The pulled Frenkel-Kontorova chain

摘要

We model the pulling of an elastic chain in apotential as a slow-fast system using dissipative dynamics, and prove that the dynamics is monotone. If the potential is periodic (the Frenkel-Kontorova model), we show the existence of the adiabatic (slow pulling) limit, describe completely the trajectory of the chain in the limit as a family of orbits of a twist diffeomorphism, and prove the existence of avalanches. Similarities with some self-organized criticality models are discussed.PACS Number: 6390