Cambridge.University.Press.Granular.Physics.Jul.2007.pdf

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Cambridge.University.Press.Granular.Physics.Jul.2007. This page intentionally left blankGRANULAR PHYSICSThe field of granular physics has burgeoned since its development in the late 1980s,when physicists first began to use statistical mechanics to study granular media.They are prototypical of complex systems, manifesting metastability, hysteresis,bistability and a range of other fascinating phenomena.This book provides a wide-ranging account of developments in granular physics,and lays out the foundations of the statics and dynamics of granular physics. Itcovers a wide range of subfields, ranging from fluidisation to jamming, and theseare modelled through a range of computer simulation and theoretical approaches.Written with an eye to pedagogy and completeness, this book will be a valuableasset for any researcher in this field.In addition to Professor Mehta’s detailed exposition of granular dynamics,the book contains contributions from Professor Sir Sam Edwards, jointly withDr Raphael Blumenfeld, on the thermodynamics of granular matter; from Profes-sor Isaac Goldhirsch on granular matter in the fluidised state; and Professor PhilippeClaudin on granular statics.Anita Mehta, a former Rhodes scholar, is currently a Radcliffe Fellow atHarvard University. She is well known for being one of the pioneers in granularphysics, and is credited with the introduction of many new concepts in this field, inparticular to do with the competition of slow and fast modes in granular dynamics.GRANULAR PHYSICSANITA MEHTAHarvard UniversityWith contributions fromSIR SAM EDWARDS AND RAPHAEL BLUMENFELDISAAC GOLDHIRSCHPHILIPPE CLAUDINCAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São PauloCambridge University PressThe Edinburgh Building, Cambridge CB2 8RU, UKFirst published in print formatISBN-13 978-0-521-66078-5ISBN-13 978-0-511-29669-7© A. Mehta 20072007Information on this title: www.cambridge.org/9780521660785This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press.ISBN-10 0-511-29669-XISBN-10 0-521-66078-5Cambridge University Press has no responsibility for the persistence or accuracy of urls for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.Published in the United States of America by Cambridge University Press, New Yorkwww.cambridge.orghardbackeBook (NetLibrary)eBook (NetLibrary)hardbackSablesIl n’est pas de d´esert si vasteQue ne puisse traverserCelui qui porte la musique des´etoiles.Poem on the Paris Underground,attributed to Michel Le SaintSandsThere is no desert so vastthat it cannot be traversedby one who carries the musicof the stars.My translationContentsPreface page x1 Introduction 11.1 Statistical mechanics framework, packing and the role of friction 21.2 Granular flow through wedges, channels and apertures 41.3 Instabilities, convection and pattern formation in vibratedgranular beds 51.4 Size segregation in vibrated powders 81.5 Self-organised criticality – theoretical sandpiles? 111.6 Cellular automaton models of sandpiles 131.7 Theoretical studies of sandpile surfaces 152 Computer simulation approaches – an overview 182.1 Granular structures – Monte Carlo approaches 182.2 Granular flow – molecular dynamics approaches 222.3 Simulations of shaken sand – some general remarks 243 Structure of vibrated powders – numerical results 273.1 Details of simulation algorithm 273.2 The structure of shaken sand – some simulation results 293.3 Vibrated powders: transient response 403.4 Is there spontaneous crystallisation in granular media? 443.5 Some results on shaking-induced size segregation 464 Collective structures in sand – the phenomenon of bridging 524.1 Introduction 524.2 On bridges in sandpiles – an overarching scenario 524.3 Some technical details 544.4 Bridge sizes and diameters: when does a bridge span a hole? 554.5 Turning over at the top; how linear bridges form domes 584.6 Discussion 61viiviii Contents5 On angles of repose: bistability and collapse 635.1 Coupled nonlinear equations: dilatancy vs the angle of repose 635.2 Bistability within δθB: how dilatancy ‘fattens’ the angle of repose 655.3 When sandpiles collapse: rare events, activated processesand the topology of rough landscapes 675.4 Discussion 695.5 Another take on bistability 696 Compaction of disordered grains in the jamming limit: sand onrandom graphs 796.1 The three-spin model: frustration, metastability and slow dynamics 816.2 How to tap the spins? – dilation and quench phases 826.3 Results I: the compaction curve 846.4 Results II: realistic amplitude cycling – how granularmedia jam at densities lower than close-packed 906.5 Discussion 937 Shaking a box of sandI–asimplelattice model 947.1 Introduction 947.2 Definition of the model 947.3 Results I: on the packing fraction 967.4 Results II: on annealed cooling, and the onset of jamming 977.5 Results III: when the sandbox is frozen 1007.6 Results IV: two nonequilibrium regimes 1027.7 Discussion 1038 Shaking a box of sand II – at the jamming limit, when shape matters! 