Thomas P. Weissert

The Genesis of Simulation in Dynamics

Pursuing the Fermi-Pasta-Ulam Problem

• Gebundenes Buch

Produktbeschreibung

This book introduces some aspects of the development of the modern theory of dynamics and simulation to a wide audience of scientifically literate readers and shows how it developed alongside the modern electronic computer. Unlike some other general texts on chaos theory and dynamical systems theory, this book follows the work on a specific problem at the very beginning of the modern era of dynamics, from its inception in 1954 through the early 1970s. It discusses such problems as the nonlinear oscillator simulation carried out by Fermi, Pasta, and Ulam at Los Alamos in the early 1950s; the mathematical rediscovery of solitons in the early 1960s; and the general problems of computability discussed by Kolmorogov, Arnold and Moser, by Ford, and by many others. In following these developments, one can see the initial development of many of the new and now standard techniques of nonlinear modeling and numerical simulation. No other text focuses so tightly and covers so completely one specific, pernicious problem at the heart of dynamics.

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We hear a lot about dynamical systems theory these days-"chaos dy namics" is the popular idiom-but very little of this abstract discipline is taught in undergraduate or even in graduate school, unless that happens to be one's own field. People may have heard some of the terms, but they may not understand what a dynamicist does. Just what does a dynamicist do? Although I've been through the training, I spend much more time talk ing and thinking about dynamics than actually doing it, which is a circum stance that affords me an interesting perspective. Some time after defending my dissertation, when I stopped back by my alma mater on a visit through Boulder, I ran into one of my advisors, a practicing dynamicist, and he was excited to show me his new workstation and its resident software. Hope fully, by relating what I experienced then, I may in part help to answer my opening question. He sat down in front of a very large screen, at least 19 inches across, so closely, that it filledhis field of view completely. At his fingertips were the usual mouse and keyboard. He fired up the software and chose a model; I think we were out to explore "just the standard map. " As the program began, the screen remained black, except for a small blinking cursor at the middle.

Produktdetails

• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-0-387-98236-6
• 1997.
• Seitenzahl: 194
• Erscheinungstermin: 10. Oktober 1997
• Englisch
• Abmessung: 241mm x 160mm x 15mm
• Gewicht: 428g
• ISBN-13: 9780387982366
• ISBN-10: 0387982361
• Artikelnr.: 09185843

Inhaltsangabe

I: History.- 1. The FPU Model and Simulation: "A Little Discovery".- 2. The FPU Research Program: Echoes on a String.- 3. The Kolmogorov-Arnold-Moser Theorem: "Here Comes the Surprise".- 4. Research Threads Come Together: Harmonic Convergence.- II: Philosophy.- 5. Steps to an Epistemology of Simulation.- Append.- A. Hamiltonian Dynamics: Language of Abstraction.- A.1. Topology and Phase-Space Trajectories.- A.2. Canonical Transformations.- A.3. Transforming the Unperturbed String.- A.4. Cyclic Coordinates.- A.5. Liouville Integrability.- A.6. The Action-Angle Variables.- A.7. Dynamics on a Torus.- A.8. Commensurability: Two Types of Motion.- A.9. Digital Representation.- A.10.Physical Reality and the Continuum.- A.11.Perturbing the String.- References.