Glasses and Grains (eBook)

Contents 6
Foreword 10
Glasses 12
1. Introduction 12
2. Crystallisation 13
3. Collective nature of solidity: Arrhenius versus super-Arrhenius 16
4. Avoiding crystallisation 19
5. Short digression: the nucleation argument 23
Two phases 23
Entropic drive 24
6. Configurational entropy and metastable states 25
Local mean-field 25
A sum rule 27
The transition 27
Reading the complexity and a coherence length from 28
7. Analogy with – and lessons from – chaotic systems 28
8. Glasses in the real world: aging 29
9. Random first-order theory 31
10. Is mean-field circumstantial or essential? 33
References 34
Colloidal Glasses 36
1. Introduction 36
2. Repulsive colloidal glasses 39
3. Attractive colloidal glasses 44
4. Conclusions 48
Acknowledgment 48
References 49
Glass and Jamming Transitions 51
1. Introduction 51
2. Basic facts 52
3. The jamming-glass transition of colloids and grains 57
4. First dialogue 60
5. Dynamical heterogeneities and dynamical correlations 63
6. Second dialogue 69
7. The Random First-Order Transition Theory Part I: Mean-field theory 71
7.1. A chaotic free energy landscape 71
7.2. Boundary pinning field and replicas 75
8. Third dialogue 78
9. The Random First-Order Transition Theory Part II: Beyond mean-field theory and the real space description 79
9.1. The Mosaic State 79
9.2. Dynamics close to 82
10. Fourth and final dialogue 83
Acknowledgment 85
Some References 85
References 85
Granular Flows 87
1. Introduction 87
2. The granular liquid 90
2.1. Local rheology 90
2.2. Example of application of the local rheology 2.2.1. Flow down an inclined plane. 95
2.2.2. Flow on a pile. 98
2.2.3. Granular collapse. 98
2.2.4. Confined flows. 99
2.3. Beyond 100
2.3.1. The solid-liquid transition: Role of the preparation, hysteresis, and finite size effects. 100
2.3.2. Quasi-static flows. 103
2.3.3. Transition liquid/gas and link with the kinetic theory. 103
2.3.4. Conclusion about the local rheology. 103
3. Depth-averaged approach 104
4. Towards more complex granular materials 107
4.1. Polydispersed media 108
4.2. Cohesive granular media 109
4.3. Immersed granular media 110
5. Conclusion 114
References 114
Theoretical Considerations for Granular Flow 120
1. Introduction 120
2. Kinematics of rolling states 123
2.1. The honeycomb lattice 125
3. Forces in rolling states 128
4. Kinematics of random grain packings 134
4.1. Three-Dimensional Case 141
5. Conclusions 142
Acknowledgment 143
References 143
Grains, Glasses and Jamming 145
1. Introduction and preliminary remarks 145
2. Glassy behaviour of vibrated grains 147
2.1. Macroscopic evidence 147
2.1.1. Slow relaxations. 148
2.1.2. Aging. 148
2.2. Microscopic Dynamics: Granular media vs Structural Glasses 150
2.2.1. Systems. 151
2.2.2. Trajectories, cage-jumps and statistics of the displacements. 151
3. Dynamical heterogeneities in glassy systems 154
3.1. Spatio-temporal organisation of the cage jumps 154
3.2. Towards the glass transition 156
3.3. Relation to the underlying structure 158
4. Summary and open questions 160
Acknowledgment 161
References 161