The Physics of Granular Media

Editors: Dr. H. Hinrichsen holds a temporary professorship at the University of Wuppertal. He is head of the DFG project "Influence of electrical charges on the stability of granular matter in suspension". Prof. Dr. D.E. Wolf is a well-known scientist from the University of Duisburg. He has worked for many years on granular matter and is a widely recognized expert within this community. Authors: Prof. Dr. Igor Aaronson Prof. Dr. R. P. Behringer Prof. Dr. Eric Clement Prof. Dr. E. Ben-Naim Prof. Dr. H. van Damme Prof. Dr. Sir Sam Edwards Prof. Dr. H. A. Makse Prof. Dr. J. D. Goddard Prof. Dr. Isaac Goldhirsch Dr. Elisabeth Guazzelli Prof. Dr. H. J. Herrmann Priv.-Doz. Dr. Haye Hinrichsen Prof. Dr. H. M. Jaeger Prof. Dr. A. Kudrolli Prof. Dr. D. Lohse Prof. Dr. S. Luding Dr. C. F. Moukarzel Priv.-Doz. Dr. T. Poschel Prof. Dr. S. Roux Dr. F. Radjai Prof. Dr. Dietrich E. Wolf

Preface.List of Contributors.I Static Properties.1 Stress in Dense Granular Materials (I. Goldhirsch and C. Goldenberg).1.1 Introduction.1.2 Continuum Mechanics: A Brief Review.1.3 Constitutive Relations for Dense Granular Materials.1.4 A Microscopic Approach.1.5 Forces, Stress and Response Functions.1.6 Concluding Remarks.References.2 Response Functions in Isostatic Packings (C. F. Moukarzel).2.1 Introduction.2.2 Rigidity Considerations for Contact Networks.2.3 Consequences of Isostaticity.2.4 Specific Examples.2.5 Discussion.References.3 Statistical Mechanics of Jammed Matter (H. A. Makse, J. Bruji-c, and S. F. Edwards).3.1 Introduction to the Concept of Jamming.3.2 New Statistical Mechanics for Granular Matter.3.3 Jamming with the Confocal.3.4 Jamming in a Periodic Box.References.II Granular Gas.4 The Inelastic Maxwell Model (E. Ben-Naim and P. Krapivsky).4.1 Introduction.4.2 Uniform Gases: One Dimension.4.3 Uniform Gases: Arbitrary Dimension.4.4 Impurities.4.5 Mixtures.4.6 Lattice Gases.4.7 Conclusions.References.5 Cluster Formation in Compartmentalized Granular Gases (K. van der Weele, R. Mikkelsen, D. van der Meer, and D. Lohse).5.1 Introduction.5.2 The Vertically Vibrated Experiment.5.3 Eggers' Flux Model.5.4 Extension to More than two Compartments.5.5 Urn Model.5.6 Horizontally Vibrated System.5.7 Double Well Model.5.8 Further Directions.References.III Dense Granular Flow.6 Continuum Modeling of Granular Flow and Structure Formation (I. S. Aranson and L. S. Tsimring).6.1 Introduction.6.2 Order Parameter Description of Partially Fluidized Granular Flows.6.3 Avalanchesonan Inclined Plane.6.4 Fitting the Theory with Molecular Dynamics Simulations.6.5 Surface-driven Shear Granular Flow Under Gravity.6.6 Stick-Slips and Granular Friction.6.7 Conclusions.References.7 Contact Dynamics Study of 2D Granular Media: Critical States and Relevant Internal Variables (F. Radjai and S. Roux).7.1 A Geometry-Mechanics Dialogue.7.2 Agranular Model.7.3 Macroscopic Continuum Description.7.4 Numerical Results.7.5 Conclusion.References.8 Collision of Adhesive Viscoelastic Particles (N. V. Brilliantov and T. Poschel).8.1 Introduction.8.2 Forces Between Granular Particles.8.3 Collision of Granular Particles.8.4 Conclusion.References.IV Hydrodynamic Interactions.9 Fluidized Beds: From Waves to Bubbles (E. Guazzelli).9.1 Introduction.9.2 Flow Regimes and Instabilities.9.3 Instability Mechanism.9.4 Governing Equations.9.5 Primary Instability.9.6 Rheology of the Particle Phase.9.7 Secondary Instability and the Formation of Bubbles.9.8 Conclusions.References.10 Wind-blown Sand (H. J. Herrmann).10.1 Introduction.10.2 The Wind Field.10.3 Aeolian Sand Transport.10.4 Dunes.10.5 Conclusion.References.V Charged and Magnetic Granular Matter.11 Electrostatically Charged Granular Matter (S. M. Dammer, J. Werth, and H. Hinrichsen).11.1 Introduction.11.2 Charged Granular Matter in Vacuum.11.3 Charged Granular Matter in Suspension.11.4 Agglomeration of Monopolar Charged Suspensions.11.5 Coating Particles in Bipolarly Charged Suspensions.11.6 Summary.References.12 Magnetized Granular Materials (D. L. Blair and A. Kudrolli).12.1 Introduction.12.2 Background: Dipolar Hard Spheres.12.3 Experimental Technique.12.4 The Phase Diagram.12.5 The Non-equipartition of Energy.12.6 Cluster Growth Rates.12.7 Compactness of the Cluster.12.8 Migration of Clusters.12.9 Summary.References.VI Computational Aspects.13 Molecular Dynamics Simulations of Granular Materials (S. Luding).13.1 Introduction.13.2 The Soft-particle Molecular Dynamics Method.13.3 Hard-sphere Molecular Dynamics.13.4 The Link between ED and MD via the TC Model.13.5 The Stress in Particle Simulations.13.6 2D Simulation Results.13.7 Large-scale Computational Examples.13.8 Conclusion.References.14 Contact Dynamics for Beginners (L. Brendel, T. Unger, and D. E. Wolf).14.1 Introduction.14.2 Discrete Dynamical Equations.14.3 Volume Exclusion in a One-dimensional Example.14.4 The Three-dimensional Single Contact Case Without Cohesion.14.5 Iterative Determination of Constraint Forces in a Multi-contact System.14.6 Computational Effort: Comparison Between CD and MD.14.7 Rolling and Torsion Friction.14.8 Attractive Contact Forces.14.9 Conclusion.References.Index.CD-ROM.The enclosed CD-ROM contains the figures of the articles, many of them colored, as well as related movies.