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Symmetry
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Scale Relativity and Fractal Space-Time Theory
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Scale Relativity and Fractal Space-Time Theory

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (15 September 2021) | Viewed by 11445

Special Issue Editors

Prof. Dr. Maricel Agop

E-Mail Website
Guest Editor
Department of Materials Science, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, Romania
Interests: drug delivery; fractal physics; non-linear dynamics; theoretical non-differentiable physics; polymer dynamics
Special Issues, Collections and Topics in MDPI journals
Dr. Stefan-Andrei Irimiciuc

E-Mail Website
Co-Guest Editor
National Institute for Laser, Plasma and Radiation Physics, 409 Atomistilor Street, 077125 Bucharest, Romania
Interests: fractal physics; laser–matter interaction; plasma diagnostics; drug delivery; polymer dynamics
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Iuliana Oprea

E-Mail Website
Co-Guest Editor
Department of Mathematics, Colorado State University, USA
Interests: hydrodynamic and hydromagnetic stability; dynamical systems; pattern formation; mathematical modelling

Special Issue Information

Dear Colleagues,

The studies of non-linear dynamics, and implicitly of chaotic behavior, are of major importance to a wide range of domains (physics, chemistry, geology, biology, economy, etc.). One of the main reasons behind the large-scale implications of non-linear analysis—particularly of scale relativity and fractal space-time theory—is the impossibility of associating non-linearity with an exact physical model or limiting it to a narrow field of science. Therefore, theoretical studies of non-linear phenomena that occur in complex system dynamics, field theories, plasma physics, quantum mechanics, and many other areas have encountered serious mathematical difficulties, as they include approximations that lead to linear or quasi-linear models. The development of new theoretical models needs to consider the arisal of deterministic chaos in associations with the emergence with spatial temporal structures are part of the complex systems dynamics. For temporal scales that are large with respect to the inverse of the highest Lyapunov exponent, the deterministic trajectories can be replaced by a collection of potential trajectories and the concept of definite position by that of probability density. Therefore, a connection be established between the scale-theory-based models and “hidden symmetries” which can generate these densities of probability.

This Special Issue aims to attract both theoretical and experimental research on a wide range of domains which are connected through the fractal approach and by respecting the explicit or implicit symmetries of complex system dynamics.

Prof. Dr. Maricel Agop
Dr. Stefan Andrei Irimiciuc
Prof. Dr. Iuliana Oprea
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. Symmetry 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 2400 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 analysis
  • complex systems
  • hidden symmetries
  • scale relativity theories
  • non-linear mathematical and physical models

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Published Papers (5 papers)

