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