随机驱动的Prandtl-Tomlinson摩擦模型
The Prandtl-Tomlinson model of friction with stochastic driving
摘要：
我们考虑经典的Prandtl-Tomlinson模型，粒子在波纹势上运动，受弹簧牵引。在通常情况下，拉力以恒定速度$\dotγ$作用，模型显示与$\dotγ$相关的平均摩擦力$σ$（对于小$\dotγ)$为$\dotγ\sim (σ-σ_c)^β$，其中$σ_c$是临界摩擦力。根据波纹势的分析性质，$β$的可能值是众所周知的。我们在这里研究的情况下，在拉，除了恒定的速度项，一个随机项的机械起源（即，总驱动是一个功能的$\dotγt$）。我们分析表明，这一项如何修改的力-速度的依赖性接近临界力，并给出的值$β$的分析性质的潜在的随机驱动的标度特性，编码在其赫斯特指数的值。
英文摘要：
We consider the classical Prandtl-Tomlinson model of a particle moving on a corrugated potential, pulled by a spring. In the usual situation in which pulling acts at constant velocity $\dotγ$, the model displays an average friction force $σ$ that relates to $\dotγ$ (for small $\dotγ)$ as $\dotγ\sim (σ-σ_c)^β$, where $σ_c$ is a critical friction force. The possible values of $β$ are well known in terms of the analytical properties of the corrugated potential. We study here the situation in which the pulling has, in addition to the constant velocity term, a stochastic term of mechanical origin (i.e, the total driving is a function of $\dotγt$). We analytically show how this term modifies the force-velocity dependence close to the critical force, and give the value of $β$ in terms of the analytical properties of the corrugation potential and the scaling properties of the stochastic driving, encoded in the value of its Hurst exponent.
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