Time asymmetry of the Kramers equation with nonlinear friction: fluctuation-dissipation relation and ratchet effect.

@article{Sarracino2013TimeAO,
  title={Time asymmetry of the Kramers equation with nonlinear friction: fluctuation-dissipation relation and ratchet effect.},
  author={Alessandro Sarracino},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2013},
  volume={88 5},
  pages={
          052124
        }
}
  • A. Sarracino
  • Published 4 November 2013
  • Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
We show by numerical simulations that the presence of nonlinear velocity-dependent friction forces can induce a finite net drift in the stochastic motion of a particle in contact with an equilibrium thermal bath and in an asymmetric periodic spatial potential. In particular, we study the Kramers equation for a particle subjected to Coulomb friction, namely a constant force acting in the direction opposite to the particle's velocity. We characterize the nonequilibrium irreversible dynamics by… 
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References

SHOWING 1-10 OF 72 REFERENCES

Ratchet effect driven by Coulomb friction: the asymmetric Rayleigh piston.

It is illustrated in the asymmetric Rayleigh piston, showing how Coulomb friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath as well as an explicit analytical expression for the average velocity of the piston in the rare collision limit.

Kinetics of a frictional granular motor.

In the large friction limit, the exact solution of a model corresponding to asymptotic behavior of the Boltzmann-Lorentz equation is obtained, and in the limit of large rotor mass and small friction, a Fokker-Planck equation is derived.

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…

Singular features in noise-induced transport with dry friction

We present an exactly solvable nonlinear model for the directed motion of an object due to zero-mean fluctuations on a uniform featureless surface. Directed motion results from the effect of dry…

Granular Brownian motion with dry friction

The interplay between Coulomb friction and random excitations is studied experimentally by means of a rotating probe in contact with a stationary granular gas. The granular material is independently…

Exact power spectra of Brownian motion with solid friction

We study a Langevin equation describing the Brownian motion of an object subjected to a viscous drag, an external constant force and a solid friction force of the Coulomb type. In a previous work…

Nonlinear dissipation effect in Brownian relaxation.

  • A. PlyukhinA. Froese
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
In an ensemble of noninteracting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially, from a small nonlinear correction to the dissipative force.

Brownian ratchet in a thermal bath driven by Coulomb friction.

A new ratchet mechanism where a thermal bath solicits the random rotation of an asymmetric wheel, which is also subject to Coulomb friction due to solid-on-solid contacts is proposed, paving the way to the realization of micro and submicrometer Brownian motors in an equilibrium fluid, based purely upon nanofriction.

A Gallavotti–Cohen-Type Symmetry in the Large Deviation Functional for Stochastic Dynamics

We extend the work of Kurchan on the Gallavotti–Cohen fluctuation theorem, which yields a symmetry property of the large deviation function, to general Markov processes. These include jump processes…

Non-linear Brownian motion: the problem of obtaining the thermal Langevin equation for a non-Gaussian bath

The non-linear dissipation corresponding to a non-Gaussian thermal bath is introduced together with a multiplicative white noise source in the phenomenological Langevin description for the velocity…
...