A new guideline for proper allocation of multipoles in the multiple multipole method (MMP) is proposed. In an ‘a posteriori’ approach, subspace fitting (SSF) is used to find the best location of multipole expansions for the two dimensional dielectric scattering problem. It is shown that the best location of multipole expansions (regarding their global approximating power) coincides with the med...

a new guideline for proper allocation of multipoles in the multiple multipole method (mmp) is proposed. in an ‘a posteriori’ approach, subspace fitting (ssf) is used to find the best location of multipole expansions for the two dimensional dielectric scattering problem. it is shown that the best location of multipole expansions (regarding their global approximating power) coincides with the med...

We present the pseudo-particle multipole method (PM), a new method to handle multipole expansion in fast multipole method and treecode. This method uses a small number of pseudo-particles to express multipole expansion. With this method, the implementation of FMM and treecode with high-order multipole terms is greatly simplified. We applied PM to treecode and combined it with special-purpose co...

We present approximate formulas for the tensor BB, EE, TT, and TE multipole coefficients for large multipole order l. The error in using the approximate formula for the BB multipole coefficients is less than cosmic variance for l > 10. These approximate formulas make various qualitative properties of the calculated multipole coefficients transparent: specifically, they show that, whatever value...

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 multipo...

We study, analytically and numerically, singularity formation in an interface flow driven by a multipole for a two-dimensional Hele–Shaw cell with surface tension. Our analysis proves that singularity formation is inevitable in the case of a dipole. For a multipole of a higher order, we show that the solution does not tend to any stationary solution as time goes to infinity if its initial cente...

2 A General Firstand Second-Order Theory of Beam Transport Optics . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 The Vector Differential Equation of Motion . . . . . . . . 2.2 The Coordinate System . . . . . . . . . . . . . . . . .’ . 2.3 Expanded Form of a Magnetic Field Having Median Plane Symmetry . . . . . . . . . . . . . . . . . . . . . . 2.4 Field Expansion to Second Order Only ....

A transformation linking spherical multipole fields with generalized spheroidal multipole fields is derived. Applications including the inverse diffraction problem for spherically-scanned near field data for sources that due to conformal considerations are efficiently described using spheroidal (either oblate or prolate) volume support regions are discussed with the aid of numerical illustratio...

Optical properties of natural or designed materials are determined by the electromagnetic multipole moments that light can excite in the constituent particles. In this paper, we present an approach to calculating the multipole excitations in arbitrary arrays of nanoscatterers in a dielectric host medium. We introduce a simple and illustrative multipole decomposition of the electric currents exc...