Modulated structures in electroconvection in nematic liquid crystals
S. Komineasa, H. Zhaob, and L. Kramera a Physikalisches Institut, Universitaet Bayreuth,
D-95440 Bayreuth, Germany b Max-Planck-Institut fuer Physik komplexer Systeme,
Noethnitzer Str. 38, D-01187 Dresden, Germany
Abstract
Motivated by experiments in electroconvection in nematic liquid crystals
with homeotropically 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").