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Coordinator

Piotr Gwiazda
Institute of Applied Mathematics and Mechanics
University of Warsaw
Banacha 2,
02-097 Warsaw
e-mail: mmns@mimuw.edu.pl
phone: +48 22 5544551
fax: +48 22 5544700
 

Analytic and numerical study of dislocation dynamics
Piotr Biler and Marco Cannone in collaboration with Regis Monneau
The project is carried out by Łukasz Paszkowski at University of Wrocław
Dislocations are line defects in crystals. When the material is submitted to shear stresses, these lines can move in the crystallographic planes and this dynamics can be observed using electron microscopy. The elementary mechanisms at the origin of the deformation of monocrystals are rather well understood, however, many questions concerning the plastic behaviour of materials containing a high density of defects are still open. The difficulty lies in the necessity of taking into account, in a three-dimensional geometry, a large number of mechanisms and interactions.

Hence, in recent years, new physical theories describing the collective behaviour of dislocations have been developed and numerical simulations of dislocations have been performed. We refer the reader to the recent publications [1, 2] for the comprehensive references about modelling of dislocation dynamics.

In this project, the Ph.D. student will study properties of solutions to equations modelling dynamics of dislocations. By using analytical and numerical methods, we expect results on the asymptotic behaviour of solutions as well as the criteria for regularity and possible singularities of solutions.

This Ph.D. project will be realized in two research centres: in Wroclaw University (Mathematical Institute) (5 semesters) and in Universite Paris-Est (in Laboratoire d'Analyse et de Mathematiques Appliquees and in CERMICS - Ecole nationale des Ponts et Chaussees) (3 semesters).

[1] O. Alvarez, P. Hoch, Y. Le Bouar and R. Monneau, (2006) Arch. Rat. Mech. Anal., 181: 449--504.
[2] N. Forcadel, C. Imbert and R. Monneau, (2009) Discrete Contin. Dyn. Syst. Ser. A, 23: 785--826.

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