606 research outputs found
On-off intermittency over an extended range of control parameter
We propose a simple phenomenological model exhibiting on-off intermittency
over an extended range of control parameter. We find that the distribution of
the 'off' periods has as a power-law tail with an exponent varying continuously
between -1 and -2, at odds with standard on-off intermittency which occurs at a
specific value of the control parameter, and leads to the exponent -3/2. This
non-trivial behavior results from the competition between a strong slowing down
of the dynamics at small values of the observable, and a systematic drift
toward large values.Comment: 4 pages, 3 figure
Low frequency noise controls on-off intermittency of bifurcating systems
A bifurcating system subject to multiplicative noise can display on-off
intermittency. Using a canonical example, we investigate the extreme
sensitivity of the intermittent behavior to the nature of the noise. Through a
perturbative expansion and numerical studies of the probability density
function of the unstable mode, we show that intermittency is controlled by the
ratio between the departure from onset and the value of the noise spectrum at
zero frequency. Reducing the noise spectrum at zero frequency shrinks the
intermittency regime drastically. This effect also modifies the distribution of
the duration that the system spends in the off phase. Mechanisms and
applications to more complex bifurcating systems are discussed
The Lorentz force effect on the On-Off dynamo intermittency
An investigation of the dynamo instability close to the threshold produced by
an ABC forced flow is presented. We focus on the on-off intermittency behavior
of the dynamo and the counter-effect of the Lorentz force in the non-linear
stage of the dynamo. The Lorentz force drastically alters the statistics of the
turbulent fluctuations of the flow and reduces their amplitude. As a result
much longer burst (on-phases) are observed than what is expected based on the
amplitude of the fluctuations in the kinematic regime of the dynamo. For large
Reynolds numbers, the duration time of the ``On'' phase follows a power law
distribution, while for smaller Reynolds numbers the Lorentz force completely
kills the noise and the system transits from a chaotic state into a ``laminar''
time periodic flow. The behavior of the On-Off intermittency as the Reynolds
number is increased is also examined. The connections with dynamo experiments
and theoretical modeling are discussed.Comment: 8 page
Effects of the low frequencies of noise on On-Off intermittency
A bifurcating system subject to multiplicative noise can exhibit on-off
intermittency close to the instability threshold. For a canonical system, we
discuss the dependence of this intermittency on the Power Spectrum Density
(PSD) of the noise. Our study is based on the calculation of the Probability
Density Function (PDF) of the unstable variable. We derive analytical results
for some particular types of noises and interpret them in the framework of
on-off intermittency. Besides, we perform a cumulant expansion for a random
noise with arbitrary power spectrum density and show that the intermittent
regime is controlled by the ratio between the departure from the threshold and
the value of the PSD of the noise at zero frequency. Our results are in
agreement with numerical simulations performed with two types of random
perturbations: colored Gaussian noise and deterministic fluctuations of a
chaotic variable. Extensions of this study to another, more complex, system are
presented and the underlying mechanisms are discussed.Comment: 13pages, 13 figure
On-off intermittency and amplitude-phase synchronization in Keplerian shear flows
We study the development of coherent structures in local simulations of the
magnetorotational instability in accretion discs in regimes of on-off
intermittency. In a previous paper [Chian et al., Phys. Rev. Lett. 104, 254102
(2010)], we have shown that the laminar and bursty states due to the on-off
spatiotemporal intermittency in a one-dimensional model of nonlinear waves
correspond, respectively, to nonattracting coherent structures with higher and
lower degrees of amplitude-phase synchronization. In this paper we extend these
results to a three-dimensional model of magnetized Keplerian shear flows.
Keeping the kinetic Reynolds number and the magnetic Prandtl number fixed, we
investigate two different intermittent regimes by varying the plasma beta
parameter. The first regime is characterized by turbulent patterns interrupted
by the recurrent emergence of a large-scale coherent structure known as
two-channel flow, where the state of the system can be described by a single
Fourier mode. The second regime is dominated by the turbulence with sporadic
emergence of coherent structures with shapes that are reminiscent of a
perturbed channel flow. By computing the Fourier power and phase spectral
entropies in three-dimensions, we show that the large-scale coherent structures
are characterized by a high degree of amplitude-phase synchronization.Comment: 17 pages, 10 figure
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