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The Genesis of Simulation in Dynamics: Pursuing the Fermi-Pasta-Ulam Problem

by Weissert, Thomas P. A

  • ISBN: 9780387982373
  • ISBN10: 038798237X

The Genesis of Simulation in Dynamics: Pursuing the Fermi-Pasta-Ulam Problem

by Weissert, Thomas P. A

  • List Price: $36.95
  • Binding: Paperback
  • Publisher: Springer-Verlag
  • Publish date: 10/01/1997
  • ISBN: 9780387982373
  • ISBN10: 038798237X
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Description: I: History.- 1. The FPU Model and Simulation: "A Little Discovery".- 1.1. Development.- 1.2. Dynamics to Statistical Mechanics.- 1.3. Surfaces of Constraint.- 1.4. Global Versus Local Analysis.- 1.5. Simulation.- 1.6. Loading the Nonlinear String.- 1.7. Modal Representation.- 1.8. Model Considerations.- 1.9. Results.- 1.10. Discussion Post Hoc.- 2. The FPU Research Program: Echoes on a String.- 2.1. The Threads of a Research Program.- 2.2. The Nonlinear Discrete Lattice.- 2.3. Ford, 1961.- 2.4. Jackson, 1963.- 2.5. Ford and Waters, 1963.- 2.6. The Continuous String.- 2.7. In the Continuous Limit.- 2.8. Discreteness as Viscosity.- 2.9. The First Soliton Paper.- 3. The Kolmogorov--Arnold--Moser Theorem: "Here Comes the Surprise".- 3.1. A Brief History of Dynamics.- 3.2. The Fundamental Problem of Dynamics.- 3.3. The Small Divisors Problem.- 3.4. Poincar to Kolmogorov.- 3.5. The Conjecture.- 3.6. Beyond the Blaze.- 3.7. The Hnon and Heiles Simulation, 1964.- 4. Research Threads Come Together: Harmonic Convergence.- 4.1. The Story Continues.- 4.2. Izrailev and Chirikov, 1966.- 4.3. Zabusky and Deem, 1967.- 4.4. Walker and Ford, 1969: Physical Review.- 4.5. Ford and Lunsford, 1970.- 4.6. Lunsford and Ford, 1972.- 4.7. The Toda Lattice Is Integrable.- II: Philosophy.- 5. Steps to an Epistemology of Simulation.- 5.1. Introduction.- 5.2. Hierarchy of Modeling.- 5.3. Historical Significance.- 5.4. Experiment.- 5.5. Epistemology.- 5.6. Preconceptions.- 5.7. Strategies for Belief and Pursuit.- 5.8. Case Study I: Fermi--Pasta--Ulam.- 5.9. Case Study II: Hnon and Heiles.- 5.10. Methodology.- 5.11. Irreversibility.- 5.12. Proof.- 5.13. Proof and 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.
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