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

Manipulating conductivity and noise for transitioning between stochastic and inverse stochastic resonances in liquid-crystal electroconvection

Noise can play a constructive role in nature and various engineering systems. Over the past four decades, noise-induced stochastic resonances (SRs) have been extensively documented, showing enhancement in system performance. Additionally, inverse SR has been observed in various systems. Typically, these resonances were studied independently. A transition between these resonances was recently observed in an alternating current-driven liquid-crystal electroconvection (EC) system using combined amplitude and phase noises. This study uses internal (material) and external (noise) parameters to demonstrate the control of this transition. Specifically, the nonmonotonic threshold voltage behavior of the EC system, indicative of the resonances, was numerically examined using additional parameters. Experimental tests were conducted to confirm the effects of these parameters. The findings reveal that the transition between these resonances can be systematically controlled to meet specific needs, whether desirable or undesirable system performances. Notably, this study illustrates how to modify the behavior of both resonances in colored noise by adjusting its cutoff frequency and steepness and phase noise, which is often overlooked. Moreover, this study provides valuable insights for various noise-related applications.

Control of stochastic and inverse stochastic resonances in a liquid-crystal electroconvection system using amplitude and phase noises

Stochastic and inverse stochastic resonances are counterintuitive phenomena, where noise plays a pivotal role in the dynamics of various biological and engineering systems. Even though these resonances have been identified in various systems, a transition between them has never been observed before. The present study demonstrates the presence of both resonances in a liquid crystal electroconvection system using combined amplitude and phase noises, which correspond to colored noises with appropriate cutoff frequencies (i.e., finite correlation times). We established the emergence of both resonances and their transition through systematic control of the electroconvection threshold voltage using these two noise sources. Our numerical simulations were experimentally confirmed and revealed how the output performance of the system could be controlled by combining the intensity and cutoff frequency of the two noises. Furthermore, we suggested the crucial contribution of a usually overlooked additional phase noise to the advancements in various noise-related fields.

Electroconvection in one-dimensional liquid crystal cells

We investigate the alternating current (ac) -driven electroconvection (EC) in one-dimensional cells (1DCs) under the in-plane switching mode. In 1DCs, defect-free EC can be realized. In the presence and absence of external multiplicative noise, the features of traveling waves (TWs), such as their Hopf frequency f_{H} and velocity, are examined in comparison with those of conventional two-dimensional cells (2DCs) accompanying defects of EC rolls. In particular, we show that the defects significantly contribute to the features of the TWs. Additionally, owing to the defect-free EC in the 1DCs, the effects of the ac and noise fields on the TW are clarified. The ac field linearly increases f_{H}, independent of the ac frequency f. The noise increases f_{H} monotonically, but f_{H} does not vary below a characteristic noise intensity V_{N}^{*}. In addition, soliton-like waves and unfamiliar oscillation of EC vortices in 1DCs are observed, in contrast to the localized EC (called worms) and the oscillation of EC rolls in 2DCs.

Traveling waves and worms in ac-driven electroconvection under external multiplicative noise

In the presence of external multiplicative noise, ac-driven electroconvection (EC) in a nematic liquid crystal is investigated. Noise-induced traveling waves (TWs) including localized ones (worms) are found with a typical, stationary wave. Three kinds of TWs are classified by their dynamic features (e.g., noise-intensity-dependent Hopf frequency and space-time map). Moreover, ac frequency-dependent threshold voltages of EC are examined in high noise intensities causing abnormal charge redistribution of the EC cell, and the roles of ac and noise fields with respect to TWs are elucidated in successive pattern evolutions. The mechanism of TWs is discussed in terms of a locally perturbed dynamic conductivity due to the noise field additionally applied to the EC; such a conductivity can be related to a weak-electrolyte model for a Hopf bifurcation to a TW.

Inverse stochastic resonance in electroconvection by multiplicative colored noise

A kind of inverse stochastic resonance (ISR) observed in ac-driven electroconvection (EC) in a nematic liquid crystal is presented. In successive pattern evolutions by increasing noise intensity V_{N}, a typical EC (with a normalized amplitude A_{0}=1 at V_{N}=0) disappears (A_{0}→0), and then the rest state (A_{0}=0) reenters into the EC (A_{0}=1); eventually, it develops into complicated EC(A_{0}>1). The reversed bell-shaped behavior of A_{0}(V_{N}) is evidence of ISR. The present ISR may be explained by taking into account colored noise characterized by its intensity and correlation time.

Multiplicative noise effects on electroconvection in controlling additive noise by a magnetic field

We report multiplicative noise-induced threshold shift of electroconvection (EC) in the presence of a magnetic field H. Controlling the thermal fluctuation (i.e., additive noise) of the rodlike molecules of nematic liquid crystals by H, the EC threshold is examined at various noise levels [characterized by their intensity and cutoff frequency (f(c))]. For a sufficiently strong H (i.e., ignorable additive noise), a modified noise sensitivity characterizing the shift problem is in good agreement with experimental results for colored as well as white noise (f(c)→∞); until now, there was a large deviation for (sufficiently) colored noises. The present study shows that H provides us with ideal conditions for studying the corresponding Carr-Helfrich theory considering pure multiplicative noise.