Scale Invariance, Self Similarity and Critical Behavior in Classical and Quantum Systems

Morales, Irving O.; Landa, Emmanuel; Fossión, Rubén; Frank, A.

doi:10.1088/1742-6596/380/1/012020

Cited by 11 publications

(5 citation statements)

References 29 publications

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“…Due to this property, the fractal systems can be investigated by analysing their parts. It is notable that scaling and fractal behaviour are associated with the system’s long memory [ 48 , 49 ] and complexity [ 48 ], where the complexity of a system indicates the existence of linear mechanisms and orderliness [ 48 ]. It is this complex orderliness that emerges as self-organisation of a system.…”

Section: Mathematical Methodsmentioning

confidence: 99%

Stochastic and Self-Organisation Patterns in a 17-Year PM10 Time Series in Athens, Greece

Nikolopoulos

Alam

Petraki

et al. 2021

Entropy

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This paper utilises statistical and entropy methods for the investigation of a 17-year PM10 time series recorded from five stations in Athens, Greece, in order to delineate existing stochastic and self-organisation trends. Stochastic patterns are analysed via lumping and sliding, in windows of various lengths. Decreasing trends are found between Windows 1 and 3500–4000, for all stations. Self-organisation is studied through Boltzmann and Tsallis entropy via sliding and symbolic dynamics in selected parts. Several values are below −2 (Boltzmann entropy) and 1.18 (Tsallis entropy) over the Boltzmann constant. A published method is utilised to locate areas for which the PM10 system is out of stochastic behaviour and, simultaneously, exhibits critical self-organised tendencies. Sixty-six two-month windows are found for various dates. From these, nine are common to at least three different stations. Combining previous publications, two areas are non-stochastic and exhibit, simultaneously, fractal, long-memory and self-organisation patterns through a combination of 15 different fractal and SOC analysis techniques. In these areas, block-entropy (range 0.650–2.924) is significantly lower compared to the remaining areas of non-stochastic but self-organisation trends. It is the first time to utilise entropy analysis for PM10 series and, importantly, in combination with results from previously published fractal methods.

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Section: Mathematical Methodsmentioning

confidence: 99%

Stochastic and Self-Organisation Patterns in a 17-Year PM10 Time Series in Athens, Greece

Nikolopoulos

Alam

Petraki

et al. 2021

Entropy

View full text Add to dashboard Cite

show abstract

“…Due to this, a fractal system can be studied by focusing on its parts. In addition, the scaling properties of a fractal system is strongly related to its long memory [55][56][57] and its complexity [56], in the sense that a complex system is described by linear mechanisms and exhibits order [58,59]. Fractality, long memory and complexity is highly associated and, as a result, the analysis of the long memory of a system, yields the analysis of its fractal behavior and the delineation of its complexity and vice versa [1,3,4,17].…”

Section: Fractal and Long Memorymentioning

confidence: 99%

Long-Lasting Patterns in 3 kHz Electromagnetic Time Series after the ML = 6.6 Earthquake of 2018-10-25 near Zakynthos, Greece

et al. 2020

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This paper reports one-month 3 kHz EM disturbances recorded at Kardamas, Ilia, Greece after a strong M L = 6.6 earthquake occurred on 2018/10/25 near Zakynthos and Ilia. During this period 17 earthquakes occurred with magnitudes M L = 4.5 and M L = 5.5 and depths between 3 km and 17 km, all near Zakynthos and Ilia. A two-stage, fully computational methodology was applied to the outcomes of five different time-evolving chaos analysis techniques (DFA, fractal dimension analysis through Higuchi, Katz and Sevcik methods and power-law analysis). Via literature-based thresholds, the out-of-threshold results of all chaos analysis methods were located and from these, the common time instances of 13 selected combinations per five, four, three and two methods. Numerous persistent segments were located with DFA exponents between 1.6 ≤ α ≤ 2.0 , fractal dimensions between 1.4 ≤ D ≤ 2.0 and power-law exponents between 2.2 ≤ β ≤ 3.0 . Out of the 17 earthquakes, six earthquakes were jointly matched by 13 selected combinations of five, four, three and two chaos analysis methods, four earthquakes by all combinations of four, three and two, while the remaining seven earthquakes were matched by at least one combination of three methods. All meta-analysis matches are within typical forecast periods.

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“…Due to this property, fractal systems can be investigated by analysing their parts. It is notable that scaling and fractal behaviour are associated with a system's long-memory [56][57][58] and complexity [57], where the complexity of a system indicates the existence of linear mechanisms and orderliness [59,60]. The complexity, fractality, and long memory of a system are closely related.…”

Section: Fractality and Long-memorymentioning

confidence: 99%

Fractal and Long-Memory Traces in PM10 Time Series in Athens, Greece

et al. 2019

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This work examines if chaos and long memory exist in PM 10 concentrations recorded in Athens, Greece. The algorithms of Katz, Higuchi, and Sevcik were employed for the calculation of fractal dimensions and Rescaled Range (R/S) analysis for the calculation of the Hurst exponent. Windows of approximately two months' duration were employed, sliding one sample forward until the end of each utilized signal. Analysis was applied to three long PM 10 time series recorded by three different stations located around Athens. Analysis identified numerous dynamical complex fractal time-series segments with patterns of long memory. All these windows exhibited Hurst exponents above 0.8 and fractal dimensions below 1.5 for the Katz and Higuchi algorithms, and 1.2 for the Sevcik algorithm. The paper discusses the importance of threshold values for the postanalysis of the discrimination of fractal and long-memory windows. After setting thresholds, computational calculations were performed on all possible combinations of two or more techniques for the data of all or two stations under study. When all techniques were combined, several common dates were found for the data of the two combinations of two stations. When the three techniques were combined, more common dates were found if the Katz algorithm was not included in the meta-analysis. Excluding Katz's algorithm, 12 common dates were found for the data from all stations. This is the first time that the results from sliding-window chaos and long-memory techniques in PM 10 time series were combined in this manner.

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Scale Invariance, Self Similarity and Critical Behavior in Classical and Quantum Systems

Cited by 11 publications

References 29 publications

Stochastic and Self-Organisation Patterns in a 17-Year PM10 Time Series in Athens, Greece

Stochastic and Self-Organisation Patterns in a 17-Year PM10 Time Series in Athens, Greece

Long-Lasting Patterns in 3 kHz Electromagnetic Time Series after the ML = 6.6 Earthquake of 2018-10-25 near Zakynthos, Greece

Fractal and Long-Memory Traces in PM10 Time Series in Athens, Greece

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