PMID: 15244815Jul 13, 2004Paper

Gaussian kinetic model for granular gases

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
James W DuftyLorena Zogaib

Abstract

A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal "homogeneous cooling solution" after a few collisions. The homogeneous cooling solution (HCS) is studied in some detail and the exact solution is compared with known results for the hard sphere Boltzmann equation. It is shown that all qualitative features of the HCS, including the nature of overpopulation at large velocities, are reproduced by the kinetic model. It is also shown that all the transport coefficients are in excellent agreement with those from the Boltzmann equation. Also, the model is specialized to one having a velocity independent collision frequency and the resulting HCS and transport coefficients are compared to known results for the Maxwell model. The potential of the model for the study of more complex spatially inhomogeneous states is discussed.

References

Jul 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·J J BreyJ W Dufty
Oct 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·J J BreyD Cubero
Aug 12, 1996·Physical Review Letters·J W DuftyJ J Brey
Oct 25, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·E Ben-Naim, P L Krapivsky
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·J J BreyF Moreno
Jun 21, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J J BreyF Moreno
Aug 22, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Javier BreyR García-Rojo
Mar 15, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Javier Brey, M J Ruiz-Montero
Oct 4, 2003·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·James W Dufty, J Javier Brey

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Citations

Mar 26, 2011·The European Physical Journal. E, Soft Matter·R Yano, K Suzuki
Oct 4, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·François CoppexEmmanuel Trizac
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Andrés Santos, Antonio Astillero
Mar 17, 2015·The European Physical Journal. E, Soft Matter·Vicente GarzóEmmanuel Trizac
Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Vicente Garzó, Emmanuel Trizac
Aug 11, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Javier Brey, James W Dufty
Aug 25, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·J Javier BreyM J Ruiz-Montero
Oct 4, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Vicente Garzó
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P M ReisM D Shattuck
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Francisco Vega ReyesAndrés Santos

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