On-Off Intermittency in Stochastically Driven Electrohydrodynamic Convection in Nematics

Abstract

We report on-off intermittency in electroconvection of nematic liquid crystals driven by a dichotomous stochastic electric voltage. With increasing voltage amplitude we observe laminar phases of undistorted director state interrupted by shorter bursts of spatially regular stripes. Near a critical value of the amplitude the distribution of the duration of laminar phases is governed over several decades by a power law with exponent −3/2. The experimental findings agree with simulations of the linearized electrohydrodynamic equations near the sample stability threshold.PACS numbers: 05.40.+j, 47.20.-k, 47.54.+r, 61.30-v Systems at a threshold of stability driven by a stochastic or chaotic process coupling multiplicatively to the system variables may exhibit on-off intermittency characterized by specific statistical properties of the intermittent signal. Quiescent (or laminar) periods (off-states) are interrupted by bursts of large variation (on-states); the duration of laminar periods is governed by power laws with exponents universal over a broad class of different systems. Early theoretical studies considered systems with few degrees of freedom modeled by differential equations [1] and mappings [2]. There is increasing interest in systems with many degrees of freedom [3], described by random map lattices [4], larger systems of coupled nonlinear elements [5], and partial differential equations [5,6]. Experimental results are available mainly for nonlinear electric circuits [7]; on-off intermittency was also observed in a spin wave experiment [8], in optical feedback [9], and a gas discharge plasma system [10]. Here we first report about on-off intermittency in a spatially extended dissipative system, viz. electroconvection (EC) in nematic liquid crystals driven by a stochastic voltage.EC in planarly aligned nematics is a standard system for pattern formation, for recent reviews see, e.g. [11]. In the presence of an electric field E a spontaneous fluctuation of the director leads due to the anisotropic conductivity to a formation of space charges which tend to destabilize the homogeneously ordered state. With increasing strength of the driving field one observes a hierarchy of convection patterns of increasing complexity. The patterns depend on external parameters such as amplitude, frequency and wave form of the driving voltage which are conveniently adjustable in the experiment. The hydrodynamic flow induces a modulation of the director field and thus of the effective indices of refraction which leads to transmission patterns easily observed with a microscope.In previous experiments, the superposition of a deterministic AC field with a stochastic field, E = E det (t) + E stoch (t), was studied. A variety of noise induced phenomena including stabilization or destabilization of the homogeneous state, and a change from continuous to discontinuous behaviour of the threshold as a function of the noise strength was observed [12][13][14][15][16] and has stimulated theoretical work [17,18].As long as the characteristi...

Effect of multiplicative noise on parametric instabilities

“…Previous studies involve electronic oscillators [6], spin waves in ferrites and antiferromagnets [7,8] and electroconvection in nematic liquid crystals [9,10], but only the effect of noise on supercritical bifurcations has been considered so far. Only recently, experiments on the effect of noise on parametrically driven surface waves have been performed in the case of a subcritical bifurcation.…”

Data-driven coarse graining in action: Modeling and prediction of complex systems

“…Figure 4(d) shows the results obtained with models M1 and M2 (both models give virtually identical results) observing that the PDF of T (which is normalized to its mean value) follows a truncated power-law, P (T ) = aT −γ exp (−T /T 0 ), with exponent γ 1.54 which does not depend on X th . Interestingly, this particular type of PDF (with exponent close to 3/2) has been observed ubiquitously in many different biological and physical systems exhibiting intermittent behavior (a signature usually of critical phenomena), from neuronal activity in the cortex [22], electroconvection of nematic liquid crystals [23], fluid flow in porous media [24] to colloidal quantum dots [25] and noise-induced transitions in infinite dimensional dissipative systems [26]. By studying the mean first passage time (MFPT) properties, the exponent 3/2 was obtained recently for SDEs of the form (5) with lineal multiplicative noise term [27].…”

Control of on-off intermittency by slow parametric modulation

“…Like the other types, on-off intermittency is characterized by fundamental statistical properties with typical power-law scalings near the onset of intermittency: (i) for the mean laminar phase as a function of the coupling parameter with a critical exponent of −1 [7], and (ii) for the probability distribution of the laminar phase versus the laminar length with exponent −3/2 [7]. The on-off intermittency has also been detected experimentally in electronic circuits [11], in a gas discharge plasma [12], in a spin wave system [13], in nematic liquid crystals [14], and in a laser [15]. In the case of periodically driven systems, the same critical exponent of −1 for the mean laminar phase has been found in laser experiments as a function of both the amplitude and frequency of the parametric modulation near the onset of intermittency [15].…”