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

Simulation of a solar funnel cooker using MATLAB

A software for the calculation of the radiation heat transfer in solar funnel cookers by means of the radiosity method has been developed in Matlab. The software has been used to study a folding solar cooker. The cooker geometry is discretized using a triangular mesh where a piecewise constant approximation is assumed for the radiosity function. Form factors, including self-occlusions, are calculated by properly refining the triangular mesh. The concentration factor of the solar cooker is estimated as a function of its position and orientation with respect to that of the Sun.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

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

Tunnelling in quantum superlattices with variable lacunarity

Quantum fractal superlattices are microelectronic devices consisting of a series of thin layers of two semiconductor materials deposited alternately on each other over a substrate following the rules of construction of a fractal set, here, a symmetrical polyadic Cantor fractal. The scattering properties of electrons in these superlattices may be modeled by using that of quantum particles in piecewise constant potential wells. The twist plots representing the reflection coefficient as function of the lacunarity parameter show the appearance of black curves with perfectly transparent tunnelling which may be classified as vertical, arc, and striation nulls. Approximate analytical formulae for these reflection-less curves are derived using the transfer matrix method. Comparison with the numerical results show their good accuracy.Comment: 12 pages, 3 figure

Unisolvency for Multivariate Polynomial Interpolation in Coatmèlec Configurations of Nodes

A new and straightforward proof of the unisolvability of the problem of multivariate polynomial interpolation based on Coatmèlec configurations of nodes, a class of properly posed set of nodes defined by hyperplanes, is presented. The proof generalizes a previous one for the bivariate case and is based on a recursive reduction of the problem to simpler ones following the so-called Radon–Bézout process.The authors thank to Drs. Mariano Gasca and Juan I. Ramos for pointing us some references and for their useful comments which have greatly improved the presentation. The authors also thank a reviewer for pointing out a mistake in the original Proof of Lemma 5. The research reported in this paper was partially supported by Project MTM2010-19969 from the Ministerio de Ciencia e Innovacion of Spain and Grant PAID-06-09-2734 from the Universidad Politecnica de Valencia. M. A. G. M. acknowledges support from the Spanish Ministry of Science and Education (MEC), Fulbright Commission, and FECYT.García March, MÁ.; Gimenez Palomares, F.; Villatoro, FR.; Pérez Quiles, MJ.; Fernández De Córdoba Castellá, PJ. (2011). Unisolvency for Multivariate Polynomial Interpolation in Coatmèlec Configurations of Nodes. Applied Mathematics and Computation. 217(18):7427-7431. https://doi.org/10.1016/j.amc.2011.02.034S742774312171