Images and animations are available. Arthur C. Smith - Chairman, Department Committee on Graduate Students Abstract Discrete models of physical phenomena are an attractive alternative to continuous models such as partial differential equations. In discrete models, such as cellular automata, space is treated as having finitely many locations per unit volume. Physical processes are modelled by rules that typically depend on a small number of nearby locations. We might well ask, on the grounds of minimalism, whether the global synchronization and crystalline lattice are inherent in any discrete formulation.
All interactions involve only a single pair of sites.
The models have the further advantage that they exactly conserve the analog of quantities such as momentum and energy which are conserved in physics. A framework for simulating the asynchronous, parallel model with irregular geometry on a sequential computer is be presented. Evidence is given that the models agree well qualitatively and quantitatively with continuous differential equations. We will draw parallels between the various kinds of physical models and various computing architectures, and show that the class of models presented corresponds to a new parallel computing architecture known as an amorphous computer. Introduction 1.1 Overview 2.