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To study the ballistic transport of charge carriers in nano-structured quantum devices, a highly efficient numerical technique is developed, which provides continuous transmission spectra for arbitrarily complex potential geometries in two…
In this paper, we investigate some properties of generalized Fibonacci quaternions and Fibonacci-Narayana quaternions.
In this paper we calculate the transfer coefficients for evaporation and condensation of mixtures. We use the continuous profiles of various thermodynamic quantities through the interface, obtained in our previous works using the square…
In this paper, we discuss a mathematical model for inverse freeform design of an optical system with two reflectors in which light transfers from a point source to a point target. In this model, the angular light intensity emitted from the…
This paper defines and develops cycle indices for the finite classical groups. These tools are then applied to study properties of a random matrix chosen uniformly from one of these groups. Properties studied by this technique will include…
We investigate the optical transmission spectra for $s$-polarized (TE) and $p$-polarized (TM) waves in one-dimensional photonic quasicrystals on a quasiperiodic multilayer structure made up by alternate layers of SiO$_{2}$ and…
Dirac-electronic tunneling and nonlinear transport properties with both finite and zero energy bandgap are investigated for graphene with a tilted potential barrier under a bias. For validation, results from a finite-difference based…
The Jacobi system with matrix-valued coefficients and with the spectral parameter depending on a matrix-valued weight factor is considered on the full-line lattice. The scattering from the full-line lattice is expressed in terms of the…
We study the electronic transmission through a graphene bilayer in the presence of an applied bias between layers. We consider different geometries involving interfaces between both a monolayer and a bilayer and between two bilayers. The…
In this work we present a theoretical study on the propagation of light in heterogeneous systems with fluctuating optical properties. To understand the consequences of the fluctuations we perform numerical calculations with uniform and non…
We analyze the transparency of a thin film of low refractive index (an optical glue or a bonding layer) placed between higher-index media and forming an opto-pair. Examples include a semiconductor light-emitting diode with attached lens or…
We use a scattering matrix approach to simulate the transmission through a hexagonal Photonic Crystal in the vicinity of the Dirac point. If the crystal is oriented so that the propagation direction perpendicular to the surface corresponds…
We consist of first presenting Zeckendorf Theorem with these two versions Fibonacci and Luca. In this document we obtain results on the generalized of the Zeckendorf theorem for Fibonacci numbers (multibonacci). Such results find…
A light ray in space is characterized by two vectors: (i) a transverse spatial-vector associated with the point where the ray intersects a given spherical cap; (ii) an angular-frequency vector which defines the ray direction of propagation.…
The modulation of the optical transmittance in multilayer graphene by means of an electrical signal in the simple configuration of coplanar electrodes is reported. Besides the fundamental frequency of modulation, higher harmonics also…
We develop a transfer matrix formalism for four-flux radiative transfer models, which is ideally suited for studying transport through multiple scattering layers. The model, derived for spherical particles within the diffusion…
Estimating the trace of the inverse of a large matrix is an important problem in lattice quantum chromodynamics. A multilevel Monte Carlo method is proposed for this problem that uses different degree polynomials for the levels. The…
In my thesis I study mesoscopic corrections on diffuse transport. I first describe the diffuse transport of light, using the scalar approximation and the radiative transfer approach. Next, I focus on the correlations in transmission, I…
We calculate the effect of a Dirac point (a conical singularity in the band structure) on the transmission of monochromatic radiation through a photonic crystal. The transmission as a function of frequency has an extremum at the Dirac…
The reflection and transmission amplitudes of waves in disordered multimode waveguides are studied by means of numerical simulations based on the invariant embedding equations. In particular, we analyze the influence of surface-type…