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 |
| 8 Oct 2024 | Nabil Fadai (Nottingham) |
Stochastic agent-based models in mathematical biology
In the last decade, there has been a movement to describe biological and social systems via agent-based models, which track individual agents (organisms, cells, people) and their environment through a set of deterministic and probabilistic rules. In this talk, we examine how local individual-based mechanisms translate into global population dynamics. In particular, we will consider the Allee effect in population models, which were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. Using stochastic individual-based models, we can obtain a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. This modelling framework is then extended to applications in the social sciences, including the modelling of sports riots and panic-buying. |
| 15 Oct 2024 | Jeremy Budd (Birmingham) |
Graph-based learning and learned adversarial regularisation
This talk is really two talks glued together under the (very!) vague theme of “learning”. In the first half, I will give an overview of the field of graph-based learning, a field that has matured over the last 15 years and is rich in both practical applications and theoretical underpinnings. The key idea of graph-based learning is to understand interrelated data as a graph, to solve variational problems and PDEs on that graph to analyse that data, and to study the limits of such models as the number of nodes goes to infinity. In the second half, I will talk about some of my recent work in learning a regulariser for inverse problems. In an inverse problem, one seeks to recover some unknown input given knowledge of some output measurement. This problem is ill-posed, as the measurement process invariably loses information. To counteract this, one must impose some prior for what the input “should” have looked like. Learned regularisation seeks to learn this prior from data. |
| 22 Oct 2024 | Geoff Vasil (Edinburgh) |
Polynomials for Fun and Profit
This talk will outline a wide range of amazing properties of a few meek little polynomials. I will briefly discuss how I came to this line of inquiry honestly via the mathematics underlying the Dedalus computational framework for solving general classes of PDEs. But after that, I’m taking the gloves off for a wild trip through the land of geometry, probability and combinatorics. |
| 29 Oct 2024 | Kasia Warburton (Cambridge) |
Water pressure evolution beneath glaciers
In Antarctica and Greenland, most ice makes its way from the interior of the ice sheet, where it falls as snow, to the margins, where it ablates, via fast flowing glaciers. These glaciers flow fast due to sliding between the ice and bed, the rate of which sensitively depends on the water pressure there. In this talk I will present models for the subglacial hydrology of ice sheets which capture tidal and seasonal water pressure fluctuations, a range of timescales for which the overlying ice goes from behaving primarily elastically to viscously. |
| 5 Nov 2024 | Keaton Burns (MIT) |
Solving PDEs exactly over polynomials
Numerical simulations of partial differential equations (PDEs) are indispensable across science and engineering. For simple geometries, spectral methods are a powerful class of techniques that produce exceptionally accurate solutions for wide ranges of equations. But many variations of these methods exist, each with distinct properties and performance, and developing the best method for a complex nonlinear problem is often quite challenging. In this context, we present a framework that unifies all polynomial and trigonometric spectral methods, from classical “collocation” to the more recent “ultraspherical” schemes. In particular, we examine the exact discrete equations solved by each method and characterize their deviation from the original PDE in terms of perturbations called “tau corrections”. By analyzing these corrections, we can precisely categorize existing methods and design new solvers that robustly accommodate new boundary conditions, eliminate spurious numerical modes, and satisfy exact conservation laws. This approach conceptually separates what discrete model a spectral scheme solves from how it solves it. This separation provides much more freedom when building and optimizing new numerical models. We will illustrate these advantages with various examples from fluid dynamics using Dedalus, an open-source package for solving PDEs with modern spectral methods. |
| 12 Nov 2024 | Lois Baker (Edinburgh) |
Lagrangian filtering for wave-mean flow decomposition
