Multiple photon Hamiltonian in linear quantum optical networks

We give an alternative derivation for the explicit formula of the effective Hamiltonian describing the evolution of the quantum state of any number of photons entering a linear optics multiport. The description is based on the effective Hamiltonian of the optical system for a single photon and comes from relating the evolution in the Lie group that describes the unitary evolution matrices in the Hilbert space of the photon states to the evolution in the Lie algebra of the Hamiltonians for one and multiple photons. We give a few examples of how a group theory approach can shed light on some properties of devices with two input ports.Comment: 6 pages. Comments welcom

Identificación y modelización de tendencias en emisiones contaminantes

El objetivo de este trabajo es el análisis de tendencias para emisiones contaminantes en España y número de horas o días en que los que se superan los umbrales de concentración permitidos por la ley (Directiva 1999/30/CE y Real Decreto 1073/2002 ) en España , Francia y Portugal. El análisis de tendencias es un área de gran relevancia en la actualidad y existen diferentes herramientas y enfoques para abordarlo. El tipo concreto de datos (reales o enteros) de que trate, además del conocimiento físico.químico del problema, será también relevante a la hora de optar por una u otra alternativa. En este trabajo se han utilizado dos herramientas: el análisis de tendencias estocásticas basado en series temporales para las emisiones contaminantes, y el basado en un modelo jerárquico bayesiano de procesos no homogéneos de Poisson unido a gráficos EWMA para las ocasiones (horas o días) en los que se superan los límites establecidos. Las especies químicas contaminantes que serán objeto de este análisis son: SO2 , NOx , PM10 , PAHs, dioxinas y VOCs y el periodo estudiado será el comprendido entre 1995 y 2008; las predicciones realizadas con ayuda de los modelos ajustados para cada tipo de datos llegarán al año 2020. Las bases de datos utilizadas para este trabajo son las siguientes: EMEP (European Monitoring and Evaluation Programme), disponible en la página web www.emep.int, que ofrece gran cantidad de datos sobre emisiones y concentraciones en los países de la Convención de Transmisión a Larga Distancia de Contaminantes Atmosféricos; estaciones españolas; agregación que se ha realizado; comparativa con Francia y Portuga

An a priori error analysis of a type III thermoelastic problem with two porosities

In this work, we study, from the numerical point of view, a type III thermoelastic model with double porosity. The thermomechanical problem is written as a linear system composed of hyperbolic partial differential equations for the displacements and the two porosities, and a parabolic partial differential equation for the thermal displacement. An existence and uniqueness result is recalled. Then, we perform its a priori error numerical analysis approximating the resulting variational problem by using the finite element method and the implicit Euler scheme. The linear convergence of the algorithm is derived under suitable additional regularity conditions. Finally, some numerical simulations are shown to demonstrate the accuracy of the approximations and the dependence of the solution on a coupling coefficient.Ministerio de Ciencia, Innovación y Universidades | Ref. PGC2018‐096696‐B‐I00Ministerio de Economía y Competitividad | Ref. MTM2016‐74934‐

A Moore‐Gibson‐Thompson heat conduction equation for non centrosymmetric rigid solids

In this paper, we propose a new thermal model based on the so‐called Moore‐Gibson‐Thompson equation for heat conduction, assuming that the material is not centrosymmetric. The existence of a unique solution is proved, although only the main steps of its proof are provided for the sake of simplicity in the presentation. A sufficient condition is proposed to guarantee the stability of the solutions. Then, a fully discrete scheme is introduced by using the classical finite element scheme and the implicit Euler scheme. A discrete stability property and an a priori error analysis are shown, from which the linear convergence of the approximations is deduced. Finally, some numerical simulations in one‐dimensional examples are performed to show the behavior of the discrete energy decay.Agencia Estatal de Investigación | Ref. PID2019-105118GB-I00Universidade de Vigo/CISU

Numerical analysis of a problem of elasticity with several dissipation mechanisms

