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Article
The Boltzmann Equation for Driven Systems of Inelastic Soft Spheres
We study a generic class of inelastic soft sphere models with a binary collision rate g^ν that depends on the relative velocity g. This includes previously studied inelastic hard spheres (ν = 1) and inelastic Max...
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Article
Introduction
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Article
Scaling Solutions of Inelastic Boltzmann Equations with Over-Populated High Energy Tails
This paper deals with solutions of the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell models for large times and for large velocities, and the nonuniform convergence to the...
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Article
Towards a Landau–Ginzburg-Type Theory for Granular Fluids
In this paper we show how, under certain restrictions, the hydrodynamic equations for the freely evolving granular fluid fit within the framework of the time dependent Landau–Ginzburg (LG) models for critical ...
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Chapter
Kinetic Theory of Granular Fluids: Hard and Soft Inelastic Spheres
The basic concept that rapid granular flows can be considered as a collection of particles with short range interactions, moving ballistically and suffering instantaneous and inelastic binary collisions, is fo...
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Chapter
Towards a Landau—Ginzburg Theory for Granular Fluids
Granular matter [1] consits of small or large macroscopic particles. When out of equilibrium, its dynamics is controlled by dissipative interactions, and distinguished in quasi-static flows or granular solids on ...
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Article
Diffusion Lattice Boltzmann Scheme on a Orthorhombic Lattice
We present a diffusion lattice Boltzmann (DLB) scheme which is derived from first principles. As opposed to the traditional lattice BGK schemes the DLB is valid for orthorhombic lattices and it has two eigenva...
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Article
Velocity distributions in homogeneous granular fluids: the free and the heated case
Non-Gaussian properties (cumulants, high energy tails) of the single particle velocity distribution for homogeneous granular fluids of inelastic hard spheres or disks are studied, based on the Enskog-Boltzman...
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Article
Thermodynamic formalism and localization in Lorentz gases and hop** models
The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure ψ(β). The inverse-temperature-like variable β allows one to scan the structure of the probability d...
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Article
Dynamical chaos in the Lorentz lattice gas
This paper provides an introduction to the applications of dynamical systems theory to nonequilibrium statistical mechanics, in particular to a study of nonequilibrium phenomena in Lorentz lattice gases with s...
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Article
Algebraic spatial correlations in lattice gas automata violating detailed balance
In this paper we discuss the existence of generic long-range correlations in spatially homogeneous and stable equilibrium states of closed lattice gas automata whose stochastic collision rules violate the symm...
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Article
Generalized Boltzmann equation for lattice gas automata
In this paper a theory is formulated that predicts velocity and spatial correlations between occupation numbers that occur in lattice gas automata violating semi-detailed balance. Starting from a coupled BBGKY...
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Chapter and Conference Paper
Chaos in Lorentz lattice gases
Lorentz lattice gases belong to the category of dynamical systems with positive Lyapunov exponents, and are therefore chaotic. We show using techniques from the kinetic theory of gases that these dynamical qua...
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Article
Relaxation and transport in FCHC lattice gases
FCHC lattice gases are the basic models for studying flow problems in three-dimensional systems. This paper presents a self-contained theoretical analysis and some computer simulations of such lattice gases, e...
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Article
Lattice gases with static disorder: Renormalization of mean field theory
Lattice gas automata are used to model transport phenomena in random media with static disorder. If the interactions are repulsive, there is a large probability of backscattering or retracing collision sequenc...
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Article
Diffusion in Lorentz lattice gas automata with backscattering
The probability of first return to the initial intervalx and the diffusion tensorD xβ are calculated exactly for a ballistic Lorentz gas on a Bethe lattice or Cayley tree. It consists of a moving particle and a f...
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Article
Stress-stress correlation functions in lattice gases beyond Boltzmann's approximation
The complete time dependence of the stress-stress correlation functions in lattice gas cellular automata is calculated from the ring kinetic theory using numerical and analytical methods. This provides correct...
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Article
Biased lattice gases with correlated equilibrium states
The approach to and structure of the equilibrium state is studied for a 7-bit lattice gas with biased forward and backward transition rates by means of mean field theory and computer simulations. If the rate c...
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Chapter and Conference Paper
Green-kubo formulas for staggered transport coefficients in CA-fluids
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Chapter and Conference Paper
Heat conductivity in a thermal LGCA
