## Granular Gases" Granular Gases" are diluted many-particle systems in which the mean free path of the particles is much larger than the typical particle size, and where particle collisions occur dissipatively. The dissipation of kinetic energy can lead to effects such as the formation of clusters, anomalous diffusion and characteristic shock waves to name but a few. The book is organized as follows: Part I comprises the rigorous theoretical results for the dilute limit. The detailed properties of binary collisions are described in Part II. Part III contains experimental investigations of granular gases. Large-scale behaviour as found in astrophysical systems is discussed in Part IV. Part V, finally, deals with possible generalizations for dense granular systems. |

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### Contents

3 | |

Free Cooling of Particles with Rotational Degrees of Freedom | 31 |

Hydrodynamic Transport Coefficients of Granular Gases | 59 |

Probing the Boundaries of Hydrodynamics | 79 |

Granular Gases with ImpactVelocityDependent Restitution Coefficient | 100 |

Boundary Conditions for Collisional Grain Flows at Bumpy Frictional Walls | 125 |

Diffusion Process in TwoDimensional Granular Gases | 140 |

Energy Loss and Aggregation Processes in Low Speed Collisions of Ice Particles Coated with Frosts or MethanolWater Mixtures | 150 |

Experimental Study of a Granular Gas Fluidized by Vibrations | 244 |

Computer Simulation of Vertically Vibrated Granular Layers in a Box with SawtoothShaped Base | 254 |

Resonance Oscillations in Granular Gases | 266 |

Dynamical Evolution of Viscous Discs Astrophysical Applications to the Formation of Planetary Systems and to the Confinement of Planetary Rings ... | 281 |

Numerical Simulations of the Collisional Dynamics of Planetary Rings | 330 |

Formation of Narrow Ringlets in Saturns Rings | 350 |

Granular Viscosity Planetary Rings and Inelastic Particle Collisions | 363 |

The Equation of State for Almost Elastic Smooth Polydisperse Granular Gases for Arbitrary Density | 386 |

Contact Mechanics and Coefficients of Restitution | 184 |

Kinetic Theory for 1D Granular Gases | 195 |

Chains of Viscoelastic Spheres | 203 |

Experimental Studies of Vibrofluidised Granular Beds | 213 |

Pattern Formation in a Vibrated Granular Layer | 233 |

Experimental Observations of Nonequilibrium Distributions and Transitions in a 2D Granular Gas | 410 |

Fermi Statistics and Condensation | 429 |

How Much Can We Simplify a Systemof Grains? | 445 |

457 | |

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### Common terms and phrases

amplitude angular momentum Boltzmann equation boundary conditions Brahic calculated clustering coefficient of restitution collisional collisions constant correlation function corresponding dense dependence diffusion disc dissipation distribution function DSMC dynamics elastic Enskog equilibrium evolution experimental Fermi fluctuations Fluid Mech frequency Gaussian Goldhirsch Goldreich grains granular gases granular materials granular systems granular temperature gravitational homogeneous cooling hydrodynamic Icarus impact velocity inelastic collisions interactions kinetic energy kinetic theory Lett linear Luding macroscopic mass mean free path mean squared displacement measurements mechanism molecular molecular dynamics motion normal number of particles numerical simulations observed obtained orbital parameters perturbations Phys planetary rings planetesimals planets Pöschel regime relative velocity resonance restitution coefficient ringlet rotational satellite Saturn’s rings scale shear solar solution speed sticking force surface theoretical tion torque Tremaine values velocity distribution vertical vibration viscoelastic viscosity volume fraction