Bipolar and Toroidal Harmonics

Ellipsoidal, Cylindrical, Bipolar and Toroidal Wormholes in 5D Gravity

In this paper we construct and analyze new classes of wormhole and flux tube-like solutions for the 5D vacuum Einstein equations. These 5D solutions possess generic local anisotropy which gives rise to a gravitational running or scaling of the Kaluza-Klein “electric” and “magnetic” charges of these solutions. It is also shown that it is possible to self–consistently construct these anisotropic ...

Bipolar Spherical Harmonics Expansions of the Boltzmann Transport Equation

An extension of the spherical harmonics expansion method for the deterministic solution of the Boltzmann transport equation for the computation of both electron and hole distribution functions is presented. The generation and recombination of carriers via traps in the band gap is considered in a way that is consistent with the Shockley-Read-Hall model. Simulation results for a pn-diode and an n...

Cortical complexity in bipolar disorder applying a spherical harmonics approach.

Recent studies using surface-based morphometry of structural magnetic resonance imaging data have suggested that some changes in bipolar disorder (BP) might be neurodevelopmental in origin. We applied a novel analysis of cortical complexity based on fractal dimensions in high-resolution structural MRI scans of 18 bipolar disorder patients and 26 healthy controls. Our region-of-interest based an...

Tokamak plasma boundary reconstruction using toroidal harmonics and an optimal control method

This paper proposes a new fast and stable algorithm for the reconstruction of the plasma boundary from discrete magnetic measurements taken at several locations surrounding the vacuum vessel. The resolution of this inverse problem takes two steps. In the first one we transform the set of measurements into Cauchy conditions on a fixed contour ΓO close to the measurement points. This is done by l...

2D interpolation and extrapolation of discrete magnetic measurements with toroidal harmonics for equilibrium reconstruction in a Tokamak