Dynamics of undulatory fluctuations of semiflexible filaments in a network
Dynamics of undulatory fluctuations of semiflexible filaments in a network
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DOI：
10.1103/physreve.102.062406
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发表时间：
2020-12-03
影响因子：
2.4
通讯作者：
Levine, Alex J.
中科院分区：
文献类型：
--
作者：
Kernes, Jonathan;Levine, Alex J.
我们研究了单根半柔性细丝在其边界处与Hookean弹簧耦合的动力学。弹簧对灯丝产生波动的拉力，其大小取决于灯丝的瞬时端到端长度。因此，弹簧引入了一种非线性，它混合了灯丝的起伏的简正模式，并改变了它们的动力学。我们用Martin-Siggia-Rose-Janssen-de Dominicis形式研究了这些动力学，计算了横向起伏和灯丝端到端距离随时间变化的关联函数。由纤维的弯曲模数kappa和弹簧重整化张力tau(R)设置的特征波长根部kappa/tau(R)以下的模式的松弛动力学被边界弹簧改变。这发生在系统以拉伸和弯曲为主的模式之间的交叉频率附近。边界弹簧可以用来表示细丝网络的其余部分的线弹性柔量，细丝被交联到该网络上。因此，我们预测这种非线性效应将在网络组成细丝的动力学关联和网络的集体剪切响应中观察到。系统的动态剪切模数预计将呈现出众所周知的交叉，频率从omega(1/2)到omega(3/4)，但在单丝动力学分析中包含网络的顺应性将这种转变转移到更高的频率。
We study the dynamics of a single semiflexible filament coupled to a Hookean spring at its boundary. The spring produces a fluctuating tensile force on the filament, the value of which depends on the filament's instantaneous end-to-end length. The spring thereby introduces a nonlinearity, which mixes the undulatory normal modes of the filament and changes their dynamics. We study these dynamics using the Martin-Siggia-Rose-Janssen-De Dominicis formalism, and compute the time-dependent correlation functions of transverse undulations and of the filament's end-to-end distance. The relaxational dynamics of the modes below a characteristic wavelength root kappa/tau(R), set by the filament's bending modulus kappa and spring-renormalized tension tau(R), are changed by the boundary spring. This occurs near the crossover frequency between tension- and bending-dominated modes of the system. The boundary spring can be used to represent the linear elastic compliance of the rest of the filament network to which the filament is cross linked. As a result, we predict that this nonlinear effect will be observable in the dynamical correlations of constituent filaments of networks and in the networks' collective shear response. The system's dynamic shear modulus is predicted to exhibit the well-known crossover with increasing frequency from omega(1/2) to omega(3/4), but the inclusion of the network's compliance in the analysis of the individual filament dynamics shifts this transition to a higher frequency.