Dynamics of fluctuations below a stationary bifurcation to electroconvection in the planar nematic liquid crystal N4

Abstract

We fitted $C({\bf k},\tau,\epsilon) \propto exp[-\sigma({\bf k},\epsilon)\tau]$ to time-correlation functions $C({\bf k},\tau,\epsilon)$ of structure factors $S({\bf k}, t, \epsilon)$ of shadowgraph images of fluctuations below a supercritical bifurcation at $V_0 = V_c$ to electro-convection of a planar nematic liquid crystal in the presence of a voltage $V = \sqrt{2}V_0 cos(2\pi f t) $[${\bf k}= (p,q)$ is the wave vector and $\epsilon \equiv V_0^2/V_{c}^2 - 1$]. There were stationary oblique (normal) rolls at small (large) $f$. Fits of a modified Swift-Hohenberg form to $\sigma({\bf k},\epsilon)$ gave $f$-dependent critical behavior for the minimum decay rates $\sigma_0(\epsilon)$ and the correlations lengths $\xi_{p,q}(\epsilon)