Bath Applied and Interdisciplinary Mathematics Seminar
Tuesdays at 13.15 at Wolfson 4W 1.7. All talks will be broadcast on Zoom (link details below).
Everyone is welcome at these talks.
| Date | Speaker | Title |
| 4 Feb 2025 | Matthew Colbrook (Cambridge) |
What can we learn about a dynamical system from data? – Impossibility results and classifications using adversarial dynamical systems.
Machine learning has emerged as a powerful tool for studying complex nonlinear systems using trajectory data, with applications spanning climate science, epidemiology, and beyond. A fundamental question arises: When can we reliably learn system behaviors from data, and when is it fundamentally impossible? In this talk, I will introduce the concept of adversarial dynamical systems-systems specifically designed to prevent learning algorithms from converging. This approach enables the development of a rigorous classification framework that identifies the intrinsic difficulty of problems and establishes what is fundamentally unattainable. These results reveal impossibility theorems for data-driven system learning, showing that such adversarial systems arise with high probability and that reliable learning can remain out of reach regardless of the algorithm, data quality, or quantity. To illustrate, I will focus on Koopman operators, which reformulate nonlinear dynamics as infinite-dimensional spectral problems (search “Koopmania” for more!). By understanding these barriers, we can design methods that provably converge, achieving breakthroughs such as state-of-the-art predictions of Arctic sea ice dynamics. |
| 11 Feb 2025 | Thomasina Ball (Warwick) |
Convergent viscous gravity driven flows as a model for mountain building
Many mountain ranges are formed when tectonic plates collide, resulting in the large-scale deformation of rock that produces topographic variations. Compression creates steep topographic gradients, whereas gravitational forces act to reduce contrasts in elevation, resulting in an evolving system that is governed by the balance of external forcing and gravity. Over sufficiently long timescales and lengthscales, this system can be modelled in a continuum manner, as a convergent viscous gravity current. In this talk I will discuss the progress we’ve made in modelling mountain building, from incorporating flexure of the underthrusting plate, to extending the rheology to yield stress fluids, both theoretically and numerically. |
| 18 Feb 2025 | Emilian Parau (University of East Anglia) |
Evolution of nonlinear waves in the marginal ice zone
Wave and sea ice properties in the Arctic and Southern Oceans are linked by feedback mechanisms, therefore the understanding of wave propagation in these regions is essential to model this key component of the Earth climate system. The most striking effect of sea ice in the marginal ice zone (MIZ) is the attenuation of waves at a rate proportional to their frequency. In this talk we will model their dynamics by the damped nonlinear Schrödinger equation (NLS), its higher order version, Dysthe’s equation, or using the spatial Zakharov equation. The evolution of energetic unidirectional random waves and the modulational instability will be discussed. |
| 25 Feb 2025 | Laura Cope (Exeter) |
The Dynamics of Stochastically-Forced Zonal Jets
Zonal jets are strong and persistent east-west flows that arise spontaneously in planetary atmospheres and oceans. They are ubiquitous, with key examples including mid-latitude jets in the troposphere, multiple jets in the Antarctic Circumpolar Current and flows on gaseous giant planets such as Jupiter and Saturn. Turbulent flows on a beta-plane lead to the spontaneous formation and equilibration of persistent zonal jets. However, the equilibrated jets are not steady and the nature of the time variability in the equilibrated phase is of interest both because of its relevance to the behaviour of naturally occurring jet systems and for the insights it provides into the dynamical mechanisms operating in these systems. I will discuss aspects of zonal jet variability using insights from a framework of idealized, stochastically-forced models in which eddy-eddy interactions are systematically neglected. |
| 4 Mar 2025 | Anand Oza (New Jersey Institute of Technology) |
Coarse-grained models for schooling swimmers in fast flows
