Physics Colloquium: Complex self-organization phenomena in physical and chemical systems: From discrete stochastic atomistic models to continuum descriptions

Statistical physics provide a powerful tool to describe cooperative many-particle phenomena both in- and out-of-equilibrium based on a detailed atomistic-level description. Rather than just phenomena conventional physical and chemical systems (thin film growth, self-assembly of nanoclusters, spatial patterns in reaction-diffusion systems,…), this approach can also be applied to diverse biological, sociological, epidemiological, etc. systems (aggregation, flocking, traffic flow, spatial epidemic spread,…). Instead of implementing Newtonian-type dynamics to track particles, we present examples utilizing stochastic models to track just particle locations, which thereby allow access to longer experimentally-relevant time- and length- scales. Specifically, we describe self-assembly and thin film growth during surface deposition, and also concentration patterns in surface and other reaction-diffusion systems.

A related basic question is whether it is possible to systematically transition from an atomistic level description to a coarse-grained continuum description (where one does not track individual particles but just coarse variables like position-dependent film height, species concentrations,…). The answer is often yes but with some difficulty.

Reviews: Evans et al. Surf. Sci. Rep 61 (206) 1; Liu et al. Chem. Rev. 115 (2015) 5979.