3 research outputs found
Stick-slip motion of solids with dry friction subject to random vibrations and an external field
We investigate a model for the dynamics of a solid object, which moves over a
randomly vibrating solid surface and is subject to a constant external force.
The dry friction between the two solids is modeled phenomenologically as being
proportional to the sign of the object's velocity relative to the surface, and
therefore shows a discontinuity at zero velocity. Using a path integral
approach, we derive analytical expressions for the transition probability of
the object's velocity and the stationary distribution of the work done on the
object due to the external force. From the latter distribution, we also derive
a fluctuation relation for the mechanical work fluctuations, which incorporates
the effect of the dry friction.Comment: v1: 23 pages, 9 figures; v2: Reference list corrected; v3: Published
version, typos corrected, references adde
Brownian motion with dry friction: Fokker-Planck approach
We solve a Langevin equation, first studied by de Gennes, in which there is a
solid-solid or dry friction force acting on a Brownian particle in addition to
the viscous friction usually considered in the study of Brownian motion. We
obtain both the time-dependent propagator of this equation and the velocity
correlation function by solving the associated time-dependent Fokker-Planck
equation. Exact results are found for the case where only dry friction acts on
the particle. For the case where both dry and viscous friction forces are
present, series representations of the propagator and correlation function are
obtained in terms of parabolic cylinder functions. Similar series
representations are also obtained for the case where an external constant force
is added to the Langevin equation.Comment: 18 pages, 13 figures (in color
Path integral approach to random motion with nonlinear friction
Using a path integral approach, we derive an analytical solution of a
nonlinear and singular Langevin equation, which has been introduced previously
by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion
of a solid object on a vibrating horizontal surface. We show that the optimal
(or most probable) paths of this model can be divided into two classes of
paths, which correspond physically to a sliding or slip motion, where the
object moves with a non-zero velocity over the underlying surface, and a
stick-slip motion, where the object is stuck to the surface for a finite time.
These two kinds of basic motions underlie the behavior of many more complicated
systems with solid/solid friction and appear naturally in de Gennes' model in
the path integral framework.Comment: 18 pages, 3 figure