28 October 2025 in Maths Room 706
Speaker: Robert B. Scott, Departement de physiques UFRS (France)
Title: Higher order viscosity in otherwise Newtonian fluids
Abstract:
We reconsider the rigorous development of the mathematical form of the viscous terms in the fluid momentum equations. In the Navier-Stokes equations, traditionally this involves expressing the stress tensor as a Taylor series of the local fluid velocity and keeping only the terms with first-order derivatives. By extending the development to consider the contributions from derivatives up to third order, we find additional viscous terms. Symmetry considerations reduce the additional viscous terms to three terms (characterized by two independent real-valued coefficients) that enter the deviatoric stress tensor, and reduce to two term terms in the momentum equations. Of the latter, one is a shear-like bi-Laplacian viscosity identical to the so-called hyperviscosity, traditionally considered artifical and introduced for convenience in mathematical analysis or used for numerical stability in geophysical fluid dynamics. Our work provides a rigorous justification for hyperviscosity, potentially for all otherwise Newtonian fluids. Furthermore, there is an independent, bulk-like viscosity that vanishes for solenoidal flow. We propose a modified boundary condition to accommodate the higher order differential equation. Finally, we sketch a plan to estimate the numerical value of the hyperviscosity coefficient for a given fluid using molecular dynamics simulations.
Tuesday 4 November 2025
NO SEMINAR - READING WEEK
Tuesday 11 November 2025 in Maths Room 706
Speaker: Kang Ren, University of Southampton
Title: Mathematical modelling of hydroelastic interactions in confined fluid domains
Abstract:
This talk presents my recent work on the mathematical modelling and analysis of fluid-structure interactions in confined fluid domains such as channels and tanks. Motivated by problems in cold-region rivers and channels, liquid sloshing in partially filled tanks, and renewable energy device development, the study employs linear potential flow theory coupled with thin elastic plate and membrane models. Semi-analytical and numerical approaches are developed to characterise the resulting dynamics.
References:
[1]. Ren, K., Wu, G.X. and Li, Z.F., 2020. Hydroelastic waves propagating in an ice-covered channel. Journal of Fluid Mechanics, 886 (A18).
[2]. Ren, K., Wu, G.X. and Li, Z.F., 2021. Natural modes of liquid sloshing in a cylindrical container with an elastic cover. Journal of Sound and Vibration, 512, 116390
[3]. Ren, K., Wu, G.X. and Yang, Y.F., 2022. Coupled free vibration of liquid in a three-dimensional rectangular container with an elastic cover. Physics of Fluids, 34, 067109.
[4]. Ren, K., Wu, G.X. and Yang, Y.F., 2024. Surface wave interaction with floating elastic plates in channels. Physics of Fluids, 36(1).
[5]. Ren, K. and Wu, G.X., 2025. Liquid motion in cylindrical containers with elastic covers under external excitation. Journal of Sound and Vibration, 119156.
Tuesday 18 November 2025 in Maths Room 706
Speaker: Kirill Cherednichenko, University of Bath
Title: Norm-resolvent convergence for Neumann Laplacians on manifolds thinning to graphs and its applications
Abstract:
I will start with a brief introduction to the subject of approximating ‘thin’ (elastic, electromagnetic) structures by ‘singular’ ones. I will then present some recent results on norm-resolvent convergence with an order-sharp error estimate for Neumann Laplacians on thin domains converging to metric graphs — these include the case of a ‘resonant’ scaling between vertex sizes and edge cross-sections, which leads to a time/frequency dispersive limit formulation. The talk will conclude with an outline of possible applications of the mathematical insights in wave propagation. This is joint work with Yulia Ershova and Alexander V. Kiselev.
Tuesday 25 November 2025 in Maths Room 706
Speaker: Helen Wilson, UCL
Title: Plate-like elastic particles in suspension
Abstract:
Viscoelastic fluids are liquids - often polymeric solutions or melts - that have some microstructure that can become stretched and aligned by flow. This gives them the ability to store energy in the microstructure, that can be released at a later time. This gives the material a mixture of liquid-like (viscous) and solid-like (elastic) properties.
The mathematical modelling of these fluids usually involves conformation tensors, and it has long been understood that only two forms of derivative are appropriate for these tensors: the convected derivatives introduced by Oldroyd in 1950.
There are two such derivatives, and coupling each to the simplest possible elastic relaxation term generates a constitutive model: Oldroyd A or Oldroyd B. Oldroyd B has been widely used ever since its introduction as it is the simplest constitutive model to capture much of the phenomenology of polymeric liquids; in particular it is an excellent model for Boger fluids, which are dilute solutions of linear polymers in a very viscous solvent, invented by David Boger in 1977. Oldroyd A, on the other hand, has been broadly neglected until recently.
In 2023 Eggers and coworkers proposed a semi-physical model based on beads and springs that was designed to conform to the Oldroyd-A constitutive model. We implemented this model in simulations and ran into difficulties, which we eventually identified as unbounded runaway of the size of the triangles.
After introducing this background, I will present the simulation results, followed by a theoretical analysis explaining how the underlying energy potential actually encourages degenerate triangle configurations. Finally we introduce a new model that also reproduces the Oldroyd-A dynamics but without the degeneracy issues of the original Eggers work.
This is joint work with Luke Debono.
Tuesday 2 December 2025 in Maths Room 706
Speaker: Ian Eames, Professor of Fluid Mechanics, Department of Mechanical Engineering, UCL
Title: The effect of turbulence on vortices
Abstract: External turbulence has a profound effect on how flow signatures (wakes, jets, vortices) spread in time. We will discuss the main conceptual building blocks (impulse, integral invariants) to understand the gross changes in the vortex and the changes to the external turbulence. A theoretical and experimental campaign to analyse these complex interactions is described. This work is collaborative with Prof Flor at LEGI.
Tuesday 9 December 2025 in Maths Room 706
Speaker: Yasemin Sengul Tezel, Cardiff University
Title: Nonlinear viscoelasticity: Modelling, analysis and applications
Abstract: In this talk I will present two approaches to nonlinear viscoelasticity, namely, the classical approach and the strain-limiting approach. I will, first, give an overview for the classical approach by considering nonlinear viscoelasticity of strain-rate type modelling solids undergoing phase transformations. For the strain-limiting approach, I will start with the elastic case and the question of modelling in the context of implicit constitutive theory. I will mention the advantages this approach brings over Cauchy elasticity. I will then move on to viscoelasticity and talk about different types of models that have been mathematically investigated. I will finish with some current open problems.