From molecular dynamics to coarse self-similar solutions: A simple example using equation-free computation

Abstract

In the context of the recently developed "equation-free" approach to the computer-assisted analysis of complex systems, we illustrate the computation of coarsely self-similar solutions. Dynamic renormalization and fixed point algorithms for the macroscopic density dynamics are applied to the results of short bursts of appropriately initialized molecular dynamics in a simple diffusion simulation. The approach holds promise for locating coarse self-similar solutions and the corresponding exponents in a variety of multiscale computational contexts.