Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena
Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These
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exander N.Gorban · Nikolaos K. Kazantzis Ioannis G. Kevrekidis · Hans Christian Öttinger Constantinos Theodoropoulos (Eds.)
Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena With 50 Figures
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Alexander N.Gorban
Nikolaos K. Kazantzis
University of Leicester Department of Mathematics University Road LE1 7RH Leicester United Kingdom e-mail: [email protected] and Institute of Computational Modeling Russian Academy of Sciences
Worcester Polytechnic Institute Department of Chemical Engineering Institute Road 100 Worcester, MA 01609-2280 USA e-mail: [email protected]
Hans Christian Öttinger ETH Zürich Institut für Polymere Wolfgang Pauli-Straße 10 CH-8093 Zürich Switzerland e-mail: [email protected]
Ioannis G. Kevrekidis Princeton University Department of Chemical Engineering Engineering Quadrangle A-217 Princeton NJ 08544-5263 USA e-mail: [email protected]
Constantinos Theodoropoulos University of Manchester School of Chemical Engineering and Analytical Science PO Box 88, Sackville St. Manchester, M60 1QD United Kingdom e-mail: [email protected]
Library of Congress Control Number: 2006929855
ISBN-10 3-540-35885-4 Springer Berlin Heidelberg New York ISBN-13 978-3-540-35885-5 Springer Berlin Heidelberg New York 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 for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2006 Printed in Germany 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. Typesetting: Data conversion by authors Production: LE-TEX Jelonek, Schmidt & Vöckler GbR, Leipzig Cover design: design & production GmbH, Heidelberg Printed on acid-free paper
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Preface
Even a cursory inspection of the content of the well-known on-line free encyclopedia Wikipedia reveals a simple classification and model typology that is frequently encountered in a wide spectrum of scientific disciplines. In particular, different types of models have traditionally been classified according to the following well-known categorization criteria [1]: 1. Linear vs. nonlinear: If the objective functions and constraints are represented entirely by linear equations, then the model is known as a linear model. If one or more of the objective functions or constraints are represented with a nonlinear
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