Forcadel, Nicolas (2007) Contribution to the analysis of partial differential equations describing front propagation and application to dislocation dynamics. PhD thesis, ENPC p.383.
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Abstract
This work deals with the modeling, the analysis and the numerical analysis of the dislocation dynamics and with the very strong links which exists with mean curvature type motion. Dislocations are linear defects which move in crystals when those are subjected to exterior stress. More precisely, the dynamics of a dislocation line is described by an eikonal equation where the speed depends in a nonlocal way on the who le line. ln the modeling, it is also possible to add a mean curvature term.
The first part of this work is devoted to the study of the qualitative properties of dynamics of a dislocation line (existence, uniqueness, asymptotic behaviour. .. ). This study relies essentiaIly on the theory of viscosity solutions. We also propose several numerical scheme for this dynamics and we show their convergence as weIl as error estimates.
ln a second part, we establish the link between the dynamics of a finite number of dislocations and the dynamics of dislocation density by showing homogenization results. We also study, in a theoretical and numerical way, a model for the dynamics of dislocation density.
| Item Type: | PhD Thesis (PhD) |
|---|---|
| PhD Supervisor: | Monneau, Régis |
| Date: | 02 July 2007 |
| Board of examiners: | Berestycki, Henri and Roquejoffre, Jean-Michel and Soner, Mete and Alvarez, Olivier and Barles, Guy and Caffarelli, Luis and Cardaliaguet, Pierre and Monneau, Régis |
| Collection (Fonds): | Ecole des Ponts ParisTech (ENPC) |
| Institution: | ENPC |
| Subjects: | 1. Mathematics and Applications |
| Uncontrolled Keywords: | Dislocation dynamics, Viscosity solutions, Mean curvature motion, Non-local equations, Dynamique des dislocations, Solutions de viscosités, Mouvement par courbure moyenne, Equations non locales |
| ID Code: | 3311 |
| Deposited By: | Anna Egea |
| Deposited On: | 17 January 2008 |
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