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  1. Article ; Online: Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics.

    Ghizdovat, Vlad / Rusu, Oana / Frasila, Mihail / Rusu, Cristina Marcela / Agop, Maricel / Vasincu, Decebal

    Entropy (Basel, Switzerland)

    2023  Volume 25, Issue 8

    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 ... ...

    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, 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).
    Language English
    Publishing date 2023-07-31
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e25081149
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  2. Article ; Online: Coherences in the Dynamics of Physical Systems from a Multifractal Perspective of Motion.

    Vasincu, Decebal / Bruma, Andreea Bianca / Rusu, Oana / Rusu, Cristina Marcela / Ghizdovat, Vlad / Agop, Maricel

    Entropy (Basel, Switzerland)

    2023  Volume 25, Issue 8

    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 ...

    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 the difference between the kinetic and potential energy of a Lagrangian, specified as a perfect square in generic coordinates.
    Language English
    Publishing date 2023-07-30
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e25081143
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  3. Article ; Online: Implications and Consequences of SL(2R) as Invariance Group in the Description of Complex Systems Dynamics from a Multifractal Perspective of Motion.

    Dobreci, Lucian / Rusu, Oana / Vasincu, Decebal / Jarcău, Mihaela / Rusu, Cristina Marcela / Gurlui, Silviu / Ghizdovat, Vlad / Gavrilut, Alina / Agop, Maricel

    Entropy (Basel, Switzerland)

    2022  Volume 24, Issue 4

    Abstract: Possible implications and consequences of using SL(2R) as invariance groups in the description at any scale resolution of the dynamics of any complex system are analyzed. From this perspective and based on Jaynes' remark (any circumstance left ... ...

    Abstract Possible implications and consequences of using SL(2R) as invariance groups in the description at any scale resolution of the dynamics of any complex system are analyzed. From this perspective and based on Jaynes' remark (any circumstance left unspecified in the description of any complex system dynamics has the concrete expression in the existence of an invariance group), in the present paper one specifies such unspecified circumstances that result directly from the consideration of the canonical formalism induced by the SL(2R) as invariance group. It follows that both the Hamiltonian function and the Guassian distribution acquire the status of invariant group functions, the parameters that define the Hamiltonian acquire statistical significances based on a principle of maximizing informational energy, the class of statistical hypotheses specific to Gaussians of the same average acts as transitivity manifolds of the group (transitivity manifolds which can be correlated with the multifractal-non-multifractal scale transitions), joint invariant functions induced through SL(2R) groups isomorphism (the SL(2R) variables group, and the SL(2R) parameters group, etc.). For an ensemble of oscillators of the same frequency, the unspecified circumstances return to the ignorance of the amplitude and phase of each of the oscillators, which forces the recourse to a statistical ensemble traversed by the transformations of the Barbilian-type group. Finally, the model is validated based on numerical simulations and experimental results that refer to transient phenomena in ablation plasmas. The novelty of our model resides in the fact that fractalization through stochasticization is imposed through group invariance, situation in which the group's transitivity manifolds can be correlated with the scale resolution.
    Language English
    Publishing date 2022-03-30
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e24040484
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  4. Article ; Online: Multifractality through Non-Markovian Stochastic Processes in the Scale Relativity Theory. Acute Arterial Occlusions as Scale Transitions.

    Tesloianu, Nicolae Dan / Dobreci, Lucian / Ghizdovat, Vlad / Zala, Andrei / Cotirlet, Adrian Valentin / Gavrilut, Alina / Agop, Maricel / Vasincu, Decebal / Nedelciuc, Igor / Rusu, Cristina Marcela / Costache, Irina Iuliana

    Entropy (Basel, Switzerland)

    2021  Volume 23, Issue 4

    Abstract: By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale's sense and/or the form of the ... ...

    Abstract By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale's sense and/or the form of the multifractal theory of motion). By operating in the context of the multifractal theory of motion, based on multifractalization through non-Markovian stochastic processes, the main results of Nottale's theory can be generalized (specific momentum conservation laws, both at differentiable and non-differentiable resolution scales, specific momentum conservation law associated with the differentiable-non-differentiable scale transition, etc.). In such a context, all results are explicated through analyzing biological processes, such as acute arterial occlusions as scale transitions. Thus, we show through a biophysical multifractal model that the blocking of the lumen of a healthy artery can happen as a result of the "stopping effect" associated with the differentiable-non-differentiable scale transition. We consider that blood entities move on continuous but non-differentiable (multifractal) curves. We determine the biophysical parameters that characterize the blood flow as a Bingham-type rheological fluid through a normal arterial structure assimilated with a horizontal "pipe" with circular symmetry. Our model has been validated based on experimental clinical data.
    Language English
    Publishing date 2021-04-09
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e23040444
    Database MEDical Literature Analysis and Retrieval System OnLINE

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  5. Article ; Online: The Role of Information in Managing Interactions from a Multifractal Perspective.

    Agop, Maricel / Irimiciuc, Stefan Andrei / Ghenadi, Adrian / Bibire, Luminita / Toma, Stefan / Petrescu, Tudor-Cristian / Vaideanu, Dorin / Rusu, Cristina Marcela / Gavrilut, Alina / Vasincu, Decebal

    Entropy (Basel, Switzerland)

    2021  Volume 23, Issue 2

    Abstract: In the framework of the multifractal hydrodynamic model, the correlations informational entropy-cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply ... ...

    Abstract In the framework of the multifractal hydrodynamic model, the correlations informational entropy-cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne's temporal measures in a more general manner. This work furthers the analysis published recently by our group in "Towards Interactions through Information in a Multifractal Paradigm".
    Language English
    Publishing date 2021-01-26
    Publishing country Switzerland
    Document type Journal Article
    ZDB-ID 2014734-X
    ISSN 1099-4300 ; 1099-4300
    ISSN (online) 1099-4300
    ISSN 1099-4300
    DOI 10.3390/e23020148
    Database MEDical Literature Analysis and Retrieval System OnLINE

    More links

    Kategorien

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    This service is chargeable due to the Delivery terms set by subito. Orders including an article and supplementary material will be classified as separate orders. In these cases, fees will be demanded for each order.

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