Coulomb Friction Driving Brownian Motors

Abstract

We review a family of models recently introduced to describe Brownian motors under the influence of Coulomb friction, or more general non-linear friction laws. It is known that, if the heat bath is modeled as the usual Langevin equation (linear viscosity plus white noise), additional non-linear friction forces are not sufficient to break detailed balance, i.e. cannot produce a motor effect. We discuss two possibile mechanisms to elude this problem. A first possibility, exploited in several models inspired to recent experiments, is to replace the heat bath's white noise by a "collisional noise", that is the effect of random collisions with an external equilibrium gas of particles. A second possibility is enlarging the phase space, e.g. by adding an external potential which couples velocity to position, as in a Klein-Kramers equation.In both cases, non-linear friction becomes sufficient to achieve a non-equilibrium steady state and, in the presence of an even small spatial asymmetry, a motor effect is produced.

Entropy production for velocity-dependent macroscopic forces: The problem of dissipation without fluctuations

“…In fig. 2 we compare the trajectories from a simulation of the macroscopic model ( 6) and a simulation of the microscopic one (10). The figure fairly demonstrates that the trajectories look quite similar if small details (as in the inset) are ignored.…”

“…When giving the parameters of simulations, we take as unit of mass M , unit of time τ and unit of length λ = k B T g /M τ (that is unit of energy k B T g ). In Figure 2 we compare the trajectories from a simulation of the macroscopic model ( 6) and a simulation of the microscopic one (10). The figure fairly demonstrates that the trajectories look quite similar if small details (as in the inset) are ignored.…”

“…We take into detailed con-sideration the force acting between two sliding solid bodies, that is the so-called dry friction, which in macroscopic systems (e.g. on scales larger than few millimeters) is well described by the law of Coulomb friction [9][10][11]. In our analysis it becomes clear that the Coulomb model is too much coarse-grained and, for this reason, it neglects the dominant contribution to the FEP [12,13].…”

“…In that case, provided that k T ≪ κL 2 /2 < 2π 2 U 0 , the stationary state is a quasi-periodic stick slip motion where, in a range of velocity v 0 ≫ U 0 /M , the average friction force F P T has a negligible (logarithmic or smaller) dependence upon v 0 . In our model (10) the velocity of the first mass is not constant but feels the slowing effect of F P T and, at random times, is instantaneously changed with probability rates given by Eq. ( 7), i.e.…”

Diffusion Properties of a Brownian Ratchet with Coulomb Friction

“…Other studies have focused on the issues related to the definition of entropy production in these systems [16]. In the specific context of models of Brownian motors, the role of Coulomb friction as a source of non-equilibrium able to induce a ratchet effect has also been investigated in different systems [7,17,18], with experimental realizations in the context of driven granular gases [19,20].…”