Unifying Concepts in Granular Media and Glasses (eBook)

Cover 1
Preface 5
Volume Contents 7
The Properties of Jamming at Zero Temperature 9
Acknowledgments 15
References 15
A Basis for the Statistical Mechanics of Granular Systems 17
Introduction 17
Classical Statistical Mechanics 18
Statistical Mechanics for Jammed Matter 18
Definition of the Volume Function, W 19
Entropy and Compactivity 20
Remarks 21
The Classical Boltzmann Equation 22
'Boltzmann Approach' to Granular Matter 24
Experimental Validation of the Statistical Mechanics Concepts 27
References 30
A Possible Experimental Test of the Thermodynamic Approach to Granular Media 33
Introduction 33
References 39
Memory and Kovacs Effects in the Parking-lot Model: An Approximate Statistical-mechanical Treatment 43
Introduction 43
The Model and its Properties 43
Statistical-mechanical Formalism with Two Thermodynamic Parameters 45
Approximate Description of the Compaction Kinetics 47
Memory and Kovacs Effects 49
Conclusion 51
References 51
Statistical Mechanics of Jamming and Segregation in Granular Media 55
Introduction 55
Granular Media 56
Approaches a la Edwards to Statistical Mechanics of Granular Media 57
Configurational Entropy of Granular Media and Glasses Frozen at T = 0 58
Lattice Models for Granular Media 59
A Monodisperse Hard-sphere System under Gravity 59
The Stationary States of the Tap Dynamics 60
Edwards' Averages 61
Relaxation during MC "Tap" Dynamics 62
A Mean Field Study of Hard Spheres under Gravity on a Random Graph 62
A Hard-sphere Binary Mixture under Gravity 65
Conclusions 68
References 68
Granular Compaction 71
Introduction 71
Experimental Set-up 71
Experimental Results on 1 mm Spheres 73
Compaction of Anisotropic Granular Media 77
Discussion 80
Packing Microstructure 80
Movement of the Grains 83
Conclusion and Open Questions 83
Acknowledgments 83
References 84
Experiments in Randomly Agitated Granular Assemblies Close to the Jamming Transition 85
Introduction 85
Vibration of a 2D model Granular Assembly 86
Experimental Set-Up 86
The Large Scale and Long Time Convection Dynamics 87
Suppression of Convection 90
Outlook 90
Compacting a 3D Granular Assembly 91
Experimental Set-up 92
Measurement Techniques 92
Preliminary Results 94
Experiment 1 - Compaction and Microscopic Dynamics 94
Experiment 2 - Dynamical Intermittency 96
Mobility of an Intruding Grain 97
Conclusions 98
References 100
An Oscillator in the Granular Matter 101
Introduction 101
Experimental 102
Granular Liquid 103
Granular Glass 104
Discussion 105
References 106
Segregation Phases in a Vibrated Binary Granular Layer 107
Introduction 107
The Experiment 108
Single Particle Motion 109
Granular Segregation 110
Segregation Phase Transition 112
Binary Gas, Segregation Liquid and Segregation Crystal Phases 113
Oscillatory States 114
Discussion and Conclusion 115
References 116
Shaken, not Stirred: why Gravel Packs Better than Bricks 117
Introduction 117
The Model: Definition and Ground States 118
Zero-temperature Dynamics: (ir)Retrievability of Ground States 119
Low-temperature Dynamics 122
Discussion 124
Acknowledgements 125
References 125
On Pre-asymptotic Aging in Finite Dimensional Spin Glasses 127
Introduction 127
Definition of the Observables 129
Results and Discussion 130
Conclusions 132
Acknowledgments 132
References 133
Stimulated and Spontaneous Relaxation in Glassy Systems 137
Introduction 137
Adiabatic Relaxation 138
Stimulated and Spontaneous Relaxation as the Origin of Intermittency 139
Statistical (Microcanonical) Description of the Aging State 140
Partial Equilibration Scenario 141
A Fluctuation Theorem in the Aging State 143
Microcanonical Relations and Effective Temperatures in the Aging State 144
The Oscillator Model (OM) 148
Energy Relaxation 148
Effective Temperature 149
The Fluctuation Theorem 149
Trapping Time Distribution 150
Microcanonical Rates for the Magnetization 150
Conclusions 151
References 152
Heterogeneities in the Dynamics of Supercooled Water 153
Introduction 153
Spatially Heterogeneous Dynamics 154
Delta t- and t-dependence of Cluster Size 156
T-dependence of Clusters 156
SHD and the Adam-Gibbs Theory 157
Transitions between Inherent Structures 158
Discussion 160
References 160
Glass States in Dense Attractive Micellar Systems 171
Introduction 171
The System 174
Experiments 176
Photon Correlation Spectroscopy 176
Small Angle Neutron Scattering (Absolute Scale) 179
The Scale Intensity Distribution Approach 181
Results and Discussion 182
Results of SANS Data 182
Scaling Plots of SANS Data 183
Intermediate Scattering Functions (ISF) 184
Conclusions 185
Acknowledgments 186
References 186
Short-ranged Attractive Colloids: What is the Gel State ? 189
Introduction 189
Model, Theory and Simulation 191
The Phase Diagram 192
Phase Separation and Gels 193
Conclusions 199
Acknowledgments 199
References 199
Structural Arrest in Chemical and Colloidal Gels 203
Introduction 203
Model and Numerical Simulations 204
Relaxation Properties 205
Conclusions 209
Acknowledgments 209
References 199
Schematic Mode Coupling Theories for Shear Thinning, Shear Thickening, and Jamming 211
Introduction 211
Arrest in Colloidal Fluids 211
Mode Coupling Theory (MCT) 212
MCT & Dynamic Heterogeneity
Shear Thinning 214
A Microscopic Approach 214
Schematic MCT Models 216
Shear Thickening and Jamming 217
Glassy Versus Hydrodynamic Thickening 220
Conclusion 221
References 222
Workshop Participants List 225
Index 227