Solitons and defects in nematic liquid crystals under a simple shear flow and in a static external magnetic field

Abstract

Under a simple shear flow and in a static external magnetic field, the production of defects in the director-aligning regime of nematic liquid crystals has been investigated in terms of the Leslie–Ericksen theory. The equation of motion of the nematic director, which conforms to the driven over-damped sine-Gordon equation, has a soliton solution of the amplitude π. We show that the stationary state with the director uniformly oriented at a Leslie angle is only a metastable state and the potential, which governs the motion of the director, has a number of stable stationary states. For a strong magnetic field, the higher energy barrier between the stable and unstable states leads the director to be locked along the magnetic field direction. However, at the appropriate shear rate and magnetic field the defects, which appear as a stable solitary solution, can be nucleated from a uniformly aligned nematic liquid crystal. We have calculated the stationary travelling velocity of the solitary waves and the distance between a pair of defects.

Ferrocholesteric–ferronematic transitions induced by shear flow and magnetic field

“…This equation determines the stationary angle φ of the director (and the magnetization) orientation in the ferrocholesteric as a function of the field strength h and the orientation angle of the magnetic field φ H , the parameter ξ of the field effect on the system, the reactive parameter λ, and the velocity gradient u of the shear flow. It can also be obtained by using the approach put forward in [ 18 , 28 – 30 ]. To do this we introduce the effective potential F eff , which can be written in the dimensionless form as follows:…”

Physical origin of observed nonlinearities in Poly (1-naphthyl methacrylate): Using a single transistor—transistor logic modulated laser beam

“…The diffraction rings have been observed in nematic liquid crystals by Zolotko et al, [21] in thermally dependent refractive index, [22] polymer films, [23] in Kerr media [24,25] and liquid crystals. [26,27] The diffraction ring pattern is understood from the spatial self-modulation effect. A pump beam with a Gaussian intensity profile should induce a phase shift ∆Φ, with a bell-shaped transverse profile.…”