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BL
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| Record Number
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860334
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| Main Entry
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Garzó, Vicente
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| Title & Author
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Granular Gaseous Flows : : a Kinetic Theory Approach to Granular Gaseous Flows /\ Vicente Garzó.
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| Publication Statement
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Cham, Switzerland :: Springer,, [2019]
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| Series Statement
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Soft and Biological Matter
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| Page. NO
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1 online resource
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| ISBN
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3030044432
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: 3030044440
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: 3030044459
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: 9783030044435
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: 9783030044442
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: 9783030044459
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9783030044435
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Foreword by James W. Dufty; Foreword by Rodrigo Soto; Preface; Acknowledgements; Contents; Acronyms; Symbols; 1 Kinetic Theory of Inelastic Hard Spheres; 1.1 Introduction; 1.2 Collisional Rules; 1.2.1 Smooth Inelastic Hard Spheres; 1.2.2 Inelastic Rough Hard Spheres; 1.2.3 Viscoelastic Particles. Velocity Dependent Coefficient of Restitution; 1.3 Derivation of the Boltzmann Kinetic Equation; 1.4 Extension to Moderate Densities. Enskog Kinetic Equation; 1.5 Macroscopic Balance Equations of the Enskog Equation; 1.6 Enskog Kinetic Theory for Granular Mixtures
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1.6.1 Enskog Kinetic Equation1.6.2 Macroscopic Balance Equations; 1.7 Kinetic Models for Monocomponent Granular Gases; 1.7.1 BMD Kinetic Model; 1.7.2 BDS Kinetic Model; 1.7.3 DBZ Kinetic Model; 1.7.4 Kinetic Models for Moderate Densities; 1.8 Kinetic Models for Granular Mixtures; References; 2 Homogeneous Cooling State; 2.1 Introduction; 2.2 Monocomponent Smooth Granular Gases; 2.2.1 Exact Results; 2.2.2 Approximate Solution; 2.3 Smooth Granular Mixtures; 2.3.1 Exact Results; 2.3.2 Leading Sonine Approximation; 2.3.3 An Illustrative Example: A Binary Mixture
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2.3.4 Tracer Limit. A Nonequilibrium Phase Transition2.4 Energy Nonequipartition in Fluids of Inelastic Rough Hard Spheres; References; 3 Navier-Stokes Transport Coefficients for Monocomponent Granular Gases. I. Theoretical Results; 3.1 Introduction; 3.2 Chapman-Enskog Method; 3.2.1 Zeroth-Order Solution; 3.3 First-Order Solution; 3.4 Constitutive Equations. Navier-Stokes Transport Coefficients; 3.4.1 Navier-Stokes Transport Coefficients; 3.4.2 First-Order Contribution to the Cooling Rate; 3.4.3 Dilute Granular Gas; 3.4.4 Kinetic Model Results; 3.5 Approximate Results
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3.5.1 Standard First Sonine Approximation3.5.2 Modified First Sonine Approximation; 3.5.3 Computer-Aided Method; 3.6 Grad's Moment Method and Green-Kubo Formula; 3.6.1 Grad's Moment Method for Granular Gases; 3.6.2 Green-Kubo Formula for Granular Gases; References; 4 Navier-Stokes Transport Coefficients for Monocomponent Granular Gases. II. Simulations and Applications; 4.1 Comparison with Computer Simulations; 4.1.1 Shear Viscosity; 4.1.2 Heat Flux Transport Coefficients; 4.2 Linear Stability Analysis of the Hydrodynamic Equations; 4.2.1 Comparison with Molecular Dynamics Simulations
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4.3 Hydrodynamic Description of the Steady State in the Presence of Gravity4.4 Transport Coefficients for Other Collisional Models; 4.4.1 Inelastic Rough Hard Spheres; 4.4.2 Viscoelastic Particles; References; 5 Navier-Stokes Transport Coefficients for Multicomponent Granular Gases. I. Theoretical Results; 5.1 Introduction; 5.2 Chapman-Enskog Method for Granular Mixtures; 5.2.1 Zeroth-Order Solution; 5.3 First-Order Solution; 5.4 Navier-Stokes Transport Coefficients and Cooling Rate; 5.5 Approximate Results. Leading Sonine Approximations; 5.5.1 Mass Flux; 5.5.2 Pressure Tensor
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| Abstract
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This book addresses the study of the gaseous state of granular matter in the conditions of rapid flow caused by a violent and sustained excitation. In this regime, grains only touch each other during collisions and hence, kinetic theory is a very useful tool to study granular flows. The main difference with respect to ordinary or molecular fluids is that grains are macroscopic and so, their collisions are inelastic. Given the interest in the effects of collisional dissipation on granular media under rapid flow conditions, the emphasis of this book is on an idealized model (smooth inelastic hard spheres) that isolates this effect from other important properties of granular systems. In this simple model, the inelasticity of collisions is only accounted for by a (positive) constant coefficient of normal restitution. The author of this monograph uses a kinetic theory description (which can be considered as a mesoscopic description between statistical mechanics and hydrodynamics) to study granular flows from a microscopic point of view. In particular, the inelastic version of the Boltzmann and Enskog kinetic equations is the starting point of the analysis. Conventional methods such as Chapman-Enskog expansion, Grad's moment method and/or kinetic models are generalized to dissipative systems to get the forms of the transport coefficients and hydrodynamics. The knowledge of granular hydrodynamics opens up the possibility of understanding interesting problems such as the spontaneous formation of density clusters and velocity vortices in freely cooling flows and/or the lack of energy equipartition in granular mixtures. Some of the topics covered in this monograph include: Navier-Stokes transport coefficients for granular gases at moderate densities Long-wavelength instability in freely cooling flows Non-Newtonian transport properties in granular shear flows Energy nonequipartition in freely cooling granular mixtures Diffusion in strongly sheared granular mixtures Exact solutions to the Boltzmann equation for inelastic Maxwell models.
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| Subject
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Granular materials.
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Kinetic theory of gases.
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Kinetic theory of matter.
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Granular materials.
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Kinetic theory of gases.
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Kinetic theory of matter.
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| Subject
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SCIENCE-- Mechanics-- General.
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| Dewey Classification
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533.7
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| LC Classification
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QC175
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