Discussion on Fresnel's mirrors and Young's double-slit interferometers

In this work, Fresnel's mirror and Young's double-slit experiments are compared. Numerical calculations show that Fresnel's experiment and Young's experiment present significant differences between their interference patterns when the optical source is extended rather than point-like. Those differences agree with the analogous between the overlapping of two quasi-monochromatic beams on the temporal domain (the analogous of Young's experiment) and these same beams superimposed previous modulation with sawtooth-wave (the analogous of Fresnel's interferometer). The implemented algorithms allow evaluating the cases of fully spatially coherence, fully spatially incoherence and spatially partially coherence. Computer simulations are presented to show the validity of our proposal.     

Quasi-steady state model determination for systems with singular perturbations modelled by bond graphs

A bond graph model for a singularly perturbed system is presented. This system is characterized by fast and slow dynamics. In addition, the bond graph can have storage elements with derivative and integral causality assignments for both dynamics. When the singular perturbation method is applied, the fast dynamic differential equation degenerates to an algebraic equation; the real roots of this equation can be determined by using another bond graph called singularly perturbed bond graph (SPBG). This SPBG has the characteristic that storage elements of the fast state and slow state have a derivative and integral causality assignment, respectively. Thus, a quasi-steady state model by using SPBG is obtained. A Lemma to get the junction structure from SPBG is proposed. Finally, the proposed methodology is applied to two examples.     

Existence and Blow-up for a Parabolic System from?Combustion Theory

We study the stability of the Solid Fuel Model, which represents a thermal reaction of a solid material. This model corresponds to a nonlinear eigenvalue problem of two strongly coupled nonlinear reaction–diffusion equations, with different boundary conditions on each unknown. We obtain a strong bifurcation criterion for the steady problem and estimates for the blow-up time in the unsteady case. In addition, numerical solutions of both the steady and unsteady problem are presented to illustrate the results.     

Bonding character of intermediates in on-surface Ullmann reactions revealed with energy decomposition analysis

On-surface synthesis has become a thriving topic in surface science. The Ullmann coupling reaction is the most applied synthetic route today, but the nature of the organometallic intermediate is still under discussion. We investigate the bonding nature of prototypical intermediate species (phenyl, naphthyl, anthracenyl, phenanthryl, and triphenylenyl) on the Cu(111) surface with a combination of plane wave and atomic orbital basis set methods using density functional theory calculations with periodic boundary conditions. The surface bonding is shown to be of covalent nature with a polarized shared-electron bond supported by π-back donation effects using energy decomposition analysis for extended systems (pEDA). The bond angle of the intermediates is determined by balancing dispersion attraction and Pauli repulsion between adsorbate and surface. The latter can be significantly reduced by adatoms on the surface. We furthermore investigate how to choose computational parameters for pEDA of organic adsorbates on metal surfaces efficiently and show that bonding interpretation requires consistent choice of the density functional.     

Multiplexing of encrypted data using fractal masks

In this Letter, we present to the best of our knowledge a new all-optical technique for multiple-image encryption and multiplexing, based on fractal encrypting masks. The optical architecture is a joint transform correlator. The multiplexed encrypted data are stored in a photorefractive crystal. The fractal parameters of the key can be easily tuned to lead to a multiplexing operation without cross talk effects. Experimental results that support the potential of the method are presented.     

Trivariate near-best blending spline quasi-interpolation operators

A method to define trivariate spline quasi-interpolation operators (QIOs) is developed by blending univariate and bivariate operators whose linear functionals allow oversampling. In this paper, we construct new operators based on univariate B-splines and bivariate box splines, exact on appropriate spaces of polynomials and having small infinity norms. An upper bound of the infinity norm for a general blending trivariate spline QIO is derived from the Bernstein-Bézier coefficients of the fundamental functions associated with the operators involved in the construction. The minimization of the resulting upper bound is then proposed and the existence of a solution is proved. The quadratic and quartic cases are completely worked out and their exact solutions are explicitly calculated.     

Spline quasi-interpolation in the Bernstein basis and its application to digital elevation models

A nonstandard low-cost spline approximation method for approximating bivariate functions is constructed. It is applied for Digital Elevation approximation and then its accuracy in the downscaling process is studied.