Frank-Oseen elastic energy governs liquid crystal orientation. The director field n̂ minimizes elastic distortion energy with splay, twist, and bend constants. Topological defects of strength ±½ are unavoidable — they carry quantized topological charge. Click to add defects; watch the texture relax.
Defect strength s: orientation rotates by 2πs around defect core. ±½ defects are the elementary excitations of nematics.