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Entropy
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Modeling, Fractal, and Multifractional Artificial Intelligence of Complex Systems
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Modeling, Fractal, and Multifractional Artificial Intelligence of Complex Systems

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (30 January 2024) | Viewed by 3912

Special Issue Editor

Dr. Alina Cristiana Gavriluţ

E-Mail Website
Guest Editor
Department of Mathematics, “Al. I. Cuza” University of Iasi, 700506 Iasi, Romania
Interests: set-valued measures; non-additive measures; set-valued integrals; non-additive integrals; topology; fractals; multifractals; nonlinear dynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

For this issue, we propose the use of fractal–multifractal theories in describing the dynamics of complex systems. By complex system, we mean the set of entities in nonlinear interaction at various scales of resolution, from the microscopic to the macroscopic scale. In such a context, dynamics at the subatomic, atomic, molecular, mesoscopic, intragalactic, and extragalactic scale will be considered. Dynamics analyses can also be extended to biological systems. All these dynamic descriptions must be based on notions and concepts such as entropy in the Shannon, Fischer, fractal sense, etc., as well as on the role of invariants that can be built based on the concepts of entropy and informational energy (multifractal entropy, informational energy in the sense of Onicescu, etc.)

Dr. Alina Cristiana Gavriluţ
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • fractal
  • multifractal
  • scale relativity
  • entropy
  • informational energy
  • scale resolution
  • harmonic mappings

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Published Papers (3 papers)

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Research

15 pages, 3030 KiB  
Article
Solar Wind Turbulence and Complexity Probed with Rank-Ordered Multifractal Analysis (ROMA)
by Marius Echim, Costel Munteanu, Gabriel Voitcu and Eliza Teodorescu
Entropy 2024, 26(11), 929; https://doi.org/10.3390/e26110929 - 30 Oct 2024
Viewed by 780
Abstract
The Rank-Ordered Multifractal Analysis (ROMA) is a tool designed to characterize scale (in)variance and multifractality based on rank ordering the fluctuations in “groups” characterized by the same mono-fractal behavior (Hurst exponent). A range-limited structure-function analysis provides the mono-fractal index for each rank-ordered range [...] Read more.
The Rank-Ordered Multifractal Analysis (ROMA) is a tool designed to characterize scale (in)variance and multifractality based on rank ordering the fluctuations in “groups” characterized by the same mono-fractal behavior (Hurst exponent). A range-limited structure-function analysis provides the mono-fractal index for each rank-ordered range of fluctuations. We discuss here two examples of multi-scale solar wind turbulence and complexity where ROMA is applied on the following: (a) data collected by Ulysses spacecraft in the fast solar wind, outside the ecliptic, between 25 and 31 January 2007, at roughly 2.5 Astronomical Units (AU) from the Sun, in the Southern heliosphere, at latitudes between −76.5 and −77.3 degrees, and (b) slow solar wind data collected in the ecliptic plane by Venus Express spacecraft, at 0.72 AU, on 28 January 2007. The ROMA spectrum of fast solar wind derived from ULYSSES data shows a scale-dependent structure of fluctuations: (1) at the smallest/kinetic range of scales (800 to 3200 km), persistent fluctuations are dominant, and (2) at the inertial range of scales (104 to 2 × 105 km), anti-persistent fluctuations are dominant, but less clearly developed and possibly indicative for the development of instabilities with cross-over behavior. The ROMA spectrum of the slow solar wind derived from Venus Express data, suggests a different structure of turbulence: (1) fully developed multifractal turbulence across scales between 5 × 104 and 4 × 105 km, with the Hurst index changing from anti-persistent to persistent values for the larger amplitude magnetic fluctuations; (2) at the smallest scales (400 to 6400 km), fluctuations are mainly anti-persistent, and the ROMA spectrum indicates a tendency towards mono-fractal behavior. Full article
(This article belongs to the Special Issue Modeling, Fractal, and Multifractional Artificial Intelligence of Complex Systems)
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14 pages, 2964 KiB  
Article
Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics
by Vlad Ghizdovat, Oana Rusu, Mihail Frasila, Cristina Marcela Rusu, Maricel Agop and Decebal Vasincu
Entropy 2023, 25(8), 1149; https://doi.org/10.3390/e25081149 - 31 Jul 2023
Viewed by 1337
Abstract
Some possible correspondences between the Scale Relativity Theory and the Space–Time Theory can be established. Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gravitational field with axial symmetry accept the same SL(2R)-type invariance, [...] Read more.
Some possible correspondences between the Scale Relativity Theory and the Space–Time Theory can be established. Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gravitational field with axial symmetry accept the same SL(2R)-type invariance, an Ernst-type potential (from General Relativity) and also a multi-fractal tensor (from Scale Relativity) are highlighted in the description of complex systems dynamics. In this way, a non-differentiable description of complex systems dynamics can become functional, even in the case of standard theories (General Relativity and Quantum Mechanics). Full article
(This article belongs to the Special Issue Modeling, Fractal, and Multifractional Artificial Intelligence of Complex Systems)
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17 pages, 1304 KiB  
Article
Coherences in the Dynamics of Physical Systems from a Multifractal Perspective of Motion
by Decebal Vasincu, Andreea Bianca Bruma, Oana Rusu, Cristina Marcela Rusu, Vlad Ghizdovat and Maricel Agop
Entropy 2023, 25(8), 1143; https://doi.org/10.3390/e25081143 - 30 Jul 2023
Viewed by 1024
Abstract
Using an analogy between the multi-fractal Schrödinger equation and the dumped oscillator equation through a special ansatz, Stoler-type coherences in the dynamics of physical systems are highlighted. Such a result implies a Ricatti-type gauge, a process that can be considered a calibration of [...] Read more.
Using an analogy between the multi-fractal Schrödinger equation and the dumped oscillator equation through a special ansatz, Stoler-type coherences in the dynamics of physical systems are highlighted. Such a result implies a Ricatti-type gauge, a process that can be considered a calibration of the difference between the kinetic and potential energy of a Lagrangian, specified as a perfect square in generic coordinates. Full article
(This article belongs to the Special Issue Modeling, Fractal, and Multifractional Artificial Intelligence of Complex Systems)
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