On Spheroidal Harmonics

Eliciting Harmonics on Strings

One may produce the qth harmonic of a string of length π by applying the ‘correct touch’ at the node π/q during a simultaneous pluck or bow. This notion was made precise by a model of Bamberger, Rauch and Taylor. Their ‘touch’ is a damper of magnitude b concentrated at π/q. The ‘correct touch’ is that b for which the modes, that do not vanish at π/q, are maximally damped. We here examine the as...

On convergence Properties of 3D spheroidal Monogenics

J. Morais has recently introduced certain complete orthogonal sets of monogenic polynomials over 3D prolate spheroids with remarkable properties. The underlying functions take on either values in the reduced and full quaternions (identified, respectively, with R3 and R4), and are generally assumed to be nullsolutions of the well known Riesz and Moisil-Théodoresco systems in R3. In continuation ...

Harmonics Theory

For most conventional analyses, the power system is essentially modeled as a linear system with passive elements excited by constantmagnitude and constantfrequency sinusoidal voltage sources. However, with the widespread proliferation of power electronics loads nowadays, significant amounts of harmonic currents are being injected into power systems. Harmonic currents not only disturb loads that...

Fluid Simulation on S using Spherical Harmonics

Random walks on simplicial complexes and harmonics†

In this paper, we introduce a class of random walks with absorbing states on simplicial complexes. Given a simplicial complex of dimension d, a random walk with an absorbing state is defined which relates to the spectrum of the k-dimensional Laplacian for 1 ≤ k ≤ d. We study an example of random walks on simplicial complexes in the context of a semi-supervised learning problem. Specifically, we...