arXiv subjects

Arturo Ortiz-Tapia

Publications and source records attributed to Arturo Ortiz-Tapia.

5 recordsLinked to original sources

arXiv2026

Green-Function and Information-Geometric Correspondences Between Inverse Eigenvalue Loci of Generalized Lucas Sequences and the Mandelbrot Set

We investigate geometric, potential-theoretic, and information-theoretic correspondences between the inverse eigenvalue loci of companion matrices associated with generalized Lucas sequences and the boundary of the Mandelbrot set. Through systematic numerical experiments, we show that these algebraic spectral loci exhibit a striking low-distortion geometric correspondence with the Mandelbrot boundary at macroscopic scales, together with a coherent organization within its external potential field, characterized by concentration along narrow equipotential annuli of the Mandelbrot Green function. This correspondence is quantified using a suite of complementary diagnostics, including optimal transport matching, Procrustes alignment, local distortion measures, fractal and spectral statistics, Green-function-based potential comparisons, and convex simplex update analyses. Taken together, these results indicate that the observed similarity extends beyond visual resemblance, reflecting shared structural organization across geometric, harmonic, and statistical levels. While the present work is entirely numerical in nature, it establishes a robust multi-scale framework for comparing algebraic spectral constructions with nonlinear dynamical fractals, and it highlights several avenues for future analytical investigation.

math.GM↗

arXiv2025

A flow and transport model for simulation of microbial enhanced oil recovery processes at core scale and laboratory conditions

A general 3D flow-and-transport model in porous media is derived using an axiomatic continuum-mechanics approach and implemented with the finite element method to simulate microbial enhanced oil recovery (MEOR) at core scale under laboratory conditions. The development pipeline (conceptual -> mathematical -> numerical -> computational) is detailed. The model captures clogging/declogging from biomass, changes in interfacial tension due to biosurfactant, and the resulting impact on relative permeability, capillary pressure, and residual oil saturation via a trapping-number framework. The flow model is validated (Buckley-Leverett and coreflood benchmarks); transport (microbes/nutrients/surfactant) is validated against Hendry et al. 1997 breakthrough data. Finally, the model accurately predicts a Berea-core MEOR case study using field microbes and brine, matching recovery histories with small RMS error. Owing to its generality, the framework can be extended to other EOR scenarios and constitutive laws.

math.GM↗

arXiv2025

Homotopies and Maps between Eigenvalues of some Generalized Lucas Sequences and the Mandelbrot Set

The eigenvalues of companion matrices associated with generalized Lucas sequences, denoted as L, exhibit a striking geometric resemblance to the Mandelbrot set M. This work investigates this connection by analyzing the statistical distribution of eigenvalues and constructing a variety of homotopies that map different regions of L to structurally corresponding subsets of M. In particular, we explore both global and piecewise homotopies, including a sinusoidal interpolation targeting the main cardioid and localized deformations aligned with the periodic bulbs. We also study a variation of the Jungreis map to better capture angular and radial structures. In addition to visual and geometric matching, we classify the eigenvalues according to their dynamical behavior, identifying subsets associated with hyperbolic, parabolic, Misurewicz, and Siegel disk points. Our findings suggest that meaningful correspondences between L and M must integrate both geometric deformation and dynamical classification. In light of these observations, we also suggest a conjectural homeomorphism between L and a dense subset of the Mandelbrot cardioid boundary, based on the behavior of the sinusoidal homotopy and the eigenvalue accumulation. Finally, we prove that the sinusoidal homotopy defines a homeomorphism (modulo countable exceptions) from L onto the boundary of the Mandelbrot cardioid, and, when composed with Douady's tuning map, extends to any baby cardioid or stable region of M, reinforcing the structural correspondence between these sets.

math.GM↗

arXiv2023

On the equidistribution properties of patterns in prime numbers Jumping Champions, metaanalysis of properties as Low-Discrepancy Sequences, and some conjectures based on Ramanujan's master theorem and the zeros of Riemann's zeta function

The Paul Erdős-Turán inequality is used as a quantitative form of Weyl' s criterion, together with other criteria to asses equidistribution properties on some patterns of sequences that arise from indexation of prime numbers, Jumping Champions (called here and in previous work, "meta-distances" or even md, for short). A statistical meta-analysis is also made of previous research concerning meta-distances to review the conclusion that meta-distances can be called Low-discrepancy sequences (LDS), and thus exhibiting another numerical evidence that md's are an equidistributed sequence. Ramanujan's master theorem is used to conjecture that the types of integrands where md's can be used more succesfully for quadratures are product-related, as opposite to addition-related. Finally, it is conjectured that the equidistribution of md's may be connected to the know equidistribution of zeros of Riemann's zeta function, and yet still have enough "information" for quasi-random integration ("right" amount of entropy).

math.GM↗

arXiv2019

Some remarks on the first Hardy-Littlewood conjecture

Starting from the first Hardy-Littlewood conjecture some topics will be covered: an empirical approach to the distribution of the twin primes in classes mod(10) and a simplified proof of the Bruns theorem . Finally, it will be explored an approach based on numerical analysis: Monte Carlo Method and Low discrepancy Sequences will be used to prove the convergence of the conjecture to the expected values.

math.HO↗