INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 17 (2005) S2705–S2713 doi:10.1088/0953-8984/17/24/021 Transient clusters in granular gases Thorsten P¨ oschel 1 , Nikolai V Brilliantov 2 and Thomas Schwager 1 1 Humboldt-Universit¨ at zu Berlin–Charit´ e, Institut f¨ ur Biochemie, Monbijoustraße 2, D-10117 Berlin, Germany 2 Institute of Physics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany Received 16 March 2005 Published 3 June 2005 Online at stacks.iop.org/JPhysCM/17/S2705 Abstract The most striking phenomenon in the dynamics of granular gases is the formation of clusters and other structures. We investigate a gas of dissipatively colliding particles with a velocity dependent coefficient of restitution where cluster formation occurs as a transient phenomenon. Although for small impact velocity the particles collide elastically, surprisingly the temperature converges to zero. 1. Introduction Granular gases, i.e. gases of dissipatively colliding particles in the absence of external forces, reveal a variety of interesting phenomena, such as characteristic deviations from the Maxwell distribution [1–3], overpopulation of the high energy tail of the distribution function [4], anomalous diffusion [5, 6], and others (see [7–9] for an overview). However, the most striking phenomenon which distinguishes granular gases from molecular gases is the self-organized formation of spatio-temporal structures such as clusters [10] and vortices [11]. The loss of mechanical energy of dissipatively colliding particles i and j is characterized by the coefficient of restitution, which relates the normal component of the relative velocity before a collision, g, to that after, g ′ : ε ≡ g ′ g =−  v ′ ij · e ij  v ij · e ij ,  e ij ≡  r i − r j    r i − r j   (1) with  v ij ≡ v i − v j and with  v ′ ij being the corresponding post-collision value. Frequently it is assumed that the coefficient of restitution is a material constant; however, this assumption contradicts experiments [12] and disagrees with a dimension analysis [13, 14]. Instead, ε is a function of the impact velocity g. The coefficient of restitution can be obtained by integrating Newton’s equation for the collision. The elastic component of the contact force for spheres of diameter σ is given by Hertz’ law F (el) = B ξ 3/2 , with ξ(t ) ≡ σ −    r i − r j   and B(σ ) being the elastic material parameter [15]. Assuming viscoelastic material properties, the dissipative part of the contact 0953-8984/05/242705+09$30.00 © 2005 IOP Publishing Ltd Printed in the UK S2705