Numerical interactions between compactons and kovatons of the Rosenau-Pikovsky K(cos) equation

A numerical study of the nonlinear wave solutions of the Rosenau-Pikovsky K(cos) equation is presented. This equation supports at least two kind of solitary waves with compact support: compactons of varying amplitude and speed, both bounded, and kovatons which have the maximum compacton amplitude, but arbitrary width. A new Pad\'e numerical method is used to simulate the propagation and, with small artificial viscosity added, the interaction between these kind of solitary waves. Several numerically induced phenomena that appear while propagating these compact travelling waves are discussed quantitatively, including self-similar forward and backward wavepackets. The collisions of compactons and kovatons show new phenomena such as the inversion of compactons and the generation of pairwise ripples decomposing into small compacton-anticompacton pairs

Numerical search for the stationary quasi-breather of the graphene superlattice equation.

The propagation of electromagnetic solitons in a graphene superlattice device is governed by a modified sine-Gordon equation, referred to as the graphene superlattice equation. Kink-antikink collisions suggest the existence of a quasi-breather solution. Here, a numerical search for static quasi-breathers is undertaken by using a new initial condition obtained by a regular perturbation of the null solution. Our results show that the frequency of the initial condition has a minimum critical value for the appearance of a robust quasi-breather able to survive during more than one thousand periods. The amplitude and energy of the quasi-breather solution decrease, but its frequency increases, as time grows. The robustness of the new quasi-breather supports its experimental search in real graphene superlattice devices.The authors thank the reviewers for their thoughtful comments and efforts toward improving our manuscript. The research reported here was supported by Project RoCoSoyCo (UMA18-FEDERJA-248) of the Consejería de Economía y Conocimiento, Junta de Andalucía, Spain. Funding for open access charge: Universidad de Málaga / CBU

Fractal structure of the soliton scattering for the graphene superlattice equation

The graphene superlattice equation, a modified sine-Gordon equation, governs the propagation of solitary electromagnetic waves in a graphene superlattice. This equation has kink solutions without explicit analytical expression, requiring the use of quadrature methods. The inelastic collision of kinks and antikinks with the same but opposite speed is studied numerically for the first time; after their interaction they escape to infinity when its speed is either larger than a critical value or it is inside a series of resonance windows; otherwise, they form a breather-like state that slowly decays by radiating energy. Here, the fractal structure of these resonance windows is characterized by using a multi-index notation and their main features are compared with the predictions of the resonant energy exchange theory showing good agreement. Our results can be interpreted as new evidence in favour of this theory.Comment: 27 pages, 10 figures, 3 table

Self-similar Radiation from Numerical Rosenau-Hyman Compactons

The numerical simulation of compactons, solitary waves with compact support, is characterized by the presence of spurious phenomena, as numerically-induced radiation, which is illustrated here using four numerical methods applied to the Rosenau-Hyman K(p,p) equation. Both forward and backward radiations are emitted from the compacton presenting a self-similar shape which has been illustrated graphically by the proper scaling. A grid refinement study shows that the amplitude of the radiations decreases as the grid size does, confirming its numerical origin. The front velocity and the amplitude of both radiations have been studied as a function of both the compacton and the numerical parameters. The amplitude of the radiations decreases exponentially in time, being characterized by a nearly constant scaling exponent. An ansatz for both the backward and forward radiations corresponding to a self-similar function characterized by the scaling exponent is suggested by the present numerical results.Comment: To be published in Journal of Computational Physic

Unemployment Duration and Attitudes Towards Work among People Over 45 Years Old

The situation of global economic crisis and the rapid increase of the unemployment rate cause changes in people's attitudes about the labor market. These changes, sometimes, are motivated by the influence of certain individual variables such as the duration of unemployment. The objective of this research is to analyze the mediator influence of unemployment duration in the attitudes towards work among unemployed people over 45 years old. The people who participate in the research are 161 unemployed that agreed voluntarily in taking part in the interview of attitudes towards work. The data took out from the interviews were analyzed with the statistical software ATLAS.ti 6.2. The results demonstrate that unemployment duration plays an important mediator role in the attitudes towards work when conditioning the job search behavior and favor the chances of finding a job. The conclusion is about practical suggestions and the continuity of research in this area

