Effect of Excluded Volume and Anisotropy on Granular Statistics: 'Fermi Statistics' and Condensation

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dc.creatorHong, Daniel C.
dc.date1999-09-16
dc.date.accessioned2026-07-07T03:14:35Z
dc.date.available2026-07-07T03:14:35Z
dc.descriptionWe explore the consequences of the excluded volume interaction of hard spheres at high densities and present a theory for excited granular materials. We first demonstrate that, in the presence of gravity, the granular density crosses over from Boltzmann to Fermi statistics, when temperature is decreased in the weak excitation limit. Comparisons of numerical simulations with our predictions concerning the scaling behavior of temperature with agitation frequency, gravity and particle-diameter show satisfying agreement. Next, within the framework of the Enskog theory of hard spheres, we interpret this crossover as a 'condensation' of hard spheres from the dilute gas-state to a high density solid-like state. In the high density, low temperature limit Enskog theory fails because it predicts densities larger than the closed packed density below a certain temperature. We show how to extend the range of applicability of the Enskoq theory to arbitrarily low temperatures by constructing a physical solution: all particles that are situated in regions with densities larger than a certain maximum density are assumed to be 'condensed.'
dc.description17 pages, 4 Figures. Lecture Note delivered at 215 WE-Heraeus Seminar, Bad Honnef(Germany). To be published in 'Granular Gases,' Springer-Verlag, edited by Luding, Poschel, and Herrmann (2,000)
dc.identifierhttps://arxiv.org/abs/cond-mat/9909252
dc.identifierhttp://arxiv.org/abs/cond-mat/9909252
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/29724
dc.subjectMaterials Science
dc.subjectStatistical Mechanics
dc.titleEffect of Excluded Volume and Anisotropy on Granular Statistics: 'Fermi Statistics' and Condensation
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