A Fast Algorithm for the Moments of Bingham Distribution

TL;DR

This paper introduces a rapid and accurate algorithm for computing moments of the Bingham distribution using piecewise rational approximation, significantly outperforming traditional methods and enabling new insights in liquid crystal modeling.

Contribution

The paper presents a novel fast algorithm for Bingham distribution moments, combining rational approximation with Gaussian integrals, improving speed and accuracy over existing methods.

Findings

Algorithm achieves maximal absolute error less than 5e-8.

Significantly faster than adaptive numerical quadrature.

Reveals new defect patterns in liquid crystal models.

Abstract

We propose a fast algorithm for evaluating the moments of Bingham distribution. The calculation is done by piecewise rational approximation, where interpolation and Gaussian integrals are utilized. Numerical test shows that the algorithm reaches the maximal absolute error less than 5e-8 remarkably faster than adaptive numerical quadrature. We apply the algorithm to a model for liquid crystals with the Bingham distribution to examine the defect patterns of rod-like molecules confined in a sphere, and find a different pattern from the Landau-de Gennes theory.