Equationfree Modeling For Complex Systems

Abstract

A persistent feature of many complex systems is the emergence of macroscopic, coherent behavior from the interactions of microscopic ``agents'' --- molecules, cells, individuals in a population --- among themselves and with their environment. The implication is that macroscopic rules (a description of the system at a coarse-grained, high-level) can somehow be deduced from microscopic ones (a description at a much finer level). For laminar Newtonian fluid mechanics, a successful coarse-grained description (the Navier-Stokes equations) was known on a phenomenological basis long before its approximate derivation from kinetic theory [1]. Today we must frequently study systems for which the physics can be modeled at a microscopic, fine scale; yet it is practically impossible to explicitly derive a good macroscopic description from the microscopic rules. Hence, we look to the computer to explore the macroscopic behavior based on the microscopic description.