Nonlinear effects in liquid crystals

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Abstract
The effects of nonlinearity in nematic liquid crystals subject to electric and magnetic fields are emphasized. For the Fréedericks transition, the distortion profile is calculated exactly. For the domain modes, the torque equation can be approximated to a high degree by the nonlinear sine-Gordon equation. An exact two-dimensional periodic solution is found whose consequences are in good quantitative agreement with all experimental observations. The possibility of a first-order transition to a vortex pattern is predicted.