Hydrodynamics of topological defects in nematic liquid crystals

We show that back-flow, the coupling between the order parameter and the velocity fields, has a significant effect on the motion of defects in nematic liquid crystals. In particular the defect speed can depend strongly on the topological strength in two dimensions and on the sense of rotation of the director about the core in three dimensions.Comment: 4 pages including two figure

Lattice Boltzmann Algorithm for three-dimensional liquid crystal hydrodynamics

We describe a lattice Boltzmann algorithm to simulate liquid crystal hydrodynamics in three dimensions. The equations of motion are written in terms of a tensor order parameter. This allows both the isotropic and the nematic phases to be considered. Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are viscoelastic effects such as shear-thinning and shear-banding. We describe the implementation of velocity boundary conditions and show that the algorithm can be used to describe optical bounce in twisted nematic devices and secondary flow in sheared nematics with an imposed twist.Comment: 12 pages, 3 figure

Numerical calculations of the phase diagram of cubic blue phases in cholesteric liquid crystals

We study the static properties of cubic blue phases by numerically minimising the three-dimensional, Landau-de Gennes free energy for a cholesteric liquid crystal close to the isotropic-cholesteric phase transition. Thus we are able to refine the powerful but approximate, semi-analytic frameworks that have been used previously. We obtain the equilibrium phase diagram and discuss it in relation to previous results. We find that the value of the chirality above which blue phases appear is shifted by 20% (towards experimentally more accessible regions) with respect to previous estimates. We also find that the region of stability of the O5 structure -- which has not been observed experimentally -- shrinks, while that of BP I (O8-) increases thus giving the correct order of appearance of blue phases at small chirality. We also study the approach to equilibrium starting from the infinite chirality solutions and we find that in some cases the disclination network has to assemble during the equilibration. In these situations disclinations are formed via the merging of isolated aligned defects.Comment: 16 pages, 5 figures. Accepted for publication in Phys. Rev.

Critical Behavior of Frustrated Josephson Junction Arrays with Bond Disorder

The scaling behavior of the current-voltage ($IV$) characteristics of a two-dimensional proximity-coupled Josephson junction array (JJA) with quenched bond disorder was investigated for frustrations $f=1/5$, 1/3, 2/5, and 1/2. For all these frustrations including 1/5 and 2/5 where a strongly first-order phase transition is expected in the absence of disorder, the $IV$ characteristics exhibited a good scaling behavior. The critical exponent $\nu$ indicates that bond disorder may drive the phase transitions of frustrated JJA's to be continuous but not into the Ising universality class, contrary to what was observed in Monte Carlo simulations. The dynamic critical exponent $z$ for JJA's was found to be only 0.60 - 0.77.Comment: RevTeX4, 4 pages, 4 figures, the manuscript is replaced with the published versio

Equilibrium properties of a Josephson junction ladder with screening effects

In this paper we calculate the ground state phase diagram of a Josephson Junction ladder when screening field effects are taken into account. We study the ground state configuration as a function of the external field, the penetration depth and the anisotropy of the ladder, using different approximations to the calculation of the induced fields. A series of tongues, characterized by the vortex density $\omega$, is obtained. The vortex density of the ground state, as a function of the external field, is a Devil's staircase, with a plateau for every rational value of $\omega$. The width of each of these steps depends strongly on the approximation made when calculating the inductance effect: if the self-inductance matrix is considered, the $\omega=0$ phase tends to occupy all the diagram as the penetration depth decreases. If, instead, the whole inductance matrix is considered, the width of any step tends to a non-zero value in the limit of very low penetration depth. We have also analyzed the stability of some simple metastable phases: screening fields are shown to enlarge their stability range.Comment: 16 pp, RevTex. Figures available upon request at [email protected] To be published in Physical Review B (01-Dec-96

