This master thesis is dealing with object tracking in high-speed camera images, within what we are trying to find their trajectory and orientation. The mathematical theory associated with this problem as well as the methods used fo image processing are described here. The main outcome is an application with a user interface through which we can calculate the desired parameters of the individual objects.

Cette thèse est constituée de deux parties indépendantes. La première partie concerne l'étude des vecteurs propres de matrices aléatoires de type Wigner. Dans un premier temps, nous étudions la distribution des vecteurs propres de matrices de Wigner déformées, elles consistent en une perturbation d'une matrice de Wigner par une matrice diagonale déterministe. Si les deux matrices sont du même ordre de grandeur, il a été prouvé que les vecteurs propres se délocalisent complètement et les valeurs propres rentrent dans la classe d'universalité de Wigner-Dyson-Mehta. Nous étudions ici une phase intermédiaire où la perturbation déterministe domine l'aléa: les vecteurs propres ne sont pas totalement délocalisés alors que les valeurs propres restent universelles. Les entrées des vecteurs propres sont asymptotiquement gaussiennes avec une variance qui les localise dans une partie explicite du spectre. De plus, leur masse est concentrée autour de cette variance dans le sens d'une unique ergodicité quantique. Ensuite, nous étudions des corrélations de différents vecteur propres. Pour se faire, une nouvelle observable sur les moments de vecteurs propres du mouvement brownien de Dyson est étudiée. Elle suit une équation parabolique close qui est un pendant fermionique du flot des moments de vecteurs propres de Bourgade-Yau. En combinant l'étude de ces deux observables, il est possible d'analyser certaines corrélations.La deuxième partie concerne l'étude de la distribution des valeurs propres de modèles non-linéaires de matrices aléatoires. Ces modèles apparaissent dans l'étude de réseaux de neurones aléatoires et correspondent à une version non-linéaire de matrice de covariance dans le sens où une fonction non-linéaire, appelée fonction d'activation, est appliquée entrée par entrée sur la matrice. La distribution des valeurs propres convergent vers une distribution déterministe caractérisée par une équation auto-consistante de degré 4 sur sa transformée de Stieltjes. La distribution ne dépend de la fonction que sur deux paramètres explicites et pour certains choix de paramètres nous retrouvons la distribution de Marchenko-Pastur qui reste stable après passage sous plusieurs couches du réseau de neurones. / This thesis consists in two independent parts. The first part pertains to the study of eigenvectors of random matrices of Wigner-type. Firstly, we analyze the distribution of eigenvectors of deformed Wigner matrices which consist in a perturbation of a Wigner matrix by a deterministic diagonal matrix. If the two matrices are of the same order of magnitude, it was proved that eigenvectors are completely delocalized and eigenvalues belongs to the Wigner-Dyson-Mehta universality class. We study here an intermediary phase where the deterministic perturbation dominates the randomness of the Wigner matrix : eigenvectors are not completely delocalized but eigenvalues are still universal. The eigenvector entries are asymptotically Gaussian with a variance which localize them onto an explicit part of the spectrum. Moreover, their mass is concentrated around their variance in a sense of a quantum unique ergodicity property. Then, we consider correlations of different eigenvectors. To do so, we exhibit a new observable on eigenvector moments of the Dyson Brownian motion. It follows a closed parabolic equation which is a fermionic counterpart of the Bourgade-Yau eigenvector moment flow. By combining the study of these two observables, it becomes possible to study some eigenvector correlations.The second part concerns the study of eigenvalue distribution of nonlinear models of random matrices. These models appear in the study of random neural networks and correspond to a nonlinear version of sample covariance matrices in the sense that a nonlinear function, called the activation function, is applied entrywise to the matrix. The empirical eigenvalue distribution converges to a deterministic distribution characterized by a self-consistent equation of degree 4 followed by its Stieltjes transform. The distribution depends on the function only through two explicit parameters. For a specific choice of these parameters, we recover the Marchenko-Pastur distribution which stays stable after going through several layers of the network.