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Research

15 pages, 5822 KiB  
Article
Novel Approach for EEG Signal Analysis in a Multifractal Paradigm of Motions. Epileptic and Eclamptic Seizures as Scale Transitions
by Stefan Andrei Irimiciuc, Andrei Zala, Dan Dimitriu, Loredana Maria Himiniuc, Maricel Agop, Bogdan Florin Toma, Laura Gabriela Gavril, Decebal Vasincu and Lucian Eva
Symmetry 2021, 13(6), 1024; https://doi.org/10.3390/sym13061024 - 7 Jun 2021
Cited by 5 | Viewed by 2384
Abstract
Two different operational procedures are proposed for evaluating and predicting the onset of epileptic and eclamptic seizures. The first procedure analyzes the electrical activity of the brain (EEG signals) using nonlinear dynamic methods (the time variations of the standard deviation, the variance, the [...] Read more.
Two different operational procedures are proposed for evaluating and predicting the onset of epileptic and eclamptic seizures. The first procedure analyzes the electrical activity of the brain (EEG signals) using nonlinear dynamic methods (the time variations of the standard deviation, the variance, the skewness and the kurtosis; the evolution in time of the spatial–temporal entropy; the variations of the Lyapunov coefficients, etc.). The second operational procedure reconstructs any type of EEG signal through harmonic mappings from the usual space to the hyperbolic one using the time homographic invariance of a multifractal-type Schrödinger equation in the framework of the scale relativity theory (i.e., in a multifractal paradigm of motions). More precisely, the explicit differential descriptions of the brain activity in the form of 2 × 2 matrices with real elements disclose, through the in-phase coherences at various scale resolutions (i.e., as scale transitions), the multitude of brain neuronal dynamics, especially sequences of epileptic and eclamptic seizures. These two operational procedures are not mutually exclusive, but rather become complementary, offering valuable information concerning epileptic and eclamptic seizures. In such context, the prediction of epileptic and eclamptic seizures becomes fundamental for patients not responding to medical treatment and also presenting an increased rate of seizure recurrence. Full article
(This article belongs to the Special Issue Scale Relativity and Fractal Space-Time Theory)
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21 pages, 6622 KiB  
Article
Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids
by Maricel Agop, Tudor-Cristian Petrescu, Dumitru Filipeanu, Claudia Elena Grigoraș-Ichim, Ana Iolanda Voda, Andrei Zala, Lucian Dobreci, Constantin Baciu and Decebal Vasincu
Symmetry 2021, 13(5), 754; https://doi.org/10.3390/sym13050754 - 27 Apr 2021
Viewed by 1834
Abstract
In the framework of the Multifractal Theory of Motion, which is expressed by means of the multifractal hydrodynamic model, complex system dynamics are explained through uniform and non-uniform flow regimes of multifractal fluids. Thus, in the case of the uniform flow regime of [...] Read more.
In the framework of the Multifractal Theory of Motion, which is expressed by means of the multifractal hydrodynamic model, complex system dynamics are explained through uniform and non-uniform flow regimes of multifractal fluids. Thus, in the case of the uniform flow regime of the multifractal fluid, the dynamics’ description is “supported” only by the differentiable component of the velocity field, the non-differentiable component being null. In the case of the non-uniform flow regime of the multifractal fluid, the dynamics’ description is “supported” by both components of the velocity field, their ratio specifying correlations through homographic transformations. Since these transformations imply metric geometries explained, for example, by means of Killing–Cartan metrics of the SL(2R)-type algebra, of the set of 2 × 2 matrices with real elements, and because these metrics can be “produced” as Cayleyan metrics of absolute geometries, the dynamics’ description is reducible, based on a minimal principle, to harmonic mappings from the usual space to the hyperbolic space. Such a conjecture highlights not only various scenarios of dynamics’ evolution but also the types of interactions “responsible” for these scenarios. Since these types of interactions become fundamental in the self-structuring processes of polymeric-type materials, finally, the theoretical model is calibrated based on the author’s empirical data, which refer to controlled drug release applications. Full article
(This article belongs to the Special Issue Scale Relativity and Fractal Space-Time Theory)
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19 pages, 4719 KiB  
Article
Novel Approach for EKG Signals Analysis Based on Markovian and Non-Markovian Fractalization Type in Scale Relativity Theory
by Maricel Agop, Stefan Irimiciuc, Dan Dimitriu, Cristina Marcela Rusu, Andrei Zala, Lucian Dobreci, Adrian Valentin Cotîrleț, Tudor-Cristian Petrescu, Vlad Ghizdovat, Lucian Eva and Decebal Vasincu
Symmetry 2021, 13(3), 456; https://doi.org/10.3390/sym13030456 - 11 Mar 2021
Cited by 2 | Viewed by 1915
Abstract
Two distinct operational procedures are proposed for diagnosis and tracking of heart disease evolution (in particular atrial fibrillations). The first procedure, based on the application of non-linear dynamic methods (strange attractors, skewness, kurtosis, histograms, Lyapunov exponent, etc.) analyzes the electrical activity of the [...] Read more.
