Dislocation dynamics in an anisotropic stripe pattern

Abstract

The dynamics of dislocations confined to grain boundaries in a striped system are studied using electroconvection in the nematic liquid crystal N4. In electroconvection, a striped pattern of convection rolls forms for sufficiently high driving voltages. We consider the case of a rapid change in the voltage that takes the system from a uniform state to a state consisting of striped domains with two different wavevectors. The domains are separated by domain walls along one axis and a grain boundary of dislocations in the perpendicular direction. The pattern evolves through dislocation motion parallel to the domain walls. We report on features of the dislocation dynamics. The kinetics of the domain motion are quantified using three measures: dislocation density, average domain wall length, and the total domain wall length per area. All three quantities exhibit behavior consistent with power law evolution in time, with the defect density decaying as t −1/3 , the average domain wall length growing as t 1/3 , and the total domain wall length decaying as t −1/5 . The two different exponents are indicative of the anisotropic growth of domains in the system.

Numerical study of domain coarsening in anisotropic stripe patterns

“…We qualitatively justify this feature from weakly nonlinear analysis arguments. The dislocation exponent is close to the value of 1 / 3 in that intermediate range, in agreement with the value measured in recent experiments [15]. Some conclusions are presented in Sec.…”

“…On the other hand, configurations of oblique rolls very similar to those observed experimentally [14,15] are always observed when setting r Ͼ 0 instead. Normal rolls were never observed in the runs presented in the following sections.…”

“…Studying the ordering dynamics on this system is motivated by various reasons. First, one can intend a comparison with available experimental data, since coarsening experiments have been recently conducted in electroconvection [14,15]. Second, the polycrystalline structures of oblique stripes have a relatively simpler geometry than those of isotropic stripes: the constraint of the fixed angle prevents the formation of disclinations.…”

Dislocations in an Anisotropic Swift-Hohenberg Equation

“…Beyond mimicking some of the features of the isotropic Swift-Hohenberg equation, the anisotropic SwiftHohenberg equation itself plays an important role in modeling anisotropic convection [11], nematic liquid crystals [1,7], or, more generally, anisotropic pattern-forming systems. The effect of anisotropy on point defects has been studied in [10].…”

Amplitude modulation and relaxation-oscillation of counterpropagating rolls within a broken-symmetry laser-induced electroconvection strip

“…The formation of spatially periodic patterns in a wide variety of media driven far from equilibrium continues to attract a great deal of attention from experiment, simulations, and theory [1,2,3,4,5,6,7,8,9,10,11,12,13]. For patterns in fluids, many important advances have relied on careful experiments with samples possessing a very high degree of spatial homogeneity in the material properties and the external control parameters.…”