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Topological defect dynamics in a thin nematic liquid crystal film under crossed polarizers. Pairs of s = ±1/2 disclinations orbit and annihilate in harmonic superposition, generating optical isogyres (Schlieren brushes) and birefringence interference bands.
A thin crystalline film stretched across the ash terrace, revealing orientation where there is no mechanical flow. 偏振光切过地表，四条暗色刷线在半整数缺陷核之间旋转并汇聚。The ground here behaves like an anisotropic continuum: molecules tilt in unison until topology forces a tear.
Simulated director field $\theta(r)$ for $s = \pm 1/2$ disclination pairs under crossed polarizers via $I = \sin^2(2\theta) \cdot \cos^2(\Delta \phi / 2)$. Calculating intensity directly from $\cos(4\theta)$ avoids branch-cut discontinuities along the $\arctan2$ seam. The brush lines (isogyres) exhibit correct 2-fold symmetry around half-integer defects, and mutual annihilation transitions smoothly into uniform homeotropic extinction without popping density.