Wolfram, Stephen, "Cellular automaton fluids 1: Basic theory," J. Stat. Phys. 45 (1986), 471--526.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... full isotropy of wavelike phenomena it turns out that one needs nondiffusive transport of horizontal momentum in the vertical direction and viceversa which is hard to achieve with 90 ffi invariance and is much easier to achieve with six particle directions and 60 ffi invariance (cf. e.g. [88]) This is why the fluid modeled by the HPP gas significantly departs from the Navier Stokes equation (cf. x5.6) and why a model such as FHP manages to achieve the goal. As for point (e ) by considerations similar to the above one can show that almost any coupling between the x and y directions ....

.... they lend themselves to very efficient computer simulations, ica are an ideal medium for the qualitative study of the connections between microscopic mechanics and statistical mechanics on one hand (cf. 43,77,85,13] and between statistical mechanics and macroscopic mechanics on the other (cf. [88]) They are also suitable for the the modeling of an increasingly important type of generalized mechanical activity, namely computation[43] In physics, additive invariants, whether represented by mechanical quantities such as energy or statistical quantities such as entropy, bear a major ....

Wolfram, Stephen, "Cellular automaton fluids 1: Basic theory," J. Stat. Phys. 45 (1986), 471--526.

.... states at the next time t 1, considering the states of the neighbored cells (f(z p 0 ; t) f(z p n Gamma1 ; t) where n = jPj) T = fT (z) S n Sjz 2 Zg (3) Particular classes of CAM are Lattice Gas (LGA) Frisch et al. 1986) and Lattice Boltzmann Automata (LBA) Succi et al. 1991; Wolfram 1986). A LGA simulates movements of an integer number of particles whereas a LBA uses the probability density of particles. Both methods fulfill conservation laws and symmetries and it can be shown that the incompressible Navier Stokes equation is fulfilled in these automata (Frisch et al. 1987) ....

Wolfram, S. (1986). Cellular Automaton Fluids 1: Basic theory. Journal of Statistical Physics 45 (3/4), 471--526.

....had already been studied in an abstract mathematical context by Hedlund and associates as early as 1963[30, 31] both Richardson s results on invertibility (x4.3) and Patt s search for ica (x5.3) had been anticipated by Hedlund s school. Wolfram s 1983 86 sortie into the cellular automata arena[85, 86, 87, 88, 89], stimulated by that workshop, was in turn a determining factor in introducing a generation of mathematical physicists to the cellular automaton paradigm. Inspired by Fredkin s billiard ball model of computation[19] Margolus arrived in 1983 at a very simple computation universal ica[41] that is ....

.... full isotropy of wavelike phenomena it turns out that one needs nondiffusive transport of horizontal momentum in the vertical direction and viceversa which is hard to achieve with 90 ffi invariance and is much easier to achieve with six particle directions and 60 ffi invariance (cf. e.g. [88]) This is why the fluid modeled by the HPP gas significantly departs from the Navier Stokes equation (cf. x5.6) and why a model such as FHP manages to achieve the goal. As for point (e ) by considerations similar to the above one can show that almost any coupling between the x and y directions ....

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Wolfram, Stephen, "Cellular automaton fluids 1: Basic theory," J. Stat. Phys. 45 (1986), 471--526.

.... full isotropy of wavelike phenomena it turns out that one needs nondiffusive transport of horizontal momentum in the vertical direction and viceversa which is hard to achieve with 90 ffi invariance and is much easier to achieve with six particle directions and 60 ffi invariance (cf. e.g. [27]) This is why the fluid modeled by the hpp gas significantly departs from the Navier Stokes equation, and why a more refined model such as fhp manages to achieve the goal. As for point (e ) by considerations similar to the above one can show that almost any coupling between the x and y ....

Wolfram, Stephen, "Cellular automaton fluids 1: Basic theory," J. Stat. Phys. 45 (1986), 471--526.

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