Energy sharing and near-recurrence in nonlinear chains
Particle chain displacement
Normal mode energies (Fourier)
In 1953, Fermi, Pasta, Ulam and Tsingou simulated a nonlinear chain expecting energy to thermalize (spread to all modes). Instead they found near-perfect recurrence — energy kept returning to the initial mode. This "FPU problem" launched the field of nonlinear dynamics and soliton theory. The FPU-α model has forces F = k(Δx + α·Δx²). At small α, the system is quasi-periodic; at large α, chaos and eventual equipartition emerge.