In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale potential problems, a fast multipole boundary element method for the problems of Laplace equation is presented. through the multipole expansion and local expansion for the basic solution of the kernel function of the Laplace equati...

We discuss low-temperature multipole states of Nd-based filled skutterudites by analyzing a multiorbital Anderson model with the use of a numerical renormalization group method. In order to determine the multipole state, we take a procedure to maximize the multipole susceptibility matrix. Then, it is found that the dominant multipole state is characterized by the mixture of 4u magnetic and 5u o...

We address the properties of nonlinear multipole modes supported by an interface between two distinct optical lattices imprinted in two-dimensional nonlinear quadratic media. Such multipole-mode solitons feature out of phase between neighboring lobes, which may be located in two different sides of the lattices. We analyze the impact of guiding parameters of lattices on the existence and stabili...

This paper presents a multipole analysis of the QRS complex of the normal magnetocardiogram (MCG) of six normal subjects. The multipole strengths up to the octupole term were determined from the measured distribution of the z-component of the cardiac magnetic field (the component perpendicular to the frontal plane). This equivalent magnetic multipole generator was found to represent the cardiac...

The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more libera...

This paper presents the generalized multipole, local and translation operators for three dimensional static potentials of the form r, where λ is any real number. Addition theorems are developed using Gegenbauer polynomials. Multipole expansions and error bounds are presented in a manner similar to those for truncated classical multipole expansions. Numerical results showing error behavior versu...

In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale potential problems, a fast multipole boundary element method for the problems of Poisson equation is presented. First of all, through the multipole expansion and local expansion for the basic solution of the kernel function of the ...

The gravitational radiation originating from a compact binary system in circular orbit is usually expressed as an infinite sum over radiative multipole moments. In a slow-motion approximation, each multipole moment is then expressed as a post-Newtonian expansion in powers of v/c, the ratio of the orbital velocity to the speed of light. The “bare multipole truncation” of the radiation consists i...

This paper presents a multipole analysis of the QRS complex of the normal magnetocardiogram (MCG) of six normal subjects. The multipole strengths up to the octupole term were determined from the measured distribution of the z-component of the cardiac magnetic field (the component perpendicular to the frontal plane). This equivalent magnetic multipole generator was found to represent the cardiac...

We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of o...