The Implementation of Brazil Sustainable Urban Mobility Policy

Institute of Transport and Logistics Studies. Faculty of Economics and Business. The University of Sydne

Quasi-mesoscopic model for ferroelectric switching in the chevron geometry

We present a theory of ferroelectric liquid crystal switching which combines elements of standard macroscopic continuum theories with mesoscopic Landau-de Gennes chevron theories. The macroscopic elements of the theory apply in the chevron arms, and are subject to a boundary condition at the chevron interface. This boundary condition can be derived from an anchoring energy associated with the director discontinuity at the chevron tip. The anchoring energy, which corresponds to the degree to which the cone mismatch condition is not satisfied, is calculated using the mesoscopic Landau-de Gennes theory. In the combined theory the frequently used cone-matching condition emerges as a thick cell limit. We are able to calculate a free energy associated with the imposition of a field on particular configurations. There follows a switching phase diagram determining the conditions for thresholdless and bistable switching. We further show that the time dependence of the switching process is determined by the slower bulk relaxation dynamics rather than by the fast chevron surface dynamics

Dynamics of chevron formation II: permeation-dominated phenomena.

This paper continues a study of the dynamics of chevron formation in smectic-A liquid crystals in samples with boundary conditions apparently favoring the bookshelf structure, with uniform layers perpendicular to the sample cell plane. The chevron structure that arises when the sample is cooled results from the mismatch between preferred bulk and surface layer thicknesses. In a previous paper we considered relaxation driven by the strong coupling between layer deformation and fluid flow. In this paper we discuss the alternative scenario in which boundary conditions suppress this coupling. Layer deformation now occurs by layer relaxation in the absence of fluid flow. This process is extremely slow and is governed by the nonlinear Fisher-Kolmogorov equation. Chevrons do form under some circumstances, but the process is irregular, and quasimetastable jagged multi-edged multi-tip-like structures can occur on intermediate time scales for suitable layer strains. In the absence of surface layer pinning, layer slippage occurs at the surfaces. We also examine the possibility that deformation may occur through a wave of invasion destroying the bookshelf region

Dynamics of chevron structure formation

The natural structure for smectic-A liquid crystals arranged in a sample with homogeneous boundary conditions is the so-called bookshelf structure with uniform layers perpendicular to the sample cell plane. However, this structure often deforms into the so-called chevron structure when the sample is cooled. This deformation is usually thought to result from the mismatch between bulk and surface layer thicknesses. In this paper we study the dynamics of chevron formation. Two possible scenarios are envisaged. In one of these there is strong coupling between layer deformation and fluid flow, and in the other the fluid essentially does not move. In this paper we examine the first scenario, leaving the second, slower relaxation mode for another paper. Analytic solutions are found for near-critical deformations, and numerical solutions are found beyond the critical regime