Gramada Apostol, Bourne Philip E
Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California San Diego, La Jolla, California 92093, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Dec;78(6 Pt 2):066601. doi: 10.1103/PhysRevE.78.066601. Epub 2008 Dec 2.
We present a method for the rankwise distributed multipole analysis of an arbitrary distribution of charge and its surrounding field. Using the superposition principle, the electrostatic field created by a distribution of charge can be resolved recursively into the contributions of a set of intrinsic multipole moments "tied to" their rank-specific multipole centers. The positions of the multipole centers, which are fixed with respect to the distribution of charge, are determined from a term-by-term optimization of the Taylor's expansion of the electrostatic potential with respect to the charge coordinates. We describe the recursive construction of the intrinsic multipole moments and derive the algebraic expression of the multipole centers. The resulting distributed multipole expansion provides a conceptual framework for the analysis and modeling of the electrostatic field and of its associated distribution of charge.
我们提出了一种对任意电荷分布及其周围场进行按阶分布式多极分析的方法。利用叠加原理，由电荷分布产生的静电场可以递归地分解为一组与它们各自阶数特定的多极中心“相关联”的本征多极矩的贡献。多极中心的位置相对于电荷分布是固定的，它是通过对静电势关于电荷坐标的泰勒展开式进行逐项优化来确定的。我们描述了本征多极矩的递归构造，并推导了多极中心的代数表达式。由此得到的分布式多极展开为静电场及其相关电荷分布的分析和建模提供了一个概念框架。
