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Seminario Dottorato: The Fermi Pasta Ulam Paradox: An Introduction to the problem and its recent developments

Wednesday 1 February 2012 - Eleni Christodoulidi

ARGOMENTI: Seminari Dottorato

SEMINARIO DOTTORATO
Wednesday 1 February 2012 h. 15:00, room 2BC30
Eleni Christodoulidi (Padova, Dip. Mat.)
"The Fermi Pasta Ulam Paradox: An Introduction to the problem and its recent developments"

-Abstract
In 1950's Fermi, motivated by fundamental questions of statistical mechanics and by ergodic properties of nonlinear dynamical systems, started a numerical experiment on a nonlinear toy model, in collaboration with Pasta and Ulam. The system was chosen to be a one dimensional chain of N nonlinear coupled oscillators, described by a quadratic potential of nearby particle interactions plus a cubic perturbation. Fermi's ergodic hypothesis states that a system under an arbitrarily small perturbing force becomes generically ergodic. Giving initial conditions to the so called FPU system on the longest wavelength normal modes, the system showed a contradicting and integrable-like behaviour. Many pioneer works followed for the explanation of this paradox, more prominent of them being the approximation of FPU dynamics in the thermodynamic limit by the integrable partial differential equation Korteweg-de Vries by Zabusky and Kruskal (1965), and the work of Flaschka et al. (1982), where the authors observed the vicinity of the integrable one dimensional Toda chain with the FPU model. Recent developments show a more complete picture of the problem and its explanation.

Rif. int. C. Marastoni, T. Vargiolu

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