GRANULAR PHYSICS

By X. DIZAR

CONTENTS INTRODUCTION STATISTICAL MECHANICS FRAMEWORK, PACKING AND THE ROLE OF FRICTION GRANULAR ?OW THROUGH WEDGES, CHANNELS AND APERTURES INSTABILITIES, CONVECTION AND PATTERN FORMATION IN VIBRATED GRANULAR BEDS SIZE SEGREGATION IN VIBRATED POWDERS SELF-ORGANISED CRITICALITY – THEORETICAL SANDPILES? CELLULAR AUTOMATON MODELS OF SANDPILES THEORETICAL STUDIES OF SANDPILE SURFACES COMPUTER SIMULATION APPROACHES – AN OVERVIEW GRANULAR STRUCTURES – MONTE CARLO APPROACHES GRANULAR ?OW – MOLECULAR DYNAMICS APPROACHES SIMULATIONS OF SHAKEN SAND – SOME GENERAL REMARKS STRUCTURE OF VIBRATED POWDERS – NUMERICAL RESULTS DETAILS OF SIMULATION ALGORITHM THE STRUCTURE OF SHAKEN SAND – SOME SIMULATION RESULTS VIBRATED POWDERS: TRANSIENT RESPONSE IS THERE SPONTANEOUS CRYSTALLISATION IN GRANULAR MEDIA? SOME RESULTS ON SHAKING-INDUCED SIZE SEGREGATION COLLECTIVE STRUCTURES IN SAND – THE PHENOMENON OF BRIDGING ON BRIDGES IN SANDPILES – AN OVERARCHING SCENARIO SOME TECHNICAL DETAILS BRIDGE SIZES AND DIAMETERS: WHEN DOES A BRIDGE SPAN A HOLE? TURNING OVER AT THE TOP; HOW LINEAR BRIDGES FORM DOMES DISCUSSION ON ANGLES OF REPOSE: BISTABILITY AND COLLAPSE COUPLED NONLINEAR EQUATIONS: DILATANCY VS THE ANGLE OF REPOSE BISTABILITY WITHIN ??B: HOW DILATANCY ‘FATTENS’ THE ANGLE OF REPOSE WHEN SANDPILES COLLAPSE: RARE EVENTS, ACTIVATED PROCESSES AND THE TOPOLOGY OF ROUGH LANDSCAPES ANOTHER TAKE ON BISTABILITY COMPACTION OF DISORDERED GRAINS IN THE JAMMING LIMIT: SAND ON RANDOM GRAPHS THE THREE-SPIN MODEL: FRUSTRATION, METASTABILITY AND SLOW DYNAMICS HOW TO TAP THE SPINS? – DILATION AND QUENCH PHASES RESULTS I: THE COMPACTION CURVE RESULTS II: REALISTIC AMPLITUDE CYCLING – HOW GRANULAR MEDIA JAM AT DENSITIES LOWER THAN CLOSE-PACKED SHAKING A BOX OF SAND I – A SIMPLE LATTICE MODEL DE?NITION OF THE MODEL RESULTS I: ON THE PACKING FRACTION RESULTS II: ON ANNEALED COOLING, AND THE ONSET OF JAMMING RESULTS III: WHEN THE SANDBOX IS FROZEN RESULTS IV: TWO NONEQUILIBRIUM REGIMES SHAKING A BOX OF SAND II – AT THE JAMMING LIMIT, WHEN SHAPE MATTERS! ZERO-TEMPERATURE DYNAMICS: (IR)RETRIEVABILITY OF GROUND STATES, DENSITY ?UCTUATIONS AND ANTICORRELATIONS RUGGED ENTROPIC LANDSCAPES: EDWARDS’ OR NOT? LOW-TEMPERATURE DYNAMICS ALONG THE COLUMN: INTERMITTENCY AVALANCHES WITH REORGANISING GRAINS AVALANCHES TYPE I – SOC AVALANCHES TYPE II – GRANULAR AVALANCHES DISCUSSION AND CONCLUSIONS 10 FROM EARTHQUAKES TO SANDPILES – STICK–SLIP MOTION AVALANCHES IN A ROTATING CYLINDER THE MODEL RESULTS 11 COUPLED CONTINUUM EQUATIONS: THE DYNAMICS OF SANDPILE SURFACES REVIEW OF SCALING RELATIONS FOR INTERFACIAL ROUGHENING CASE A: THE EDWARDS–WILKINSON EQUATION WITH ?OW CASE B: WHEN MOVING GRAINS ABOUND CASE C: TILT COMBINED WITH ?OWING GRAINS A MORE COMPLICATED EXAMPLE: THE FORMATION OF RIPPLES CONCLUSIONS 12 THEORY OF RAPID GRANULAR ?OWS ISAAC GOLDHIRSCH QUALITATIVE CONSIDERATIONS KINETIC THEORY BOUNDARY CONDITIONS WEAKLY FRICTIONAL GRANULAR GASES CONCLUSION 13 THE THERMODYNAMICS OF GRANULAR MATERIALS SIR SAM EDWARDS AND RAPHAEL BLUMENFELD STATISTICAL MECHANICS VOLUME FUNCTIONS AND FORCES IN GRANULAR SYSTEMS THE STRESS ?ELD FORCE DISTRIBUTION 14 STATIC PROPERTIES OF GRANULAR MATERIALS PHILIPPE CLAUDIN STATICS AT THE GRAIN SCALE LARGE-SCALE PROPERTIES REFERENCES