Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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MPI Kolloquium

Thursday, 02.06.2005 17 c.t.

The Fermi-Pasta-Ulam Problem: A Watershed in Computational and Nonlinear Physics

by Prof. Dr. David K. Campbell
from Boston University, USA

Contact person: Theo Geisel

Location

Seminarraum Haus 2, 4. Stock (Bunsenstr.)

Abstract

This year marks the 50th anniversary of the publication of a Los Alamos preprint modestly entitled “Studies of Nonlinear Problems: I” and written by Enrico Fermi, John Pasta, and Stan Ulam. Now universally known as the “FPU Problem,” this investigation produced results characterized by Fermi as a “little discovery” and was a in fact a defining event in computational and nonlinear physics. It marked the first systematic study of a nonlinear system by digital computers (“experimental mathematics”) and led directly to the development of the concept of “solitons” and indirectly to the modern understanding of “deterministic chaos.” On the occasion of its 50th anniversary, it is timely to review the origins, examine the present intellectual descendants, and predict the future implications of this watershed problem. Beginning with a discussion of the nature of the FPU problem and the results of the original simulations, including the remarkable “FPU recurrences,” I show how a continuum limit analysis clarifies the nature of these recurrences and leads directly to the equations to which the concept of solitons was first applied. I next establish the existence of deterministic chaos in the FPU problem and discuss briefly recent attempts to clarify the transition between the solitonic and chaotic regimes. I close by discussing the consequences of the interplay between solitons and chaos for several outstanding problems in physics, including anomalous heat transport in FPU-like model systems and real low-dimensional materials, “intrinsic localized modes,” and the origins of statistical mechanics.

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