Abstract
The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a similarity form in the simple cases of uniform or steady-state flows. This determines the region of validity of hydrodynamic description. The latter is used to construct the phase diagram of granular systems and discriminate between clustering instability and inelastic collapse. The molecular dynamics results support analytical results, but also exhibit a novel fluctuational breakdown of mean-field descriptions.
Article PDF
Avoid common mistakes on your manuscript.
References
R. P. Behringer,Nonlinear Sci. Today 3:2 (1993); H. Jaeger, S. Nagel, and R. P. Behringer, to be published.
H. A. Weaver and L. Danly, eds.,The Formation and Evolution of Planetary Systems (Cambridge University Press, Cambridge, 1989).
J. K. Knight, C. G. Fandrich, C. N. Liu, H. M. Jaeger, and S. R. Nagel,Phys. Rev. E 51:3957 (1995).
C. K. K. Lun and S. B. Savage,J. Appl. Math. 54:47 (1987).
P. K. Haff,J. Fluid Mech. 134:401 (1983);J. Rheol. 30:931 (1986).
I. Goldhirsch and G. Zanetti,Phys. Rev. Ltt. 70:1619 (1993).
S. McNamara and W. R. Young,Phys. Rev. E 50:R28 (1994).
S. E. Esipov and T. Pöschel, Unpublished.
E. M. Lifshitz and L. P. Pitaevskii,Physical kinetics (Pergamon Press, New York, 1981).
Y. Du, H. Li, and L. P. Kadanoff,Phys. Rev. Lett. 74:1268 (1995).
L. Boltzmann,Vorlesungen über Gastheorie, ed. J. A. Barth (Leipzig, 1923).
Y. Pomeau and P. Résibois,Phys. Rep. 19:63 (1975).
V. L. Gurevich,Kinetika Fononnyh Sistem (Nauka, Moscow, 1982);Transport in Phonon Systems (North-Holland, Amsterdam, 1986).
A. Isihara,Statistical Physics (Academic Press, New York, 1971).
S. McNamara, Ph.D. Thesis Scripps Institute of Oceanology, San Diego, California (1995).
C.-H. Wang, R. Jackson, and S. Sundaresan,J. Fluid Mech. (1996), in press, and references therein.
S. R. de Groot and P. Mazur,Non-equilibrium Thermodynamics (Dover, New York, 1981), pp. 304–311.
Y. B. Levinson,Zh. Eksp. Teor. Fiz. 79:1394 (1980);Sov. Phys. JETP 52:704 (1980); S. E. Esipov and Y. B. Levinson,Pis'ma Zh. Eksp. Teor. Fiz 34:218 (1981);JETP Lett. 34:210 (1981).
Author information
Authors and Affiliations
Additional information
Communicated by D. Stanffer
Rights and permissions
About this article
Cite this article
Esipov, S.E., Pöschel, T. The granular phase diagram. J Stat Phys 86, 1385–1395 (1997). https://doi.org/10.1007/BF02183630
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02183630