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The pulled Frenkel-Kontorova chain

S Slijepcevic

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Recommended by S Aubry

We model the pulling of an elastic chain in a potential 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


PACS

05.65.+b Self-organized systems

02.30.Em Potential theory

MSC

37E30 Homeomorphisms and diffeomorphisms of planes and surfaces

37E45 Rotation numbers and vectors

37E40 Twist maps

Subjects

Mathematical physics

Statistical physics and nonlinear systems

Dates

Issue 4 (July 1998)

Received 18 August 1997, in final form 17 February 1998



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