Thomas P. Weissert

The Genesis of Simulation in Dynamics (eBook, PDF)

Pursuing the Fermi-Pasta-Ulam Problem

• Format: PDF

Produktbeschreibung

An introduction to certain aspects of developments in the modern theory of dynamics and simulation for a wide audience of scientifically literate readers. Unlike 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, the seminal discoveries at MIT in the early 1950s, the mathematical rediscovery of solitons in the late 1950s and the general problems of computability. In following these developments, the initial development of many of the now standard techniques of nonlinear modelling and numerical simulation are seen. No other text focuses so tightly and covers so completely one specific, pernicious problem at the heart of dynamics.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 176
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461219569
• Artikelnr.: 44184932

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.