Luis G. D. C. Borges | Searcharxiv

arXiv2013

On the Evolution of Structure in Turbulence Phenomena

We study the evolution of coherent structures in arbitrary turbulence phenomena, developing some tools, from non-archimedean analysis and algebraic geometry, in order to model its display. We match the scale-dependent, topological structure of the physical fields subsumed by these coherent structures with the phase portraits of some convenient, non-archimedean dynamical systems whose set we endow with a law of action. Finally, we obtain the proposition of an extremum principle for this action to define a geodesic path, as the modelized coherent structures evolve, and we delineate the conception of two experiments, derived from the fields of fluid and plasma turbulence, to test its efectiveness.

math-ph↗

arXiv2013

On turbulence: deciphering a renormalization flow out of an elliptic curve, II

Reaching for a better understanding of turbulence, a line of investigation was followed, its main presupposition being that each scale dependent state, in a general renormalization flow, is a state that can be modeled using a class of ninth degree polynomials. These polynomials are deduced from the Weierstrass models of a certain kind of elliptic curves. As the consequences of this presupposition unfolded, leading to the numerical study of a few samples of elliptic curves, the L functions associated with these later were considered. Their bifurcation diagrams were observed and their escape rates were determined. The consistency of such an approach was put to a statistical test, measuring the rank correlation between escape rates and values taken by these L functions on the point z=1+0i. In the most significant case, the rank correlation coefficient found, r_s, was about r_s=-0.78, with an associated p-value of an order of magnitude close to the (-69) power of 10.

math-ph↗