Discussion of “What can we hope for from cellular automata”

Abstract

Brian CantweIl: I was curious to know how energy dissipation is actually accomplished. Is the method exactly energy conserving? It s got an isothermal equation of state. How is energy dissipated and where does it go? Uriei Frisch: Energy is conserved but in a trivial way. In the simplest lattice gas schemes, energy is conserved because all the particles have the same speed, say unity. Kinetic energy per particle is the same as its mass; therefore mass conservation and energy conservation are not independent. The kinetic energy is just a very tiny perturbation on top of the microscopic world, and the kinetic energy just randomizes into equilibrium motion. You have the same apparent paradox in the real world. If you look at kinetic energy, in the incompressible limit you have to go to very low Mach number. Therefore the kinetic energy is a negligible part of the total energy. Brian Cantwen: But that is my question. What is a measure of the temperature? Uriel Friseh: It is more interesting to point out that when one does combustion or compressible flow-there are lots of models which were not presented here which have several speeds and which have a genuine energy equation which is not identical with the mass equation-one can have burned and unburned gases and have expansion just the same as in the real world-with the mass and energy and momentum relations being 426