Departamento de Física

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http://repositorioabierto.uantof.cl/handle/uantof/221

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Accurate Analytical Approximation for the Bessel Function J2(x)
(2024) Pablo Martin; Juan Pablo Ramos Andrade; Fabián Caro Pérez; Freddy Lastra
We obtain an accurate analytic approximation for the Bessel function 𝐽2(𝑥) using an improved multipoint quasirational approximation technique (MPQA). This new approximation is valid for all real values of the variable x, with a maximum absolute error of approximately 0.009. These errors have been analyzed in the interval from 𝑥=0 to 𝑥=1000, and we have found that the absolute errors for large x decrease logarithmically. The values of x at which the zeros of the exact function 𝐽2(𝑥) and the approximated function 𝐽˜2(𝑥) occur are also provided, exhibiting very small relative errors. The largest relative error is for the second zero, with 𝜀rel=0.0004 , and the relative errors continuously decrease, reaching 0.0001 for the eleventh zero. The procedure to obtain this analytic approximation involves constructing a bridge function that connects the power series with the asymptotic approximation. This is achieved by using rational functions combined with other elementary functions, such as trigonometric and fractional power functions.
Casimir effect of a rough membrane in 2 + 1 Hořava Lifshitztheory
(2024) Claudio Bórquez; Byron Droguett
We investigate the Casimir effect of a rough membrane within the framework of the Hořava–Lifshitz the-ory in 2+1 dimensions. Quantum fluctuations are induced by an anisotropic scalar field subject to Dirichlet boundary conditions. We implement a coordinate transformation to render the membrane completely flat, treating the remaining terms associated with roughness as a potential. The spectrum is obtained through perturbation theory and regularized usingtheζ-function method. We present an explicit example of a membrane with periodic border. Additionally, we consider the effect of temperature. Our findings reveal that the Casimir energy and force depend on roughness, the anisotropic scaling factor and temperature.
Description of Parameter Variation Learning with Artificial Intelligence and GeoGebra in Students of a Differential Equations Course
(2024) Jorge Olivares Funes; Elvis R. Valero Kari; Pablo Martin
In this era of social and technological change, the advent of AI has had great impact on the lives of many people and especially in the educational field, as mentioned in [1], wich prove that the perceptions that students and instructors have about artificial intelligence are very positive to implement them in learning. In this [2] assert that it is possible to have a collaborations between the fields of mathematics and artificial intelligence AI.
Fractional Einstein–Gauss–Bonnet Scalar Field Cosmology
(2024) Bayron Micolta Riascos; Alfredo D. Millano; Genly Leon; Byron Droguett; Esteban González; Juan Magaña
fractional calculus; dynamical systems; scalar field cosmology; modified gravity
Geogebra in the visualization of integrating factors in non-exact differential equations
(2024) Jorge Olivares; P. Martin; E. Valero
In the present work, integrating factors used in the solution of non-exact differential equations will be shown with general examples through software application of dynamic geometry GeoGebra. Now these applets are part of theteaching support material in the eigineering careers of the University of Antofagasta on 2020.
MPQA method applied to the plasma dispersion function
(2024) E. Morales Campaña; P. Martin
A new approximation method for the plasma dispersion function Z(ζ) is presented. Multipoint quasi-rational approximation technique is used to find a bridge function that connects the power series and the asymptotic expansion of the function Z(ζ) using rational functions combined with exponential functions. An approximation with a polynomial of degree 10 is performed for the function Z(ζ), and the results obtained are compared with those of previous approximations from the literature. The results of this approximation were a relative error of ε = 0.0035 for Re[˜Z(ζ)] and a relative error of ε = 0.0011 for Im[˜Z(ζ)], which are lower than those of the other existing approximations
Nonreciprocal spin wave channeling in ferromagnetic/heavy-metal nanostrips
(2024) R.A. Gallardo; P. Alvarado Seguel; F. Brevis; C. Gonzalez-Fuentes; J.W. González; K. Lenz; J. Lindner; A. Roldán-Molina
Nonreciprocity, unidirectionality, and channeling are essential concepts for potential magnonic applications. Nonreciprocity and unidirectionality ensure the efficient propagation of spin waves along predetermined paths with preferential directions, disrupting the symmetry of counterpropagating waves. Channeling fosters the development of intricate spin-wave networks, enabling more sophisticated functionalities. Integrating these concepts into practical applications will shape the future of spin-wave-based information processing devices. This article theoretically studies the dynamics of spin waves in a ferromagnetic strip coupled to a heavy-metal strip, where the nonreciprocity, unidirectionality, and channeling effects are analyzed. Both backward volume (BV) and Damon–Eshbach (DE) configurations are considered, where the lateral dimensions of the heavy-metal and ferromagnetic strips can differ. Calculations show notable nonreciprocal channeling of spin waves in both DE and BV modes. In the BV configuration, the dispersion is reciprocal with nontrivial localization of lateral confined modes. It is shown that the waves can be channeled into the zones in contact with the HM, where the Dzyaloshinskii–Moriya interaction is active. In the DE configuration, the waves exhibit nonreciprocal spin-wave dispersion, allowing unidirectional and channeled spin-wave propagation. The main results are compared to micromagnetic simulations, where an excellent agreement between both methods is obtained. These findings are relevant for envisioning advanced magnonic devices, enabling precise control over spin-wave propagation for innovative, low-power, high-speed information processing.
Precise analytical approximations of the eigenvalues of the decatic anharmonic potential
(2024) M. T. Veliz; P. Martín
Precise analytical approximations have been determined for the eigenvalues of the ground state of the decatic anharmonic potential x2+λx10 in the one-dimensional Schrodinger equation. The results have been found using the technique multipoint quasirational approximation (MPQA). With the new method, power and asymptotic expansions have been determined. The analytic function here obtained is derived connecting both expansions. The maximum relative error of the best analytical approximation here determined is 0.04. However, most of the relative errors for other values of λ, are smaller than 1% (less than 0.01).
Renormalization of the nonprojectable Hořava theory
(2024)
We present the proof of renormalization of the Hořava theory in the non projectable version. We obtain a form of the quantum action that exhibits a manifest Becchi-Rouet-Stora-Tyutin–symmetry structure. Previous analysis has shown that the divergences produced by irregular loops cancel completely between them. The remaining divergences are local. The renormalization is achieved by using the approach developed by Barvinsky et al. with the background-field formalism.
Self duality in unconventional conformal supersymmetry
(2024) Pedro D. Alvarez; Cristóbal Corral; Jorge Zanelli
In this work, we study (anti-)self duality conditions in unconventional conformal supersymmetry. We focus on a theory constructed in a Townsend-MacDowell-Mansouri form for anSU(2,2|N)gauge connection with matter fields in the adjoint representation. We findbo sonic solutions that correspond to analytic gravitational instantons with nontrivial torsion.These configurations can be regarded as the torsional generalization of the Taub-NUT/Bolt-AdS and Eguchi-Hanson metric and they are (anti-)self-dual with respect to a generalized dual operator. We explore their global properties and show that they saturate a BPS bound.

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