Noise-induced threshold shift and pattern formation in electroconvection by controlling characteristic time scales

Abstract

We report external noise-induced threshold shift and pattern formation in ac-driven electroconvection (EC) in nematic liquid crystals. We investigate the noise intensity dependence of the threshold and determine the relationship f(c)(*)=hf(cd)(a) (α ∼ 1.4, h ∼ 0.1) between the characteristic cutoff frequency (f(c)(*)) of the noise and the characteristic ac frequency (f(cd)) of EC. For f(c)>f(c)(*), the noise contributes to stabilizing EC (i.e., upward threshold shift), whereas for f(c)<f(c)(*), it contributes to destabilizing EC (i.e., downward threshold shift). For f(c)=f(c)(*), the noise makes no contribution to the threshold shift. However, the characteristic wavelength of EC strongly depends on the noise intensity but not on f(c).

Multiplicative Noise-Induced Electrohydrodynamic Pattern Formations by Controlling Electric Conductivity

“…[10][11][12] Very recently, it has been discovered that in addition to the external timescale N of noise, a certain internal timescale (a charge relaxation time) characterizing ECs plays a crucial role in the threshold problems and phase diagrams (pattern structures). 13) In particular, the sensitivity b ¼ bð Þ for white-limit noise ( N ! 0) was modified into b ¼ bð ; N Þ for colored noise ( N ≠ 0);…”

“…13) Indeed, there exist some characteristic (internal) times d ($ 10 À1 s, a relaxation time of the director), ($ 10 À3 s), and f À1 ($ 10 À3 {10 À1 s) in conventional ECs, 14) and also the characteristic external time N ($ 10 À6 {10 À3 s) of colored noise. [11][12][13] Practically, when the timescale of N overlaps with the internal timescales ( d , , and f À1 ), a remarkable variation for noise-induced phenomena can be expected, similarly to the usual resonance. Very recently, on the other hand, by taking into account the additive noise ðr; tÞ (i.e., thermal fluctuations of LC molecules) that can be controlled by a magnetic field, its effect on the threshold shift problems [Eq.…”

“…16) In particular, high-conductivity cells (HCCs, $ 10 À6 À1 m −1 ) are examined; their conductivity is unusually larger than that of the conventional, typical conductivity cells (TCCs, $ 10 À8 {10 À7 À1 m −1 ). 13) Thus, (¼ " 0 "= $ 10 À5 s) for HCCs becomes much smaller than that for TCCs ($ 10 À4 {10 À3 s), and then a high EC-critical frequency f cd [¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi…”

“…is realized ( f cd $ 10 4 Hz), compared with f cd $ 10 2 Hz for TCCs with $ 10 À8 À1 m −1 . 13) Notice that the timescale of overlaps with that of N . Here, 2 denotes a dimensionless parameter of LCs (e.g., 1:5 < 2 < 4 for the present LC, MBBA).…”

“…The results of threshold shifts in σ-controlled cells have already been reported in our previous papers. 13) Accordingly, in this paper, actual pattern formations are presented with many real pictures. For HCCs, in particular, completely different behaviors of the EC threshold and pattern formations such as noise-dominated patterns are found.…”