Stationary states and energy cascades in inelastic gases

Abstract

We find a general class of nontrivial stationary states in inelastic gases where, due to dissipation, energy is transfered from large velocity scales to small velocity scales. These steady-states exist for arbitrary collision rules and arbitrary dimension. Their signature is a stationary velocity distribution f(v) with an algebraic high-energy tail, f(v) ~ v^{-sigma}. The exponent sigma is obtained analytically and it varies continuously with the spatial dimension, the homogeneity index characterizing the collision rate, and the restitution coefficient. We observe these stationary states in numerical simulations in which energy is injected into the system by infrequently boosting particles to high velocities. We propose that these states may be realized experimentally in driven granular systems.

4 pages, 4 figures

Cited by in corpus (16)

• The Boltzmann equation for driven systems of inelastic soft spheres
• The rich behavior of the Boltzmann equation for dissipative gases
• Power-law velocity distributions in granular gases
• Phase Transition with Non-Thermodynamic States in Reversible Polymerization
• Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems
• Anomalous Diffusion in a Bench-Scale Pulsed Fluidized Bed
• The Self-Similarity of Shear-Dominated Viscous Stirring
• Angular velocity distribution of a granular planar rotator in a thermalized bath
• Maxwell and very hard particle models for probabilistic ballistic annihilation: hydrodynamic description
• Granular gases under extreme driving
• Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction
• Application of the Gillespie algorithm to a granular intruder particle
• Aggregation-fragmentation-diffusion model for trail dynamics
• A Collisional-Energy-Cascade Model for Nonthermal Velocity Distributions of Neutral Atoms in Plasmas
• Monotonicity in the averaging process
• 1D inelastic relativistic-collision