Mathematical Models of Granular Matter

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Gianfranco Capriz, Pasquale Giovine, Paolo Maria Mariano
Springer, Apr 20, 2008 - Technology & Engineering - 216 pages

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
References
209
Index
211
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