Frenkel-Kontorova-Tomlinson Model for Sliding Friction
![](/img/demonstrations-branding.png)
Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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.
Contributed by: Enrique Zeleny (September 2012)
Open content licensed under CC BY-NC-SA
Snapshots
Details
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.
Permanent Citation