Configuration of a smectic A liquid crystal due to an isolated edge dislocation

Abstract

We discuss the static configuration of a smectic A liquid crystal subject to an edge dislocation under the assumption that the director and layer normal fields ([Formula: see text] and [Formula: see text], respectively) defining the smectic arrangement are not, in general, equivalent. After constructing the free energy for the smectic, we obtain exact solutions to the equilibrium equations which result from its minimisation at quadratic order in the variables which describe the distortion, and hence a complete description of the smectic configuration across the domain of the sample. We also examine the effect of relaxing the constraint [Formula: see text] for different values of the constants which characterise the response of the material to distortions, and compare these results with the 'classical' case considered by previous authors, in which equivalence of [Formula: see text] and [Formula: see text] is enforced.

Two-dimensional flow and linear stability properties of smectic A liquid crystals

“…Alternatively, it may be of interest to work in two dimensions but relax the assumptions leading to the linearity of the system. This would lead to significantly more complicated governing equations, potentially resulting in the need to appeal to computational methods to obtain the resultant flow pattern and SmA configuration; however, such a framework might enable us to consider flow in the presence of defects, for example an edge dislocation [18,19,27], for which a key assumption regarding the validity of the linear model, that of flat layers, must break down, at least in a small region of the sample. For a problem such as this, an asymptotic approach should enable one to utilise equations (3.7), (2.12), (3.16), (3.18), and (3.21) in regions sufficiently far from the defect core, but a modified nonlinear system in a small neighbourhood around this core.…”