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A fluctuation formula for the non-galilean factor in lattice gas automata

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Brito, Ricardo and Bussemaker, H. J. and Ernst, M. H. (1992) A fluctuation formula for the non-galilean factor in lattice gas automata. Journal of physics A: Mathematical and general, 25 (15). L949-L954. ISSN 0305-4470

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Official URL: http://dx.doi.org/10.1088/0305-4470/25/15/009


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Abstract

A lattice gas automaton lacks Galilei invariance, and equilibria of systems moving with a finite speed \u -->\ are not simply related by a Galilei transformation to the equilibrium distribution in the rest frame. In the hydrodynamic description of low speed equilibria in lattice gas automata a factor G(rho) appears in the nonlinear convective term, del --> . G(rho)rho-u --> u -->, of the Navier-Stokes equation, that differs from unity due to lack of Galilei invariance. For this non-Galilean factor an expression in terms of fluctuating quantities is derived, in a grand ensemble where the total momentum is fluctuating around a zero average. The formula is valid as long as there exists a unique equilibrium state. Consequently, the results can also be used for a direct simulation of G(rho) in lattice gas models where the explicit form of the equilibrium distribution is not known, such as in models that violated semi-detailed balance.


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© 1992 IOP Publishing Lld. One of us (MHE) would like to thank J W Dufty, U Frisch, M Henon, A Noullez and J P Rivet for stimulating discussions, and I'Observatoire de Nice, where this research was initiated, for its hospitality in the spring of 1991. HJB is financially supported by the Stichting voor Fundamenteel Onderzoek der Materie (FOM), which is sponsored by de Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). RB is sponsored by the DGICYT (Spain) grant PB88-0140, FOM and Universidad Complutense through the program 'Bolsas 92'.

Subjects:Sciences > Physics > Thermodynamics
ID Code:22130
Deposited On:07 Jul 2013 16:59
Last Modified:24 Jul 2018 10:50

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