The Fermi-Pasta-Ulam problem: Simulation and modern dynamics
In 1952, Enrico Fermi, John Pasta and Stanislaw Ulam (FPU) simulated the loaded string model, perturbed with small, nonlinear interaction terms. Because Poincare's theorem guarantees the non-existence of a complete set of integrals for three-body problem, they expected to see the diffusion of energy from its single-mode initial condition to all other modes of the string. But for every combination of initial conditions, the energy remained bounded within the lowest few modes. No theoretical explanation existed for this failure of the underlying hypothesis that erogidicity follows from the lack of a complete set of integrals of the motion in a Hamiltonian model. The author traces the history of this problem from the FPU simulation to the point that a consensus was reached concerning its solution twenty years later. During this period, the simulation of nonlinearly-perturbed integral models became the methodology for a new era in dynamics. Through the use of simulation, dynamicists discovered deterministic chaos, in which the exponential separation of pair orbits generate randomness in deterministic macroscopic systems, and a new kind of structure-related to the KAM theorem-that provides limited order in the absence of analytic integrals of the motions. The author maps the set of conceptually-related journal articles into a chronological inference topology that tracks the understanding of this problem of dynamics. Simulating non-integrable models on a digital computer requires the discretization of time and space. These approximations affect what the simulation can reveal about the model, and the model about reality. Simulations play the role of experiments on mathematical models. A discussion is presented of the issues that emerge with the use of simulation as a heuristic device and the groundwork is laid for an epistemology of simulation.
- Research Organization:
- Colorado Univ., Boulder, CO (United States)
- OSTI ID:
- 5145113
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
NONLINEAR PROBLEMS
HISTORICAL ASPECTS
STRING MODELS
COMPUTERIZED SIMULATION
COMPOSITE MODELS
EXTENDED PARTICLE MODEL
MATHEMATICAL MODELS
PARTICLE MODELS
QUARK MODEL
SIMULATION
662110* - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)