Strong anomalous diffusion of the phase of a chaotic pendulum

Cagnetta, Francesco; Gonnella, Giuseppe; Mossa, Alessandro; Ruffo, Stefano

doi:10.1209/0295-5075/111/10002

Cited by 9 publications

(5 citation statements)

References 43 publications

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“…Remarkably, these non-universal distributions, which feature non-analytic behaviors, are obtained from the general principle of single big jump, which provides a unique physical explanation of the process driving the rare events. Finally, we also derive the scaling of all the moments of the distribution that, interestingly, feature strong anomalous diffusion [28][29][30]. All our analytical results are in very good agreement with extensive numerical simulations.…”

Section: Introductionsupporting

confidence: 58%

“…In Figure 5 we consider the super-diffusive regime α > 1, ν > α/2 and ν > η. In panel (a) we plot R q (T ) and in panel (b) we plot the function γ(q) , that shows strong anomalous diffusion [28,29]. Far away from the transition where preasymptotic effects are expected to be stronger, simulations displays a nice agreements with theoretical values:…”

Section: The Moments Of the Distributionmentioning

confidence: 76%

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Rare events in generalized Lévy Walks and the Big Jump principle

Vezzani

Barkai

Burioni

2020

Sci Rep

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The prediction and estimate of rare events is an important task in disciplines that range from physics and biology, to economics and social science. A peculiar aspect of the mechanism that drives rare events is described by the so called Big Jump Principle. According to the principle, in heavytailed processes a rare huge fluctuation is caused by a single event and not by the usual coherent accumulation of small deviations. We consider generalized Lévy walks, a class of stochastic models with wide applications, from complex transport to search processes, that accounts for complex microscopic dynamics in the single stretch. We derive the bulk of the probability distribution and using the big jump principle, the exact form of the tails that describes rare events. We show that the tails of the distribution feature non-universal and non-analytic behaviors, that crucially depend on the dynamics of the single step. The big jump estimate also provides a physical explanation of the processes driving the rare events, opening new possibilities for their correct prediction.

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Section: Introductionsupporting

confidence: 58%

Section: The Moments Of the Distributionmentioning

confidence: 76%

Rare events in generalized Lévy Walks and the Big Jump principle

Vezzani

Barkai

Burioni

2020

Sci Rep

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“…This in turn implies that the single jump is needed, at least in some cases, for the investigation of the mean square displacement of the spreading process, which is easily considered the main quantifier of diffusion. Since strong anomalous diffusion is observed in a wide range of systems, we believe the principle of large jump has wide spread applications [57][58][59][60][61].…”

Section: Discussion and Open Problemsmentioning

confidence: 99%

Single-big-jump principle in physical modeling

2019

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The big jump principle is a well established mathematical result for sums of independent and identically distributed random variables extracted from a fat tailed distribution. It states that the tail of the distribution of the sum is the same as the distribution of the largest summand. In practice, it means that when in a stochastic process the relevant quantity is a sum of variables, the mechanism leading to rare events is peculiar: instead of being caused by a set of many small deviations all in the same direction, one jump, the biggest of the lot, provides the main contribution to the rare large fluctuation. We reformulate and elevate the big jump principle beyond its current status to allow it to deal with correlations, finite cutoffs, continuous paths, memory and quenched disorder. Doing so we are able to predict rare events using the extended big jump principle in Lévy walks, in a model of laser cooling, in a scattering process on a heterogeneous structure and in a class of Lévy walks with memory. We argue that the generalized big jump principle can serve as an excellent guideline for reliable estimates of risk and probabilities of rare events in many complex processes featuring heavy tailed distributions, ranging from contamination spreading to active transport in the cell. PACS numbers:

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“…For example, in piecewise linear one-dimensional chaotic maps it has been found that the diffusion coefficient is a fractal function of control a e-mail: s.gilgallegos@qmul.ac.uk b e-mail: r.klages@qmul.ac.uk c e-mail: janne@solanpaa.fi d e-mail: esa.rasanen@tut.fi parameters [4,5,6]. A relatively simple two-dimensional map with similarly irregular diffusion coefficients is the standard map [7,8], which can be derived as a time discrete version of a chaotic nonlinear pendulum equation [9,10]. Here it has been observed that normal diffusion is interrupted by regions in parameter space which are related to accelerator modes yielding superdiffusive transport [11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Energy-dependent diffusion in a soft periodic Lorentz gas

Gil-Gallegos

Klages

Solanpää

et al. 2019

Eur. Phys. J. Spec. Top.

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The periodic Lorentz gas is a paradigmatic model to examine how macroscopic transport emerges from microscopic chaos. It consists of a triangular lattice of circular hard scatterers with a moving point particle. Recently this system became relevant as a model for electronic transport in low-dimensional nanosystems such as molecular graphene. However, to more realistically mimic such dynamics, the hard Lorentz gas scatterers should be replaced by soft potentials. Here we study diffusion in a soft Lorentz gas with Fermi potentials under variation of the total energy of the moving particle. Our goal is to understand the diffusion coefficient as a function of the energy. In our numerical simulations we identify three different dynamical regimes: (i) the onset of diffusion at small energies; (ii) a transition where for the first time a particle reaches the top of the potential, characterized by the diffusion coefficient abruptly dropping to zero; and (iii) diffusion at high energies, where the diffusion coefficient increases according to a power law in the energy. All these different regimes are understood analytically in terms of simple random walk approximations. arXiv:1811.11661v1 [cond-mat.stat-mech]

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Strong anomalous diffusion of the phase of a chaotic pendulum

Cited by 9 publications

References 43 publications

Rare events in generalized Lévy Walks and the Big Jump principle

Rare events in generalized Lévy Walks and the Big Jump principle

Single-big-jump principle in physical modeling

Energy-dependent diffusion in a soft periodic Lorentz gas

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