Titlebook: Introduction to Topological Defects and Solitons; In Liquid Crystals, Jonathan V. Selinger Textbook 2024 The Editor(s) (if applicable) and

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Prequel to Defects: Variable Magnitude of Order find the core structure of a defect. The theory also predicts the free energy cost of a defect, and the drag force acting on a defect. Based on these results, the chapter compares the unit-vector and variable-magnitude theories, and comments on the general relationship between topology and physics.

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2D Nematic Order, Active Liquid Crystalsmatic case. If a system has both strong nematic order and weak polar order, then it may form complex string defects. The chapter further explores two further issues that often occur with 2D nematic order: unequal elastic constants for splay and bend, and active materials with topological defects out of thermal equilibrium.

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Free Energy energy of the system. This chapter explains how to minimize the elastic free energy around a defect or soliton, calculate the optimum configuration of orientational order, and hence determine the free energy associated with the defect or soliton. It further shows how to minimize the elastic free en

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Prequel to Defects: Variable Magnitude of Order magnitude as well as direction. The free energy can be expressed in terms of this variable-magnitude order parameter, and it can then be minimized to find the core structure of a defect. The theory also predicts the free energy cost of a defect, and the drag force acting on a defect. Based on these