An efficient simulation technique for calculating the current distribution in a Vertical Cavity Surface Emitting Laser (VCSEL) is proposed and implemented. The technique consists of a hybrid 1D/3D approach to the problem. The 3D aspect of simulation is essential for devices like a photonic crystal VCSEL where the existing 2D simulation techniques are inadequate. The modular approach of the technique is advantageous, as it provides exibility in dealing with device simulations of varying complexity. It also provides a relatively short simulation time, beneficial for exploring a large design parameter space. The box integration technique is used for discretizing the equations and sparse matrix methods are used in solving the matrices. Simulation results and comparisons are provided for various aspects and modules of the simulator. The results for a few sample simulations indicate that the analysis has reasonable agreement with experimental results. The simulation error can be reduced using more accurate models for the active region of the laser.

No description available.

In an optimal visiting problem, we want to control a trajectory that has to pass as close as possible to a collection of target points or regions. We introduce a hybrid control-based approach for the classic problem where the trajectory can switch between a group of discrete states related to the targets of the problem. The model is subsequently adapted to a mean-field game framework, that is when a huge population of agents plays the optimal visiting problem with a controlled dynamics and with costs also depending on the distribution of the population. In particular, we investigate a single continuity equation with possible sinks and sources and the field possibly depending on the mass of the agents. The same problem is also studied on a network framework. More precisely, we study a mean-field game model by proving the existence of a suitable definition of an approximated mean-field equilibrium and then we address the passage to the limit.

Le but de ce travail est d’étudier la faisabilité de la détection de mouvements dans des séquences d’images en utilisant l’équation de continuité et la dynamique de supraconductivité. Notre approche peut être motivée par le fait que l’équation de continuité apparait dans plusieurs techniques qui estiment le flot optique. Un grand nombre de techniques qui utilisent les flots optiques utilisent une contrainte appelée contrainte de l’invariance lumineuse. La dynamique de supraconductivité nous permet de nous affranchir de la contrainte de l’invariance lumineuse. Les expériences se feront avec la base de données de séquences d’images CDNET 2014. Pour obtenir les résultats numériques en terme de score F1, une combinaison sera faite par la suite entre la dynamique de supraconductivité et un méchanisme d’attention qui est un résumé des vérites de terrain. / The goal of this work is to study the feasibility of motion detection in images sequences by using the continuity equation and superconductivity dynamics. Our approach can be motivated by the fact that many techniques that compute the optic flow use the continuity equation combined with a constraint that is called the brightness constancy constraint. The dynamics of superconductivity allows us to escape from the brightness consistency constraint. The experiments will be done with a database of images sequences named CDNET 2014. To obtain the numerical results in terms of F1 score a combination will be done between the dynamics of superconductivity and a mechanism of attention which is a resume of the ground truth.

This MA thesis focuses on the aerodynamic measurement in the teaching of physics using the Leybold Didactic didactic set. The thesis consists of instructions for solving 4 basic problems using the Leybold set; every problem comprises theoretical instructions for students and an experimental verification of the problem. The thesis should contribute to wider use of experimental teaching of physics in schools; also, it is supposed to serve teachers and students as a source of interesting laboratory assignments verifying aerodynamic laws and quantities. After minor adjustments, the thesis can be used in all types of schools, from elementary physics at primary schools to advanced physics at technical universities.

The master's thesis deals with Navier-Stokes equations in curvilinear coordinates and their solution for quasi-potential flow. The emphasis is on detailed description of curvilinear space and its expression using Bézier curves, Bézier surfaces and Bézier bodies. Further, fundamental concepts of hydromechanics are defined, including potential and quasi-potential flow. Cauchy equations are derived as a result of the law of momentum conservation and continuity equation is derived as a result of principle of mass conservation. Navier-Stokes equations are then derived as a special case of Cauchy equations using Cauchy stress tensor of Newtonian compressible fluid. Further transformation into curvilinear coordinates is accomplished through differential operators in curvilinear coordinates and by using curvature vector of space curve. In the last section we use results from previous chapters to solve boundary value problem of quasi-potential flow, which was solved by finite difference method using Matlab environment.