论文标题
网络中半串眼细丝的不断散发波动的动力学
Dynamics of undulatory fluctuations of semiflexible filaments in a network
论文作者
论文摘要
我们研究了一个半融灯丝的动力学，该动力学耦合到其边界处的胡克恩弹簧。弹簧在细丝上产生了波动的拉伸力，其价值取决于灯丝的瞬时端到端长度。春季因此引入了一种非线性，它混合了细丝的流动正常模式并改变其动力学。我们使用Martin-Siggia-Rose-Janssen-De-De-Demincis形式主义研究这些动力学，并计算横向起伏的时间依赖性相关功能和细丝的端到端距离。由细丝的弯曲模量$κ$和春季肾上腺呈张力$τ_{r} $设置的特征波长$ \ sqrt {κ/τ_r} $下方模式的松弛动力学。这发生在系统的张力和弯曲主导模式之间的交叉频率附近。边界弹簧可用于表示灯丝交联的细丝网络的线性弹性依从性。结果，我们预测，这种非线性效应将在网络组成丝和网络的集体剪切响应中的动态相关性中观察到。预计系统的动态剪切模量将展示众所周知的跨界车，其频率从$ω^{1/2} $增加到$ω^{3/4} $，但是将网络的依从性纳入了单个丝状动力学的分析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, whose value 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-Domincis 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 $\sqrt{κ/τ_R}$, set by the filament's bending modulus $κ$ and spring-renormalized tension $τ_{R}$, are changed by the boundary spring. This occurs near the cross-over 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 $ω^{1/2}$ to $ω^{3/4}$, but the inclusion of the the network's compliance in the analysis of the individual filament dynamics shifts this transition to a higher frequency.
