Phase transitions in models of Vlasov-McKean type

June 1, 2012
3:00PM - 4:00PM
Seminar

PDE/Applied Math/Complex Science Seminar

DAY : Friday, June 1

ROOM : SH 4607

Vladislav Panferov
Department of Mathematics
California State University, Northridge

Title: Phase transitions in models of Vlasov-McKean type

Abstract: I will discuss the problem of non-uniqueness and stability
of steady states for equations of Vlasov-McKean type.
These equations provide a mean-field description of a system of
interacting diffusions; particularly we consider the problem with
the spatial variable in a periodic box of size L and particles
interacting through a pairwise potential V. If the Fourier transform
of V has a negative minimum, the system has a critical threshold
for the diffusion constant beyond which the trivial uniform steady
state becomes unstable and the system experiences a phase transition.
We show that for a large class of interactions, when the size of the
domain is sufficiently large, the transition is always discontinuous
and is characterized by coexistence of several stable states in a
certain interval of parameter space.The transition is also shown to
occur at a value of the diffusion constant strictly greater than the
critical threshold.