Models and Asymptotics of Non-equilibrium Steady States in Driven Diffusive Systems

University Of Arizona, Tucson AZ

Investigators

Abstract

This award will support the analysis of non-equilibrium steady states (NESS) in driven diffusive systems. Physical systems of interest in this general class are typically modeled either deterministically by diffusive nonlinear evolution equations or stochastically by certain types of Markov processes. The NESS referred to here differ from the equilibria of linear dynamics or the invariant measures of detailed balance in that the non-equilibrium steady states exhibit phase separation (often driven by boundary dynamics), spontaneous symmetry breaking and/or long range correlations away from critical transitions. Specific contexts to be explored include the strong bending regime of striped pattern formation, spatial random partitions, and random matrix ensembles. Non-equilibrium steady states are typical for a number of physical systems and models, including defect condensation in pattern forming systems driven far from threshold, classical molecule formation, a system of interacting Bose particles, shaken granular gasses, infinite allele models, network formation by preferential attachment or rewiring, stochastic growth models and two-dimensional quantum gravity. The award will support research approaches on the behavior of such systems that uses deterministic (non-random) as well as stochastic (random) techniques.