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Cluster-growth in freely cooling granular media

Chaos 9, 673 (1999); doi:10.1063/1.166441

Issue Date: September 1999

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S. Luding and H. J. Herrmann
Institute for Computer Applications 1, Pfaffenwaldring 27, D-70569 Stuttgart, Germany
When dissipative particles are left alone, their fluctuation energy decays due to collisional interactions, clusters build up and grow with time until the system size is reached. When the effective dissipation is strong enough, this may lead to the "inelastic collapse," i.e., the divergence of the collision frequency of some particles. The cluster growth is an interesting physical phenomenon, whereas the inelastic collapse is an intrinsic effect of the inelastic hard sphere (IHS) model used to study the cluster growth—involving only a negligible number of particles in the system. Here, we extend the IHS model by introducing an elastic contact energy and the related contact duration tc. This avoids the inelastic collapse and allows to examine the long-time behavior of the system. For a quantitative description of the cluster growth, we propose a burning-like algorithm in continuous space, that readily identifies all particles that belong to the same cluster. The criterion for this is here chosen to be only the particle distance. With this method we identify three regimes of behavior. First, for short times a homogeneous cooling state (HCS) exists, where a mean-field theory works nicely, and the clusters are tiny and grow very slowly. Second, at a certain time which depends on the system's properties, cluster growth starts and the clusters increase in size and mass until, in the third regime, the system size is reached and most of the particles are collected in one huge cluster. ©1999 American Institute of Physics.
History: Received 8 January 1999; accepted 18 May 1999
Permalink: http://link.aip.org/link/?CHAOEH/9/673/1
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KEYWORDS and PACS

Keywords
PACS
  • 45.70.-n
    Classical mechanics of discrete systems Granular systems
  • 05.45.-a
    Statistical physics, thermodynamics, and nonlinear dynamical systems Nonlinear dynamics and nonlinear dynamical systems
  • 05.40.-a
    Statistical physics, thermodynamics, and nonlinear dynamical systems Fluctuation phenomena, random processes, noise, and Brownian motion
  • YEAR: 1999

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PUBLICATION DATA

ISSN:
1054-1500 (print)   1089-7682 (online)
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REFERENCES (33)
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