On The Brink Of Chaos: Study Of Fermi-Pasta-Ulam Effects In 2D

This work represents an extended computational study of the Fermi-Pasta-Ulam experiment for the dynamical nature of energy transfer among normal modes. A 2D lattice system with 40 particles is placed on a torus, where each particle is allowed to interact with its six nearest neighbors under the Lennard-Jones potential force law. Trajectories of the particles are analyzed through a Fourier transform method that calculates the amplitude and phase of each normal mode as a function of time. Results of the normal mode analyses and basic applications of the Lyapunov exponents show that Fermi-Pasta-Ulam effects are absent at small and large extremes of amplitude displacements. At an intermediate amplitude displacement, quasi-periodic behavior of the phase is seen initially and a secondary normal mode dominates the first one at irregular intervals. However, contrary to prediction, the system eventually reaches limited thermalization. This behavior resembles but is not characteristic of classical FPU effects.