Formation of the shock pressure regime in the form of a traveling wave in nematic twisted cells

The paper presents a numerical study, within a nonlinear generalization of the classical Ericksen–Leslie theory, of a new nonlinear mechanism for the formation of the regime of shock pressure on the boun-ding walls of a microsized twisted nematic cell (TNC), realized in the form of the kinklike traveling wave $\mathscr{P}(z-vt)$ under the effect of the externally applied electric field and induced by a strong local distribance of the director field in the form of a Gaussian (normal) distribution. The mechanisms responsible for the formation of the traveling wave of shock pressure propagating in the $T_{\mathrm{NA}}$ from one of its boundaries to another are studied, and it is shown how the magnitude of the electric field and the shape of the localized initial perturbation of the director field affect the similarity of the traveling wave to the kinklike wave. Studies of the dynamic relaxation of the director field in TNCs also showed that, at temperatures exceeding the temperature for the nematic–smectic $A$ (NA) $T_{\mathrm{NA}}$ phase transition by several dozen mK, fluctuations in the order parameter of the emerging smectic phase suppress the effect of the electric field and favor the singular behavior of the azimuthal anchoring energy density as $T\to T_{\mathrm{NA}}$.