We study the action minimization problem which is formally associated to phase transformation in the stochastically perturbed Allen-Cahn equation. The sharp-interface limit is related to (but… (More)

There has been a recent burst of activity in the atmosphere-ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degrees of freedom in stochastic climate… (More)

The problem of turbulent transport of a scalar field by a random velocity field is considered. The scalar field amplitude exhibits rare but very large fluctuations whose typical signature is fatter… (More)

A statistical theory is developed for the stochastic Burgers equation in the inviscid limit. Master equations for the probability density functions of velocity, velocity difference, and velocity… (More)

A systematic analysis is carried out for the randomly forced Burgers equation in the infinite Reynold number (inviscid) limit. No closure approximations are made. Instead the probability density… (More)

A modification of Kraichnan’s direct interaction approximation ~DIA ! @R. H. Kraichnan, J. Math. Phys. 2, 124 ~1961!# for random linear partial differential equations is proposed. The approximation… (More)

ABSTRACT The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows which are families of probability distributions on the space of… (More)

The study of passive scalar transport in a turbulent velocity field leads naturally to the notion of generalized flows, which are families of probability distributions on the space of solutions to… (More)

A periodic Kolmogorov type ̄ow is implemented in a lattice gas automaton. For given aspect ratios of the automaton universe and within a range of Reynolds number values, the averaged ̄ow evolves… (More)