In this paper we describe an efficient algorithm for computing the potentials of the form r−λ where λ ≥ 1. This treecode algorithm uses spherical harmonics to compute multipole coefficients that are used to evaluate these potentials. The key idea in this algorithm is the use of Gegenbauer polynomials to represent r−λ in a manner analogous to the use of Legendre polynomials for the expansion of ...

A new fast multipole formulation for the hypersingular BIE (HBIE) for 2D elasticity is presented in this paper based on a complex-variable representation of the kernels, similar to the formulation developed earlier for the conventional BIE (CBIE). A dual BIE formulation using a linear combination of the developed CBIE and HBIE is applied to analyze multi-domain problems with thin inclusions or ...

Possible con®gurations of the magnetic ®eld in the outer magnetosphere during geomagnetic polarity reversals are investigated by considering the idealized problem of a magnetic multipole of order m and degree n located at the centre of a spherical cavity surrounded by a boundless perfect diamagnetic medium. In this illustrative idealization, the ®xed spherical (magnetopause) boundary layer beha...

A fast multipole boundary element method (BEM) for solving large-scale thin plate bending problems is presented in this paper. The method is based on the Kirchhoff thin plate bending theory and the biharmonic equation governing the deflection of the plate. First, the direct boundary integral equations and the conventional BEM for thin plate bending problems are reviewed. Second, the complex not...

Highly accurate computations of surface plasmons in metallic nanostructures with various geometries are presented. Calculations for cylinders with irregular cross section, coupled structures, and periodic gratings are shown. These systems exhibit a resonant behavior with complex field distribution and strong field enhancement, and therefore their computation requires a very accurate numerical m...

The existence of multipole surface-plasmon modes at simple-metal surfaces is demonstrated both experimentally and theoretically. Inelastic reAection electron-scattering experiments on smooth films of K and Na show loss peaks originating from the ordinary surface plasmon as well as from a higher-energy multipole mode. Microscopic density-functional calculations of the electron-loss function repr...

Recent work on designs of dipoles, quadrupoles and sextupoles for the NLC Main Damping Ring has led to estimates of the systematic multipole components in the fields of these magnets. We report on studies of the effects of these multipoles on the dynamic aperture of the damping ring, and show that the systematic multipole components in the present magnet designs are unlikely to be a severe limi...

A method for designing magnetic shields that do not perturb applied multipole fields in the static regime is developed. Cylindrical core-shell structures with two layers characterized by homogeneous isotropic permeabilities are found to support neutral shielding of multipole fields and unique cloaking solutions of arbitrary multipole order. An extra degree of freedom is provided by every layer ...

Abstract: The transition of molecular crystals into a polar state is modeled by a one-dimensional Ising Hamiltonian in multipole expansion and a suitable order parameter. Two symmetry breakings are necessary for the transition: the translational and the spin flip invariance—the former being broken by geometric constraints, the latter by the interaction of the first non-zero multipole with the n...