Odd-parity bipolar spherical harmonics

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...

Spherical Harmonics

5 Spherical Harmonics 7 5.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5.2 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.1 Harmonic expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5.2.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

3 Generalized Spherical Harmonics

Optimal Spherical Harmonics Projection

We introduce the reader to the mathematics behind projection of n-dimensional vectors into a basis on n-dimensional space, where n can be anything upto and including infinity. We show how ideally one wants to project into the duals of a basis if this basis is not orthonormal, and provide the mathematics to formulate this operation in matrix form. The second part of the article discusses spheric...