Avalanches in the weakly driven Frenkel-Kontorova model

Abstract

A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly, which acts as a weak driving mechanism. The numerical study was performed in the limit of infinitely weak driving. The model exhibits avalanches starting at the pulled end of the chain. The dynamics of the avalanches and their size and strength distributions are studied in detail. The behavior depends on the value of the damping constant. For moderate values an erratic sequence of avalanches of all sizes occurs. The avalanche distributions are power laws, which are a key feature of self-organized criticality. It will be shown that the system selects a state where perturbations are just able to propagate through the whole system. For large damping a regular behavior occurs, where a sequence of states reappears periodically but shifted by an integer multiple of the period of the external potential. There is a broad transition regime between regular and irregular behavior, which is characterized by multistability between regular and irregular behavior. The avalanches are built up by sound waves and shock waves. Shock waves can change their direction of propagation, or they can split into two pulses propagating in opposite directions leading to transient spatiotemporal chaos.