Explicit vector spherical harmonics on the 3-sphere

3 Generalized Spherical Harmonics

A Nonlinear Galerkin Scheme Involving Vector and Tensor Spherical Harmonics for Solving the Incompressible Navier-Stokes Equation on the Sphere

The first part of this talk is dedicated to the introduction of the nonlinear Galerkin method applied to the Navier-Stokes equation on the rotating sphere. The Navier-Stokes equation plays a fundamental role in meteorology by modelling meso-scale (stratified) atmospherical flows. The nonlinear Galerkin method is implemented by using type three vector spherical harmonics, and convergence is sket...

Resonance energy transfer: The unified theory via vector spherical harmonics.

In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in...

Spherical Minimal Immersions of the 3-sphere

In 1966 Takahashi [11] proved that a minimal isometric immersion f : S(1) → S(r) of round spheres exists iff r = √ m/λp, where λp is the pth eigenvalue of the Laplacian on S; in this case, the components of f are spherical harmonics on S of order p. This immersion is unique up to congruence on the range and agrees with the generalized Veronese map if m = 2 as was shown in 1967 by Calabi [1]. In...

Orthogonal radiation patterns for three-dimensional noise sources based on the spherical harmonics of sphere(s)

The control and thus sensing of radiation from three-dimensional noise sources has become a topic of strong interest as investigation moves away from the laboratory. Furthermore, the advance in signal processing power has facilitated the real-time fusion of a large number of sensor signals, which are typically required to give an accurate estimate of global error signals. Current state-of-the-a...