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Frenkel-Kontorova-Tomlinson Model for Sliding Friction

The Frenkel–Kontorova–Tomlinson model is used to study the interface between two rigid sliding bodies. It consists of a chain of equal particles of mass connected by springs of strengths and damping force proportional to velocity. Each mass is coupled with a spring to the body at the top that moves at constant velocity . The interaction with the body at the bottom is represented with a periodic potential of amplitude , with equal to the ratio of lattice constants. Open boundary conditions are used.

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The equations of motion are
,
where is the position of the particle relative to its equilibrium position.
References
[1] M. Weiss and F. Elmer, "Dry Friction in the Frenkel–Kontorova–Tomlinson Model: Dynamical Properties." arxiv.org/abs/cond-mat/9704110.
[2] O. Braun and Y. Kivshar, The Frenkel–Kontorova Model: Concepts, Methods, and Applications, New York: Springer, 2004.
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