Relaxation-Oscillation and Eckhaus -Unstable Roll Dynamics Observed Within Laser-Localized Electroconvection Spots.

We use modest laser powers to create slightly warmed regions within a nematic liquid crystal to generate localized electrconvection patterns [1]. Using a laser profile with an intensity that varies linearly with position, we observe counterpropagating waves with nonzero group and phase velocity; the latter is the largest and increases significantly if the applied frequency and voltage are increased in a manner that holds the control parameter fixed. The temporal dependence of the amplitude at a point is periodic but not sinusoidal: its temporal profile is that of a relaxation-oscillator. Measurement of the wavevector profiles shows the wavevector range for the traveling waves extends well beyond the Eckhaus-stable band. This type of measurement can in principle be used to provide an experimental system-size control parameter for spatial-temporal chaos; results of preliminary experiments on this problem will be presented.