Les conditions à la surface de Vénus sont infernales : température de plus de 400 C, pression atmosphérique 90 fois celle sur Terre dans une atmosphère composée à 96 % de dioxyde de carbone. Une particularité de cette planète est la couche opaque nuageuse de 20 km d'épaisseur qui couvre toute la planète. Les nuages ont un rôle crucial pour le transfert de rayonnement, la dynamique atmosphérique, dans le cycle de certaines espèces chimiques comme le soufre et plus généralement pour le climat de Vénus. Malgré de nombreuses missions spatiales consacrées à cet astre depuis 1961, il y a peu de mesures in-situ. Les couches basses des nuages sont diciles à étudier par satellite, par conséquent il existe encore de nombreuses questions au sujet des nuages : leurs propriétés et leurs impacts radiatifs, dynamiques et chimiques sont mal contraints. Composées majoritairement d'acide sulfurique en solution, les particules sont supposées sphériques et liquides et composent des nuages étalés verticalement entre 50 et 70 km d'altitude environ, entourés par des brumes entre 30 et 50 km et au-dessus de 70 km. Les gouttelettes ont été classées, d'après des observations, en trois modes en fonction de leur taille et de leur composition : les modes 1 et 2 respectivement pour les petites (r = 0.2 μm) et moyennes particules (r = 1.0 μm), et un troisième mode qui contiendrait les plus grandes particules (r = 3.5 μm). Ce dernier mode, qui a été détecté par la sonde Pioneer Venus, demeure de composition et d'existence incertaines, et il n'est pas pris en compte dans notre étude. Afin de compléter et de mieux comprendre les données obtenues par l'observation spatiale, un modèle modal de microphysique, nommé MADMuphy (Modal Aerosol Dynamics with Microphysics), a été développé. L'objectif est d'intégrer MAD-Muphy dans le modèle de climat global vénusien (IPSL-VGCM), il faut donc limiter le nombre de variables que le VGCM doit suivre dans le temps et l'espace (également appelé traceurs). La méthode des moments est déjà utilisée dans les GCM de Titan et de Mars et constitue un bon compromis entre la précision des résultats et le temps de calcul. MAD-Muphy est donc basé sur cette représentation pour une pression et une température dé nies pour une couche de l'atmosphère (ou 0D). La thèse présentée ici détaille le développement des expressions mathématiques des équations de la microphysique avec les moments, présente le nouveau modèle MAD-Muphy ainsi que les hypothèses qui ont été nécessaires pour son développement. Tout d'abord, nous déterminerons le temps caractéristique de chaque processus microphysique et nous étudierons leur comportement en 0D. Ensuite, nos résultats seront comparés avec ceux du modèle sectionné SALSA en 0D. / The conditions on the surface of Venus are infernal: temperature of more than 400 C, 90 times the Earth's atmospheric pressure in an atmosphere composed of 96 % of carbon dioxide. A distinctive characteristic of this planet is the 20 km thick opaque cloud layer, which enshrouds the planet. Clouds have a crucial role in radiative transfer, atmospheric dynamics, in the cycle of some chemical species like sulphur and more generally in the climate of Venus. Despite the numerous space missions devoted to this object since 1961, there are few in-situ measurements. The lower cloud layers are di cult to study by satellite, so there are still many questions about clouds: their properties and their radiative, dynamic and chemical impacts are poorly constrained. Predominantly composed of sulphuric acid solution, the particles are supposed to be spherical and liquid and compose the clouds that are vertically spread between approximately 50 and 70 km of altitude, surrounded by hazes between approximately 30 and 50 km and above 70 km. Based on observations the droplets have been classied into three modes according to their size and composition: modes 1 and 2 respectively for small (r = 0.2 μm) and medium particles (r = 1.0 μm), and a third mode that would contain the largest particles (r = 3.5 μm). The latter mode, which has been detected by the Pioneer Venus probe, remains uncertain in composition and existence, and is not taken into account in our study. To complete and better understand the observational data, a modal microphysical model, called MAD-Muphy (Modal Aerosol Dynamics with Microphysics), has been developed. The goal is to integrate MAD-Muphy into the venusian global climate model (IPSL-VGCM), so we must limit the number of variables that the VGCM must follow in time and space (also called tracers). The moment method is already used in the Titan and Mars GCMs and is a good compromise between the accuracy of the results and the computation time. MAD-Muphy is the refore based on this representation for a pressure and a temperature of one atmospheric layer (or 0D). The thesis presented here details the derivation of the mathematical expressions of the microphysical equations with moments, presents the new MAD-Muphy model as well as the hypotheses that were necessary for its development. We will first determine the characteristic timescale of each microphysical process and we will study their behaviour in 0D. Then, our results will be compared with those of the SALSA sectional model in 0D.

