14:00 – 15:00 Nadia Sidorova (University College London)
Localisation and ageing in the parabolic Anderson model
The parabolic Anderson problem is the Cauchy problem for the heat equation on the d-dimensional integer lattice with random potential. It describes the behaviour of branching random walks in a random environment (represented by the potential) and is being actively studied by mathematical physicists. One of the most important situations is when the potential is time-independent and is a collection of independent identically distributed random variables. We discuss the intermittency effect occurring for such potentials and consisting in increasing localisation and randomisation of the solution. We also discuss the ageing behaviour of the model showing that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly over time.
15:00 – 16:00 Mike Field (Rice University)
Asynchronous networks and event driven dynamics
The talk is intended to be a general (and gentle) introduction to models of network dynamics that are applicable to contemporary problems in biology, engineering and technology. In particular, we will discuss the limitations of classical models and how to deal with networks where, for example, connection structure may vary in time and nodes may stop and later restart.
Further info on the Dynamical Systems webpage.