Mankin Romi, Laas Katrin, Lumi Neeme
Institute of Mathematics and Natural Sciences, Tallinn University, 29 Narva Road, 10120 Tallinn, Estonia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Oct;88(4):042142. doi: 10.1103/PhysRevE.88.042142. Epub 2013 Oct 28.
The long-time limit behavior of the positional distribution for an underdamped Brownian particle in a fluctuating harmonic potential well, which is simultaneously exposed to an oscillatory viscoelastic shear flow is investigated using the generalized Langevin equation with a power-law-type memory kernel. The influence of a fluctuating environment is modeled by a multiplicative white noise (fluctuations of the stiffness of the trapping potential) and by an additive internal fractional Gaussian noise. The exact expressions of the second-order moments of the fluctuating position for the Brownian particle in the shear plane have been calculated. Also, shear-induced cross correlation between particle fluctuations along orthogonal directions as well as the angular momentum are found. It is shown that interplay of shear flow, memory, and multiplicative noise can generate a variety of cooperation effects, such as energetic instability, multiresonance versus the shear frequency, and memory-induced anomalous diffusion in the direction of the shear flow. Particularly, two different critical memory exponents have been found, which mark dynamical transitions from a stationary regime to a subdiffusive (or superdiffusive) regime of the system. Similarities and differences between the behaviors of the models with oscillatory and nonoscillatory shear flow are also discussed.
利用具有幂律型记忆核的广义朗之万方程，研究了在波动的谐振势阱中同时受到振荡粘弹性剪切流作用的欠阻尼布朗粒子位置分布的长时间极限行为。波动环境的影响通过乘性白噪声（捕获势刚度的波动）和加性内部分数高斯噪声来建模。计算了布朗粒子在剪切平面内波动位置的二阶矩的精确表达式。此外，还发现了沿正交方向的粒子波动之间以及角动量之间的剪切诱导互相关。结果表明，剪切流、记忆和乘性噪声之间的相互作用可以产生各种协同效应，如能量不稳定性、与剪切频率的多重共振以及在剪切流方向上的记忆诱导反常扩散。特别地，发现了两个不同的临界记忆指数，它们标志着系统从平稳状态到亚扩散（或超扩散）状态的动力学转变。还讨论了具有振荡和非振荡剪切流的模型行为之间的异同。
