Applied Mathematics Seminar
University of Leeds
Welcome to the Leeds Applied Mathematics Seminar
Spring 2017
Monday 30 January 2017
Peter Hydon (University of Kent)
Variations on a theme of Noether
Famously, Noether's (First) Theorem uses symmetries of a variational problem to generate conservation laws of the corresponding Euler-Lagrange equations. Her less well-known Second Theorem links symmetries to differential relations between the Euler-Lagrange equations.
In this talk, I describe a simple approach to Noether’s theorems that has unexpected rewards. A new result bridges the gap between Noether’s First and Second Theorems. It transfers immediately to difference equations, leading to finite difference approximations that preserve particular conservation laws and generalized Bianchi identities. If time allows, I will add a third variation.
This talk is intended for a general mathematical audience; it covers the theory and some nice applications. No prior knowledge of Noether’s theorems is needed.
Monday 24 April 2017
Xiaoyu Luo (University of Glasgow)
Soft tissue mechanics applie to myocardial infaction
This talk will start with an overview of the invariant-based continuum mechanics approach for anisotropic soft tissues that undergo nonlinear large deformation. I will then report how we model the cardiac system using the invariant-based constitutive laws and a fluid-structure interaction solver, and how we model the myocardial infarction with different levels of sophistication. The models will be patient-specific derived from in vivo clinical magnetic resonance images (MRI), with material parameters determined using inverse and statistical approaches so that the model results agree with in vivo observations. We model the cardiac function both in diastole and in systole and consider agent-based modelling for myocardial infarction, soft tissue changes informed by MRI perfusion measurements. Finally, I will briefly introduce the EPSRC funded SofTMech Centre and the ongoing research themes in the Centre.