A novel full wave analysis method to determine the scattering parameters and the radiation field intensities of arbitrary Body of Revolution (BOR) radiators consisting of impenetrable media is explored through derived components of modal analysis and the method of moments (MoM). Modal excitation is utilized to excite the structural feed; allowing for a more accurate measure of the scattering parameters of the total structure as opposed to the use of external excitation sources. The derivation of the mode matching method introduces a novel approach to achieving a frequency independent coupling matrix that will reduce the computational requirements for iterations utilized in the solution of multi-step discontinuous junctions. An application of interpolation functions across a single element of the MoM's traditional basis function approach allows for the ability to facilitate the meshing of complex structures. The combined field integral equation method is implemented in the analysis method to assure the mitigation of spurious solutions that can be problematic for electric field integral equation solutions that are predominant in many MoM based codes. The structures of interest represent bodies of revolution (BOR), which maintains that the structures must exhibit rotational symmetry about the longitudinal, or directional, axis. The complexity of the domain of structures that can be treated with the analysis method will be significantly reduced through the use of BOR symmetry of the structure. The proposed method for the solution of structures will include the comprehensive treatment of Boundary Value Problems (BVP's) through modal analysis, aperture treatment, and an application of the method of moments. Solutions for BOR radiating structures can be divided into two regions of analytical concern, the inner guided wave region and the outer radiating region. Modal analysis will be used to determine the scattering matrix of the inner guided wave region. The modal analysis will consist of subdividing the inner region into a number of finite step discontinuities, and the method of mode matching will be implemented to numerically solve the BVP's at each step discontinuity for a finite number of modal field distributions. The surface field equivalence principle will be applied to treat the aperture in order to produce an equivalent problem that supplants a source magnetic current density and an induced electric current density across the aperture that will radiate in the presence of the outer structural material of the BOR radiator. An algorithm utilizing the MoM is applied to solve integral equations that are defined to treat the surfaces of the BOR structure using electromagnetic boundary conditions. The application of the MoM will develop the field intensities on the aperture with complete consideration of the outer structural boundaries of the BOR radiator. The field intensities on the aperture will be related to the inner guided wave region through electromagnetic boundary conditions, and an admittance matrix will be numerically calculated. The admittance matrix will then apply to the inner guided wave region's scattering matrix to determine the reflection and transmission coefficients at the input of the BOR radiator. The comprehensive solution method will be applied to a variety of BOR structures; the electromagnetic solutions of the structures as obtained by the proposed method shall be verified for accuracy against comparative analysis of the structures using known computational packages that have been generally accepted throughout industry with respect to design capabilities.

No description available.

No / A heterogeneous hybrid computational electromagnetics method is presented, which enables different parts of an antenna simulation problem to be treated by different methods, thus enabling the most appropriate method to be used for each part. The method uses a standard frequency-domain moment-method program and a finite-difference time-domain program to compute the fields in two regions. The two regions are interfaced by surfaces on which effective sources are defined by application of the Equivalence Principle. An extension to this permits conduction currents to cross the boundary between the different computational domains. Several validation cases are examined and the results compared with available data. The method is particularly suitable for simulation of the behavior of an antenna that is partially buried, or closely coupled with lossy dielectric volumes such as soil, building structures or the human body.

