Homogénéisation de l'effet Hall et de la magnétorésistance dans des composites

Abstract : A composite conductor is composed of microscopic heterogeneities but appears as a homogeneous medium on the macroscopic scale. Describing the behavior of such materials requires the homogenization of the conduction equations which rule each of their phases. In this PhD thesis, we study a few effective laws for composite conductors in the presence of a constant magnetic field. In the first chapter, we recall a few results on electro-physics (Hall effect, magneto-resistance) and on the homogenization theory (H-convergence) as well as its extension to high-conductivity problems. In the second chapter, we study the Hall effect in two-dimensional high-contrast two-phase composites and we compare the result to the one obtained with a three-dimensional fibre-reinforced structure. The third chapter generalizes this particular case and extends the perturbation law to non-periodic cylindrical composites without any geometrical assumption on their cross section. The chapters two and three underline the gap between dimension two and dimension three in high-conductivity problems. The fourth chapter analyses the magneto-resistance in a three-dimensional composite medium and outlines a strong interaction between the direction of the magnetic field and the dissipated energy in the material; this completes a previous work on the two-dimensional case.
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Laurent Pater. Homogénéisation de l'effet Hall et de la magnétorésistance dans des composites. Mathématiques générales [math.GM]. Université Rennes 1, 2013. Français. ⟨NNT : 2013REN1S101⟩. ⟨tel-00835958v2⟩

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