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

Alexandra Saviuc, Manuela Gîrțu, Liliana Topliceanu, Tudor-Cristian Petrescu and Maricel Agop
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Alexandra Saviuc: Faculty of Physics, Alexandru Ioan Cuza University of Iași, 700506 Iasi, Romania
Manuela Gîrțu: Department of Mathematics and Informatics, Vasile Alecsandri University of Bacau, 600114 Bacau, Romania
Liliana Topliceanu: Faculty of Engineering, Vasile Alecsandri University of Bacau, 600115 Bacau, Romania
Tudor-Cristian Petrescu: Department of Structural Mechanics, Gheorghe Asachi Technical University of Iasi, 700050 Iasi, Romania
Maricel Agop: Department of Physics, Gheorghe Asachi Technical University of Iași, 700050 Iasi, Romania

Mathematics, 2021, vol. 9, issue 18, 1-20

Abstract: 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.

Keywords: differentiability; fractal hydrodynamic regimes; fractal Schrödinger regimes; fractal soliton; fractal kink; “holographic implementations”; cubics; apolar transport; harmonic mapping principle; period doubling scenario (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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