2003/10/17 by Ricardo Brito, R. Brito, M. H. Ernst +2 · 1 citation
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Earthquake Detection and Analysis #FOS: Physical sciences #Granular flow and fluidized beds #High-pressure geophysics and materials #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0310406
Version 2 (minor corrections) of a review chapter to appear in Advances in Condensed Matter and Statistical Mechanics, ed. by E. Korutcheva and R. Cuerno, Nova Science Publishers, 2003
openalex publication_date 2003/10/17 · arxiv created 2004/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This review is a kinetic theory study investigating the effects of inelasticity on the structure of the non-equilibrium states, in particular on the behavior of the velocity distribution in the high energy tails. Starting point is the nonlinear Boltzmann equation for spatially homogeneous systems, which supposedly describes the behavior of the velocity distribution function in dissipative systems as long as the system remains in the homogeneous cooling state, i.e. on relatively short time scales before the clustering and similar instabilities start to create spatial inhomogeneities. This is done for the two most common models for dissipative systems, i.e. inelastic hard spheres and inelastic Maxwell particles. In systems of Maxwell particles the collision frequency is independent of the relative velocity of the colliding particles, and in hard sphere systems it is linear. We then demonstrate the existence of scaling solutions for the velocity distribution function, F(v,t) ∼ v0(t)-d f((v/v0(t)), where v0 is the r.m.s. velocity. The scaling form f(c) shows overpopulation in the high energy tails. In the case of freely cooling systems the tails are of algebraic form, f(c)∼ c-d-a, where the exponent a may or may not depend on the degree of inelasticity, and in the case of forced systems the tails are of stretched Gaussian type f(v)∼exp[-β(v/v0)b] with b <2.