Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids
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...
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| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/5/754 |
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| author | Maricel Agop Tudor-Cristian Petrescu Dumitru Filipeanu Claudia Elena Grigoraș-Ichim Ana Iolanda Voda Andrei Zala Lucian Dobreci Constantin Baciu Decebal Vasincu |
| author_facet | Maricel Agop Tudor-Cristian Petrescu Dumitru Filipeanu Claudia Elena Grigoraș-Ichim Ana Iolanda Voda Andrei Zala Lucian Dobreci Constantin Baciu Decebal Vasincu |
| author_sort | Maricel Agop |
| collection | DOAJ |
| description | 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 <i>SL</i>(2<i>R</i>)-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. |
| first_indexed | 2024-03-10T11:55:36Z |
| format | Article |
| id | doaj.art-01d8bf2dac0b4d81813293a5be51fab0 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T11:55:36Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-01d8bf2dac0b4d81813293a5be51fab02023-11-21T17:19:51ZengMDPI AGSymmetry2073-89942021-04-0113575410.3390/sym13050754Toward Complex Systems Dynamics through Flow Regimes of Multifractal FluidsMaricel Agop0Tudor-Cristian Petrescu1Dumitru Filipeanu2Claudia Elena Grigoraș-Ichim3Ana Iolanda Voda4Andrei Zala5Lucian Dobreci6Constantin Baciu7Decebal Vasincu8Department of Physics, “Gh. Asachi” Technical University of Iasi, 700050 Iasi, RomaniaDepartment of Structural Mechanics, “Gh. Asachi” Technical University of Iasi, 700050 Iasi, RomaniaDepartment of Concrete Structures, Building Materials, Technology and Management, “Gh. Asachi” Technical University of Iasi, 700050 Iasi, RomaniaDepartment of Accounting, Audit and Financing, “Ștefan cel Mare” University of Suceava, 720229 Suceava, RomaniaSocial Sciences and Humanities Research Department, Institute for Interdisciplinary Research, Alexandru Ioan Cuza University of Iasi, Lascăr Catargi Street, NO. 54, 700107 Iaşi, RomaniaMunicipal Emergency Hospital Moineşti, 1 Zorilor Street, 605400 Iasi, RomaniaDepartment of Physical and Occupational Therapy, “Vasile Alecsandri” University of Bacau, 600115 Bacau, RomaniaDepartment of Material Science and Engineering, “Gh. Asachi” Technical University of Iasi, 700050 Iasi, RomaniaSurgery Department, University of Medicine and Farmacy “Grigore T. Popa” Iași, 700050 Iași, RomaniaIn 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 <i>SL</i>(2<i>R</i>)-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.https://www.mdpi.com/2073-8994/13/5/754complex systemmultifractal fluids<i>SL</i>(2<i>R</i>)–algebraCayleyan metricsdrug release applications |
| spellingShingle | Maricel Agop Tudor-Cristian Petrescu Dumitru Filipeanu Claudia Elena Grigoraș-Ichim Ana Iolanda Voda Andrei Zala Lucian Dobreci Constantin Baciu Decebal Vasincu Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids Symmetry complex system multifractal fluids <i>SL</i>(2<i>R</i>)–algebra Cayleyan metrics drug release applications |
| title | Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids |
| title_full | Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids |
| title_fullStr | Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids |
| title_full_unstemmed | Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids |
| title_short | Toward Complex Systems Dynamics through Flow Regimes of Multifractal Fluids |
| title_sort | toward complex systems dynamics through flow regimes of multifractal fluids |
| topic | complex system multifractal fluids <i>SL</i>(2<i>R</i>)–algebra Cayleyan metrics drug release applications |
| url | https://www.mdpi.com/2073-8994/13/5/754 |
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