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Singular Perturbation of the Dirac Hamiltonian
(2017-12-15)
This thesis is devoted to the study of the Dirac Hamiltonian perturbed by delta-type potentials and Coulomb-type potentials.
We analysed the delta-shell interaction on bounded and smooth domains and its approximation by ...
Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$
(2017-11)
Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ...
Absence of eigenvalues of two-dimensional magnetic Schr ̈odinger operators
(2017-10-17)
By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schr ̈odinger operator possesses no point ...
Asymptotic behaviour for fractional diffusion-convection equations
(2017-10)
We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ...
Existence of weak solutions for a general porous medium equation with nonlocal pressure
(2017-10)
We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ...
Three-dimensional coarsening dynamics of a conserved, nematic liquid crystal-isotropic fluid mixture
(2017-09)
We present a numerical investigation of the three-dimensional coarsening dynamics of a nematic liquid crystal-isotropic fluid mixture using a conserved phase field model. The model is a coupled system for a generalized ...
The relativistic spherical $\delta$-shell interaction in $\mathbb{R}^3$: spectrum and approximation
(2017-08-03)
This note revolves on the free Dirac operator in $\mathbb{R}^3$ and its $\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ...
An efficient multigrid strategy for large-scale molecular mechanics optimization
(2017-08-01)
Static mechanical properties of materials require large-scale nonlinear optimization of the molecular mechanics model under various controls. This paper presents an efficient multigrid strategy to solve such problems. This ...
Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications
(2017-07-18)
Let $I_{v}\left( x\right) $ be modified Bessel functions of the first
kind. We prove the monotonicity property of the function $x\mapsto
I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left(
x\right) ...
El efecto de Talbot: de la óptica a la ecuación de Schrödinger
(2017-07)
El objetivo de este artículo es dar a conocer un bello efecto óptico que se denomina efecto de Talbot. Primero, describiremos el fenómeno y comentaremos su descubrimiento a mediados del siglo XIX. A continuación, analizaremos ...