Brownian motion with dry friction: Fokker-Planck approach
Brownian motion with dry friction: Fokker-Planck approach
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DOI：
10.1088/1751-8113/43/44/445002
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发表时间：
2010-11-05
影响因子：
2.1
通讯作者：
Just, Wolfram
中科院分区：
文献类型：
--
作者：
Touchette, Hugo;Van der Straeten, Erik;Just, Wolfram
我们解决了朗之万方程，首先研究了德Gennes，其中有一个固体固体或干摩擦力作用在布朗粒子上，除了粘性摩擦通常认为在布朗运动的研究。通过求解相应的含时Fokker-Planck方程，我们得到了该方程的含时传播子和速度相关函数。精确的结果被发现的情况下，只有干摩擦作用在颗粒上。对于干摩擦力和粘性摩擦力都存在的情况下，传播函数和相关函数的级数表示的抛物柱面函数。类似的级数表示也得到的情况下，外部恒定的力被添加到朗之万方程。
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 the study of Brownian motion. We obtain both the time-dependent propagator of this equation and the velocity correlation function by solving the associated time-dependent Fokker-Planck equation. Exact results are found for the case where only dry friction acts on the particle. For the case where both dry and viscous friction forces are present, series representations of the propagator and correlation function are obtained in terms of parabolic cylinder functions. Similar series representations are also obtained for the case where an external constant force is added to the Langevin equation.