publication . Article . 1993

STATISTICAL HYDRODYNAMICS OF LATTICE-GAS AUTOMATA

P. Grosfils; Jean-Pierre Boon; Ricardo Brito; Matthieu H. Ernst;
Open Access
  • Published: 01 Oct 1993
  • Country: Spain
Abstract
We investigate the space and time behavior of spontaneous thermohydrodynamic fluctuations in a simple fluid modeled by a lattice-gas automaton and develop the statistical-mechanical theory of thermal lattice gases to compute the dynamical structure factor, i.e., the power spectrum of the density correlation function. A comparative analysis of the theoretical predictions with our lattice gas simulations is presented. The main results are (i) the spectral function of the lattice-gas fluctuations is fully compatible with the spectrum obtained from experimental measurements performed in real fluids; (ii) in the long-wavelength limit, the correlations of lattice-gas ...
Persistent Identifiers
Subjects
free text keywords: Termodinámica, Termodinámica, Boltzmann constant, symbols.namesake, symbols, Mathematics, Wavelength, Correlation function, Structure factor, Statistical physics, Lattice (order), Lattice gas automaton, HPP model, Spectral density
17 references, page 1 of 2

[1] J. P. Boan and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980) (Reprinted by Dover, New York, 1991).

[2] Microscopic Simulations of Complex Hydrodynamic Phc nomena, edited by M. Mareschal and B. L. Holian (Plenum, New York, 1992).

[3] Lattice Gas Automata: Theory, Implementation, Simula tion8, edited by J. P. Boon, special issue of J. Stat. Phys. 38 (1992).

[4] M. H. Ernst, in Liquids, Freezing and the Glass Tran 8ition, Les Houches, Session LI, 1989, edited by D. Levesque, J. P. Hansen, and 3. Zinn-Justin (Elsevier Science, Amsterdam, 1991), p. 43.

[5] P. Grosfils, J. P. Boon, and P. Lallemand, Phys. Rev. Lett. 68, 1077 (1992).

[6] See, e.g. , 3. P. Boon and S. Yip, Molecular Hydrodynam i cs (Ref. [1]), Chap. 5.

[7] M. H. Ernst and S. P. Das, 3. Stat. Phys. 66, 465 (1992).

[8] R. Brito, M. H. Ernst, and T. R. Kirkpatrick, 3. Stat Phys. 62, 283 (1991).

[9] P. Resibois and M. de Leener, Classical Kinetic Theory of Fluids (John Wiley, New Yark, 1977).

[10] G. A. van Velzen, R. Brito, and M. H. Ernst, J. Stat. Phys. 70, 811 (1993).

[ll] S. P. Das, H. J. Bussemaker, and M. H. Ernst, Phys. Rev. E 48, 245 (1993).

[12] This is only correct if the imaginary part of the factors in (3.12) is small.

[13] S. H. Luo, H. Chen, S. Chen, G. D. Doolen, and Y. C. Lee, Phys. Rev. A 48, 7097 (1991).

[14] The A: values of the different regimes can vary with the direction of the k vector.

[15] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, MA, 1988).

17 references, page 1 of 2
Abstract
We investigate the space and time behavior of spontaneous thermohydrodynamic fluctuations in a simple fluid modeled by a lattice-gas automaton and develop the statistical-mechanical theory of thermal lattice gases to compute the dynamical structure factor, i.e., the power spectrum of the density correlation function. A comparative analysis of the theoretical predictions with our lattice gas simulations is presented. The main results are (i) the spectral function of the lattice-gas fluctuations is fully compatible with the spectrum obtained from experimental measurements performed in real fluids; (ii) in the long-wavelength limit, the correlations of lattice-gas ...
Persistent Identifiers
Subjects
free text keywords: Termodinámica, Termodinámica, Boltzmann constant, symbols.namesake, symbols, Mathematics, Wavelength, Correlation function, Structure factor, Statistical physics, Lattice (order), Lattice gas automaton, HPP model, Spectral density
17 references, page 1 of 2

[1] J. P. Boan and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980) (Reprinted by Dover, New York, 1991).

[2] Microscopic Simulations of Complex Hydrodynamic Phc nomena, edited by M. Mareschal and B. L. Holian (Plenum, New York, 1992).

[3] Lattice Gas Automata: Theory, Implementation, Simula tion8, edited by J. P. Boon, special issue of J. Stat. Phys. 38 (1992).

[4] M. H. Ernst, in Liquids, Freezing and the Glass Tran 8ition, Les Houches, Session LI, 1989, edited by D. Levesque, J. P. Hansen, and 3. Zinn-Justin (Elsevier Science, Amsterdam, 1991), p. 43.

[5] P. Grosfils, J. P. Boon, and P. Lallemand, Phys. Rev. Lett. 68, 1077 (1992).

[6] See, e.g. , 3. P. Boon and S. Yip, Molecular Hydrodynam i cs (Ref. [1]), Chap. 5.

[7] M. H. Ernst and S. P. Das, 3. Stat. Phys. 66, 465 (1992).

[8] R. Brito, M. H. Ernst, and T. R. Kirkpatrick, 3. Stat Phys. 62, 283 (1991).

[9] P. Resibois and M. de Leener, Classical Kinetic Theory of Fluids (John Wiley, New Yark, 1977).

[10] G. A. van Velzen, R. Brito, and M. H. Ernst, J. Stat. Phys. 70, 811 (1993).

[ll] S. P. Das, H. J. Bussemaker, and M. H. Ernst, Phys. Rev. E 48, 245 (1993).

[12] This is only correct if the imaginary part of the factors in (3.12) is small.

[13] S. H. Luo, H. Chen, S. Chen, G. D. Doolen, and Y. C. Lee, Phys. Rev. A 48, 7097 (1991).

[14] The A: values of the different regimes can vary with the direction of the k vector.

[15] W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, MA, 1988).

17 references, page 1 of 2
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