A Celebration of Mathematical Modeling: The Joseph B. Keller Anniversary Volume PDF
Preview A Celebration of Mathematical Modeling: The Joseph B. Keller Anniversary Volume
A Celebration of Mathematical Modeling A Celebration of Mathematical Modeling The Joseph B. Keller Anniversary Volume Edited by DAN GIVOLI Department of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa, Israel MARCUS J. GROTE Department of Mathematics, University of Basel, Basel, Switzerland and GEORGE C. PAPANICOLAOU Department of Mathematics, Stanford University, Stanford, California, U.S.A. SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-90-481-6526-1 ISBN 978-94-017-0427-4 (eBook) DOI 10.1007/978-94-017-0427-4 Printed on acid-free paper All Rights Reserved ©2004 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2004 Softcover reprint of the hardcover 1st edition 2004 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. For Joe Keller, colleague, teacher and friend, on the occasion of his eightieth birthday Table of Contents Preface ix Publications of Joseph B. Keller xiii Monte Carlo Simulation for American Options 1 R. Caflisch and S. Chaudhary Some Problems in Electromagnetics 17 M. Cheney Pattern Formation in a Suspension of Swimming Microorganisms: Nonlinear Aspects 33 R. Childress and E. Spiegel Non-Reflecting Boundaries: High-Order Treatment 53 D. Givoli Nonreflecting Boundary Conditions for Time Dependent Waves 73 M. Grote Weak Shock Reflection 93 J. Hunter and A.M. Tesdall Bifurcation Theory, Symmetry Breaking and Homogenization in Continuum Mechanics Descriptions of DNA 113 J. Maddocks On Flames as Discontinuity Surfaces in Gasdynamic Flows 137 B.J. Matkowsky Contact Lines 161 M. Miksis Eikonal Functions: Old and New 181 J. Rubinstein and G. Wolansky vii viii Physical Insight, Mathematical Modeling and Asymptotics 199 L. Ting Waves, Bubbles and Jets 221 J.-M. Vanden-Broeck Index 239 Preface ThisvolumecelebratestheeightiethbirthdayofJosephB.Keller. The authors who contributed to this volume belong to what can be called the “Keller school of applied mathematics.” They are former students, postdoctoral fellows and visiting scientists who have collaborated with Joe (some of them still do) during his long career. They all look at Joe as their ultimate (role) model. JoeKeller’sdistinguishedcareerhasbeendividedbetweentheCourant Institute of Mathematical Sciences at New York University, where he received all his degrees (his PhD adviser being the great R. Courant himself) and served as a professor for 30 years, and Stanford University, where he has been since 1978. The appended photos highlight some scenes from the old days. Those who know Joe Keller’s work have been always amazed by its diversity and breadth. It is considered a well-known truth that there is not a single important area in applied mathematics or physics which Keller did not contribute to. This can be appreciated, for example, by glancing through his list of publication included in this volume. Appro- priately, the papers in this book, written with Joe’s inspiration, cover a variety of application areas; together they span the broad subject of mathematical modeling. The models discussed in the book describe the behavior of various systems such as those related to finance, waves, mi- croorganisms, shocks, DNA, flames, contact, optics, fluids, bubbles and jets. Joe’s activity includes many more areas, which unfortunately are not represented here. Joe Keller is undoubtly one of the greatest applied mathematicians of the 20th century, and has won almost any possible prize. His consider- able abilities have been well summarized by Bernard Matkowsky in the June 1996 issue of SIAM News: “He has the ability to see clearly the essential elements of a physical phenomenon in a particular discipline, and then to pose the simplest possible mathematical model to describe the phenomenon. Keller then uses (and more often than not invents) sophisticated mathematical methods to solve the problem. These meth- ods can be used for problems other than the one for which they were developed, and thus become available to mathematicians, scientists, and engineers worldwide. Finally he extracts the physical implications of his mathematical results, so that his work is appreciated not only by math- ematicians, but also by people in the discipline in which the problem originated.” ix x One major field of interest of Joe is wave propagation. His famous invention of the Geometrical Theory of Diffraction (GTD) for solving problems of high-frequency waves started during World War II while he was working on sonar problems for the Columbia University Division of War Research. Since then GTD has become an indispensable tool for waveproblemsinavarietyofapplicationareassuchaselectromagnetics, acoustics, non-destructive testing of structures, earthquake engineering and oil exploration. Joe’s contributions include many other important inventions and methods that will not be mentioned here. A talk by Joe at a seminar or a conference is an event that should never be missed. Here is just one example out of many. In a special lecture which he gave just before Christmas 1987 in his department, Joe started by saying that during Christmas time many people bring home toy models (like model airplanes, etc.), and so he would like to give his audience as a Christmas present a bunch of mathematical models. The talk itself was superb as always. Some of his “models” were serious but amusing (like a model for ordering teams in a tournament and a model for the way a worm advances using a one-dimensional wave equation), while others were simply jokes. One model concerned a proof that if one flips a perfect coin one has a 50% chance of getting Head. Joe showed this by performing the entire calculation of the nonlinear dynamics of the coin, from the initial flip to the landing on the floor! For many years Joe received constant funding from federal agencies, including ONR, AFOSR and the Army. This in itself is not that unique. Whatisuniqueisthathiscontractwiththeseagenciessimplysaid“Prof. J.B. Kellerwill study various problems in applied mathematics.” That’s it! Probably Joe is one of the few researchers in the world who have received this kind of freedom from the funding agencies, and rightly so. It is a great honor for the editors and authors of this book to be associated with this publication. We present this volume to Joe with infiniteappreciationandaffection,andwishhimmanymorehappyyears of mathematical modeling. Dan Givoli, Haifa Marcus Grote, Basel George Papanicolaou, Stanford October 2003 Biographical Sketch of Joseph B. Keller Joseph B. Keller was born in Paterson, New Jersey in 1923 and ed- ucated at New York University (Ph.D. 1948). He remained there as a Professor of Mathematics in the Courant Institute of Mathematical Sci- ences until 1979. Then he moved to Stanford University where he was Professor of Mathematics and Mechanical Engineering until 1993, when he became Professor Emeritus. His research concerns the use of mathematics to solve problems of science and engineering. For example, he developed the Geometrical Theory of Diffraction to describe the propagation of waves. It is widely used to analyze radar reflection from objects, to calculate elastic wave scattering from flaws in solids, to study acoustic wave propagation in the ocean, etc. Another example is his formulation of the EBK method of quantization to determine energy levels of atoms and molecules in quantum mechanics and to solve characteristic value problems in other fields. Other problems he has worked on are described in his list of publications. Professor Keller is a member of the National Academy of Science, a Foreign Member of the Royal Society of London, and he was Honorary Professor of Mathematical Sciences at the University of Cambridge. He is a recipient of the Wolf Prize (1997), the Frederick E. Nemmers Prize (1996),theNASAwardinAppliedMathematicsandNumericalAnalysis (1995), the National Medal of Science (1988), the Timoshenko Medal (1984), the Eringen Medal (1981), the von Karman Prize (1979) and he was the Gibbs Lecturer of the American Mathematical Society (1977), and the von Neumann Lecturer of SIAM (1983). xi
The list of books you might like
