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

Abstract

We fitted $C(\mathbf{k},\tau ,\epsilon )\propto exp[-\sigma (\mathbf{k},\epsilon )\tau ]$ to time-correlation functions $C(\mathbf{k},\tau ,\epsilon )$ of structure factors $S(\mathbf{k},t,\epsilon )$ 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 $V=\sqrt{2}{V}_{0}cos(2\pi ft)$[$\mathbf{k}=(p,q)$ 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 $\sigma (\mathbf{k},\epsilon )$ gave $f$-dependent critical behavior for the minimum decay rates ${\sigma }_0(\epsilon )$ and the correlations lengths $ξ_{p,q}(ε)