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A Langevin Description for Driven GranularGases

Published online by Cambridge University Press:  18 July 2011

P. Maynar  and
M. I. García de Soria
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Abstract

The study of the fluctuations in the steady state of a heated granular system isreviewed. A Boltzmann-Langevin description can be built requiring consistency with theequations for the one- and two-particle correlation functions. From the Boltzmann-Langevinequation, Langevin equations for the total energy and the transverse velocity field arederived. The existence of a fluctuation-dissipation relation for the transverse velocityfield is also studied.

Keywords

kinetic theoryBoltzmann equationgranular gaseshydrodynamics
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 4: Granular hydrodynamics , 2011 , pp. 87 - 117
Copyright
© EDP Sciences, 2011

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References

Baskaran, A., Dufty, J. W., Brey, J. J.. Transport coefficients for the hard-sphere granular fluid. Phys. Rev. E, 77 (2008), No. 3, 031311. CrossRefGoogle ScholarPubMed
Bixon, M., Zwanzig, R.. Boltzmann-Langevin Equation and Hydrodynamic Fluctuations. Phys. Rev., 187 (1969), No. 1, 267–272. CrossRefGoogle Scholar
J. J. Brey, J. W. Dufty, M. J. Ruiz-Montero, in Granular Gas Dynamics, edited by T. Pöschel and N. Brilliantov. Springer, Berlin, 2003.
Brey, J. J., García de Soria, M. I., Maynar, P.. Breakdown of hydrodynamics in the inelastic Maxwell model of granular gases. Phys. Rev. E, 82 (2010), No. 2, 021303. CrossRefGoogle Scholar
Brey, J. J., García de Soria, M. I., Maynar, P.. Breakdown of the fluctuation-dissipation relations in granular gases. EPL, 84 (2008), No. 2, 24002. CrossRefGoogle Scholar
Brey, J. J., Maynar, P., García de Soria, M. I.. Fluctuating hydrodynamics for dilute granular gases. Phys. Rev. E, 79 (2009), No. 5, 051305. CrossRefGoogle ScholarPubMed
Brey, J. J., García de Soria, M. I., Maynar, P., Ruiz-Montero, M. J.. Energy fluctuations in the homogeneous cooling state of granular gases. Phys. Rev. E, 70 (2004), No. 1, 011302. CrossRefGoogle Scholar
Brey, J. J., Ruiz-Montero, M. J., Moreno, F.. Boundary conditions and normal state for a vibrated granular fluid. Phys. Rev. E, 62 (2000), No. 4, 5339–5346. CrossRefGoogle ScholarPubMed
Cafiero, R., Luding, S., Herrmann, H. J.. Two-Dimensional Granular Gas of Inelastic Spheres with Multiplicative Driving. Phys. Rev. Lett., 84 (2000), No. 26, 6014–6017. CrossRefGoogle ScholarPubMed
Ernst, M. H., Trizac, E., Barrat, A.. The Boltzmann Equation for Driven Systems of Inelastic Soft Spheres. J. Stat. Phys., 124 (2006), No. 2–4, 549–586. CrossRefGoogle Scholar
Ernst, M. H., Trizac, E., Barrat, A.. The rich behavior of the Boltzmann equation for dissipative gases. Europhys. Lett., 76 (2006), No. 1, 56–62. CrossRefGoogle Scholar
Fiege, A., Aspelmeier, T., Zippelius, A.. Long-Time Tails and Cage Effect in Driven Granular Fluids. Phys. Rev. Lett., 102 (2009), No. 9, 098001. CrossRefGoogle ScholarPubMed
García de Soria, M. I., Maynar, P., Schehr, G., Barrat, A., Trizac, E.. Dynamics of annihilation. II. Fluctuations of global quantities. Phys. Rev. E, 77 (2008), No. 5, 051128. Google Scholar
