Alexandre Chorin, University of California, Berkeley

Abstract:

I will present a mathematical derivation of equations of motion for the conditional averages of dynamical variables in stochastic multiscale problems. The surprising feature of the resulting formalism is that it yields exact reduction schemes for the dynamics of multiscale problems, and also reduces the problem of evaluating the marginals in large sampling problems to the much easier problem of evaluating conditional expectations. The resulting formulas are of course too complex to be fully evaluated, but having an exact result to start with makes it easier to find good approximations.

I will focus on two applications: the derivation of simplified dynamics for systems with long memory (thus, no separation of scales), with an application to hydrodynamics, and the development of effective chain-free sampling schemes, with an application to glassy systems.