Une étude de l'impact des mascarets sur le transport des sédiments à l'aide de la simulation numérique a été réalisée dans ce travail. En utilisant le logiciel OpenFOAM CFD, nous avons généré 17 simulations numériques de mascaret avec divers nombres de Froude Fr, allant de 0,99 à 1,66. Deux types de mascarets, ondulant et déferlant, ont été couverts dans ces 17 simulations numériques. Pour les particules sédimentaires non cohésives, nous avons utilisé les équations de Maxey et Riley pour déterminer la trajectoire des particules sédimentaires non cohésives sous l’influence d’un mascaret ondulant. En utilisant le schéma Runge-Kutta du quatrième ordre, une méthode tracker résout les équations de Maxey et Riley qui nécessitent l’information des champs de vitesse au temps t. Pour les particules sédimentaires cohésives, nous avons calculé la distribution des particules sédimentaires cohésives en utilisant un modèle de transport de flocs, présenté par Winterwerp (2001). Dans ce modèle, la concentration volumique solide des sédiments et le diamètre des flocs D sont estimés. Les équations de transport de et D sont résolues en utilisant la méthode des moments présentée par Beaudoin et al. (2002 et 2004). La méthode des moments permet de réduire le temps CPU rendant possible une étude paramétrique. De ce travail, nous avons trouvé une classification du mascaret en fonction du nombre de Froude Fr. Cette classification est également basée sur l’étude menée par Furgerot (2014). Pour un nombre de Froude 1,04 < Fr < 1,43, le mascaret est ondulant. Pour un nombre de Froude 1,43 < Fr < 1,57, le mascaret est partiellement déferlant, similaire à la transition de mascaret définie par Furgerot (2014). Pour un nombre de Froude Fr > 1,57, le mascaret est totalement déferlant. Une analyse de la distribution de la pression a été effectuée par Baddour et Song (1990). Nous avons trouvé que les pressions totales et hydrostatiques d’un mascaret ondulant ont de grandes valeurs sous la crête et le creux. Dans le cas d’un mascaret ondulant, les pressions totales ne sont pas égales à les pressions hydrostatiques. Cela provoque la présence de pressions dynamiques. Dans le cas de mascaret déferlant, les pressions totales deviennent égales aux pressions hydrostatiques. La turbulence réduit les pressions dynamiques. L'impact des mascarets sur le transport de particules sédimentaires non cohésives et cohésives a été étudié dans ce travail. Pour les particules sédimentaires non cohésives, nous avons observé que la trajectoire utilisant l’écoulement généré par OpenFOAM est similaire à la trajectoire de type e proposée par Chen et al. (2010). Des modifications du modèle de Chen ont été faites en incluant les effets de la gravité, l’élévation et l’atténuation pour reproduire des trajectoires de particules non cohésives sous un mascaret ondulant. Nous avons obtenu des relations linéaires entre les paramètres du modèle de Chen modifié (β1 , β2 et β3) et le nombre de Froude Fr. C’est parce que le niveau de la turbulence du mascaret ondulant est faible. L’écoulement induit par mascaret ondulant n’est pas complexe. Ce phénomène physique est quasi linéaire. Le paramètre β1, lié à la célérité avant du mascaret ondulant, diminue lorsque le nombre de Froude Fr augmente. Les paramètres β2 et β3, liés respectivement à l’élévation et à l’atténuation du mascaret déferlant, augmentent lorsque le nombre de Froude Fr augmente. Enfin, pour les particules sédimentaires cohésives, nous avons calculé la distribution de la taille des flocs D sous deux types de mascaret, ondulant et déferlant. Nous avons utilisé le diamètre initial de la particule sédimentaire cohésive d = 4 μm. La taille du floc initial D est égale à 10 μm avec la concentration du floc c = 0,5 kg/m3 . Et nous avons limité la taille maximale du floc à 2000 μm. Nous avons observé que la valeur maximal de la taille des flocs Dmax augmente de façon exponentielle par rapport au nombre de Froude Fr. / A study of the impact of tidal bores on sediment transport by using the numerical simulation has been done in this work. Using OpenFOAM CFD software, we have generated 17 numerical simulations of tidal bores with various values of Froude number Fr, ranging from 0.99 to 1.66. Two types of tidal bores, undular and breaking, have been covered in these 17 numerical simulations. We have studied the behavior of two types of sediment particles, non-cohesive and cohesive sediment particles. For the non-cohesive sediment particles, we have resolved the Maxey and Riley equations to study the influence of undular tidal bores on the trajectory of non cohesive sediment particles. Using the fourth order Runge-Kutta scheme, the method tracker can solve the Maxey and Riley equations that requires the information of velocity fields at time t. For the cohesive sediment particles, we have calculated the distribution of cohesive sediment particles using a floc model that allows to estimate the sediment solid volume concentrationand the diameter of flocs D, presented by Winterwerp (2001). The transport equations of and D are solved using the moment method presented by Beaudoin et al. (2002 and 2004). The moment method has been used because it allows to reduce the CPU time, making feasible a parametric study. From this work, we have found a classification of tidal bores as a function of Froude number Fr. This classification is also based on the study conducted by Furgerot (2014). We have obtained that for a Froude number 1.04 < Fr < 1.43, the tidal bore is undular. For 1.43 < Fr < 1.57, the tidal bore is partially breaking that is similar with the tidal bore transtition defined by Furgerot (2014). For Fr > 1.57, the tidal bore is totally breaking. An analysis of pressure distributions has been performed by Baddour and Song (1990). We found that the total and hydrostatic pressures of undular tidal bores have great values under the crest and the trough wave. In the case of undular tidal bores, the total pressures are not equal to the hydrostatic pressures. In the case of breaking tidal bores, the total pressures become equal to the hydrostatic pressures when the tidal bores are totally breaking. The turbulence reduces the dynamic pressures. The impact of tidal bores on the transport of non-cohesive and cohesive sediment particles have been studied in this work. For the non-cohesive sediment particles, we have observed that the trajectory using the flow generated by OpenFOAM is similar with the type e trajectory proposed by Chen et al. (2010). The modifications of Chen’s model have been done by including the effects of gravity, elevation and attenuation to reproduce non-cohesive particle trajectories under an undular tidal bore. We have obtained that the relationship between the Chen’s parameters (β1 , β2 and β3) and the Froude number Fr are linear. This is because the level of turbulence for undular tidal bores is low. The flow induced by an undular tidal bore is not complex. This physical phenomenon is quasi linear. The parameter β1 , related to the front celerity of tidal bores, decreases when the Froude number Fr increases. The parameters, β2 and β3, related to the elevation and attenuation of tidal bores respectively, increase when the Froude number Fr increases. Finally, for the cohesive sediment particles, we have calculated the distribution of floc size D under two types of tidal bore, undular and breaking. We have used the initial diameter of cohesive sediment particles d = 4 μm. The initial floc size D is equal to 10 μm with the consentration of floc c = 0.5 kg/m3. And we have limited the maximum floc size equal to 2000 μm. We have obtained that the maximum value of floc size Dmax increases exponentially with the Froude number Fr.

