Modulated structures in electroconvection in nematic liquid crystals
arXiv:nlin/0212028 · doi:10.1103/PhysRevE.67.031701
Abstract
Motivated by experiments in electroconvection in nematic liquid crystals with homeotropic alignment we study the coupled amplitude equations describing the formation of a stationary roll pattern in the presence of a weakly-damped mode that breaks isotropy. The equations can be generalized to describe the planarly aligned case if the orienting effect of the boundaries is small, which can be achieved by a destabilizing magnetic field. The slow mode represents the in-plane director at the center of the cell. The simplest uniform states are normal rolls which may undergo a pitchfork bifurcation to abnormal rolls with a misaligned in-plane director.We present a new class of defect-free solutions with spatial modulations perpendicular to the rolls. In a parameter range where the zig-zag instability is not relevant these solutions are stable attractors, as observed in experiments. We also present two-dimensionally modulated states with and without defects which result from the destabilization of the one-dimensionally modulated structures. Finally, for no (or very small) damping, and away from the rotationally symmetric case, we find static chevrons made up of a periodic arrangement of defect chains (or bands of defects) separating homogeneous regions of oblique rolls with very small amplitude. These states may provide a model for a class of poorly understood stationary structures observed in various highly-conducting materials ("prechevrons" or "broad domains").
13 pages, 13 figures
References in corpus (9)
- Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
- Weakly Nonlinear Theory of Pattern-Forming Systems with Spontaneously Broken Isotropy
- Pattern Formation from Defect Chaos --- A Theory of Chevrons
- Order Parameter Equations for Front Transitions: Planar and Circular Fronts
- Secondary instabilities form a codimension-2 point accompanied by a homoclinic bifurcation
- Abnormal Rolls and Regular Arrays of Disclinations in Homeotropic Electroconvection
- Deviations from linear theory for fluctuations below the supercritical primary bifurcation to electroconvection
- Director precession and nonlinear waves in nematic liquid crystals under elliptic shear
- Three-dimensional pattern formation, multiple homogeneous soft modes, and nonlinear dielectric electroconvection