Cover 1
Half-title 3
Title 5
Copyright 6
Dedication 7
Contents 9
Preface 12
1 Introduction 15
1.1 Statistical mechanics framework, packing and the role of friction 16
1.2 Granular flow through wedges, channels and apertures 18
1.3 Instabilities, convection and pattern formation in vibrated granular beds 19
1.4 Size segregation in vibrated powders 22
1.5 Self-organised criticality \u2013 theoretical sandpiles? 25
1.6 Cellular automaton models of sandpiles 27
1.7 Theoretical studies of sandpile surfaces 29
2 Computer simulation approaches \u2013 an overview 32
2.1 Granular structures \u2013 Monte Carlo approaches 32
2.2 Granular flow \u2013 molecular dynamics approaches 36
2.3 Simulations of shaken sand \u2013 some general remarks 38
3 Structure of vibrated powders \u2013 numerical results 41
3.1 Details of simulation algorithm 41
3.2 The structure of shaken sand \u2013 some simulation results 43
3.3 Vibrated powders: transient response 54
3.4 Is there spontaneous crystallisation in granular media? 58
3.5 Some results on shaking-induced size segregation 60
4 Collective structures in sand \u2013 the phenomenon of bridging 66
4.1 Introduction 66
4.2 On bridges in sandpiles \u2013 an overarching scenario 66
4.3 Some technical details 68
4.4 Bridge sizes and diameters: when does a bridge span a hole? 69
4.5 Turning over at the top; how linear bridges form domes 72
4.6 Discussion 75
5 On angles of repose: bistability and collapse 80
5.1 Coupled nonlinear equations: dilatancy vs the angle of repose 80
5.2 Bistability within Delta Theta B: how dilatancy \u2018fattens\u2019 the angle of repose 82
5.3 When sandpiles collapse: rare events, activated processes and the topology of rough landscapes 84
5.4 Discussion 86
5.5 Another take on bistability 86
6 Compaction of disordered grains in the jamming limit: sand on random graphs 96
6.1 The three-spin model: frustration, metastability and slow dynamics 98
6.2 How to tap the spins? \u2013 dilation and quench phases 99
6.3 Results I: the compaction curve 101
6.3.1 Fast dynamics till SPRT: every grain for itself! 101
6.3.2 Slow dynamics of granular clusters: logarithmic compaction 103
6.3.3 Cascades at the dynamical transition 104
6.4 Results II: realistic amplitude cycling \u2013 how granular media jam at densities lower than close-packed 107
6.5 Discussion 110
7 Shaking a box of sand I \u2013 a simple lattice model 111
7.1 Introduction 111
7.2 Definition of the model 111
7.3 Results I: on the packing fraction 113
7.4 Results II: on annealed cooling, and the onset of jamming 114
7.5 Results III: when the sandbox is frozen 117
7.6 Results IV: two nonequilibrium regimes 119
7.7 Discussion 120
8 Shaking a box of sand II \u2013 at the jamming limit, when shape matters! 121
8.1 Definition of the model 122
8.2 Zero-temperature dynamics: (ir)retrievability of ground states, density fluctuations and anticorrelations 123
8.3 Rugged entropic landscapes: Edwards\u2019 or not? 125
8.4 Low-temperature dynamics along the column: intermittency 130
8.5 Discussion 131
9 Avalanches with reorganising grains 132
9.1 Avalanches type I \u2013 SOC 132
9.1.1 Review of sandpile cellular automata \u2013 Type I 133
9.2 Avalanches type II \u2013 granular avalanches 135
9.2.1 Dynamical scaling for sandpile cellular automata 136
9.2.2 Qualitative effects of avalanching on surfaces 137
9.2.3 The effect of avalanching on sandpile surfaces \u2013 some observations of material properties 142
9.2.4 Spatial and temporal roughening of sandpile surfaces 146
9.3 Discussion and conclusions 148
10 From earthquakes to sandpiles \u2013 stick\u2013slip motion 149
10.1 Avalanches in a rotating cylinder 149
10.2 The model 150
10.3 Results 152
10.3.1 Rotated sandpile 152
10.3.2 Sandpile driven by random deposition 158
10.4 Discussion 163
11 Coupled continuum equations: the dynamics of sandpile surfaces 165
11.1 Introduction 165
11.1.1 Some general remarks 165
11.1.2 Sand in rotating cylinders; a paradigm 166
11.2 Review of scaling relations for interfacial roughening 167
11.3 Case A: the Edwards\u2013Wilkinson equation with flow 168
11.3.1 Analysis of the decoupled equation in h 168
11.3.2 Some caveats 171
11.4 Case B: when moving grains abound 173
11.4.1 Numerical analysis 174
11.4.2 Homing in on the physics: a discussion of smoothing in Case B 178
11.5 Case C: tilt combined with flowing grains 179
11.5.1 Results for the single Fourier transforms 180
11.5.2 Results for the double Fourier transforms 181
11.6 Discussion 184
11.7 A more complicated example: the formation of ripples 185
11.8 Conclusions 191
12 Theory of rapid granular flows 193
12.1 Introduction 193
12.2 Qualitative considerations 194
12.2.1 Clustering 195
12.2.2 Collapse 198
12.2.3 Granular gases are mesoscopic 199
12.3 Kinetic theory 201
12.3.1 Some technical details and constitutive relations 207
12.4 Boundary conditions 213
12.5 Weakly frictional granular gases 217
12.6 Conclusion 223
13 The thermodynamics of granular materials 226
13.1 Introduction 226
13.2 Statistical mechanics 228
13.3 Volume functions and forces in granular systems 232
13.4 The stress field 239
13.4.1 First approach 240
13.4.2 Second approach \u2013 coarse-graining a microscopic theory 243
13.5 Force distribution 247
14 Static properties of granular materials 250
14.1 Statics at the grain scale 250
14.1.1 Static solutions 250
Equilibrium conditions 250
Multiplicity of static solutions 252
14.1.2 Force probability distribution 254
14.1.3 Texture and force networks 257
14.1.4 The q-model 259
Presentation of the model 259
Force distribution and the exponential tail 261
14.2 Large-scale properties 262
14.2.1 Stress measurements in static pilings 263
Silos 263
Sandpiles 265
Response functions 267
14.2.2 From micro-to macroscopic scales 270
From contact forces to stresses 270
The effective medium theory 276
14.2.3 Theoretical descriptions 278
Elasto-plasticity 279
Elasticity formalism 281
Mohr\u2013Coulomb yield criterion 285
Janssen\u2019s approach 287
OSL model 288
14.3 Conclusion 290
References 291
Index 314