Anomalous velocity fluctuation in one-dimensional defect turbulence

Uchiyama, Yusuke; Kadoya, Takanori; Konno, Haruyoshi

doi:10.1103/physreve.91.022127

Cited by 5 publications

(3 citation statements)

References 35 publications

(49 reference statements)

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“…An explosive soliton is a stable solution, as opposed to other structures that may vanish or annihilate. For instance, for the same model, equation (2), holes were found to annihilate with each other, but during the transients, a rich anomalous dynamics appears [28]; normal diffusion of solitons in a Bose-Einstein condensate induced by heterogeneities has been reported [29]; transient anomalous diffusion of solitons has been found [30] in nonlocal random media. Figure 2 shows the evolution of a soliton for a longer time window including 6 explosions.…”

Section: Explosions Of Dissipative Solitonsmentioning

confidence: 94%

A new kind of chaotic diffusion: anti-persistent random walks of explosive dissipative solitons

2019

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The solitons that exist in nonlinear dissipative media have properties very different from the ones that exist in conservative media and are modeled by the nonlinear Schrödinger equation. One of the surprising behaviors of dissipative solitons is the occurrence of explosions: sudden transient enlargements of a soliton, which as a result induce spatial shifts. In this work using the complex Ginzburg-Landau equation in one dimension, we address the long-time statistics of these apparently random shifts. We show that the motion of a soliton can be described as an anti-persistent random walk with a corresponding oscillatory decay of the velocity correlation function. We derive two simple statistical models, one in discrete and one in continuous time, which explain the observed behavior. Our statistical analysis benchmarks a future microscopic theory of the origin of this new kind of chaotic diffusion.

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Section: Explosions Of Dissipative Solitonsmentioning

confidence: 94%

A new kind of chaotic diffusion: anti-persistent random walks of explosive dissipative solitons

2019

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“…Related to comprehensive studies of the SSDE, their fluctuations are assumed to follow the Gaussian distribution. However, we can observe anomalous fluctuations following non-Gaussian distributions in the real world: fluid particle transport in a rotating cylinder [16], a hopping cold atom in optical lattices [17], wave propagation in dissipative media [18], etc. For the sake of identifying the anomalous fluctuations on random time durations, the SSDE is a suitable model to describe non-Gaussian distributions.…”

Section: Introductionmentioning

confidence: 99%

Fractional generalized Cauchy process

2019

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This paper presents a fractional generalized Cauchy process (FGCP) with an additive and a multiplicative Gaussian white noise for describing subordinated anomalous fluctuations. The FGCP displays intermittent dynamics during random time durations, whose analytical representation is given by the Itô stochastic integral. The associated probability density function is given by the Tsallis q-Gaussian distribution at the stationary state. The method of fractional Feynman-Kac formula shows that weak ergodicity breaking of the FGCP depends on the existence of the subordinator and/or the divergence of variance.

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“…To catch the true dynamical features of PSs, it is necessary to get the information on (i) the PS number distribution, (ii) the waiting time (lifetime) distribution, (iii) the velocity distribution of PS. For the case of 1D CGLE in a region of the amplitude turbulence, we could describe the related stochastic processes having a long-memory through the three distributions (i), (ii) and (iii) by taking a birth-death process (λ n =ν and μ n =μn) of the PS number n [14], and a generalized Cauchy process of the velocity of PS [15].…”

Section: Introductionmentioning

confidence: 99%

Approximate time-dependent solution of a master equation with full linear birth-death rates

Konno

Tamura

2018

J. Phys. Commun.

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There are growing interests on dynamics of phase-singularities (PSs) in complex systems such as ventricular fibrillation, defect in fluids and liquid crystals, living creatures, quantum vortex and so on. A master equation approach on the number of PS for studying birth-death dynamics of PSs is invented first by Gil, Lega and Meunier. Although their approach is applied to various complex systems including non-linear birth-death rates, time-dependent solution of related master equation is obtained only rarely. Even a master equation with full linear birth-death rates, time-dependent solution is not also given due to the analytical complexity and the existence of singularity in the probability generating function. In this paper, an approximate time-dependent solution of the master equation and the associated waiting time distribution are obtained explicitly with the aid of the method of the Poisson transform. Numerical evaluation of the obtained approximate solution teaches us that there exists the universal scaling law in the waiting time distribution.

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Anomalous velocity fluctuation in one-dimensional defect turbulence

Cited by 5 publications

References 35 publications

A new kind of chaotic diffusion: anti-persistent random walks of explosive dissipative solitons

A new kind of chaotic diffusion: anti-persistent random walks of explosive dissipative solitons

Fractional generalized Cauchy process

Approximate time-dependent solution of a master equation with full linear birth-death rates

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