La présence d'objets métalliques en Imagerie par Résonance Magnétique provoque des dysfonctionnements qui peuvent se manifester par des artefacts, des échauffements, ... Dans le présent travail, on construit et étudie des modèles mettant en évidence le phénomène d'échauffement.<br /><br />Dans la première partie, on étudie l'antenne cage d'oiseau. On montre que les pulsations de résonance sont les valeurs propres d'un problème aux valeurs propres généralisé et on développe une méthode de calcul efficace de celles-ci. On étudie ensuite les propriétés du champ radiofréquence à l'aide de simulations numériques : mouvement de rotation en tout point et homogénéité au centre de l'antenne.<br /><br />Dans la deuxième partie, on modélise le problème magnétique associé à l'IRM par les équations de Maxwell avec le champ radiofréquence comme condition aux limites. On montre que ce problème est bien posé en dimension 3 et qu'il est équivalent à une série de problèmes axisymétriques bidimensionnels découplés. Des calculs numériques sont effectués sur les problèmes axisymétriques, qui confirment les résultats théoriques obtenus.

The orbit of Phobos exhibits an along-track acceleration, which suggests energy dissipation in the Mars-Phobos system. We hypothesize that the inferred dissipation occurs within Mars. We explore the response of a layered, incompressible Maxwell viscoelastic Mars to tidal forcing by Phobos using normal mode relaxation theory. Our results elucidate the general behavior of a tidally forced viscoelastic body, and have implications for the viscoelastic structure of Mars. We find the real and imaginary part of the degree-two tidal Love number for Mars to be 0.168 and -9.32x10^−4 respectively. Models which satisfy these and other constraints have either: a fluid core with radius 2040 km and density 5410 kg/m^3; or an elastic inner core with radius 1200 km and density 6700 kg/m^3, along with a fluid outer core with thickness 850 km and density 4850 kg/m^3. These findings support previous hypotheses that Mars has at least a fluid outer core.

The orbit of Phobos exhibits an along-track acceleration, which suggests energy dissipation in the Mars-Phobos system. We hypothesize that the inferred dissipation occurs within Mars. We explore the response of a layered, incompressible Maxwell viscoelastic Mars to tidal forcing by Phobos using normal mode relaxation theory. Our results elucidate the general behavior of a tidally forced viscoelastic body, and have implications for the viscoelastic structure of Mars. We find the real and imaginary part of the degree-two tidal Love number for Mars to be 0.168 and -9.32x10^−4 respectively. Models which satisfy these and other constraints have either: a fluid core with radius 2040 km and density 5410 kg/m^3; or an elastic inner core with radius 1200 km and density 6700 kg/m^3, along with a fluid outer core with thickness 850 km and density 4850 kg/m^3. These findings support previous hypotheses that Mars has at least a fluid outer core.

A numerical method based on the the method of characteristics for hyperbolic systems of partial differential equations in four independent variables is developed and used for solving time domain Maxwell's equations. The method uses the characteristic hypersurfaces and the characteristic conditions to derive a set of independent equations relating the electric and magnetic field components on these hypersurfaces. A discretization scheme is developed to solve for the unknown field components at each time step. The method retains many of the good features of the original method of characteristics for hyperbolic systems in two independent variables, such as optimal time step, good behavior near data discontinuities and the ability to treat general boundary conditions. The method is exemplified by calculating the time domain response of a few typical planar interconnect structures to Gaussian and unit step excitations. Although the general emphasis is on interconnect problems, the method is applicable to a number of other transient electromagnetic field problems governed by Maxwell's equations. In addition to the method of characteristics a finite difference scheme, known in mathematic circles as the modified Richtmyer scheme, is applied to the time domain solution of Maxwell's equations. Both methods should be useful for efficient full wave analysis of three dimensional electromagnetic field problems. / Graduation date: 1994

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In the modern world, because of increasing oil prices and the need to control greenhouse gas emission, a new interest in the production of electric cars is coming about. One of the products is a charging point for electric cars, at which electric cars can be recharged by a plug in cable. Usually people are required to pay for the electricity after recharging the electric cars. Today, the payment is handled by using SMS or through the parking system. There is now an opportunity, in cooperation with AES (the company with which we are working), to equip the pole with GPRS, and this requires development and maintenance of the antenna. The project will include data analysis of the problem, measurements and calculations. In this work, we are computing energy flow of the wave due to the location of the antenna inside the box. We need to do four steps. First, we take a set of points (determined by the computational mesh) that have the same distance from the antenna in the domain. Second, we calculate the angles between the ground and the points in the set. Third, we do an angle-energy plot, to analyse which angle can give the maximum energy. And last, we need to compare the maximum energy value of different position of the antenna. We are going to solve the problem in Matlab, based on the Maxwell equation and the Helmholtz equation, which is not time-dependent.

The problem is effect of electromagnetic wave. When electromagnetic wave obliquely transmitted through two different medias ,electromagnetic wave undergoes reflection and refraction at the interface and inside the media. Computation of electromagnetic wave is well known by Maxwell`s equation. There are two cases solving questions. One is constant of £g¡B£`¡B£m.Another is variable of £g¡B£`¡B£m. In case one, use D`Alembertian equation and Helmholtz equation transforming Maxwell`s equation. And solve by ILHI`s(incomplete Lips-chitz-Hankel integrals) and FFT(fast Fourier transform). In case two,if £g¡B£`¡B£m are variables ,we can simplify Maxwell`s equation. It is similar to wave equation with source. We use Finite Element Method(FEM) getting Numerical solution by setting absorbing boundary and mesh. Using results by ILHI`s would get exact solution obliquely incident on two medias. Proof numerical solution by exact solution.

Cette thèse se rapporte à certaines de nos publications (avant 1995) concernant des solutions explicites exactes ou asymptotiques pour des problèmes variés de diffraction par un dièdre imparfaitement conducteur.

Texte remanié de: Thesis--Sydney--University of New South Wales. / Bibliogr. p. 229-253.

Dissertation--Oldenburg, 2002. / Bibliogr. p. 327-349.