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Article

“Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm

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Faculty of Physics, Alexandru Ioan Cuza University of Iași, 700506 Iasi, Romania
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Department of Mathematics and Informatics, Vasile Alecsandri University of Bacau, 600114 Bacau, Romania
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Faculty of Engineering, Vasile Alecsandri University of Bacau, 600115 Bacau, Romania
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Department of Structural Mechanics, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, Romania
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Department of Physics, Gheorghe Asachi Technical University of Iași, 700050 Iasi, Romania
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Romanian Scientists Academy, 050094 Bucharest, Romania
*
Author to whom correspondence should be addressed.
Academic Editors: Catalin I. Pruncu and Efstratios Tzirtzilakis
Mathematics 2021, 9(18), 2273; https://doi.org/10.3390/math9182273
Received: 8 July 2021 / Revised: 6 September 2021 / Accepted: 14 September 2021 / Published: 16 September 2021
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems)
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. View Full-Text
Keywords: differentiability; fractal hydrodynamic regimes; fractal Schrödinger regimes; fractal soliton; fractal kink; “holographic implementations”; cubics; apolar transport; harmonic mapping principle; period doubling scenario differentiability; fractal hydrodynamic regimes; fractal Schrödinger regimes; fractal soliton; fractal kink; “holographic implementations”; cubics; apolar transport; harmonic mapping principle; period doubling scenario
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MDPI and ACS Style

Saviuc, A.; Gîrțu, M.; Topliceanu, L.; Petrescu, T.-C.; Agop, M. “Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm. Mathematics 2021, 9, 2273. https://doi.org/10.3390/math9182273

AMA Style

Saviuc A, Gîrțu M, Topliceanu L, Petrescu T-C, Agop M. “Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm. Mathematics. 2021; 9(18):2273. https://doi.org/10.3390/math9182273

Chicago/Turabian Style

Saviuc, Alexandra, Manuela Gîrțu, Liliana Topliceanu, Tudor-Cristian Petrescu, and Maricel Agop. 2021. "“Holographic Implementations” in the Complex Fluid Dynamics through a Fractal Paradigm" Mathematics 9, no. 18: 2273. https://doi.org/10.3390/math9182273

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