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| Introduction | |
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| Kinetic gas theory for dissipative particles | |
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| Atomic level of material deformation | |
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| Continuum description of particles | |
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| Pairwise collision of particles | |
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| Many-particle systems | |
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| Hydrodynamics description | |
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| Experimental investigation of granular gases | |
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| Some remarks | |
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| Mechanics of Particle Collisions | |
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| Particle collisions | |
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| Collision on a line | |
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| Collision in space | |
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| Does the coefficient of restitution suffice to describe granular gas dynamics? | |
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| Coefficient of restitution | |
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| Forces between colliding spheres | |
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| Derivation of the coefficient of restitution | |
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| Pad� approximation | |
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| Coefficient of tangential restitution | |
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| Application to few-particle systems | |
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| Inelastic collapse | |
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| Collision cannon | |
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| Summary | |
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| Granular Gases - Velocity Distribution | |
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| Cooling granular gas - Haff's law | |
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| Homogeneous cooling state | |
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| Haff's law for the evolution of the granular temperature | |
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| Boltzmann equation | |
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| Velocity distribution function | |
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| Direct and inverse collisions | |
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| Collision integral and Boltzmann-Enskog equation | |
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| An important property of the collision integral | |
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| Sonine polynomials expansion of the velocity distribution function | |
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| Velocity distribution and temperature of a granular gas for the case � =const. | |
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| Decomposition of the Boltzmann equation | |
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| The second Sonine coefficient and the moments of the collision integral | |
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| Linear approximation of the second Sonine coefficient | |
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| Complete solution for the second Sonine coefficient | |
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| Time-dependent scaled velocity distribution function | |
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| Evolution of temperature for � = const. | |
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| Stability analysis of the Boltzmann equation | |
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| High-order coefficients of the Sonine polynomials expansion | |
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| Velocity distribution function and temperature for viscoelastic particles | |
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| Why do we expect qualitatively different distribution functions for the cases � = const. and � = � (g)? | |
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| Collision integral for a gas of viscoelastic particles | |
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| Moments of the collision integral for viscoelastic particles | |
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| Equations for temperature and for the shape of the velocity distribution function | |
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| Velocity distribution and temperature in O (�<sup>0</sup>) | |
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| Velocity distribution and temperature in O (�<sup>1</sup>) | |
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| Beyond the linear theory | |
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| Age of granular gases | |
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| High-energy tail of the velocity distribution function | |
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| Overpopulation of the high-velocity tail | |
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| High-velocity tail for � = const. | |
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| High-velocity tail for viscoelastic particles | |
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| Two-dimensional granular gases | |
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| Summary | |
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| Single-Particle Transport. Self-Diffusion and Brownian Motion | |
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| Diffusion and self-diffusion | |
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| Transport in granular gases | |
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| Diffusion coefficient and mean square displacement | |
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| Diffusion coefficient and velocity-time correlation function | |
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| Pseudo-Liouville and binary collision operators in dissipative gas dynamics | |
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| Liouville operator in classical mechanics | |
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| Derivation of the binary-collision operator | |
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| Application of the pseudo-Liouville operator to standard problems | |
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| Coefficient of self-diffusion | |
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| Velocity correlation time | |
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| Constant coefficient of restitution | |
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| Coefficient of self-diffusion for gases of viscoelastic particles | |
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| Inherent time scales | |
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| Coefficient of self-diffusion beyond the adiabatic approximation | |
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| Brownian motion in granular gases | |
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| Boltzmann equation for the velocity distribution function of Brownian particles | |
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| Fokker-Planck equation for Brownian particles | |
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| Velocity distribution function for Brownian particles | |
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| Diffusion of Brownian particles | |
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| Two-dimensional granular gases | |
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| Summary | |
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| Transport Processes and Kinetic Coefficients | |
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| Granular gas as a continuum: hydrodynamic equations | |
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| Macro- and microscales of inhomogeneous granular gas | |
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| Hydrodynamic fields | |
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| Hydrodynamic equations for granular gases | |
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| Chapman-Enskog approach for non-uniform granular gases | |
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| Basic idea of the Chapman-Enskog scheme | |
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| Equations of zeroth order of the Chapman-Enskog expansion | |
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| First-order equations of the Chapman-Enskog expansion | |
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| Solution of the first-order equation | |
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| Kinetic coefficients expressed by the velocity distribution function | |
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| Kinetic coefficients and velocity distribution for gases of elastic particles | |
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| First-order Chapman-Enskog equations | |
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| Coefficient of viscosity | |
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| Coefficient of thermal conductivity | |
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| Velocity distribution function of an inhomogeneous gas of elastic particles | |
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| Kinetic coefficients for granular gases of simplified particles (� =const) | |
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| Viscosity coefficient | |
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| Thermal conductivity coefficient � and transport coefficient � | |
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| Velocity distribution function | |
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| Kinetic coefficients for granular gases of viscoelastic particles | |
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| Chapman-Enskog approach for gases of viscoelastic particles | |
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| Viscosity coefficient | |
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| Coefficients � and � | |
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| Chapman-Enskog method for the self-diffusion coefficient | |
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| Constant coefficient of restitution | |
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| Viscoelastic particles | |
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| Two-dimensional granular gases | |
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| Constant coefficient of restitution | |
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| Granular gases of viscoelastic particles | |
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| Summary | |
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| Structure Formation | |
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| Instability of the homogeneous cooling state | |
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| Arguments for the instability of the homogeneous cooling state | |
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| Linearized hydrodynamic equations | |
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| Structure formation for � = const. | |
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| Linearized hydrodynamic equations for � = const. | |
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| Hydrodynamic modes | |
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| Vortex formation due to the instability of the transverse modes | |
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| Cluster formation due the instability of the other hydrodynamic modes | |
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| Structure formation in granular gases of viscoelastic particles | |
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| Linearized equations for the hydrodynamic modes | |
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| Stability analysis of the hydrodynamic modes and structure formation | |
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| Structure formation as a transient process | |
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| Nonlinear mechanisms of structure formation | |
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| Two-dimensional granular gases | |
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| Summary | |
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| Appendix | |
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| Functions of the collision integral | |
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| Kinetic integrals and basic integrals | |
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| Evaluation of the basic integral | |
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| Computational formula manipulation of kinetic integrals | |
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| Molecular dynamics of granular gases | |
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| Event-driven molecular dynamics | |
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| A simple event-driven algorithm | |
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| A simple program for event driven simulations | |
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| Efficient algorithms | |
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| Solutions to problems | |
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| References | |
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| Symbol index | |
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| Index | |