Mathematical Models of Granular Matter
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows
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1937
Gianfranco Capriz · Pasquale Giovine Paolo Maria Mariano (Eds.)
Mathematical Models of Granular Matter With Contributions by: A. Barrat · A.V. Bobylev · C. Cercignani · I.M. Gamba R. Garcia-Rojo · J.D. Goddard · H.J. Herrmann S. McNamara · A. Puglisi · T. Ruggeri · G. Toscani · E. Trizac P. Visco · F. van Wijland
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Editors Gianfranco Capriz
Pasquale Giovine
Department of Mathematics University of Pisa largo Bruno Pontecorvo 5 56127 Pisa Italy and Accademia Nazionale dei Lincei via della Lungara 10 00165 Roma Italy [email protected]
Dipartimento di Meccanica e Materiali Università “Mediterranea” di Reggio Calabria via Graziella, località Feo di Vito 89060 Reggio Calabria Italy [email protected]
Paolo Maria Mariano DICeA University of Florence via Santa Marta 3 50139 Firenze Italy paolo.mariano@unifi.it
ISBN 978-3-540-78276-6 DOI 10.1007/978-3-540-78277-3
e-ISBN 978-3-540-78277-3
Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2008921365 Mathematics Subject Classification (2000): 76T25, 74E20, 74E25, 82D30 c 2008 Springer-Verlag Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH Coverart “Without title”, xilo-picture by Luigi Mariano, 1973, private collection Printed on acid-free paper 987654321 springer.com
Preface
The adjective ‘granular’ is attributed to materials when they are made of sets of unfastened discrete solid particles (granules) of a size larger than one micron, a length scale above which thermal agitation is negligible. In fact, the dominant energy scale in granular materials is the one of a single grain under gravity. Granular matter is common and we meet it everyday. Examples range from the dust settled on the books of our libraries, to the sand in the desert, to the meal used in cooking, itself obtained from grain, often stored in silos. Granular matter displays a variety of peculiarities that distinguish it from other substances studied by condensed matter physics and renders its overall mathematical modeling arduous. In a review paper of 1999 [dG] P.G. de Gennes writes: “granular matter is a new type of condensed matter, as fundamental as a liquid or a solid
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