Polymers consisting of rigid segments connected by flexible joints (needle chains) constitute an important class of biopolymers. Using kinetic theory as a starting point, we first derive the generalized coordinate-space diffusion (Fokker-Planck) equation for the needle chain polymer model. Next, the equivalent generalized coordinate Ito stochastic differential equation is established. Nonlinear transformations of variables finally yield a stochastic differential equation for the needle chain spatial coordinates in the laboratory coordinate system where the coefficients are expressed in terms of the chain constraint conditions. This latter equation constitutes the basis for our needle chain Brownian dynamics (BD) algorithm. The used needle chain model includes needle translation-translation and rotation-rotation hydrodynamic interactions, a homogeneous solvent flow field, external forces, excluded volume effects, and bending and twisting stiffness between nearest neighbor segments. For this chain model we find that by proper generalization of the involved parameters the mathematical analysis of the polymer dynamics, in great detail, maps onto the analysis of the bead-rod-spring polymer chain model with constraints presented by Ottinger in Phys. Rev. E 50, 2696 (1994). Preliminary numerical simulation data show that for a three segment needle chain, with needle axial ratio equal to five, our new needle chain BD algorithm is, in general, more than about 10(3) times more efficient than the bead-spring polymer chain BD algorithm commonly used as an approximation for studies of such polymer chains, This efficiency ratio increases asymptotically proportional to approximately the fourth power of the needle axial ratio. In addition to this major gain in efficiency, the needle chain model for segmented polymers, in general, incorporates a more realistic hydrodynamic description of the individual segments and, in particular, the joints between the segments than the bead-rod-spring models. (C) 1996 American Institute of Physics. [References: 8]
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机译：由通过柔性接头（针链）连接的刚性链段组成的聚合物构成了一类重要的生物聚合物。以动力学理论为出发点，我们首先推导了针链聚合物模型的广义坐标空间扩散（Fokker-Planck）方程。接下来，建立等效的广义坐标伊藤随机微分方程。变量的非线性变换最终产生实验室坐标系中针链空间坐标的随机微分方程，其中系数根据链约束条件表示。后一个方程式构成了我们的针链布朗动力学（BD）算法的基础。使用的针链模型包括针的平移-平移和旋转-旋转流体动力相互作用，均匀的溶剂流场，外力，排除的体积效应以及最近邻段之间的弯曲和扭曲刚度。对于此链模型，我们发现通过适当地概括所涉及的参数，可以对聚合物动力学进行数学分析，其中更详细地将其映射到由Ottinger在Phys中提出的约束的珠-杆-弹簧聚合物链模型的分析。 E 50，2696（1994）。初步的数值模拟数据表明，对于三段式针链，针轴比等于5，我们的新针链BD算法通常比珠状弹簧聚合物链BD的效率高出约10（3）倍。通常用作研究此类聚合物链的近似算法。此效率比渐近增加，大约与针轴向比的四次方成正比。除了提高效率外，通常，用于分段聚合物的针链模型还结合了单个节段的流体力学描述，尤其是节段之间的接头，而不是珠-杆-弹簧模型。 （C）1996年美国物理研究所。 [参考：8]
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