## Mathematical Models of Granular MatterGianfranco Capriz, Pasquale Giovine, Paolo Maria Mariano Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed. |

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### Contents

Contents | 1 |

Conclusions | 17 |

Models with Multiple Interactions | 30 |

Main Results for Maxwell Models with Multiple Interactions | 45 |

References | 56 |

Hydrodynamic Limit and the Euler Equations | 65 |

Conclusions | 71 |

A Shadow Speck of Matter | 79 |

The Dynamics of a Tracer Particle as a NonEquilibrium | 157 |

An Extended Continuum Theory for Granular Media | 167 |

Balance of Interactions for Material Bodies with Affine Microstructure | 173 |

Observers | 175 |

Dilatant Granular Materials with Rotating Grains | 177 |

Inertia Forces and Balance of Granular Energy | 179 |

Constitutive Restrictions in the Thermoelastic Case | 182 |

Suspension of Rigid Granules in a Fluid Matrix | 185 |

Balance of Kinetic Energy | 86 |

Boltzmann Equation and Moments | 92 |

Maximum Characteristic Velocity in Classical Theory | 98 |

Sound Waves and Light Scattering | 104 |

Influence of Contact Modelling on the Macroscopic Plastic | 108 |

Results | 116 |

Conclusions | 123 |

Total Energy Fluctuations in Vibrated | 131 |

A Large Deviation Theory for the Injected Power Fluctuations | 138 |

Two Examples | 146 |

Kinetic Energy Coefficients | 187 |

References | 190 |

Slow Motion in Granular Matter Paolo Maria Mariano | 193 |

Representation of the Granularity | 194 |

R3 SO3 Invariance | 200 |

Evolution of the Local Numerosity of Granules | 204 |

A Single Granule Coinciding with the Generic Material Element | 207 |

209 | |

211 | |

### Other editions - View all

Mathematical Models of Granular Matter Gianfranco Capriz,Pasquale Giovine,Paolo Maria Mariano Limited preview - 2008 |

Mathematical Models of Granular Matter Gianfranco Capriz,Pasquale Giovine,Paolo Maria Mariano No preview available - 2009 |