聚合物膜的动力学本征模
Dynamical Eigenmodes of a Polymerized Membrane
摘要：
我们研究了在过阻尼极限下聚合体膜的珠-弹簧模型，它是著名的聚合物Rouse模型的二维推广。我们推导出膜动力学的{ \it精确}本征模（“劳斯模式”）。这使我们能够获得精确的解析表达式几乎任何平衡或动态量的膜。作为例子，我们确定的回转半径，均方位移的标记珠，和两个标记珠之间的差异矢量的自相关函数。有趣的是，即使在存在任何大小的拉力的情况下，劳斯模式仍然是膜的精确本征模式。随着更强的力量，膜变得基本上是平的，并没有机会相交本身，在这种情况下，我们的分析提供了一个有用的和精确的解决方案的动态下一个现实的模型平面膜张力。
英文摘要：
We study the bead-spring model for a polymerized phantom membrane in the overdamped limit, which is the two-dimensional generalization of the well-known Rouse model for polymers. We derive the {\it exact} eigenmodes of the membrane dynamics (the "Rouse modes"). This allows us to obtain exact analytical expressions for virtually any equilibrium or dynamical quantity for the membrane. As examples we determine the radius of gyration, the mean square displacement of a tagged bead, and the autocorrelation function of the difference vector between two tagged beads. Interestingly, even in the presence of tensile forces of any magnitude the Rouse modes remain the exact eigenmodes for the membrane. With stronger forces the membrane becomes essentially flat, and does not get the opportunity to intersect itself; in such a situation our analysis provides a useful and exactly soluble approach to the dynamics for a realistic model flat membrane under tension.
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