The beautiful displays exhibited by fish schools and bird flocks have long fascinated scientists, but the role of their complex behavior remains largely unknown. In particular, the influence of hydrodynamic interactions on schooling and flocking has been the subject of debate in the scientific literature. I will present a model for flapping wings that interact hydrodynamically in an inviscid fluid, wherein each wing is represented as a plate that executes a prescribed time-periodic kinematics. The model generalizes and extends thin-airfoil theory by assuming that the flapping amplitude is small, and permits consideration of multiple wings through the use of conformal maps and multiply-connected function theory. We find that the model predictions agree well with experimental data on freely-translating, flapping wings in a water tank. The results are then used to motivate a reduced-order model for the temporally nonlocal interactions between schooling wings, which consists of a system of nonlinear delay-differential equations. We obtain a PDE as the mean-field limit of these equations, which we find supports traveling wave solutions. Generally, our results indicate how hydrodynamics may mediate schooling and flocking behavior in biological contexts. |
| 11 Mar 2025 | Stephen Wilson (Bath) |
Mathematical Modelling of the Evaporation of Sessile Droplets
The evaporation of a sessile droplet is a multifaceted problem of enduring scientific interest that is key to a wide range of everyday and industrial situations, such as protein crystallography, surface patterning, ink-jet printing, and agrochemical spraying of plants. In this talk I shall review some of the recent developments in the study of evaporating droplets, focusing on situations in which relatively simple mathematical models can give new insights into this fascinating multidisciplinary problem, including the competitive evaporation of multiple droplets, the evaporation of a droplet on a non-planar substrate, the effect of the spatial distribution of the local evaporative flux on the deposit left on the substrate by a particle-laden droplet, and the effect of gravity on the evaporation of a sessile droplet. The results presented in this talk are the outcomes of joint work with a large number of collaborators, including Drs Brian Duffy, David Pritchard and Alexander Wray (University of Strathclyde), Professor Khellil Sefiane (University of Edinburgh) and Professor Colin Bain (University of Durham), and past and present research students Gavin Dunn, Jutta Stauber, Feargus Schofield, Hannah-May D’Ambrosio, Laura Mills, David Craig and Henry Sharp, all of whose invaluable contributions are gratefully acknowledged. |
| 18 Mar 2025 | Andrew Wells (Oxford) |
TBD
TBD |
| 25 Mar 2025 | Duncan Hewitt (Cambridge) |
Swimming in mud: modelling locomotion in cohesive materials
TBD |
| 1 Apr 2025 | Daphné Lemasquerier (St Andrews) |
TBD
TBD |
| 22 Apr 2025 | Jacob Page (Edinburgh) |
Nonlinear travelling waves in viscoelastic shear flows
Viscoelastic fluids are common in industry and nature. They are characterised by a complex microstructure which gives rise to many counter-intuitive effects at the macroscale. This includes the creation of new types of self-sustaining |
| 29 Mar 2025 | Ruth Baker (Oxford) |
TBD
TBD |
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Zoom meeting links
Join Zoom Meeting
https://bath-ac-uk.zoom.us/j/99753762534?pwd=4gMpJvORysHydzEzym33HsBuS0Vg2H.1
Meeting ID: 997 5376 2534
Passcode: 411754
How to get to Bath
See here for instructions how to get to Bath. Please email Phil Trinh (hppt20@bath.ac.uk), Eric Hester (eh2450@bath.ac.uk), and Alex Doak (Alex Doak <add49@bath.ac.uk>) if you intend to come by car and require a parking permit for Bath University Campus for the day.Tips for giving talks
Tips for new students on giving talks
Since the audience of the AIMS seminar contains both PhD students and staff with quite wide interests and backgrounds, the following are some guidelines/hints to make sure people don't give you evil looks at lunch afterwards.
Before too much time passes in your talk, ideally the audience should know the answers to the following 4 questions:
- What is the problem you're considering?
- Why do you find this interesting?
- What has been done before on this problem/what's the background?
- What is your approach/what are you going to talk about?
There are lots of different ways to communicate this information. One way, if you're doing a slide show, could be for the first 4 slides to cover these 4 questions; although in this case you may want to revisit these points later on in the talk (e.g. to give more detail).
Remember:
- "vertebrate style" (structure hidden inside - like the skeleton of a vertebrate) = good for detective stories, bad for maths talks.
- "crustacean style" (structure visible from outside - like the skeleton of a crustacean) = bad for detective stories, good for maths talks.