Computers in Physics From Newton to Mandelbrot : A Primer in Theoretical Physics D. Stauffer, H. E. Stanley, John Gastineau, A. John Mallinckrodt, and Susan McKay Citation: Computers in Physics 6, 424 (1992); doi: 10.1063/1.4823092 View online: http://dx.doi.org/10.1063/1.4823092 View Table of Contents: http://scitation.aip.org/content/aip/journal/cip/6/4?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Benoit Mandelbrot Phys. Today 64, 63 (2011); 10.1063/1.3603925 A Primer on Work-Energy Relationships for Introductory Physics Phys. Teach. 43, 10 (2005); 10.1119/1.1845983 Mandelbrot and Zewail Win 1993 Wolf Prizes in Physics, Chemistry Phys. Today 46, 109 (1993); 10.1063/1.2808949 Newton is Editor of Mathematical Physics Phys. Today 45, 64 (1992); 10.1063/1.2809803 Statistical Physics and the Atomic Theory of Matter, from Boyle and Newton to Landau and Onsager Am. J. Phys. 54, 477 (1986); 10.1119/1.14572
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BOOKS Department Editors: A. John Mallinckrodt Susan R. McKay
Reviews on System Modeling and Theoretical Physics
To submit a book review to Computers in Physics, please contact either John Mallinckrodt, Physics Department, California State Polytechnic University, Pomona, CA 91768; e-mail: ajmallinckro@csupomona,edu, or Susan McKay (address below).
The Art 01 Modeling Dynamic Systems : Forecasting lor Chaos, Randomness, and Determinism Foster Morrison John Wiley & Sons, Inc., New York, 1991; ISBN 0-471-52004-7 387 pp., hardcover, $54.95
Reviewed by Susan R. McKay any technical professionals, such as astronomers, physicists, ecologists, biologists, economists, and sociologists, find themselves involved in model building. Foster Morrison offers general guidance and specific examples for this diverse readership. He gives what he describes as a "field guide for the modeler of dynamic systems." In an informal style, he describes general features and approaches that have proved useful in a variety of disciplines. Analogies and examples from the fields of population biology, astronomy, physics, and economics are plentiful. The book begins with a brief introduction to dynamics and computing and then moves quickly into a five-chapter "thumbnail sketch of applied mathematics." Highlights from calculus, linear algebra, complex analysis, ordinary and partial differential equations,
Susan R. McKay is Assistant Professor of Physics at the University of Maine, Orono, ME 04469; e-mail: [email protected]
numerical analysis, and statistical methods are discussed, using many examples and avoiding a theorem / proof format. Morrison's perspective is fresh, intuitive, and applicationoriented, so even the reader who is fluent in these topics will find much of this section interesting. Some of the treatment is surprisingly basic, such as defining a derivative and a differential equation, although the mathematical pace of the book quickly accelerates and, overall, the level seems best for someone who has had most of a typical engineering / science college math sequence. The math review is followed by a four-chapter section in which Morrison discusses examples of dynamic systems and feedback mechanisms, including thermostats, the logistic curve, linear oscillators, Volterra's predator-prey equations, and the two-body orbit problem of celestial mechanics. The treatment of each system is self-contained and notation is clearly explained; fieldspecific technical jargon is avoided. General approaches, such as finding the system's fixed points and looking at their stability, are emphasized. Although none of this information is new, this particular collection provides a valuable, concise description which is not found elsewhere. Morrison then introduces what he calls "a hierarchy of dynamic systems," a "taxonomy" to help recognize similar systems from different fields. There are five levels in the hierarchy, ranging from static to stochastic systems, with solvable systems, perturbations on solvable systems, and chaotic systems forming the intermediate levels. For each level, analytical as well as numerical ap-
proaches are described. A weakness of this hierarchy is its fuzziness. For example, a perturbation added to a solvable system can lead to chaos, as in the case of two quasi linear coupled oscillators. The treatment of chaotic systems is only about 20 pages long and discusses primarily the logistic map and the Lorenz equations. Much more could be said here, especially about intermittency and coexisting attractors, which arise in even weakly nonlinear systems. In producing a field guide, though, Morrison has done an admirable job. This book includes many of the types of dynamic system that may be encountered, their distinguishing features, and suggestions for modeling them. Both beginning and experienced modelers of dynamic systems will benefit from its practical tips and general perspective. •
