Work

Relations between angular and Cartesian orientational expansions

Year: 2020

Type: article

Abstract: Orientational expansions, which are widely used in natural sciences, exist in angular and Cartesian forms. Although these expansions are orderwise equivalent, it is difficult to relate them in practice. In this article, both types of expansions and their relations are explained in detail. We give explicit formulas for the conversion between angular and Cartesian expansion coefficients for functions depending on one, two, and three angles in two and three spatial dimensions. These formulas are useful, e.g., for comparing theoretical and experimental results in liquid crystal physics. The application of the expansions in the definition of orientational order parameters is also discussed.

Source: AIP Advances

DOI: 10.1063/1.5141367

Authors: Michael te Vrugt, Raphael Wittkowski

Institution: University of Münster

Language: English

Topic: Liquid Crystal Research Advancements

Subfield: Electronic, Optical and Magnetic Materials

Field: Materials Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,350

Funder: Deutsche Forschungsgemeinschaft