Two distinct operational procedures are proposed for diagnosis and tracking of heart disease evolution (in particular atrial fibrillations). The first procedure, based on the application of non-linear dynamic methods (strange attractors, skewness, kurtosis, histograms, Lyapunov exponent, etc.) analyzes the electrical activity of the heart (electrocardiogram signals). The second procedure, based on multifractalization through Markovian and non-Markovian-type stochasticizations in the framework of the scale relativity theory, reconstructs any type of EKG signal by means of harmonic mappings from the usual space to the hyperbolic one. These mappings mime various scale transitions by differential geometries, in Riemann spaces with symmetries of SL(2R)-type. Then, the two operational procedures are not mutually exclusive, but rather become complementary, through their finality, which is gaining valuable information concerning fibrillation crises. As such, the author’s proposed method could be used for developing new models for medical diagnosis and evolution tracking of heart diseases (patterns dynamics, signal reconstruction, etc.). Full article
(This article belongs to the Special Issue Scale Relativity and Fractal Space-Time Theory)
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26 pages, 24496 KiB  
Article
Dynamic Evaluation of Traffic Noise through Standard and Multifractal Models
by Alina Petrovici, Jose Luis Cueto, Valentin Nedeff, Enrique Nava, Florin Nedeff, Ricardo Hernandez, Carmen Bujoreanu, Stefan Andrei Irimiciuc and Maricel Agop
Symmetry 2020, 12(11), 1857; https://doi.org/10.3390/sym12111857 - 11 Nov 2020
Cited by 4 | Viewed by 2061
Abstract
Traffic microsimulation models use the movement of individual driver-vehicle-units (DVUs) and their interactions, which allows a detailed estimation of the traffic noise using Common Noise Assessment Methods (CNOSSOS). The Dynamic Traffic Noise Assessment (DTNA) methodology is applied to real traffic situations, then compared [...] Read more.
Traffic microsimulation models use the movement of individual driver-vehicle-units (DVUs) and their interactions, which allows a detailed estimation of the traffic noise using Common Noise Assessment Methods (CNOSSOS). The Dynamic Traffic Noise Assessment (DTNA) methodology is applied to real traffic situations, then compared to on-field noise levels from measurement campaigns. This makes it possible to determine the influence of certain local traffic factors on the evaluation of noise. The pattern of distribution of vehicles along the avenue is related to the logic of traffic light control. The analysis of the inter-cycles noise variability during the simulation and measurement time shows no influence from local factors on the prediction of the dynamic traffic noise assessment tool based on CNOSSOS. A multifractal approach of acoustic waves propagation and the source behaviors in the traffic area are implemented. The novelty of the approach also comes from the multifractal model’s freedom which allows the simulation, through the fractality degree, of various behaviors of the acoustic waves. The mathematical backbone of the model is developed on Cayley–Klein-type absolute geometries, implying harmonic mappings between the usual space and the Lobacevsky plane in a Poincaré metric. The isomorphism of two groups of SL(2R) type showcases joint invariant functions that allow associations of pulsations–velocities manifolds type. Full article
(This article belongs to the Special Issue Scale Relativity and Fractal Space-Time Theory)
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17 pages, 4248 KiB  
Article
Non-Linear Behaviors of Transient Periodic Plasma Dynamics in a Multifractal Paradigm
by Stefan-Andrei Irimiciuc, Alexandra Saviuc, Florin Tudose-Sandu-Ville, Stefan Toma, Florin Nedeff, Cristina Marcela Rusu and Maricel Agop
Symmetry 2020, 12(8), 1356; https://doi.org/10.3390/sym12081356 - 13 Aug 2020
Cited by 5 | Viewed by 2266
Abstract
In a multifractal paradigm of motion, nonlinear behavior of transient periodic plasmas, such as Schrodinger and hydrodynamic-type regimes, at various scale resolutions are represented. In a stationary case of Schrodinger-type regimes, the functionality of “hidden symmetry” of the group SL (2R) is implied [...] Read more.
In a multifractal paradigm of motion, nonlinear behavior of transient periodic plasmas, such as Schrodinger and hydrodynamic-type regimes, at various scale resolutions are represented. In a stationary case of Schrodinger-type regimes, the functionality of “hidden symmetry” of the group SL (2R) is implied though Riccati–Gauge different “synchronization modes” among period plasmas’ structural units. These modes, expressed in the form of period doubling, damped oscillations, quasi-periodicity, intermittences, etc., mimic the various non-linear behaviors of the transient plasma dynamics similar to chaos transitions scenarios. In the hydrodynamic regime, the non-Newtonian behavior of the transient plasma dynamics can be corelated with the viscous tension tensor of the multifractal type. The predictions given by our theoretical model are confronted with experimental data depicting electronic and ionic oscillatory dynamics seen by implementing the Langmuir probe technique on transient plasmas generated by ns-laser ablation of nickel and manganese targets. Full article
(This article belongs to the Special Issue Scale Relativity and Fractal Space-Time Theory)
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