1048.1 Definition of the model 1058.2 Zero-temperature dynamics: (ir)retrievability of groundstates, density fluctuations and anticorrelations 1068.3 Rugged entropic landscapes: Edwards’ or not? 1088.4 Low-temperature dynamics along the column: intermittency 1138.5 Discussion 1149 Avalanches with reorganising grains 1159.1 Avalanches typeI–SOC 1159.2 Avalanches type II – granular avalanches 1189.3 Discussion and conclusions 13110 From earthquakes to sandpiles – stick–slip motion 13210.1 Avalanches in a rotating cylinder 13210.2 The model 13310.3 Results 13510.4 Discussion 146 . CLAUDIN CAMBRIDGE UNIVERSITY PRESSCambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São PauloCambridge University PressThe Edinburgh Building, Cambridge. without the written permission of Cambridge University Press. ISBN-10 0-511-29669-XISBN-10 0-521-66078- 5Cambridge University Press has no responsibility
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Xem thêm: Cambridge.University.Press.Granular.Physics.Jul.2007.pdf, Cambridge.University.Press.Granular.Physics.Jul.2007.pdf, Cambridge.University.Press.Granular.Physics.Jul.2007.pdf, Statistical mechanics framework, packing and the role of friction, Granular flow 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, Granular structures – Monte Carlo approaches, Granular flow – molecular dynamics approaches, Simulations of shaken sand – some general remarks, Details of simulation algorithm, The structure of shaken sand – some simulation results, such that the j th element of b, Vibrated powders: transient response, Is there spontaneous crystallisation in granular media?, Some results on shaking-induced size segregation, On bridges in sandpiles – an overarching scenario, Bridge sizes and diameters: when does a bridge span a hole?, Turning over at the top; how linear bridges form domes, Coupled nonlinear equations: dilatancy vs the angle of repose, When sandpiles collapse: rare events, activated processes and the topology of rough landscapes, Another take on bistability, The three-spin model: frustration, metastability and slow dynamics, How to tap the spins? – dilation and quench phases, Fast dynamics till SPRT: every grain for itself, Slow dynamics of granular clusters: logarithmic compaction, Cascades at the dynamical transition, Definition 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, Definition of the model, Rugged entropic landscapes: Edwards’ or not?, Low-temperature dynamics along the column: intermittency, Review of sandpile cellular automata – Type I, Dynamical scaling for sandpile cellular automata, Qualitative effects of avalanching on surfaces, The effect of avalanching on sandpile surfaces – some observations of material properties, Spatial and temporal roughening of sandpile surfaces, Avalanches in a rotating cylinder, Sandpile driven by random deposition, Sand in rotating cylinders; a paradigm, Review of scaling relations for interfacial roughening, Analysis of the decoupled equation in h, Some caveats Case A: the Edwards–Wilkinson equation with flow, Numerical analysis Case B: when moving grains abound, Results for the single Fourier transforms, Results for the double Fourier transforms, A more complicated example: the formation of ripples, Granular gases are mesoscopic, Some technical details and constitutive relations, Weakly frictional granular gases, Volume functions and forces in granular systems, First approach The stress field, Second approach – coarse-graining a microscopic theory, Force probability distribution Statics at the grain scale .1 Static solutions, Texture and force networks, The q-model Statics at the grain scale .1 Static solutions, Stress measurements in static pilings, From micro-to macroscopic scales, Theoretical descriptions Large-scale properties

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