OCCAM

In this talk we will present results concerning the large scale long time behaviour of particles moving in a periodic (random) velocity field subject to molecular diffusion. The particle can be considered massless (passive tracer) or not (inertial particle). Under appropriate assumptions for the velocity field the large scale long time behavior of the particle is described by a Brownian motion with an effective diffusivity matrix K.

We then present some numerical algorithms concerning the calculation of the effective diffusivity in the limit of vanishing molecular diffusion (stochastic geometric integrators). Time permitting we will discuss the case where the driving noise is no longer white but colored and study the effects of this change to the effective diffusivity matrix.

 We examine several aspects of introducing stochasticity into dynamical systems, with specific applications to modelling
populations of neurons. In particular, we use the example of a interacting
populations of excitatory and inhibitory neurons (E-I networks). As each
network consists of a large but finite number of neurons that fire
stochastically, we can study the effect of this intrinsic noise using a master
equation formulation. In the parameter regime where each E-I network acts as a
limit cycle oscillator, we combine phase reduction and averaging to study the
stationary distribution of phase differences in an ensemble of uncoupled E-I
oscillators, and explore how the intrinsic noise disrupts synchronization due
to a common external noise source.

TBA

The paper for this first session is "Every discrete, finite image is uniquely determined by its dipole histogram" by Charles Chubb and John I. Yellott