García de Soria, M. I., Maynar, P., Trizac, E.. Energy fluctuations in a randomly driven granular fluid. Mol. Phys., 107 (2009), No. 4–6, 383–392. CrossRefGoogle Scholar
Garzó, V., Montanero, J. M.. Transport coefficients of a heated granular gas. Physica A, 313 (2002), No. 3–4, 336–356. CrossRefGoogle Scholar
Goldhirsch, I., Zanetti, G.. Clustering instability in dissipative gases. Phys. Rev. Lett., 70 (1993), No. 11, 1619–1622. CrossRefGoogle ScholarPubMed
Goldshtein, A., Shapiro, M.. Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid. Mech., 282 (1995), 75–114. CrossRefGoogle Scholar
Haff, P. K.. Grain flow as a fluid-mechanical phenomenon. J. Fluid. Mech., 134 (1983), 401–430. CrossRefGoogle Scholar
Maaß, C. C., Isert, N., Maret, G., Aegerter, C. M.. Experimental Investigation of the Freely Cooling Granular Gas. Phys. Rev. Lett., 100 (2008), No. 24, 248001. CrossRefGoogle ScholarPubMed
Maynar, P., García de Soria, M. I., Trizac, E.. Fluctuating hydrodynamics for driven granular gases. EPJ ST, 179 (2009), 123–139. Google Scholar
McNamara, S., Young, W. R.. Dynamics of a freely evolving, two-dimensional granular medium. Phys. Rev. E, 53 (1996), No. 5, 5089–5100. CrossRefGoogle Scholar
Montanero, J. M., Santos, A.. Computer simulation of uniformly heated granular fluids. Granular Matter, 2 (2000), No. 2, 53–64. CrossRefGoogle Scholar
Moon, S. J., Shattuck, M. D., Swift, J. B.. Velocity distributions and correlations in homogeneously heated granular media. Phys. Rev E, 64 (2001), No. 3, 031303. CrossRefGoogle ScholarPubMed
Pagonabarraga, I., Trizac, E., van Noije, T. P. C., Ernst, M. H.. Randomly driven granular fluids: Collisional statistics and short scale structure. Phys. Rev. E, 65 (2001), No. 1, 011303. CrossRefGoogle ScholarPubMed
Painter, B., Dutt, M., Behringer, R.. Energy dissipation and clustering for a cooling granular material on a substrate. Physica D, 175 (2003), No. 1–2, 43–68. CrossRefGoogle Scholar
Prevost, A., Egolf, D. A., Urbach, J. S.. Forcing and Velocity Correlations in a Vibrated Granular Monolayer. Phys. Rev. Lett., 89 (2002), No. 8, 084301. CrossRefGoogle Scholar
Puglisi, A., Loreto, V., Marconi, U. M. B., Vulpiani, A.. Kinetic approach to granular gases. Phys. Rev E, 59 (1999), No. 5, 5582–5595. CrossRefGoogle ScholarPubMed
P. Résibois, M. de Leener. Classical Kinetic Theory of Fluids. Wiley, New York, 1977.
N. G. van Kampen. Stochastic Proccesses in Physics and Chemistry. North-Holland, Amsterdam, 1992.
van Noije, T. P. C., Ernst, M. H.. Velocity distributions in homogeneous granular fluids: the free and the heated case. Granular Matter, 1 (1998), No. 2, 57–64. CrossRefGoogle Scholar
van Noije, T. P. C., Ernst, M. H., Trizac, E., Pagonabarraga, I.. Randomly driven granular fluids: Large-scale structure. Phys. Rev. E, 59 (1999), No. 4, 4326–4341. CrossRefGoogle Scholar
Visco, P., Puglisi, A., Barrat, A., van Wijland, F., Trizac, E.. Energy fluctuations in vibrated and driven granular gases. Eur. Phys. J. B, 51 (2006), No. 3, 377–387. CrossRefGoogle Scholar
Williams, D. R. M., MacKintosh, F. C.. Driven granular media in one dimension: Correlations and equation of state. Phys. Rev. E, 54 (1996), No. 1, R9–R12. CrossRefGoogle ScholarPubMed