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 solitons, fractal solitons-fractal kinks, and fractal minimal vortices. Complex fluid dynamics in the form of Schrodinger 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.

Automated summary

The text discusses analyzing the non-differentiable behaviors in the dynamics of a complex fluid combined with a fractal object, implementing holographic regimes through fractal solitons, fractal kinks, and Airy functions. The in-phase coherence among structural units of the complex fluid induces various operational procedures, leading to a possible scenario towards chaos without necessarily concluding in chaos. Special cubic structures, differential geometries, and harmonic mapping principles are utilized to mimic this chaotic scenario.