Universality of rare fluctuations in turbulence and critical phenomena

Bramwell, S. T.; Holdsworth, Peter; Pinton, Jean‐François

doi:10.1038/25083

Cited by 291 publications

(411 citation statements)

References 18 publications

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“…Large scale fluctuations in many correlated systems are described by the generalized Gumbel distribution [45]. It is further the asymptotic distributions of the extreme values of sequences correlated over a 'distance' 1/a (eq.15) [46] and the asymptotic distribution of sums of independent non identically distributed random variables or of correlated variables which do not verify the conditions of validity of the central limit theorem [47].…”

Section: 4the Relation Between a Gg Distribution And A Generalizedmentioning

confidence: 99%

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

Caër¹,

Male²,

Delannay³

2007

Physica A: Statistical Mechanics and its Applications

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Section: 4the Relation Between a Gg Distribution And A Generalizedmentioning

confidence: 99%

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

Caër¹,

Male²,

Delannay³

2007

Physica A: Statistical Mechanics and its Applications

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“…In this class of systems, the relevant macroscopic observable is not only the current: the dissipated energy is also expected to play a main role. These systems include granular media [16], dissipative biophysical systems [18], turbulent fluids [19], active matter [20], chemical reactions [21], population dynamics [22], etc. In general, this class comprises all sort of reaction-diffusion systems where dissipation, diffusion and driving are the main physical mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Renormalized time scale for anticipating and lagging synchronization

2016

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We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven dissipative media, starting from the fluctuating hydrodynamic equations describing the system mesoscopic evolution. Interestingly, the action associated to a path in mesoscopic phase-space, from which large-deviation functions for macroscopic observables can be derived, has the same simple form as in non-dissipative systems. This is a consequence of the quasi-elasticity of microscopic dynamics, required in order to have a nontrivial competition between diffusion and dissipation at the mesoscale. Euler-Lagrange equations for the optimal density and current fields that sustain an arbitrary dissipation fluctuation are also derived. A perturbative solution thereof shows that the probability distribution of small fluctuations is always gaussian, as expected from the central limit theorem. On the other hand, strong separation from the gaussian behavior is observed for large fluctuations, with a distribution which shows no negative branch, thus violating the Gallavotti-Cohen fluctuation theorem as expected from the irreversibility of the dynamics. The dissipation large-deviation function exhibits simple and general scaling forms for weakly and strongly dissipative systems, with large fluctuations favored in the former case but heavily supressed in the latter. We apply our results to a general class of diffusive lattice models for which dissipation, nonlinear diffusion and driving are the key ingredients. The theoretical predictions are compared to extensive numerical simulations of the microscopic models, and excellent agreement is found. Interestingly, the large-deviation function is in some cases non-convex beyond some dissipation. These results show that a suitable generalization of macroscopic fluctuation theory is capable of describing in detail the fluctuating behavior of nonlinear driven dissipative media.

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“…In these cases, anomalous values of a are found for Gumbel's asymptote, and we plot a = 1 and 2 along with the Fréchet curve a = 1.1 for comparison with the X-ray data. Also, since our global quantity is emitted flux rather than absorbed power, our curves show the opposite handedness to the results of Bramwell et al (1998).…”

Section: Non-gaussian Statistical Propertiesmentioning

confidence: 66%

“…In this case, they would be the brightest among multiple events (whose PDF could be power-law) occuring within each observational time window. Interestingly, extremal statistics in a global measure are found in turbulent fluids and other highly-correlated systems (Bramwell et al 1998(Bramwell et al , 2000(Bramwell et al , 2001. In these cases, anomalous values of a are found for Gumbel's asymptote, and we plot a = 1 and 2 along with the Fréchet curve a = 1.1 for comparison with the X-ray data.…”

Section: Non-gaussian Statistical Propertiesmentioning

confidence: 99%

“…We note that the PDF was used by Antar et al (2001) to characterise turbulent fluctuations in tokamak edge plasmas, and by Bhavsar & Barrow (2001) to model the magnitude distribution of the brightest cluster galaxies. Bramwell et al (1998Bramwell et al ( , 2000Bramwell et al ( , 2001) discuss the PDFs of fluctuations in highly-correlated systems (see Sect. 4), and Burlaga (2001) presents a review of log-normal distributions in the turbulent solar wind.…”

Section: The Probability Density Function (Pdf)mentioning

confidence: 99%

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Characterising Anomalous Transport in Accretion Disks from X-ray Observations

Greenhough¹,

Chapman²,

Chaty³

et al.

Statistical Challenges in Astronomy

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Abstract. Whilst direct observations of internal transport in accretion disksare not yet possible, measurement of the energy emitted from accreting astrophysical systems can provide useful information on the physical mechanisms at work. Here we examine the unbroken multi-year time variation of the total X-ray flux from three sources: Cygnus X-1, the microquasar GRS1915+105, and for comparison the nonaccreting Crab nebula. To complement previous analyses, we demonstrate that the application of advanced statistical methods to these observational time-series reveals important contrasts in the nature and scaling properties of the transport processes operating within these sources. We find the Crab signal resembles Gaussian noise; the Cygnus X-1 signal is a leptokurtic random walk whose self-similar properties persist on timescales up to three years; and the GRS1915+105 signal is similar to that from Cygnus X-1, but with self-similarity extending possibly to only a few days. This evidence of self-similarity provides a robust quantitative characterisation of anomalous transport occuring within the systems.

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Universality of rare fluctuations in turbulence and critical phenomena

Cited by 291 publications

References 18 publications

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

Renormalized time scale for anticipating and lagging synchronization

Characterising Anomalous Transport in Accretion Disks from X-ray Observations

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