2019 Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA) colloquium

ICMS, The Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT

Friday 20th September

 

Speakers include

  • Professor Beth Wingate (University of Exeter)
  • Professor Adriana Garroni (University of Rome)
  • Professor Johannes Zimmer (University of Bath)

This event is now full. If you wish to join the waiting list, please send an email to robyn.stewart-evans@icms.org.uk

Programme

The timings for the event are shown below.

13:00-14:00

Lunch

14:00-14:50

Garroni, Adriana (University of Rome)

Variational models in Materials Science: the importance of having defects

14:50-15:40

Wingate, Beth (University of Exeter)

On the way to the limit: oscillations in fluids and their role in the creation of low frequency dynamics

15:40-16:10

Coffee/Tea

16:10-17:00

Zimmer, Johannes (University of Bath)

Averaging of fast-slow Hamiltonian systems and a thermodynamic interpretation

17:00

Poster Presentations and Informal Reception

 

Abstracts

Adriana Garroni (University of Rome)
Variational models in Materials Science: the importance of having defects
Many modern problems in Applied Mathematics and the Calculus of Variations are connected to important issues in Materials Science. The study of behaviors of matter beyond elasticity (such as in damage, plasticity or fracture) requires multi-scale analysis which is strongly influenced by the presence of defects and their interaction. These defects may be represented as 0-dimensional, 1-dimensional or 2-dimensional (codimension-1) structures on which energy is concentrated and that interact in a complex, sometimes unexpected, manner. The variational treatment of these defects can be performed using tools of Geometric Measure Theory (such as functions of bounded variations and rectifiable currents), while their interaction (static and dynamic) and the formation of complex structures may be described by means of the theory of Relaxation and Homogenization.

Beth Wingate (University of Exeter)
On the way to the limit: oscillations in fluids and their role in the creation of low frequency dynamics
Working in the framework of fast singular limits (Bogoliubov and Mitropolsky [1961], Klainerman and Majda [1981], Shochet [1994], Embid and Majda [1996] and others) I will discuss the role of dispersive waves on the creation of long-time dynamics for simple geometries in rotating and stratified fluids. In particular, asking the question: what can be learned about finite versus infinite frequencies? I will discuss how we can understand this more generally in the context of wave and mean flow interactions, as well as its potential impact on time stepping methods.

Johannes Zimmer (University of Bath)
Averaging of fast-slow Hamiltonian systems and a thermodynamic interpretation.
Atoms and molecules are on a microscopic scale governed by Hamiltonian dynamics, namely Newton's equations of motion.  Their dynamics is thus invariant under time reversal. Yet, the collective macroscopic evolution has a direction of time, usually interpreted as an entropic effect. How does this transition from reversible Hamiltonian dynamics to irreversible thermodynamic macroscopic evolution happen?  In this talk, we consider a hugely simplified situation, namely a fast-slow Hamiltonian system of two particles. This system does not include the many-particle aspect one usually associated with thermodynamics, but captures the most fundamental aspect of thermodynamic systems, namely a separation of scales. The talk will first revisit work of Bornemann, which derives an effective macroscopic evolution of Hamiltonian type. We will then study a higher order expansion, which can be derived rigorously via two-scale convergence.  Finally, a thermodynamic interpretation of the resulting system is given, where entropic effects appear as higher-order corrections to energetic ones.
This is joint work with Matthias Klar and Karsten Matthies (Bath).