Analysis of a class of granular motors in the brownian limit

Attractor nonequilibrium stationary states in perturbed long-range interacting systems

Isolated long-range interacting particle systems appear generically to relax to nonequilibrium states ("quasistationary states" or QSSs) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one-dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSSs we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique nonequilibrium stationary state, completely different from its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g., spatial density or velocity distribution) of the system itself.

Fluctuation theorems for an asymmetric rotor in a granular gas

We investigate the validity of fluctuation theorems for an asymmetric rotor experiment in a granular gas. A first state, with a Gaussian distribution of the angular velocity, is found to be well described by a first order Langevin equation. We show that fluctuation theorems are valid for the injected work and for the total entropy production. In a second state, the angular velocity distribution is double peaked due to a spontaneous symmetry breaking: A convection roll develops in the granular gas, which strongly couples to the rotor. Surprisingly, in this case, similar symmetry relations hold, which lead to a good prediction for the height ratio of the two peaks.

Momentum transfer in nonequilibrium steady states

When a Brownian object interacts with noninteracting gas particles under nonequilibrium conditions, energy dissipation associated with Brownian motion causes an additional force on the object as a "momentum transfer deficit." This principle is demonstrated first by a new nonequilibrium steady state model and then applied to several known models such as an adiabatic piston for which a simple explanation has been lacking.

Effect of dynamic and static friction on an asymmetric granular piston

We investigate the influence of dry friction on an asymmetric, granular piston of mass M, composed of two materials, undergoing inelastic collisions with bath particles of mass m. Numerical simulations of the Boltzmann-Lorentz equation reveal the existence of two scaling regimes depending on the friction strength. In the large friction limit, we introduce an exact model giving the asymptotic behavior of the Boltzmann-Lorentz equation. For small friction and for large mass ratio M/m, we derive a Fokker-Planck equation for which the exact solution is also obtained. Static friction attenuates the motor effect and results in a discontinuous velocity distribution.

Kinetics of a frictional granular motor

Within the framework of a Boltzmann-Lorentz equation, we analyze the dynamics of a granular rotor immersed in a bath of thermalized particles in the presence of a frictional torque on the axis. In numerical simulations of the equation, we observe two scaling regimes at low and high bath temperatures. In the large friction limit, we obtain the exact solution of a model corresponding to asymptotic behavior of the Boltzmann-Lorentz equation. In the limit of large rotor mass and small friction, we derive a Fokker-Planck equation for which the exact solution is also obtained.