Bibliographic record and links to related information available from the Library of Congress catalog
Note: Electronic data is machine generated. May be incomplete or contain other coding.
From Granular Matter to Generalized Continuum J.D. Goddard .................................................... 1 1 Introduction .............................................. 1 1.1 Mathematical Preliminaries ................................ 3 1.2 Balances ................................................. 4 2 Micromechanics ........................................... 5 2.1 Granular Microstructure and Rotation ....................... 5 2.2 Graph Theory for Extrinsic Modes .......................... 7 2.3 Extrinsic Power........................................ ...12 3 Energy-Based Homogenization ................................ 13 3.1 Intrinsic Moments and Continuum Fields. .................... 15 4 Conclusions ...................................... ... 17 Appendix: Simplex and Edge-Complex Gradients .................... 17 References ....................................... 20 Generalized Kinetic Maxwell Type Models of Granular Gases A. V. Bobylev, C. Cercignani, and I.M. Gamba .................... 23 1 Introduction................. ............................ 23 2 Maxwell Models of the Boltzmann Equation ...................... 26 3 Isotropic Maxwell Model in the Fourier Representation. ............ 28 4 Models with Multiple Interactions ............................ 30 4.1 Statement of the General Problem ........................... 31 5 The General Problem in Fourier Representation ................... 33 5.1 Existence and Uniqueness of Solutions ....................... 33 5.2 Large Time Asymptotics ................................ 34 5.3 Existence of Self-Similar Solutions .......................... 41 5.4 Properties of Self-Similar Solutions .......................... 42 6 Main Results for Maxwell Models with Multiple Interactions ........ 45 6.1 Self-Similar Asymptotics ................ ................ 45 6.2 Distribution Functions, Moments and Power-Like Tails......... 47 6.3 Applications to the Conservative or Dissipative Boltzmann Equation ....................................... 51 References ........................................ 56 Hydrodynamics from the Dissipative Boltzmann Equation Giuseppe Toscani ........................................... 59 1 Introduction..................................... 59 2 Modeling Dissipative Boltzmann Equation ....................... 62 3 Hydrodynamic Limit and the Euler Equations .................... 65 4 Hydrodynamics from Homogeneous Cooling States ................ 67 5 Conclusions ...................................... ......... 71 References ...................................................... 72 Bodies with Kinetic Substructure Gianfranco Capriz .............. ............................. 77 1 Kinetics................................... 77 2 A Shadow Speck of Matter ................................. 79 3 Straining and Allied Notions .................................. 81 4 Balance Laws ........................................... 84 5 Balance of Kinetic Energy ........ ............................. 86 6 The First Principle ....................................... 89 References .......................... ....................... 90 From Extended Thermodynamics to Granular Materials Tommaso Ruggeri ........................................... 91 1 Introduction............................... 91 2 Boltzmann Equation and Moments .............................. 92 2.1 The Closure of Extended Thermodynamics ................... 93 2.2 Macroscopic Approach of ET in the 13 Fields ................. 93 3 Extended Thermodynamics of Moments ......................... 94 4 Maximization of Entropy ......................... .......... 97 5 Maximum Characteristic Velocity in Classical Theory .............. 98 6 Nesting Theories and Principal Subsystems ....................... 99 6.1 Example of 13-Moments Principal Subsystems ................ 99 6.2 Lower Bound Estimate and Characteristic Velocities for Large n ......................................... 100 7 Qualitative Analysis ...........................................102 7.1 Shizuta-Kawashima Condition .......................... 103 7.2 Global Existence of Smooth Solutions ........................ 103 8 Comparison with Experiments: Sound Waves and Light Scattering .. 104 References ...................................... ................ 105 Influence of Contact Modelling on the Macroscopic Plastic Response of Granular Soils Under Cyclic Loading R. Garcia-Rojo, S. McNamara, and H.J. Herrmann .................. 109 1 Introduction ................... ...............................109 2 Discrete Element Methods ................. ................ 111 2.1 Boundary Conditions: Biaxial Test .......................... 112 2.2 Molecular Dynamics .....................................113 2.3 The Normal-Dashpot Model ............................ 114 2.4 Contact Dynamics ........................................ 115 3 Results ........................................116 3.1 Comparing MD and CD ...................................117 3.2 Comparing Different Visco-Elastic Laws ................... ... 118 4 Conclusions ................................................. 123 References ................ ................................123 Fluctuations in Granular Gases A. Barrat, A. Puglisi, E. Trizac, P. Visco, and F. van Wijland ........ 125 1 Introduction ................ ................... ............125 2 A Brief Introduction to Granular Gases .......................... 127 2.1 Boundary Driven Gases .................................... 128 2.2 Randomly Driven Gases ................................... 129 3 Total Energy Fluctuations in Vibrated and Driven Granular Gases ................ .................. 131 3.1 The Inhomogeneous Boundary Driven Gas ................... 131 3.2 The Homogeneously Driven Case ........................... 135 4 A Large Deviation Theory for the Injected Power Fluctuations in the Homogeneous Driven Granular Gas ........................ 138 4.1 The Cumulants ..........................................141 4.2 The Solvable Infinite Dimension Limit ....................... 145 5 Fluctuations of Injected Power at Finite Times: Two Examples ..... 146 5.1 The Homogeneous Driven Gas of Inelastic Hard Disks ......... 146 5.2 The Boundary Driven Gas of Inelastic Hard Disks ............. 153 6 The Dynamics of a Tracer Particle as a Non-Equilibrium Markov Process ..............................................157 6.1 Detailed Balance ............................................158 6.2 Action Functionals ....................................... . 160 7 Conclusions ................................................. 161 References ....................................................... 162 An Extended Continuum Theory for Granular Media Pasquale Giovine ...............................................167 1 Introduction ................................................... 167 2 A First Model ................... ............................ 169 3 Rotations ..................................................... 171 4 Balance of Interactions for Material Bodies with Affine Microstructure ..................................... 173 5 O bservers ..................................... . .............175 6 Dilatant Granular Materials with Rotating Grains ................. 177 7 Inertia Forces and Balance of Granular Energy .................... 179 8 Constitutive Restrictions in the Thermoelastic Case ............... 182 9 Suspension of Rigid Granules in a Fluid Matrix ................... 185 Appendix: Kinetic Energy Coefficients .......................... 187 References ................ ................................... 190 Slow Motion in Granular Matter Paolo Maria Mariano ............................................193 1 Introduction .............................................193 2 Representation of the Granularity ............................... 194 3 Balance of Interactions: RJ3 x SO(3) Invariance ................... 200 4 Evolution of the Local Numerosity of Granules .................... 204 5 A Single Granule Coinciding with the Generic Material Element .... 207 References ......... . ..................................... 209