In this work, we numerically study a problem including several dissipative mechanisms. A particular case involving the symmetry of the coupling matrix and three mechanisms is considered, leading to the exponential decay of the corresponding solutions. Then, a fully discrete approximation of the general case in two dimensions is introduced by using the finite element method and the implicit Euler scheme. A priori error estimates are obtained and the linear convergence is derived under some appropriate regularity conditions on the continuous solution. Finally, some numerical simulations are performed to illustrate the numerical convergence and the behavior of the discrete energy depending on the number of dissipative mechanisms.Universidade de Vigo/CISUGAgencia Estatal de Investigación | Ref. PID2019-105118GB-I0

A MGT thermoelastic problem with two relaxation parameters

In this paper, we consider, from both analytical and numerical viewpoints, a thermoelastic problem. The so-called MGT model, with two different relaxation parameters, is used for both the displacements and the thermal displacement, leading to a linear coupled system made by two third-order in time partial differential equations. Then, using the theory of linear semi-groups the existence and uniqueness to this problem is proved. If we restrict ourselves to the one-dimensional case, the exponential decay of the energy is obtained assuming some conditions on the constitutive parameters. Then, using the classical finite element method and the implicit Euler scheme, we introduce a fully discrete approximation of a variational formulation of the thermomechanical problem. A main a priori error estimates result is shown, from which we conclude the linear convergence under suitable additional regularity conditions. Finally, we present some one-dimensional numerical simulations to demonstrate the convergence of the fully discrete approximation, the behavior of the discrete energy decay and the dependence on a coupling parameter.Agencia Estatal de Investigación | Ref. PID2019-105118GB-I00Universidade de Vigo/CISU

Numerical analysis of a thermoelastic dielectric problem arising in the Moore–Gibson–Thompson theory

Financiado para publicación en acceso aberto: Universidade de Vigo/CISUGIn this paper, we numerically study a thermoelastic problem arising in the Moore– Gibson–Thompson theory. Dielectrics effects are also included within the model. The corresponding problem is written in terms of the displacement field, the temperature and the electric potential. A viscous term is added in the heat equation to provide the numerical analysis of the corresponding variational problem. Then, by using the finite element method and the implicit Euler scheme fully discrete approximations are introduced. A discrete stability property and a priori error estimates are obtained. Finally, one- and two-dimensional numerical simulations are shown to demonstrate the accuracy of the approximation and the behavior of the solutionMinisterio de Ciencia; Innovación y Universidades | Ref. PGC2018-096696-B-I00Ministerio de Ciencia; Innovación y Universidades | Ref. PID2019-105118GB-I0

Method to determine which quantum operations can be realized with linear optics with a constructive implementation recipe

The evolution of quantum light through linear optical devices can be described by the scattering matrix S of the system. For linear optical systems with m possible modes, the evolution of n input photons is given by a unitary matrix U=φm,M(S), derived from a known homomorphism, φm,M, which depends on the size of the resulting Hilbert space of the possible photon states, M. We present a method to decide whether a given unitary evolution U for n photons in m modes can be achieved with linear optics or not and the inverse transformation φ−1m,M when the transformation can be implemented. Together with previous results, the method can be used to find a simple optical system which implements any quantum operation within the reach of linear optics. The results come from studying the adjoint map between the Lie algebras corresponding to the Lie groups of the relevant unitary matrices

Numerical analysis of a swelling poro-thermoelastic problem with second sound

In this paper, we analyze, from the numerical point of view, a swelling porous thermo-elastic problem. The so-called second-sound effect is introduced and modeled by using the simplest Maxwell–Cattaneo law. This problem leads to a coupled system which is written by using the displacements of the fluid and the solid, the temperature and the heat flux. The numerical analysis of this problem is performed applying the classical finite element method with linear elements for the spatial approximation and the backward Euler scheme for the discretization of the time derivatives. Then, we prove the stability of the discrete solutions and we provide an a priori error analysis. Finally, some numerical simulations are performed to demonstrate the accuracy of the approximations, the exponential decay of the discrete energy and the dependence on a coupling parameter