Topological defects are very well understood so long as the medium in which they exist is isotropically-elastic. They lead to director fields which are easy to calculate and superpose linearly so that a system with any number of defects is analytically treatable. They also have an interaction which is simple in form and can be accurately described by the Peach-Koehler force. In an anisotropically-elastic medium, however, such defects are very poorly understood outside of the single-defect case which was solved by Dzyaloshinskii. In this project, numerical and approximate analytical techniques are applied in order to better understand the interaction between two defects in an anisotropically-elastic medium and how it differs from the well understood isotropically-elastic case.
Swift, Carter J.
"The Interaction of Topological Defects in Anisotropically-Elastic Nematic Liquid Crystals,"
Macalester Journal of Physics and Astronomy: Vol. 10:
1, Article 12.
Available at: https://digitalcommons.macalester.edu/mjpa/vol10/iss1/12