The Mathematics and Physics of Disordered Media: Percolation, Random Walk, Modeling, and Simulation
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The Mathematics and Physics of Disordered Media: Percolation, Random Walk, Modeling, and Simulation Proceedings of a Workshop held at the IMA, University of Minnesota, Minneapolis February 13-19,1983
Edited by B. D. Hughes and B. W. Ninham
Springer-Verlag Berlin Heidelberg New York Tokyo 1983
Editors
B.D. Hughes B.W. Ninham Department of Applied Mathematics, Institute for Advanced Studies Australian, National University Canberra, A.CI. 2600, Australia
AMS Subject Classifications (1980): 60J15, 60J20, 76S05, 82A42 ISBN 3-540-12707-0 Springer-Verlag Berlin Heidelberg New York Tokyo ISBN 0-387-12707-0 Springer-Verlag New York Heidelberg Berlin Tokyo This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopyinq machine Dr similar means, and storaqe in data banks. Under § 54 of the German Copyriqht Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft WDrt", Munich.
© by Springer-Verlag Berlin Heidelberg 1983 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2146/3140-543210
The Mathematics and Physics of Disordered Media PREFACE
The successes of the new physics in the 17th and 18th centuries were inextricably interwoven with the discovery of the calculus.
Following Newton, Leibniz,
and Laplace, the scientific rationalists, in a burst of enthusiasm over the omnipotence of deductive reasoning, made mathematics Big Bird of the Sciences.
The
orderliness of that God who made this best of all possible deterministic worlds stood revealed.
In the words of Descartes, Cum Deus caZcuZat, fit mundus!
Then carne Gauss and Riemann with non-Euclidean geometries, Cantor with nite sets and a host of logicians with the axiomatization of mathematics. these developments challenged preconceived notions, and many researchers
infiAll of
went
deeper and deeper into the foundations of mathematics, trying to find The Perch for Big Bird.
These hopes, along with the dreams of the rationalists, ended
suddenly when Godel showed that any sufficiently rich system of axioms contains undecidable propositions.* This loss of faith, like the dread acciditas, that dry soul-witherino wind which afflicted the good monks of Eqypt so many centuries ago, resulted in a crisis of confidence.
Coincident with this internal attack on the foundations, one
also finds many applied scientists viewing mathematics as irrelevant to the real world.
These developments are in no small measure responsible for the present
separation between pure mathematics, applied mathematics,and the sciences generally.
Unlike their counterparts in nuclear and particle physics, astronomy
and space sciences, biology, and computer and earth sciences, who trumpeted their triumphs real or imagined, mathematicians sat mute and musing. Awareness of the increasing gap between science and mathematics prompted the National Science
