Capturing rogue waves by multi-point statistics

Hadjihosseini, Ali; Wächter, Matthias; Hoffmann, Norbert; Peinke, Joachim

doi:10.1088/1367-2630/18/1/013017

Cited by 15 publications

(23 citation statements)

References 42 publications

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“…To convert the series of sea-level height measurements in time to its scale or increment counterparts has profound consequences, as the latter now turns out to be Markovian [5,6]. As a consequence the full analysis of the data, based on the computation of the N -point propagator p(h t |h t−τ1 , ..., h t−τ N −1 ) that predicts the time series of heights, can be decomposed into N − 2 increment propagators p(∆h k,t |∆h k+1,t , h t ) for each scale k together with the initial distribution, p(∆h 0 , τ, h t ) [6], see also supplementary material I.…”

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confidence: 99%

Rogue waves and entropy consumption

Hadjihoseini¹,

Lind²,

Mori³

et al. 2017

EPL

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Based on data from the Japan Sea and the North Sea the occurrence of rogue waves is analyzed by a scale dependent stochastic approach, which interlinks fluctuations of waves for different spacings. With this approach we are able to determine a stochastic cascade process, which provides information of the general multipoint statistics. Furthermore the evolution of single trajectories in scale, which characterize wave height fluctuations in the surroundings of a chosen location, can be determined. The explicit knowledge of the stochastic process enables to assign entropy values to all wave events. We show that for these entropies the integral fluctuation theorem, a basic law of non-equilibrium thermodynamics, is valid. This implies that positive and negative entropy events must occur. Extreme events like rogue waves are characterized as negative entropy events. The statistics of these entropy fluctuations changes with the wave state, thus for the Japan Sea the statistics of the entropies has a more pronounced tail for negative entropy values, indicating a higher probability of rogue waves.

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confidence: 99%

Rogue waves and entropy consumption

Hadjihoseini¹,

Lind²,

Mori³

et al. 2017

EPL

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“…As this is a stochastic model, involving a deterministic as well as a random part, the two time series diverge quite fast. But the stochastic content in the sense of multi-point statistics is the same, which can be verified by reanalyising these surrogate data (22,21,32). Another interesting point is that apparently typical structures of a wave pattern could be reproduced by the stochastic method (58), thus it seems that the multi-point approach is capable to grasp the statistics as well as coherent structures.…”

Section: Surrogate Data and Forecastingmentioning

confidence: 71%

“…As mentioned for turbulence the Markov properties are found for both the multi-point p(ξ3|ξ2, ξ1, qN ) and the multi-scale p(ξ3|ξ2, ξ1) statistics. For surface waves we found that Markov properties are only valid for the multi-point statistics (32). If the joint probabilities W (ξ3, ξ2, ξ1, qN ) can be written as W (ξ3, ξ2, ξ1, qN ) = W (ξ3, ξ2, ξ1)W (qN ), one Markov property always follows from the other.…”

Section: Closures Of Multi-point Statisticsmentioning

confidence: 97%

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The Fokker–Planck Approach to Complex Spatiotemporal Disordered Systems

Peinke

Tabar

Wächter

2019

Annu. Rev. Condens. Matter Phys.

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When the complete understanding of a complex system is not available, as, e.g., for systems considered in the real-world, we need a top-down approach to complexity. In this approach one may start with the desire to understand general multi-point statistics. Here such a general approach is presented and discussed based on examples from turbulence and sea waves. Our main idea is based on the cascade picture of turbulence, entangling fluctuations from large to small scales. Inspired by this cascade picture, we express the general multi-point statistics by the statistics of scale-dependent fluctuations of variables and relate it to a scale-dependent process, which finally is a stochastic cascade process. We show how to extract from empirical data a Fokker-Planck equation for this cascade process, which allows to generate surrogate data to forecast extreme events as well as to develop a non-equilibrium thermodynamics for the complex systems. For each cascade events an entropy production can be determined. These entropies fulfil accurately a rigorous law, namely the integral fluctuations theorem. 2Peinke Tabar Waechter

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“…Predictability of RWs is also a recently debated feature with obvious applications in the control or forecasting of rare events. Although it is widely accepted that RWs are chaotic to a large extent, there have been some studies that successfully argue their deterministic character in optical systems [4] and even suggest ways to foretell their occurrence [5,7,8]. The key element for the characterization of extreme events is the understanding of the underlying mechanism leading to the formation of optical RWs [6].…”

Section: Introductionmentioning

confidence: 99%

Optical turbulence and transverse rogue waves in a cavity with triple-quantum-dot molecules

et al. 2017

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This version is available at https://strathprints.strath.ac.uk/61943/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. We show that optical turbulence extreme events can exist in the transverse dynamics of a cavity containing molecules of triple quantum dots under conditions close to tunneling-induced transparency. These nanostructures, when coupled via tunneling, form a four-level configuration with tunable energy-level separations. We show that such a system exhibits multistability and bistability of Turing structures in instability domains with different critical wave vectors. By numerical simulation of the mean-field equation that describes the transverse dynamics of the system, we show that the simultaneous presence of two transverse solutions with opposite nonlinearities gives rise to a series of turbulent structures with the capability of generating two-dimensional rogue waves.

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Capturing rogue waves by multi-point statistics

Cited by 15 publications

References 42 publications

Rogue waves and entropy consumption

Rogue waves and entropy consumption

The Fokker–Planck Approach to Complex Spatiotemporal Disordered Systems

Optical turbulence and transverse rogue waves in a cavity with triple-quantum-dot molecules

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