Cusp Catastrophe Model for Description of Bistability in Ferroelectric Liquid Crystals

Abstract

We propose a new theoretical approach for description of the equilibrium and bistable states of ferroelectric liquid crystal. A sample of ferroelectric liquid crystal is considered in the “bookshelf” geometry under the influence of electric field. Continuum and perturbation theories are used in order to establish the relation between the scale coefficients in the expansion for the azimuthal angle. The equilibrium states of ferroelectric SmC* are determined in the framework of the catastrophe theory.

Caustics, catastrophes, and symmetries in curved beams

“…The caustic-symmetry correspondence is rigorously demonstrated within both complementary frames, the geometric as well as the ondulatory frame. The findings of this work could be useful in the application of the catastrophe theory to other areas beyond the optical beams since the fold and cusp catastrophes are a powerful tool in diverse areas of chemistry [25,26], physics [27][28][29], and cosmology [30,31], in addition to other sciences such as medicine [32,33].…”

Application of Catastrophe Theory to Instabilities Description of Ferroelectric Liquid Crystals in Magnetic Field

“…Одним из основных преимуществ применения методов теории бифуркаций к нелинейным задачам устойчивости является то, что в целом можно уменьшить размерность исходной системы до низкоразмерной системы, главным образом в окрестности критических точек. Этот подход успешно реализован в исследовании С*ЖК для случая внешнего электрического поля в работе [4].…”