[pt] Os sistemas que operam em banda larga necessitam de radiadores que atendam eletricamente a banda de frequência utilizada. As antenas com características de independência da frequência, em particular as antenas espirais, têm encontrando cada vez mais utilização nesses sistemas, seja em aplicações comercias ou militares. Esta dissertação tem por objetivo a análise de desempenho de antenas espirais do tipo fenda em cavidades, pela aplicação do método dos momentos. Serão consideradas cavidades com a face oposta à antena constituída por um condutor perfeito ou acoplada a uma estrutura de microondas com matriz de espalhamento conhecida. Essa estrutura de microondas, poderá simular, por exemplo, uma ou mais camadas de material absorvente.Um modelo numérico foi desenvolvido, e a partir dele foi elaborado um programa de computador, para determinar as características de radiação de antenas espirais em cavidade. São apresentados e comparados os resultados obtidos para três configurações de antenas espirais de Arquimedes do tipo fenda: sem cavidade, com cavidade condutora e com um material absorvente colocado sobre a face da cavidade oposta a abertura da antena. / [en] Broad band systems need radiators to operate over the entire frequency band. Frequency independent antennas, in particular spiral antennas, are finding increasing application in such systems, for commercial or military purposes. This dissertation has for objective the analysis of performance of cavity-backed slot spiral antenna, by applying the moment method . For this study it will be taken into account cavities with the face opposing to the antenna consisting of a perfect conductor or connected to a structure of microwaves with known scattering matrix. This microwave structure will be able to simulate, for example, one or more layers of absorbing material. A numerical model was developed, and based on it, it was elaborated a computer program to determine the radiation characteristics of cavity-backed spiral antennas. The results surveyed for three configurations of slot Archimedean spiral antenna are presented and compared: without cavity, with conducting cavity, and with an absorbing material placed on the cavity opposite to the antenna.

In this study, the mapped Galerkin method was applied to solve the vector wave equation based on H&amp / #8722 / field and to obtain the propagation constant in x &amp / #8722 / y space. The vector wave equation was solved by the transformation of the infinite x &amp / #8722 / y plane onto a unit square. Two-dimensional Fourier series expansions were used in the solutions. Modal fields and propagation constants of dielectric waveguides were calculated. In the first part of the study, all of the calculations were made in step index fibers. Transverse magnetic fields were obtained in the u &amp / #8722 / v and x &amp / #8722 / y space through the solution of the matrix eigenvalue equation. Some graphics were plotted in the light of the results obtained. The results are found to be in accord with the results of other numerical techniques and exact solutions. After that, the propagation constant in x&amp / #8722 / y space was calculated with ease using the solution of the modal field components. In the second part of the study, the similar calculations were made in graded index fibers.

No / The probability density and exceedance probability functions of the induced currents in a screened cable connecting two enclosures, resulting from the close. presence of single and multiple mobile phones working at 900 MHz, are investigated. The analysis of the problem is undertaken using the Method of Moments, but due to weak coupling, the impedance matrix was modified to reduce the memory and time requirements for the problem, to enable it to be executed multiple times. The empirical probability distribution functions (PDFs) and exceedance probabilities for the induced currents are presented. The form of the PDFs is seen to be quite well approximated by a log-normal distribution for a single source and by a Weibull distribution for multiple sources