From NeWlon to Mandelbrot : APrimer in Theoretical Physics D. Stauffer and H. E. Stanley Springer-Verlag, New York, 1991 ISBN 0-387-52661-7 191 pp., softcover, $19.95
Reviewed by John Gastineau his is a strange little book that I wish I'd had in graduate school. The subtitle, "A Primer in Theoretical Physics," only begins to convey the scope and brevity of the work. In fewer than 200 pages, the
John Gastineau is Assistant Professor of Physics at Lawrence University, Appleton, WI 54912; e-mail: [email protected]
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reader is instructed in the essentials of classical mechanics, electricity and magnetism, quantum theory, statistical mechanics, and fractals in physics. Along the way, the authors provide ten short (10- to 20-line) BASIC programs to illustrate selected topics. There are discussion questions and conventional problems as well, but they do not make use of the computer. Written in a chatty, informal style sprinkled with off-center humor, the text may not appeal to all readers. (In the discussion of the motion of a top, one finds an illustration introduced with "For the reader whose youth was so occupied with video games that he [sic] had no time for such toys, Fig 1.15 shows a sketch of this experimental apparatus.") With its compact chapters, the book is not likely to be useful to the student learning quantum mechanics, or the other three standard topics, for the first time. At times, the short presentations are insufficient; the twin paradox of special relativity is mentioned, but not from the perspective of the rocketborne twin. However, the graduate student needing to review for qualifying examinations, and lacking the time to reread the standard texts, will find the book an admirable summary of theoretical physics. For example, in a spare 29 pages, the authors manage to discuss much of nonrelativistic quantum mechanics. They begin at the beginning with a discussion of why one needs the quantum theory, state the basic axioms, including the Schr6dinger equation, and then derive the Uncertainty Principle. The standard topics of barrier penetration, potential wells and energy quantization, the harmonic oscillator, angular momentum, and the hydrogen atom are quickly addressed. Finally, the essentials of timeindependent and -dependent perturbation theory are covered, including the Born approximation.
Some of the short programs are effective in building physical intuition in ways in which inspecting equations is not. After reading a derivation of the Euler equations for the rotation of a rigid body, we are treated to a numerical simulation of such a rotation. The user may choose the initial angular velocity about each principal axis; the motion is clearly unstable for a rotation about the principal axis of intermediate moment of inertia. Another program illustrates the Ising model of spontaneous magnetization, demonstrating the existence of the Curie temperature. With the addition of two lines, the program also nicely makes plausible the otherwise only axiomatic Boltzmann factor and partition function of statistical physics. One might wish for more powerful algorithms, graphical displays, and richer simulations, but refinements such as these are contrary to the spirit of a program written quickly to explore a new topic. Although the programs are supplied in the Apple lIe dialect of BASIC, I encountered few problems running them as listed under Microsoft Quick-BASIC for Macintosh. There were more (but still minor) syntax changes needed to run under TrueBASIC. The listings are devoid of comments, and make regl1lar use of GOTO statements, so are ill suited to be examples of modern programming style. The concluding chapter, which is accompanied by numerous color plates that are barely discussed, is an entertaining freestanding introduction to fractal systems in science. The reader will learn enough to nod knowingly when theoretical-physicist friends mention self-avoiding walks and diffusion-limited aggregation, but will almost certainly want to learn more from other, more detailed, accounts. Perhaps that is the point of the chapter, and more generally, the book. •
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