Mankin Romi, Laas Katrin, Lumi Neeme, Rekker Astrid
Institute of Mathematics and Natural Sciences, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Oct;90(4):042127. doi: 10.1103/PhysRevE.90.042127. Epub 2014 Oct 20.
The long-time limit behavior of velocity correlation functions (VCFs) for an underdamped Brownian particle in an oscillatory viscoelastic shear flow is investigated using the generalized Langevin equation with a power-law memory kernel. The influence of a fluctuating environment is modeled by an additive external fractional Gaussian noise. The exact expressions of the correlation functions of the fluctuating components of velocity for the Brownian particle in the shear plane have been calculated. Also, the particle's angular momentum is found. It is shown that in a certain region of the system parameters an interplay of the shear flow, memory effects, and external noise can induce a bounded long-time behavior of the VCFs, even in the shear flow direction, where in the case of internal noise the velocity process is subdiffusive, i.e., unbounded in time. Moreover, we find resonant behavior of the VCFs and the angular momentum versus the shear oscillation frequency, implying that they can be efficiently excited by oscillatory shear. The role of the initial positional distribution of particles is also discussed.
利用具有幂律记忆核的广义朗之万方程，研究了欠阻尼布朗粒子在振荡粘弹性剪切流中速度相关函数（VCFs）的长时间极限行为。波动环境的影响通过加性外部分数高斯噪声来建模。已计算出布朗粒子在剪切平面中速度波动分量相关函数的精确表达式。此外，还求出了粒子的角动量。结果表明，在系统参数的特定区域内，剪切流、记忆效应和外部噪声的相互作用可导致VCFs出现有界的长时间行为，即使在剪切流方向上也是如此，而在内部噪声情况下，速度过程是次扩散的，即在时间上是无界的。此外，我们发现VCFs和角动量相对于剪切振荡频率存在共振行为，这意味着它们可以被振荡剪切有效地激发。还讨论了粒子初始位置分布的作用。
