Calculus of Variations and Geometric Measure Theory

PhD posts in Bath/Eindhoven

created by stefanell on 09 Oct 2011

Deadline: 7 apr 2010

We have a PhD position open in the area of variational evolution.

Could you please make this known to possible candidates? I send some more details below to give an idea of what the project is about.

Yours sincerely,

Johannes Zimmer

-- Project description

In 1940, H. A. Kramers, introduced a macroscopic equation to describe Brownian motion in the presence of a force field; what is now knows as Kramers' equation is a fundamental model of diffusion in chemical reactions. It describes in phase space the evolution of the probability density for a stochastic process associated with the Langevin equation.

A fundamental insight by Jordan, Kinderlehrer and Otto in the late 1990s was that the standard diffusion equation can be formulated as a gradient flow of an entropy functional. A similar gradient flow formulation can be given for Kramers' equation.

Kramers' equation is what is in statistical physics often called the Master Equation for the associated microscopic model of Brownian motion. The aim of this project is to derive the gradient flow formulation in a rigorous manner from the microscopic model, and thus to establish a micro-macro passage for chemical reactions.

The details are as follows. This project is funded by the EU project FIRST, see www.mat.ucm.es FIRST . It will be jointly supervised by Mark Peletier (Eindhoven) and Johannes Zimmer (Bath). The first two years are to be spent in Bath, where in 201011 both supervisors will be present. The third year will be spent at the Technical University Eindhoven. The project is open to applicant who have not lived in the UK or the Netherlands for more than 12 months out of the last five years.

Start: October 2010 deadline for applications: 15 June 2010

-- Johannes Zimmer
zimmer@maths.bath.ac.uk Reader in Applied Mathematics
phone ++44 1225 386-097, fax -492 University of Bath, Bath BA2 7AY, UK
http:/www.maths.bath.ac.uk zimmer