2D Nematic Order, Active Liquid Crystals

This chapter presents the distinction between 2D nematic order and 2D polar order, and then discusses topological defects and solitons in 2D nematic order. They are generally similar to topological defects and solitons in 2D polar order, except that the winding number may be a half-integer in the nematic 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.