Stick-slip motion of solids with dry friction subject to random vibrations and an external field
arXiv:1008.3531 · doi:10.1088/0951-7715/24/2/001
Abstract
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.
arXiv commentv1: 23 pages, 9 figures; v2: Reference list corrected; v3: Published version, typos corrected, references added
References in corpus (15)
- The large deviation approach to statistical mechanics
- Dynamical Ensembles in Nonequilibrium Statistical Mechanics
- A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
- Fluctuation theorem for stochastic dynamics
- Fluctuation theorems for stochastic dynamics
- Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle
- Power and heat fluctuation theorems for electric circuits
- Injected Power Fluctuations in Langevin Equation
- Nonlinear Dynamics of Dry Friction
- Observable and hidden singular features of large fluctuations in nonequilibrium systems
- Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems
- Langevin equation with Coulomb friction
- Fluctuation properties of an effective nonlinear system subject to Poisson noise
- Path integral approach to random motion with nonlinear friction
- Nonequilibrium steady state thermodynamics and fluctuations for stochastic systems
Cited by in corpus (25)
- Tuned, driven, and active soft matter
- Entropic bounds on currents in Langevin systems
- Large deviations conditioned on large deviations I: Markov chain and Langevin equation
- Clausius relation for active particles: what can we learn from fluctuations?
- Kinetics of a frictional granular motor
- Granular Brownian motion with dry friction
- Singular features in noise-induced transport with dry friction
- Time asymmetry of the Kramers equation with nonlinear friction: fluctuation-dissipation relation and ratchet effect
- Ratchet effect driven by Coulomb friction: the asymmetric Rayleigh piston
- Weak-noise limit of a piecewise-smooth stochastic differential equation
- Exact power spectra of Brownian motion with solid friction
- Roles of Dry Friction in Fluctuating Motion of Adiabatic Piston
- Rectification of asymmetric surface vibrations with dry friction: an exactly solvable model
- Nonequilibrium dynamics of a pure dry friction model subjected to coloured noise
- First-passage time of Brownian motion with dry friction
- Effect of dynamic and static friction on an asymmetric granular piston
- Most probable transition paths in piecewise-smooth stochastic differential equations
- Entropy production for velocity-dependent macroscopic forces: the problem of dissipation without fluctuations
- On large deviation properties of Brownian motion with dry friction
- Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed
- Response function of turbulence computed via fluctuation-response relation of a Langevin system with vanishing noise
- Single Particle Brownian Motion with Solid Friction
- Numerical solutions of Fokker-Planck equations with drift-admitting jumps
- Thermodynamic uncertainty relations in the presence of non-linear friction and memory
- Diffusion Properties of a Brownian Ratchet with Coulomb Friction