二维胶体液体中涡旋协同运动的位移关联张量计算
Calculation of displacement correlation tensor indicating vortical cooperative motion in two-dimensional colloidal liquids
摘要：
作为一个指标的合作运动在一个系统的布朗粒子模型的二维胶体液体，位移相关张量的解析计算和数值结果进行了比较。解析计算的核心思想是将位移关联张量（一种四点时空关联）与变形梯度张量的拉格朗日两时关联联系起来。张量处理的统计量，包括位移相关性本身，允许捕获的合作运动的旋涡结构。计算的位移相关性也暗示了速度自相关中的负长尾，这是笼效应的表现。位移相关性的纵向和横向分量都可以用相似性变量来表示，表明笼是嵌套的，在时空中形成自相似结构。
英文摘要：
As an indicator of cooperative motion in a system of Brownian particles that models two-dimensional colloidal liquids, displacement correlation tensor is calculated analytically and compared with numerical results. The key idea for the analytical calculation is to relate the displacement correlation tensor, which is a kind of four-point space-time correlation, to the Lagrangian two-time correlation of the deformation gradient tensor. Tensorial treatment of the statistical quantities, including the displacement correlation itself, allows capturing the vortical structure of the cooperative motion. The calculated displacement correlation also implies a negative longtime tail in the velocity autocorrelation, which is a manifestation of the cage effect. Both the longitudinal and transverse components of the displacement correlation are found to be expressible in terms of a similarity variable, suggesting that the cages are nested to form a self-similar structure in the space-time.
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