Amplitude Modulation and Relaxation-Oscillation of Counterpropagating Rolls within a Broken-Symmetry Laser-Induced Electroconvection Strip

Abstract

We report a liquid-crystal pattern-formation experiment in which we break the lateral (translational) symmetry of a nematic medium with a laser-induced thermal gradient. The work is motivated by an improved measurement (reported here) of the temperature dependence of the electroconvection threshold voltage in planar-nematic 4-methoxybenzylidene-4-butylaniline (MBBA). In contrast with other broken-symmetry-pattern studies that report a uniform drift, we observe a strip of counterpropagating rolls that collide at a sink point, and a strong temporally periodic amplitude modulation within a width of 3-4 rolls about the sink point. The time dependence of the amplitude at a fixed position is periodic but displays a nonsinusoidal relaxation-oscillation profile. After reporting experimental results based on spacetime contours and wavenumber profiles, along with a measurement of the change in the drift frequency with applied voltage at a fixed control parameter, we propose some potential guidelines for a theoretical model based on saddle-point solutions for Eckhaus-unstable states and coupled complex Ginzburg-Landau equations. Published in PRE 73, 036317 (2006).