Showing papers by "Stephen Wolfram published in 1986"
TL;DR: In this article, a model of cellular automata is presented, in which particles with discrete velocities populate the links of a fixed array of sites, and equations for microscopic particle distributions are derived.
Abstract: Continuum equations are derived for the large-scale behavior of a class of cellular automaton models for fluids. The cellular automata are discrete analogues of molecular dynamics, in which particles with discrete velocities populate the links of a fixed array of sites. Kinetic equations for microscopic particle distributions are constructed. Hydrodynamic equations are then derived using the Chapman-Enskog expansion. Slightly modified Navier-Stokes equations are obtained in two and three dimensions with certain lattices. Viscosities and other transport coefficients are calculated using the Boltzmann transport equation approximation. Some corrections to the equations of motion for cellular automaton fluids beyond the Navier-Stokes order are given.
621 citations
TL;DR: A 1-dimensional cellular automaton which generates random sequences is discussed, and an efficient random sequence generator based on them is suggested.
472 citations
Book•
01 Jun 1986
67 citations
66 citations