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Nonlinearity, Complexity and Foundations in Mathematics

Burgers equation and the Fermi-Pasta-Ulam-Tsingou lattice

speaker: Stefano Ruffo (Scuola Internazionale Superiore di Studi Avanzati )

abstract: The study of thermalization processes in isolated systems is of broad interest.

It was pioneered by Fermi-Pasta-Ulam-Tsingou (FPUT), who discovered the “paradoxical” absence

of thermalization in a one-dimensional lattice of coupled nonlinear oscillators.

In this talk I will present a new avenue towards the understanding of thermalization,

the presence of a power-law in the Fourier energy spectrum. A universal scaling exponent is obtained

by mapping the FPUT model onto a pair of Burgers equations. Energy is transferred to higher Fourier modes

like in “Burgers turbulence”, while a ``shock” develops on the lattice, and only at much longer

times the systems reaches energy equipartition.

timetable:
Thu 12 Sep, 18:20 - 18:55, Aula Dini
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