Deep learning of curvature features for shape completion

The paper presents a novel solution to the issue of incomplete regions in 3D meshes obtained through digitization. Traditional methods for estimating the surface of missing geometry and topology often yield unrealistic outcomes for intricate surfaces. To overcome this limitation, the paper proposes a neural network-based approach that generates points in areas where geometric information is lacking. The method employs 2D inpainting techniques on color images obtained from the original mesh parameterization and curvature values. The network used in this approach can reconstruct the curvature image, which then serves as a reference for generating a polygonal surface that closely resembles the predicted one. The paper’s experiments show that the proposed method effectively fills complex holes in 3D surfaces with a high degree of naturalness and detail. This paper improves the previous work in terms of a more in-depth explanation of the different stages of the approach as well as an extended results section with exhaustive experiments.Spanish Ministry of Science and Technology under projects PID2020-119478GB-I00TED2021-132702B-C21MCIN/AEI/10.13039/501100 011033European Regional Development Fund (ERDF

Dissipative perturbations for the K(n,n) Rosenau-Hyman equation

Compactons are compactly supported solitary waves for nondissipative evolution equations with nonlinear dispersion. In applications, these model equations are accompanied by dissipative terms which can be treated as small perturbations. We apply the method of adiabatic perturbations to compactons governed by the K(n,n) Rosenau-Hyman equation in the presence of dissipative terms preserving the "mass" of the compactons. The evolution equations for both the velocity and the amplitude of the compactons are determined for some linear and nonlinear dissipative terms: second-, fourth-, and sixth-order in the former case, and second- and fourth-order in the latter one. The numerical validation of the method is presented for a fourth-order, linear, dissipative perturbation which corresponds to a singular perturbation term

El circo: una practica corporal <i>alternativa - emergente</i>, en la Ciudad de La Plata

El presente trabajo se inscribe en el área de estudios socioculturales en relación con practicas corporales del orden de lo alternativo – emergente como es el caso del Circo. Será entonces clave, iniciar clarificando desde donde comprenderemos las practicas corporales en ese doble sentido, y a partir de allí indagar sobre: la lógica interna, los sentidos sociales que se producen en función de los actores, como se construye y constituye la practica y los saberes de la misma, como “circulan” y se transmiten éstos entre los participantes, los diferentes roles que asumen los actores, los usos del cuerpo y los sentidos en torno a este. En el caso particular de nuestra ciudad, dicha practica corporal ha tenido un crecimiento importante que conoceremos a partir de dialogar con algunos de los actores y recorrer aquellos nuevos espacios que se han ido gestando.Facultad de Humanidades y Ciencias de la Educació

El circo: una practica corporal <i>alternativa - emergente</i>, en la Ciudad de La Plata

El presente trabajo se inscribe en el área de estudios socioculturales en relación con practicas corporales del orden de lo alternativo – emergente como es el caso del Circo. Será entonces clave, iniciar clarificando desde donde comprenderemos las practicas corporales en ese doble sentido, y a partir de allí indagar sobre: la lógica interna, los sentidos sociales que se producen en función de los actores, como se construye y constituye la practica y los saberes de la misma, como “circulan” y se transmiten éstos entre los participantes, los diferentes roles que asumen los actores, los usos del cuerpo y los sentidos en torno a este. En el caso particular de nuestra ciudad, dicha practica corporal ha tenido un crecimiento importante que conoceremos a partir de dialogar con algunos de los actores y recorrer aquellos nuevos espacios que se han ido gestando.Facultad de Humanidades y Ciencias de la Educació