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

Abstract

We fitted $C({\bf k},τ,ε) \propto exp[-σ({\bf k},ε)τ]$ to time-correlation functions $C({\bf k},τ,ε)$ of structure factors $S({\bf k}, t, ε)$ 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(2πf t) $[${\bf k}= (p,q)$ is the wave vector and $ε\equiv V_0^2/V_{c}^2 - 1$]. There were stationary oblique (normal) rolls at small (large) $f$. Fits of a modified Swift-Hohenberg form to $σ({\bf k},ε)$ gave $f$-dependent critical behavior for the minimum decay rates $σ_0(ε)$ and the correlations lengths $ξ_{p,q}(ε)