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multipole
multipole, n. and a. Physics. (ˈmʌltɪpəʊl) [f. multi- 2 + pole n.2] A. n. A system of 2{supl} monopoles (l = 1, 2, 3,{ddd}) with no net charge or pole strength and no moment of a lower order than l (cf. moment n. 8 c); the dipole (l = 1) is often treated as a special case and the quadrupole (l = 2) ... Oxford English Dictionary
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Multipole density formalism
The Multipole Density Formalism (also referred to as Hansen-Coppens Formalism) is an X-ray crystallography method of electron density modelling proposed Multipole description In the multipole model description, the charge density around a nucleus is given by the following equation: The spherical part wikipedia.org
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Multipole magnet
Multipole magnets are magnets built from multiple individual magnets, typically used to control beams of charged particles. Now for an electromagnet with a cylindrical bore of radius , producing a pure multipole field of order , this integral becomes: Ampere's Law for multipole wikipedia.org
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octupole
octupole Physics. (ˈɒktuːpəʊl) Also octa-, octo-. [f. octu- (in octuple a. (n.), octuplet: cf. quadrupole), octa-, octo- + pole n.2] A multipole of order l = 3. Freq. attrib. or as adj. Cf. multipole n.1929 P. Debye Polar Molecules ii. 26 The next configuration, constructed by a displacement of the ... Oxford English Dictionary
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Multipole radiation
Multipole radiation is analyzed using similar multipole expansion techniques that describe fields from static sources, however there are important differences See near and far field and multipole expansion. wikipedia.org
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Multipole expansion
In the first (more common) case, the coefficients of the series expansion are called exterior multipole moments or simply multipole moments whereas, in The most common expansions include: Axial multipole moments of a potential; Spherical multipole moments of a potential; and Cylindrical multipole wikipedia.org
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Fast algorithm for computing forces between $n$ point in the plane I have a set of distinct particles $\\{z_k\\}_{k=1}^n\subseteq\mathbb{R}^2$ with dynamics $$\dot{z_k} = \sum_{k'\not= k}V(z_k-z_{k'}),$$ where $V$ i...
This paper seems quite relevant: > A Fast Adaptive Multipole Algorithm for Calculating Screened Coulomb (Yukawa) Interactions, _Journal of Computational
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Quadrupole
sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole See also Multipole expansion Multipole moments Solid harmonics Axial multipole moments Cylindrical multipole moments Spherical multipole moments wikipedia.org
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Fast multipole method
JAVA Animation of the Fast Multipole Method Nice animation of the Fast Multipole Method with different adaptations. KIFMM3d The Kernel-Independent Fast Multipole 3d Method (kifmm3d) is a new FMM implementation which does not require the explicit multipole expansions wikipedia.org
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chap3: multipole expansion - 知乎
在最粗糙的近似下, 一个距离很远且电量很小的电荷分布就是可以看成一个点电荷. 第二项是偶极矩, 可以看到算子是分解到三个坐标轴上的, 也就是描述了电荷分布在三个轴方向上的形状, 逐渐立体起来. 四极矩形式比较复杂, 我们以 \alpha=\beta=z 为例. \hat {\Theta ...
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Distributed multipole analysis
Multipole expansion The DMA method was devised by Prof. If the overlap center is not at an atom, one can move the origin of the multipole expansion to the nearest distributed multipole site, re-expressing the wikipedia.org
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Cylindrical multipole moments
Interior cylindrical multipole moments Similarly, the interior cylindrical multipole expansion has the functional form where the moments are defined See also Axial multipole moments Potential theory Quantum cylindrical quadrupole Multipole expansion Spherical multipole moments Electromagnetism wikipedia.org
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多极展开相对于泰勒展开有什么优势？为何FMM（快速多极子算法）要采用多极展开而非泰勒展开？
Multipole expansion 在直角坐标下是对格林函数的各坐标分量做泰勒展开（Multipole expansion），整理成球坐标的参量后r的多项式的阶数体现在各阶的球面波里。 zhihu
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Axial multipole moments
General axial multipole moments To get the general axial multipole moments, we replace the point charge of the previous section with an infinitesimal See also Potential theory Multipole expansion Spherical multipole moments Cylindrical multipole moments Solid harmonics Laplace expansion References wikipedia.org
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多极展开相对于泰勒展开有什么优势？为何FMM（快速多极子算法）要采用多极展开而非泰勒展开？
因为fast multipole method 可以转移多极距，直接降低复杂度，结果就是加快速度，所以叫fast。 Taylor展开太单一，至少我是没想出办法去加速它的。 zhihu
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