OBJECTIVES: In this paper, we present an exact analytical solution to surface current density for a spherical shaped magnetic field coil, that is capable of producing axially (z) directed field which varies linearly as well as according to the other pure zonal harmonics along the z direction inside the spherical coil. The other aim is to obtain an analytic expression for the surface current den...

Numerous vibrational modes of spherical submicrometer particles in fabricated soft opals are experimentally detected by Brillouin light scattering and theoretically identified by their spherical harmonics by means of single-phonon scattering-cross-section calculations. The particle size polydispersity is reflected in the line shape of the low-frequency modes, whereas lattice vibrations are prob...

We present a method for solving the Stokes problem in unbounded domains. It relies on the coupling of the transparent boundary operator and a spectral method in spherical coordinates. It is done explicitly by the use of vector-valued spherical harmonics. A uniform inf-sup condition is proved, which provides an optimal error estimate.

1. Calculus on spheres 2. Spherical Laplacian from Euclidean 3. Eigenvectors for the spherical Laplacian 4. Invariant integrals on spheres 5. L spectral decompositions on spheres 6. Sup-norms of spherical harmonics on Sn−1 7. Pointwise convergence of Fourier-Laplace series 8. Irreducibility of representation spaces for O(n) 9. Hecke’s identity • Appendix: Bernstein’s proof of Weierstraß approxi...

We introduce a new basis function (the spherical Gaussian) for electronic structure calculations on spheres of any dimension D. We find general expressions for the one- and two-electron integrals and propose an efficient computational algorithm incorporating the Cauchy-Schwarz bound. Using numerical calculations for the D = 2 case, we show that spherical Gaussians are more efficient than spheri...

The description of 3D shapes using features that possess descriptive power and are invariant under similarity transformations is one of the most challenging issues in contentbased 3D model retrieval. Spherical harmonics-based descriptors have been proposed for obtaining rotation invariant representations. However, spherical harmonic analysis is based on a latitude-longitude parameterization of ...

In this work, we present a novel cortical correspondence method with application to the macaque brain. The correspondence method is based on sulcal curve constraints on a spherical deformable registration using spherical harmonics to parameterize the spherical deformation. Starting from structural MR images, we first apply existing preprocessing steps: brain tissue segmentation using the Automa...

Standard and non-standard associated Legendre equations and supersymmetric quantum mechanics Abstract. A simple supersymmetric approach recently used by Dutt, Gan-gopadhyaya, and Sukhatme (hep-th/9611087, Am. J. Phys., to appear) for spherical harmonics is generalized to Gegenbauer and Jacobi equations. The coordinate transformation procedure is well known to the authors writing on supersymmetr...

The spatial orientation of vectors rigidly embedded in polymer chains are described in terms of time-dependent joint probability distribution functions. Serial expansion in terms of double spherical harmonics is adopted for the probability distribution functions, with the coefficients therein evaluated from Brownian dynamics simulations. Truncation of the series after the second-order harmonics...