Topological defects in liquid crystal orientation field — core energy and winding number
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In nematic liquid crystals, the director field n̂(r) (headless unit vector) can have
topological defects called disclinations with half-integer winding numbers s = ±½, ±1.
The Frank elastic energy scales as F ~ πKs²ln(R/rc). The +½ and −½ disclinations
are topologically stable in nematics (π₁(RP²) = Z₂); they attract and annihilate in pairs.
The core energy regularizes the logarithmic divergence. Click the canvas to add a defect.