Discrete, Amorphous Physical Models

Erik Rauch

How minimal can a discrete model be?

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 and time is discrete, whereas continuous models (e.g. Schroedinger's equation, and most field theories) specify detail down to infinitesimal spatial and time scales. But all existing discrete models depend critically on a regular (crystalline) lattice, as well as the global synchronization of all sites. We should ask, on the grounds of minimalism, whether the global synchronization and regular lattice are inherent in any discrete formulation. Is it possible to do without these conditions and still have a useful physical model? Or are they somehow fundamental?

Transcript (with slides) of invited talk given at the NSF Digital Perspectives on Physics workshop, July 25, 2001

Discrete, Amorphous Physical Models - paper to appear in International Journal of Theoretical Physics (also in pdf format)

Animations of amorphous models