Relations between angular and Cartesian orientational expansions
Source abstract
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.
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Research context
OpenAlex topics: Liquid Crystal Research Advancements · Mathematics and Applications · Quasicrystal Structures and Properties
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Affiliations
Institut für Theoretische Physik, Center for Soft Nanoscience, Westfälische Wilhelms-Universität Münster , D-48149 Münster, Germany
Funding
Deutsche Forschungsgemeinschaft
References (59)
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