In geophysical and astrophysical flows, we are often interested in understanding the impact of internal waves on the non-wavelike flow. For example, oceanic internal waves generated at the surface and the seafloor transfer energy from the large scale flow to dissipative scales, thereby influencing the global ocean state. A primary challenge in the study of wave-flow interactions is how to separate these processes – since waves and non-wavelike flows can vary on similar spatial and temporal scales in the Eulerian frame. However, in a Lagrangian flow-following frame, temporal filtering offers a convenient way to isolate waves. In this talk I’ll present and discuss some recently developed methods for evolving Lagrangian mean fields alongside the governing equations in a numerical simulation, allowing effective filtering of waves from non-wavelike processes. |
| 13 Nov 2024 | Peter Constantin (Princeton) |
Global regularity for critical SQG in bounded domains
The critical SQG (surface quasi-geostrophic) equation is widely studied in relation to rapid formation of small scales in fluids. In the whole space or on the torus, this dissipative equation has been shown to have global smooth solutions some fifteen years ago by Caffarelli–Vasseur and, independently, by Kiselev–Nazarov–Volberg. The problem of existence and uniqueness of global smooth solution in bounded domains remained open until now. I will present a proof of global regularity obtained recently with Ignatova and Q-H. Nguyen. We introduce a new methodology of transforming the single nonlocal nonlinear evolution equation in a bounded domain into an interacting system of extended nonlocal nonlinear evolution equations in the whole space. The proof uses the method of the nonlinear maximum principle for nonlocal operators in the extended system. |
| 19 Nov 2024 | Alexander Mietke (Oxford) |
Spontaneous shape transformations of active surfaces
Biological matter has the fascinating ability to autonomously generate material deformations via intrinsic active forces, where the latter are often present within effectively two-dimensional structures. The dynamics of such “active surfaces” inevitably entails a complex, self-organized interplay between geometry of a surface and its mechanical interactions with the surrounding. The impact of these factors on the self-organization capacity of surfaces made of an active material, and how related effects are exploited in biological systems, is largely unknown. In this talk, we will focus on active surfaces with broken up-down symmetry, of which the eukaryotic cell cortex and epithelial tissues are highly abundant biological examples. In such surfaces, a natural interplay arises between active stresses and surface curvature. We demonstrate that this interplay leads to a comprehensive library of spontaneous shape transformations that resemble stereotypical morphogenetic processes. These include cell-division-like invaginations and the autonomous formation of tubular surfaces of arbitrary length, both of which robustly overcome well-known shape instabilities that would arise in analogue passive systems. |
| 26 Nov 2024 | Angela Busse (Glasgow) |
The imprint of roughness topography on near wall-turbulence
When we consider wall-bounded flows, rough-wall conditions can be considered the norm rather than the exception – surfaces are rarely perfectly smooth, and they tend to acquire blemishes over time. One of the key challenges in investigating rough-wall turbulence is that roughness can occur in many different forms. In recent years, the influence of roughness topography has received increased attention and parameters such as the skewness of the roughness height distribution and the effective slope have been identified as having a strong influence on the fluid dynamic roughness effect. In this talk, I will discuss different roughness topographical parameters and their effect on the near wall flow as well as the challenges in finding a comprehensive set of topographical parameters for the empirical prediction of roughness effects on wall-bounded turbulence. |
| 10 Dec 2024 | Carlos Jerez-Hanckes (Universidad Adolfo Ibáñez) |
Cell Electro-permeabilization Modeling Via Multiple Traces Formulation and Time Semi-Implicit Multistep Coupling
I will present new results concerning the simulation of the electrical response of multiple disjoint biological 3D cells undergoing an electro-permeabilization (enhancing ion transfer across cellular membrane) process. Instead of solving the boundary value problem in the unbounded volume, we reduce it to a system of boundary integrals equations–the local Multiple Traces Formulation–coupled with nonlinear dynamics on the cell membranes. Though in time the model is highly non-linear and poorly regular, the smooth geometry allows for boundary unknowns to be spatially approximated by spherical harmonics. This leads to spectral convergence rates in space. In time, we use a multistep semi-implicit scheme. Numerical results are provided to validate our claims and future enhancements are pointed out. |
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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 Josh Shelton (js2317@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.