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.

arXiv comment4 pages, 4 figures

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• Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems
• Particle kinematics in a dilute, 3-dimensional, vibration-fluidized granular medium
• Anomalous Diffusion in a Bench-Scale Pulsed Fluidized Bed
• The Self-Similarity of Shear-Dominated Viscous Stirring
• Maxwell and very hard particle models for probabilistic ballistic annihilation: hydrodynamic description
• Angular velocity distribution of a granular planar rotator in a thermalized bath
• Universality properties of steady driven coagulation with collisional evaporation
• Granular gases under extreme driving
• Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction
• Truncated Levy distributions in an inelastic gas
• Power law in the angular velocity distribution of a granular needle
• Aggregation-fragmentation-diffusion model for trail dynamics
• Application of the Gillespie algorithm to a granular intruder particle
• Nonequilibrium steady solutions of the Boltzmann equation
• Velocity distribution of driven granular gases
• Radiation influence on the temperature-dependent parameters of fluids
• Driven inelastic Maxwell gas in one dimension
• Singular Energy Distributions in Granular Media
• Monotonicity in the averaging process
• A Collisional-Energy-Cascade Model for Nonthermal Velocity Distributions of Neutral Atoms in Plasmas
• 1D inelastic relativistic-collision