“Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm
Assimilating a complex fluid with a fractal object, non-differentiable behaviors in its dynamics are analyzed. Complex fluid dynamics in the form of hydrodynamic-type fractal regimes imply “holographic implementations” through velocity fields at non-differentiable scale resolution, via fractal solit...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/18/2273 |
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| author | Alexandra Saviuc Manuela Gîrțu Liliana Topliceanu Tudor-Cristian Petrescu Maricel Agop |
| author_facet | Alexandra Saviuc Manuela Gîrțu Liliana Topliceanu Tudor-Cristian Petrescu Maricel Agop |
| author_sort | Alexandra Saviuc |
| collection | DOAJ |
| description | Assimilating a complex fluid with a fractal object, non-differentiable behaviors in its dynamics are analyzed. Complex fluid dynamics in the form of hydrodynamic-type fractal regimes imply “holographic implementations” through velocity fields at non-differentiable scale resolution, via fractal solitons, fractal solitons–fractal kinks, and fractal minimal vortices. Complex fluid dynamics in the form of Schrödinger type fractal regimes imply “holographic implementations”, through the formalism of Airy functions of fractal type. Then, the in-phase coherence of the dynamics of the complex fluid structural units induces various operational procedures in the description of such dynamics: special cubics with SL(2R)-type group invariance, special differential geometry of Riemann type associated to such cubics, special apolar transport of cubics, special harmonic mapping principle, etc. In such a manner, a possible scenario toward chaos (a period-doubling scenario), without concluding in chaos (nonmanifest chaos), can be mimed. |
| first_indexed | 2024-03-10T07:28:08Z |
| format | Article |
| id | doaj.art-8696387560b249aa86ae62415e40c378 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T07:28:08Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8696387560b249aa86ae62415e40c3782023-11-22T14:05:55ZengMDPI AGMathematics2227-73902021-09-01918227310.3390/math9182273“Holographic Implementations” in the Complex Fluid Dynamics through a Fractal ParadigmAlexandra Saviuc0Manuela Gîrțu1Liliana Topliceanu2Tudor-Cristian Petrescu3Maricel Agop4Faculty of Physics, Alexandru Ioan Cuza University of Iași, 700506 Iasi, RomaniaDepartment of Mathematics and Informatics, Vasile Alecsandri University of Bacau, 600114 Bacau, RomaniaFaculty of Engineering, Vasile Alecsandri University of Bacau, 600115 Bacau, RomaniaDepartment of Structural Mechanics, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, RomaniaDepartment of Physics, Gheorghe Asachi Technical University of Iași, 700050 Iasi, RomaniaAssimilating a complex fluid with a fractal object, non-differentiable behaviors in its dynamics are analyzed. Complex fluid dynamics in the form of hydrodynamic-type fractal regimes imply “holographic implementations” through velocity fields at non-differentiable scale resolution, via fractal solitons, fractal solitons–fractal kinks, and fractal minimal vortices. Complex fluid dynamics in the form of Schrödinger type fractal regimes imply “holographic implementations”, through the formalism of Airy functions of fractal type. Then, the in-phase coherence of the dynamics of the complex fluid structural units induces various operational procedures in the description of such dynamics: special cubics with SL(2R)-type group invariance, special differential geometry of Riemann type associated to such cubics, special apolar transport of cubics, special harmonic mapping principle, etc. In such a manner, a possible scenario toward chaos (a period-doubling scenario), without concluding in chaos (nonmanifest chaos), can be mimed.https://www.mdpi.com/2227-7390/9/18/2273differentiabilityfractal hydrodynamic regimesfractal Schrödinger regimesfractal solitonfractal kink“holographic implementations” |
| spellingShingle | Alexandra Saviuc Manuela Gîrțu Liliana Topliceanu Tudor-Cristian Petrescu Maricel Agop “Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm Mathematics differentiability fractal hydrodynamic regimes fractal Schrödinger regimes fractal soliton fractal kink “holographic implementations” |
| title | “Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm |
| title_full | “Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm |
| title_fullStr | “Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm |
| title_full_unstemmed | “Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm |
| title_short | “Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm |
| title_sort | holographic implementations in the complex fluid dynamics through a fractal paradigm |
| topic | differentiability fractal hydrodynamic regimes fractal Schrödinger regimes fractal soliton fractal kink “holographic implementations” |
| url | https://www.mdpi.com/2227-7390/9/18/2273 |
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