Superstatistical analysis of sea-level fluctuations

Rabassa, Pau; Beck, Christian

doi:10.1016/j.physa.2014.08.068

Cited by 16 publications

(16 citation statements)

References 40 publications

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“…(4), allowing a mapping to a q-Gaussian distribution of vehicle speeds Eq. (14). Some work in the literature assume that once a chi-square distribution manifests itself, a fit from chi-square distribution of inverse temperature values generates a q value that could be assumed to be the same coming out of Eq.…”

Section: Discussion: the Coexistence Of Different Q Valuesmentioning

confidence: 99%

“…(4) and (14) have yielded different values, but finally a shuffled speed data analysis too produced a third and different q value, emphatically different from the one by Eq. (14).…”

Section: Discussionmentioning

confidence: 99%

“…There are numerous applications of superstatistical theory on data analyses, such as sea-level fluctuations [14], high energy physics [15], modeling train delays [16], environmental atmospheric turbulence [17], temperature fluctuations [18], metastasis and cancer survival [19], currents in complex polymers [20], and headway distributions [21].…”

Section: Introductionmentioning

confidence: 99%

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A superstatistical model of vehicular traffic flow

Koşun

Ozdemir

2016

Physica A: Statistical Mechanics and its Applications

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In the analysis of vehicular traffic flow, a myriad of techniques have been implemented. In this study, superstatistics is used in modeling the traffic flow on a highway segment. Traffic variables such as vehicular speeds, volume, and headway were collected for three days. For the superstatistical approach, at least two distinct time scales must exist, so that a superposition of nonequilibrium systems assumption could hold. When the slow dynamics of the vehicle speeds exhibit a Gaussian distribution in between the fluctuations of the system at large, one speaks of a relaxation to a local equilibrium. These Gaussian distributions are found with corresponding standard deviations 1/β. This translates into a series of fluctuating beta values, hence the statistics of statistics, superstatistics. The traffic flow model has generated an inverse temperature parameter (beta) distribution as well as the speed distribution. This beta distribution has shown that the fluctuations in beta are distributed with respect to a chi-square distribution. It must be mentioned that two distinct Tsallis q values are specified: one is time-dependent and the other is independent. A ramification of these q values is that the highway segment and the traffic flow generate separate characteristics. This highway segment in question is not only nonadditive in nature, but a nonequilibrium driven system, with frequent relaxations to a Gaussian

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Section: Discussion: the Coexistence Of Different Q Valuesmentioning

confidence: 99%

“…(4) and (14) have yielded different values, but finally a shuffled speed data analysis too produced a third and different q value, emphatically different from the one by Eq. (14).…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A superstatistical model of vehicular traffic flow

Koşun

Ozdemir

2016

Physica A: Statistical Mechanics and its Applications

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“…The method proposed here would be to first analyse which type of superstatistics is realized, and to then conclude onto the relevant extreme value distribution from our general result derived in this paper. So for example for temporal changes in sea levels measured at various coastal locations in the UK (surges as produced by meteorological changes), after subtracting the mean sea level and the astronomical tide, a recent analysis [19] shows that the dynamics is best described by a χ 2 -superstatistics. Our result derived here then implies that the extreme value statistics relevant for these sea level changes is given by a Fréchet distribution.…”

Section: Discussionmentioning

confidence: 99%

“…Ultimately all expectation values relevant for the complex system under consideration are averaged over this distribution g(β). Many applications have been described in the past, including modeling the statistics of classical turbulent flow [2,[13][14][15], quantum turbulence [16], space-time granularity [17], stock price changes [8], wind velocity fluctuations [18], sea level fluctuations [19], infection pathways of a virus [20], and much more [5,[21][22][23][24][25][26][27]. Superstatistical systems, when integrated over the fluctuating parameter, are effectively described by more general entropy measures than the Boltzamnn-Gibbs entropy [10,12].…”

Section: Introductionmentioning

confidence: 99%

Extreme Value Laws for Superstatistics

Rabassa

Beck

2014

Entropy

Self Cite

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Abstract:We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible, namely: Gumbel, Fréchet and Weibull distribution. On the other hand, superstatistics contains three important universality classes, namely χ 2 -superstatistics, inverse χ 2 -superstatistics, and lognormal superstatistics, all maximizing different effective entropy measures. We investigate how the three classes of extreme value theory are related to the three classes of superstatistics. We show that for any superstatistical process whose local equilibrium distribution does not live on a finite support, the Weibull distribution cannot occur. Under the above mild asymptotic independence assumptions, we also show that χ 2 -superstatistics generally leads an extreme value statistics described by a Fréchet distribution, whereas inverse χ 2 -superstatistics, as well as lognormal superstatistics, lead to an extreme value statistics associated with the Gumbel distribution.

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The Superstatistical Nature and Interoccurrence Time of Atmospheric Mercury Concentration Fluctuations

et al. 2018

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The probability density function (PDF) of the time intervals between subsequent extreme events in atmospheric Hg0 concentration data series from different latitudes has been investigated. The Hg0 dynamic possesses a long‐term memory autocorrelation function. Above a fixed threshold Q in the data, the PDFs of the interoccurrence time of the Hg0 data are well described by a Tsallis q‐exponential function. This PDF behavior has been explained in the framework of superstatistics, where the competition between multiple mesoscopic processes affects the macroscopic dynamics. An extensive parameter μ, encompassing all possible fluctuations related to mesoscopic phenomena, has been identified. It follows a χ2 distribution, indicative of the superstatistical nature of the overall process. Shuffling the data series destroys the long‐term memory, the distributions become independent of Q, and the PDFs collapse on to the same exponential distribution. The possible central role of atmospheric turbulence on extreme events in the Hg0 data is highlighted.

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Superstatistical analysis of sea-level fluctuations

Cited by 16 publications

References 40 publications

A superstatistical model of vehicular traffic flow

A superstatistical model of vehicular traffic flow

Extreme Value Laws for Superstatistics

The Superstatistical Nature and Interoccurrence Time of Atmospheric Mercury Concentration Fluctuations

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