A novel technique to accelerate the aggregation and disaggregation stages in evanescent plane wave methods is presented. The new method calculates the six plane wave radiation patterns from a multipole expansion (aggregation) and calculates the multipole expansion of an incoming field from the six plane wave incoming field patterns. It is faster than the direct approach for multipole orders lar...

The observed spectra and X-ray luminosities of millisecond pulsars in 47 Tuc can be interpreted in the context of theoretical models based on strong, small-scale, multipole fields on the neutron star surface. For multipole fields that are relatively strong compared to the large-scale dipole field, the emitted X-rays are thermal and likely result from polar cap heating associated with the return...

The Earth’s gravitational field is represented by its multipole moments. Multipole moments have two kinds of equivalent forms, that is, the Cartesian symmetric and tracefree tensors and the spherical harmonic coefficients. The relation between these two forms is interesting and useful for some practical problems. Under Newtonian approximation, there exists a simple relation between the aforesai...

In standard treatments of atomic multipole models, interaction energies, total molecular forces, and total molecular torques are given for multipolar interactions between rigid molecules. However, if the molecules are assumed to be flexible, two additional multipolar atomic forces arise because of (1) the transfer of torque between neighboring atoms and (2) the dependence of multipole moment on...

An electrostatic model based on charge density is proposed as a model for future force fields. The model is composed of a nucleus and a single Slater-type contracted Gaussian multipole charge density on each atom. The Gaussian multipoles are fit to the electrostatic potential (ESP) calculated at the B3LYP/6-31G* and HF/aug-cc-pVTZ levels of theory and tested by comparing electrostatic dimer ene...

A new definition of the interaction list in the fast multipole method (FMM) is introduced in this paper, which can reduce the moment-to-local (M2L) translations by about 30-40% and therefore improve the efficiency for the FMM. In addition, an adaptive tree structure is investigated, which is potentially more efficient than the oct-tree structure for thin and slender domains as in the case of mi...

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order , is represented by , unit vectors pointing in directions on the sky and an overall magnitude. These ‘‘multipole vectors and scalars’’ transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group SO(3). H...

A formal multipole expansion of tensor functions dependent on several vector parameters is obtained in an invariant differential form. We apply this result to derive multipole expansions of finite rotation matrices in terms of finite sums of bipolar harmonics. The multipole expansion in terms of bipolar harmonics of unit vectors r̂1 and r̂2 are analyzed for functions of the type f (r)Ylm(r̂) (with...

A fast multipole formulation for 2D linear viscoelastic problems is presented in this paper by incorporating the elastic–viscoelastic correspondence principle. Systems of multipole expansion equations are formed and solved analytically in Laplace transform domain. Three commonly used viscoelastic models are introduced to characterize the time-dependent behavior of the materials. Since the trans...

We have studied the multipole polarizability of a graded spherical particle in a nonuniform electric field, in which the conductivity can vary radially inside the particle. The main objective of this work is to access the effects of multipole interactions at small interparticle separations, which can be important in non-dilute suspensions of functionally graded materials. The nonuniform electri...