Boltzmann equation for dissipative gases in homogeneous states with nonlinear friction.

Combining analytical and numerical methods, we study within the framework of the homogeneous nonlinear Boltzmann equation a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the method presented in a previous paper [J. Stat.

Generalized Green-Kubo formulas for fluids with impulsive, dissipative, stochastic, and conservative interactions.

We present a generalization of the Green-Kubo expressions for thermal transport coefficients mu in complex fluids of the generic form [equation see text], i.e., a sum of an instantaneous transport coefficient muinfinity, and a time integral over a time correlation function in a state of thermal equilibrium between a current J and its conjugate current Jepsilon.

Power law tails of time correlations in a mesoscopic fluid model.

In a quenched mesoscopic fluid, modeling transport processes at high densities, we perform computer simulations of the single particle energy autocorrelation function C(e) (t) , which is essentially a return probability. This is done to test the predictions for power law tails, obtained from mode coupling theory. We study both off and on-lattice systems in one- and two-dimensions.

Model system for classical fluids out of equilibrium.

A model system for classical fluids out of equilibrium, referred to as a dissipative particles dynamics (DPD) solid, is studied by analytical and simulation methods. The time evolution of a DPD particle is described by a fluctuating heat equation. This DPD solid with transport based on collisional transfer (high-density mechanism) is complementary to the Lorentz gas with only kinetic transport (low-density mechanism).

Universal power law tails of time correlation functions.

The universal power law tails of single particle and multiparticle time correlation functions are derived from a unifying point of view, solely using the hydrodynamic modes of the system. The theory applies to general correlation functions and to systems more general than classical fluids. Moreover, it is argued that the collisional transfer part of the stress-stress correlation function in dense classical fluids has the same long-time tail approximately t(-1-d/2) as the velocity autocorrelation function in Lorentz gases.

Exact steady-state solution of the Boltzmann equation: a driven one-dimensional inelastic Maxwell gas.

The exact nonequilibrium steady-state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier transform of distribution function f(c).

Driven inelastic Maxwell models with high energy tails.

The solutions of the homogeneous nonlinear Boltzmann equation for inelastic Maxwell models, when driven by different types of thermostats, show, in general, overpopulated high energy tails of the form approximately exp(-ac), with power law tails and Gaussian tails as border line cases. The results are compared with those for inelastic hard spheres, and a comprehensive picture of the long time behavior in freely cooling and driven inelastic systems is presented.

Randomly driven granular fluids: collisional statistics and short scale structure.

We present a molecular-dynamics and kinetic theory study of granular material, modeled by inelastic hard disks, fluidized by a random driving force. The focus is on collisional averages and short-distance correlations in the nonequilibrium steady state, in order to analyze in a quantitative manner the breakdown of molecular chaos, i.e.

Cahn-hilliard theory for unstable granular fluids.

A Cahn-Hilliard-type theory for hydrodynamic fluctuations is proposed that gives a quantitative description of the slowly evolving spatial correlations and structures in density and flow fields in the early stages of evolution of freely cooling granular fluids. Two mechanisms for pattern selection and structure formation are identified: unstable modes leading to density clustering (mechanismlike spinodal decomposition, or "uplifting" in structural geology), and selective noise reduction (mechanismlike peneplanation in structural geology) leading to vortex patterns. As time increases, the structure factor for the density field develops a maximum, which shifts to smaller wave numbers.