Publication: Statistical hydrodynamics of lattice-gas automata
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1993-10
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American Physical Society
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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 fluctuations are well described by the Landau-Placzek theory; (iii) at short wavelengths and/or at low densities, good agreement is obtained between the lattice-gas simulation results and the Boltzmann theory. These results provide solid support to the validity of the thermal-lattice-gas automaton as a consistent model system for real fluids.
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©1993 The American Physical Society. P.G. and J.P.B. acknowledge Pierre Lallemand for valuable discussions. R.B. wants to thank G. Szamel for his patient help and explanations. The authors acknowledge support from the Institute for Scientific Interchange, Torino (Italy) where this research was started. P.G. has benefited from support by "Direction des Recherches Etudes et Techniques" (DRET, France). J.P.B acknowledges support from the "Fond National de la Recherche Scientifique" (FNRS, Belgium). R.B. thanks the Institute for Theoretical Physics of Utrecht (where part of this research was carried out) for its hospitality. He further acknowledges support by DGICYT (Spain) under
Contract No. PB91-0378 and a grant of the Ministerio de Educacion (Spain). Part of this work was supported by the EC under Contract No. SC1-0212.
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[1] J. P. Boon and S. Yip, Molecular Hydrodynamics (McGraw-Hill, New York, 1980) (Reprinted by Dover, New York, 1991).
[2] Microscopic Simulations of Complex Hydrodynamic Phenomena, edited by M. Mareschal and B. L. Holian (Plenum, New York, 1992).
[3] Lattice Gas Automata: Theory, Implementation, Simulations, edited by J. P. Boon, special issue of J. Stat. Phys. 38 (1992).
[4] M. H. Ernst, in Liquids, Freezing and the Glass Transition, Les Houches, Session LI, 1989, edited by D. Levesque, J. P. Hansen, and J. 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., J. P. Boon and S. Yip, Molecular Hydrodynamics (Ref. [1]), Chap. 5.
[7] M. H. Ernst and S. P. Das, J. Stat. Phys. 66, 465 (1992).
[8] R. Brito, M. H. Ernst, and T. R. Kirkpatrick, J. 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).
[11] 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 k 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).
[16] In this k-value range, the simulated spectra are quite noisy and the comparative analysis requires smoothing of the data; while eliminating the high frequency noise, this procedure leaves the spectrum with spurious lower frequency oscillations [see Fig. 2(b)] to be discarded in the analysis.
[17] R. Brito and M. H. Ernst, J. Phys. A 24, 3331 (1991).