Stationary state of thermostated inelastic hard spheres

Biben, Thierry; Martin, Ph. A.; Piasecki, J.

doi:10.1016/s0378-4371(02)00779-3

Cited by 30 publications

(70 citation statements)

References 7 publications

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“…has also been studied where the origin of the dissipation is due to either near-elastic wall collisions [62] or thermostatting [63,64]. By balancing the second and third terms and ignoring inter-particle collisions, one obtains β = 2.…”

Section: A T E X I T S H a 1 _ B A S E 6 4 = " 1 5 E X E L 9 V F F mentioning

confidence: 99%

Velocity distribution of driven granular gases

Prasad¹,

Das²,

Sabhapandit³

et al. 2019

J. Stat. Mech.

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The granular gas is a paradigm for understanding the effects of inelastic interactions in granular materials. Kinetic theory provides a general theoretical framework for describing the granular gas. Its central result is that the tail of the velocity distribution of a driven granular gas is a stretched exponential that, counterintuitively, decays slower than that of the corresponding elastic gas in equilibrium. However, a derivation of this result starting from a microscopic model is lacking. Here, we obtain analytical results for a microscopic model for a granular gas where particles with two-dimensional velocities are driven homogeneously and isotropically by reducing the velocities by a factor and adding a stochastic noise. We find two universal regimes. For generic physically relevant driving, we find that the tail of the velocity distribution is a Gaussian with additional logarithmic corrections. Thus, the velocity distribution decays faster than the corresponding equilibrium gas. The second universal regime is less generic and corresponds to the scenario described by kinetic theory. Here, the velocity distribution is shown to decay as an exponential with additional logarithmic corrections, in contradiction to the predictions of the phenomenological kinetic theory, necessitating a re-examination of its basic assumptions. arXiv:1804.02558v2 [cond-mat.stat-mech]

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Section: A T E X I T S H a 1 _ B A S E 6 4 = " 1 5 E X E L 9 V F F mentioning

confidence: 99%

Velocity distribution of driven granular gases

Prasad¹,

Das²,

Sabhapandit³

et al. 2019

J. Stat. Mech.

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“…In this section, we investigate the properties of vibrated binary mixtures; such systems have recently attracted much attention, both on the experimental [5,12,13] and theoretical side [14,15,16,17,18,19,20,21,22,31,32]. In particular the breakdown of energy equipartition between the two constituents of the mixture has been thoroughly investigated.…”

Section: Molecular Dynamics Simulations For the Binary Mixturementioning

confidence: 99%

Molecular dynamics simulations of vibrated granular gases

2002

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We present molecular dynamics simulations of mono-or bidisperse inelastic granular gases driven by vibrating walls, in two dimensions (without gravity). Because of the energy injection at the boundaries, a situation often met experimentally, density and temperature fields display heterogeneous profiles in the direction perpendicular to the walls. A general equation of state for an arbitrary mixture of fluidized inelastic hard spheres is derived and successfully tested against numerical data. Single-particle velocity distribution functions with non-Gaussian features are also obtained, and the influence of various parameters (inelasticity coefficients, density. . . ) analyzed. The validity of a recently proposed Random Restitution Coefficient model is assessed through the study of projected collisions onto the direction perpendicular to that of energy injection. For the binary mixture, the non-equipartition of translational kinetic energy is studied and compared both to experimental data and to the case of homogeneous energy injection ("stochastic thermostat"). The rescaled velocity distribution functions are found to be very similar for both species.

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“…Although the measured velocity distribution F (v) generically deviates from the Maxwellian, its functional form depends on material property and on the forcing mechanism used to compensate for collisional loss of energy [6,7,8,9]. A similar picture emerges from numerical simulations and analytical studies [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33], where in addition to the more common stretched exponential behavior, power-law distributions have also been reported [13,20,21,22,31].…”

Section: Introductionmentioning

confidence: 93%

Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction

2007

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Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism, namely a deterministic non-linear friction force. We derive analytically the high energy tail of the velocity distribution and compare the theoretical predictions with high precision numerical simulations. Stretched exponential forms are obtained when the non-equilibrium steady state is stable. We derive sub-leading corrections and emphasize their relevance. In marginal stability cases, power-law behaviors arise, with exponents obtained as the roots of transcendental equations. We also consider some simple BGK (Bhatnagar, Gross, Krook) models, driven by similar heating devices, to test the robustness of our predictions.

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Stationary state of thermostated inelastic hard spheres

Cited by 30 publications

References 7 publications

Velocity distribution of driven granular gases

Velocity distribution of driven granular gases

Molecular dynamics simulations of vibrated granular gases

Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction

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