Rheology of distorted nematic liquid crystals

We use lattice Boltzmann simulations of the Beris--Edwards formulation of nematodynamics to probe the response of a nematic liquid crystal with conflicting anchoring at the boundaries under shear and Poiseuille flow. The geometry we focus on is that of the hybrid aligned nematic (HAN) cell, common in devices. In the nematic phase, backflow effects resulting from the elastic distortion in the director field render the velocity profile strongly non-Newtonian and asymmetric. As the transition to the isotropic phase is approached, these effects become progressively weaker. If the fluid is heated just above the transition point, however, another asymmetry appears, in the dynamics of shear band formation.Comment: 7 pages, 4 figures. Accepted for publication in Europhys. Let

Domain Walls and Phase Transitions in the Frustrated Two-Dimensional XY Model

We study and compare the critical properties of the two-dimensional (2D) XY model in a transverse magnetic field with magnetic filling factors f=1/3 and f=2/5. In addition to the spin waves, the low energy excitations of the system consist of various domain walls between degenerate ground states. The lowest energy domain wall has a similar structure for both f=1/3 and f=2/5 and its properties dictate the nature of the phase transition. For f=2/5 these lowest energy walls have a negative energy for binding to each other, giving rise to a branching domain-wall structure and leading to a first order phase transition. For f=1/3 this binding energy is positive, resulting in a linear critical interface. In order to make a comparison to recent experiments, we investigate the effect of small quenched bond disorder for f=2/5. A finite-size scaling analysis of extensive Monte Carlo simulations strongly suggests that the critical exponents of the phase transition for f=1/3, and for f=2/5 with disorder, fall into the universality class of the two-dimensional Ising model.Comment: 5 pages, 3 eps figures, REVTEX, revised version with new figure

Objective quantification of vitreous haze on optical coherence tomography scans: no evidence for relationship between uveitis and inflammation in multiple sclerosis

BACKGROUND AND PURPOSE: The occurrence of intermediate uveitis, which is characterized by the presence of vitreous haze (VH), in patients with multiple sclerosis (MS) may be a sign of coexistent inflammatory central nervous system (CNS) disease activity. Using an automated algorithm to quantify VH on optical coherence tomography (OCT) scans, the aim was to investigate whether VH in MS patients is associated with signs of inflammatory CNS disease activity. METHODS: Vitreous haze was quantified on OCT macular volume scans of 290 MS patients and 85 healthy controls (HCs). The relationship between VH and clinical, retinal OCT and magnetic resonance imaging parameters of inflammatory disease activity was investigated using generalized estimating equations. RESULTS: Mean VH scores did not differ between patients and HCs (P = 0.629). Six patients (2.1%) showed values higher than the highest of the controls by HCs. VH scores did not differ between the different disease types or between eyes with and without a history of optic neuritis (P = 0.132). VH was not associated with inner nuclear layer volume on OCT (P = 0.233), cerebral T2 lesion load on magnetic resonance imaging (P = 0.416) or the development of new relapses (P = 0.205). CONCLUSION: In this study, OCT-based automated VH estimation did not detect increased vitreous inflammation in MS patients compared to HCs and did not find an association with CNS inflammatory burden

Optimizing OCT acquisition parameters for assessments of vitreous haze for application in uveitis

Detection and evaluation of inflammatory activity in uveitis is essential to the management of the condition, and yet continues to be largely dependent on subjective clinical measures. Optical coherence tomography (OCT) measurement of vitreous activity is an alternative to clinical vitreous haze scoring and has passed a number of early validation studies. In this study we aimed to evaluate the impact of ‘operator factors’ on the variability of the technique as part of the validation process, and to help evaluate its suitability for ‘real world’ use. Vitreous haze index was calculated as a ratio between the reflectivity of the vitreous and of the outer retina in each scan. Different scanning conditions were tested and their effect on the measurement is reported. Our results show that the ‘quantitative imaging’ technique of OCT-measured vitreous activity had good reliability in normal subjects under a range of ‘real world’ conditions, such as when the operator changes the averaging value. The technique was however vulnerable to highly inaccurate focussing or abnormal downward displacement of the image. OCT-based quantification of vitreous activity is a promising alternative to current subjective clinical estimates, with sufficient ‘tolerance’ to be used in routine clinical practice as well as clinical trials