Fri, 10 Mar 2023

14:00 - 15:00
L4

Modelling the impact of rock heterogeneity on geological CO2 storage

Catrin Harris
(Imperial College)
Abstract

Permanent geological carbon storage will reduce greenhouse gas emissions and help mitigate climate change. Storage security is increased by CO2 capillary trapping in cm-to-m scale, layered rock heterogeneities; features that are ubiquitous across storage sites worldwide. This talk will outline the challenges associated with modelling the impact of small-scale heterogeneity on large scale saturation distributions and trapping during geological CO2 storage, including the difficulties in incorporating petrophysical and geological uncertainty into field-scale numerical models. Experimental results demonstrate the impact of cm-scale heterogeneity on pore-scale processes, which in turn influence large scale behaviour. Heterogeneity is shown to have a leading order impact on saturation distribution and storage capacity during geological CO2 storage.

Mon, 23 Jan 2023
16:30
L4

Analysis of multi-phase PDE models: from fluids to crowds

Ewelina Zatorska
(Imperial College)
Abstract

This talk will be devoted to our recent developments in the analysis of emerging models for complex flows. I will start from presenting a general PDE system describing two-fluid flows, for which we prove existence of global in time weak solutions for arbitrary large initial data. I will explain where the famous approach of Lions developed for the compressible Navier-Stokes equations fails and how to use a more direct, weighted Kolmogorov criterion to prove compactness of approximating sequences of solutions. Through a formal limit, I will link the two-fluid model to the constrained two-phase models. Applications of such models include modelling of granular flows, crowd motion, or shallow water flow through a channel. The last part of my talk will focus on the rigorous derivation of these models from the compressible Navier-Stokes equations via the vanishing singular pressure or viscosity limit.

Thu, 02 Feb 2023
12:00
L1

Copolymer templating from a mathematical and physical perspective

Thomas Ouldridge and Benjamin Qureshi
(Imperial College)
Further Information

 

Thomas is a Reader in Biomolecular Systems in the Department of Bioengineering at Imperial College. He leads the "Principles of Biomolecular Systems" group. 'His group probes the fundamental principles underlying complex biochemical systems through theoretical modelling, simulation and experiment.' (Taken from his website: https://www.imperial.ac.uk/principles-of-biomolecular-systems/)

You can also learn more about their work via their blog here

Abstract

Biological systems achieve their complexity by processing and exploiting information stored in molecular copolymers such as DNA, RNA and proteins. Despite the ubiquity and power of this approach in natural systems, our ability to implement similar functionality in synthetic systems is very limited. In this talk, we will first outline a new mathematical framework for analysing general models of colymerisation for infinitely long polymers. For a given model of copolymerisation, this approach allows for the extraction of key quantities such as the sequence distribution, speed of polymerisation and the rate of molecular fuel consumption without resorting to simulation. Subsequently, we will explore mechanisms that allow for reliable copying of the information stored in finite-length template copolymers, before touching on recent experimental work in which these ideas are put into practice.  

Thu, 15 Sep 2022

17:00 - 18:00
Lecture Theatre 1, Mathematical Institute, Radcliffe Observatory Quarter, Woodstock Road, OX2 6GG

A mathematical journey through scales - Martin Hairer

Martin Hairer
(Imperial College)
Further Information

Oxford Mathematics Public Lecture

A mathematical journey through scales - Martin Hairer

The tiny world of particles and atoms and the gigantic world of the entire universe are separated by about forty orders of magnitude. As we move from one to the other, the laws of nature can behave in drastically different ways, sometimes obeying quantum physics, general relativity, or Newton’s classical mechanics, not to mention other intermediate theories.

Understanding the transformations that take place from one scale to another is one of the great classical questions in mathematics and theoretical physics, one that still hasn't been fully resolved. In this lecture, we will explore how these questions still inform and motivate interesting problems in probability theory and why so-called toy models, despite their superficially playful character, can sometimes lead to certain quantitative predictions.

Professor Martin Hairer is Professor of Pure Mathematics at Imperial College London. He was awarded the Fields Medal in 2014.

Please email @email to register.

The lecture will be available on our Oxford Mathematics YouTube Channel on 22 September at 5 pm.

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

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Tue, 08 Feb 2022
12:00
L5

A Mathematical Study of Hawking Radiation for Reissner Nordstrom black holes

Fred Alford
(Imperial College)
Abstract

In the first part of this talk, we will (briefly) derive the original calculation by Hawking in 1974 to determine the radiation given off by a black hole, giving the result in the form of an integral of a classical solution to the linear wave equation.
In the second part of the talk, we will take this integral as a starting point, and rigorously calculate the radiation given off by a forming spherically symmetric, charged black hole. We will then show that for late times in its formation, the radiation given off approaches the limit predicted by Hawking, including the extremal case. We will also calculate a bound on the rate at which this limit is approached.

Mon, 18 Oct 2021

16:00 - 17:00
L3

On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions

GREG PAVLIOTIS
(Imperial College)
Abstract

I will present recent results on the statistical behaviour of a large number of weakly interacting diffusion processes evolving under the influence of a periodic interaction potential. We study the combined mean field and diffusive (homogenisation) limits. In particular, we show that these two limits do not commute if the mean field system constrained on the torus undergoes a phase transition, i.e., if it admits more than one steady state. A typical example of such a system on the torus is given by mean field plane rotator (XY, Heisenberg, O(2)) model. As a by-product of our main results, we also analyse the energetic consequences of the central limit theorem for fluctuations around the mean field limit and derive optimal rates of convergence in relative entropy of the Gibbs measure to the (unique) limit of the mean field energy below the critical temperature. This is joint work with Matias Delgadino (U Texas Austin) and Rishabh Gvalani (MPI Leipzig).

 

 

Mon, 18 Oct 2021
14:15
L4

Higher rank DT theory from curve counting

Richard Thomas
(Imperial College)
Abstract

Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X.
Along the way we also show they are determined by rank 0 invariants counting sheaves supported on surfaces in X. These invariants are predicted by S-duality to be governed by (vector-valued, mock) modular forms.

Tue, 01 Jun 2021
12:00
Virtual

The nonlinear stability of the Schwarzschild family of black holes

Martin Taylor
(Imperial College)
Abstract

I will present a theorem on the full finite codimension nonlinear asymptotic stability of the Schwarzschild family of black holes.  The proof employs a double null gauge, is expressed entirely in physical space, and utilises the analysis of Dafermos--Holzegel--Rodnianski on the linear stability of the Schwarzschild family.  This is joint work with M. Dafermos, G. Holzegel and I. Rodnianski.

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