The Fermi-Pasta-Ulam (FPU) problem, 1 first written up in a Los Alamos report in May 1955, marked the beginning of both a new field, nonlinear physics, and the age of computer simulations of scientific problems. The idea was to simulate the one-dimensional analogue of atoms in a crystal: a long chain of masses linked by springs that obey Hooke’s law (a linear interaction), but with a weak nonlinear term. A purely linear interaction would ensure that energy introduced into a single Fourier vibrational mode always remains in that mode; the nonlinear term allows the transfer of energy between modes. Under certain conditions, the weakly nonlinear system exhibits surprising behavior: The energy does not drift toward the equipartition predicted by statistical physics but periodically returns to the original mode. That highly remarkable result, known as the FPU paradox, shows that nonlinearity is not enough to guarantee the equipartition of energy.

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