Spectral entropy as a flow state indicator

Abdelsamie, Abouelmagd; Janiga, Gábor; Thévenin, Dominique

doi:10.1016/j.ijheatfluidflow.2017.09.013

Cited by 13 publications

(2 citation statements)

References 60 publications

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“…In the scenario described above, it is necessary to identify entropy measures that are effective in characterizing spatiotemporal patterns of complex processes typically observed or simulated in 2D + 1 and 3D + 1: following the notation of the amplitude equation theory, where D corresponds to the spatial dimension in which the amplitude of a variable fluctuates over time. This need is justified by the great advances in the generation of Big Data in computational physics, with emphasis on Direct Numerical Simulation (DNS) of turbulence [17,18], ionized fluids [19,21,22,26,27], reactive-diffusive processes [14], to highlight a few.…”

Section: Introductionmentioning

confidence: 99%

Characterizing Spatiotemporal Complex Patterns from Entropy Measures

Barauna,

Sautter,

Rosa

et al. 2024

Preprint

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In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method to classify spatiotemporal processes based on entropy measurements. To test and validate the method, we selected four classes of similar processes related to the evolution of random patterns: dynamic colored noises ((i)~white and (ii)~red); (iii)~weak turbulence from reaction-diffusion; (iv)~hydrodynamic fully developed turbulence, and (v)~plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon Permutation Entropy ($S^p_H$) and a new approach based on Tsallis Spectral Permutation Entropy ($S^s_q$). Notably, our observations reveal the segregation of reaction terms in this $S^p_H \times S^s_q$ space, a result that identifies specific sectors for each class of dynamic process, and can be used to train machine learning models for automatic classification of complex spatiotemporal patterns.

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Section: Introductionmentioning

confidence: 99%

Characterizing Spatiotemporal Complex Patterns from Entropy Measures

Barauna,

Sautter,

Rosa

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…In the scenario described above, it is necessary to identify entropy measures that are effective in characterizing the spatiotemporal patterns of complex processes typically observed or simulated in

: following the notation of the amplitude equation theory, where D corresponds to the spatial dimension in which the amplitude of a variable fluctuates over time. This need is justified by the great advances in the generation of big data in computational physics, with emphasis on the direct numerical simulation (DNS) of turbulence [ 8 , 9 ], ionized fluids [ 10 , 11 , 12 , 13 , 14 ], and reactive–diffusive processes [ 15 ] to highlight a few.…”

Section: Introductionmentioning

confidence: 99%

Characterizing Complex Spatiotemporal Patterns from Entropy Measures

Barauna,

Sautter,

Rosa

et al. 2024

Entropy

View full text Add to dashboard Cite

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method for classifying spatiotemporal processes based on entropy measurements. To test and validate the method, we selected five classes of similar processes related to the evolution of random patterns: (i) white noise; (ii) red noise; (iii) weak turbulence from reaction to diffusion; (iv) hydrodynamic fully developed turbulence; and (v) plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon permutation entropy (SHp) and a new approach based on Tsallis Spectral Permutation Entropy (Sqs). Notably, our observations reveal the segregation of reaction terms in this SHp×Sqs space, a result that identifies specific sectors for each class of dynamic process, and it can be used to train machine learning models for the automatic classification of complex spatiotemporal patterns.

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