Grebenkov Denis S, Vahabi Mahsa
Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, 91128 Palaiseau, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012130. doi: 10.1103/PhysRevE.89.012130. Epub 2014 Jan 21.
We consider a generalized Langevin equation that can be used to describe thermal motion of a tracer in a viscoelastic medium by accounting for inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. We derive a Laplace-type integral representation for the linear response function that governs the diffusive dynamics. This representation is particularly well suited for rapid numerical computation and theoretical analysis. In particular, we deduce explicit formulas for the mean and variance of the time averaged (TA) mean square displacement (MSD) and velocity autocorrelation function (VACF). The asymptotic behavior of the TA MSD and TA VACF is investigated at different time scales. Some biophysical and microrheological applications are discussed, with an emphasis on the statistical analysis of optical tweezers' single-particle tracking experiments in polymer networks and living cells.
我们考虑一个广义朗之万方程，通过考虑短时间内的惯性和流体动力学效应、中间时间的亚扩散标度以及长时间的最终光学捕获，该方程可用于描述示踪剂在粘弹性介质中的热运动。我们推导了控制扩散动力学的线性响应函数的拉普拉斯型积分表示。这种表示特别适合快速数值计算和理论分析。具体而言，我们推导出了时间平均（TA）均方位移（MSD）和速度自相关函数（VACF）的均值和方差的显式公式。在不同时间尺度下研究了TA MSD和TA VACF的渐近行为。讨论了一些生物物理和微观流变学应用，重点是聚合物网络和活细胞中光镊单粒子跟踪实验的统计分析。
