Chirikjian GS, Wang Y
Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jul;62(1 Pt B):880-92. doi: 10.1103/physreve.62.880.
Partial differential equations (PDE's) for the probability density function (PDF) of the position and orientation of the distal end of a stiff macromolecule relative to its proximal end are derived and solved. The Kratky-Porod wormlike chain, the Yamakawa helical wormlike chain, and the original and revised Marko-Siggia models are examples of stiffness models to which the present formulation is applied. The solution technique uses harmonic analysis on the rotation and motion groups to convert PDE's governing the PDF's of interest into linear algebraic equations which have mathematically elegant solutions.
推导并求解了描述刚性大分子远端相对于近端位置和取向的概率密度函数（PDF）的偏微分方程（PDE）。克拉特基-波洛德蠕虫状链、山川螺旋蠕虫状链以及原始和修正的马尔科-西吉亚模型都是应用本公式的刚度模型示例。求解技术利用旋转和运动群上的调和分析，将控制相关PDF的PDE转换为具有数学优美解的线性代数方程。
