Talbot Julian, Viot Pascal
Laboratoire de Physique Théorique de la Matière Condensée, UPMC, CNRS UMR 7600, 4, place Jussieu, 75252 Paris Cedex 05, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Feb;85(2 Pt 1):021310. doi: 10.1103/PhysRevE.85.021310. Epub 2012 Feb 29.
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.
我们研究了干摩擦对一个质量为M、由两种材料组成的不对称颗粒活塞的影响，该活塞与质量为m的浴粒子发生非弹性碰撞。玻尔兹曼-洛伦兹方程的数值模拟揭示了根据摩擦强度存在两种标度律。在大摩擦极限下，我们引入了一个精确模型来给出玻尔兹曼-洛伦兹方程的渐近行为。对于小摩擦和大质量比M/m，我们推导了一个福克-普朗克方程，并且也得到了其精确解。静摩擦会减弱电机效应并导致速度分布不连续。
