Crystal dislocations with different orientation and collisions
Homogenization and Random Phenomenon
09 October 14:00 - 14:55
Stefania Patrizi - Weierstrass Institute
We consider a parabolic differential equation whose solution represents the atom dislocation in a crystal for a general type of Peierls-Nabarro model with possibly long range interactions and an external stress. Differently from the previous literature, we treat here the case in which such dislocation is not the superpositions of transitions all occurring with the same orientations (i.e. opposite orientations are allowed as well). We show that, at a long time scale, and at a macroscopic space scale, the dislocations have the tendency to concentrate as pure jumps at points which evolve in time, driven by the external stress and by a singular potential. Due to differences in the dislocation orientations, these points may collide in finite time. The results that will be presented have been obtained in collaboration with Prof. Enrico Valdinoci.
KTH Royal Institute of Technology
The University of Chicago