Numerical studies of granular gases
In this dissertation, we study velocity distributions in granular gases. For granular systems at low density, kinetic theory reduces to the Boltzmann equation which is based on the assumption of molecular chaos. At large velocity scales, stationary solutions with power-law tails, f( v) ∼ v–σ, have been derived from the Boltzmann equation for spatially homogeneous granular systems . The behavior of power-law tail is complete generic, holding for arbitrary dimension, arbitrary collision rules, and general collision rates.
We find the non-Maxwellian steady states using event-driven molecular dynamics simulations. Firstly, power-law steady states are observed in driven systems where energy is injected rarely at large velocity scale V . The range of power-law tail shrinks when we increase the heating-dissipation ratio [special characters omitted], where NI and NC are number of injections and number of collisions, respectively. Then a crossover from a power-law to a stretched exponential distribution is developed when the heating-dissipation ratio [special characters omitted] is close to 1.
It is the energy cascade from a few energetic particles to the overwhelming majority of slowly moving particles that causes the non-Maxwellian velocity distributions. Steady states with power-law tail are robust as long as the injection velocity scale V is essentially separated from the typical velocity scale v0. These steady states are shown to exist for a wide range of number densities, different combinations of injection velocities and injection rates. The injection velocity scale V, the typical velocity scale v0, and the injection rate per particle are related by energy balance. This energy balance relation is confirmed by data collapse of velocity distributions for various choices of parameters.
0753: Theoretical physics