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Teaching

Dislocations dynamics: from microscopic models to macroscopic crystal plasticity By Dr. Stefania Patrizi  (WIAS-Berlin) 

  • Class schedule:  Wednesday, March 25th, 2015 from 03:00 pm to 04:00 pm
  • Location: Building 1, Room 2202
  • Refreshments: Available at 02:45​​

Abstract 
Dislocations are moving defects in crystals that can be described at several scales by different models. 
We first consider a 1D evolution equation arising in the Peierls-Nabarro model, which is a phase field model describing dislocation dynamics  at a microscopic scale. Differently from the previous literature, we treat the case in which dislocations do not occur all  with the same orientations (i.e. opposite orientations are allowed as well). We show that, at a long time scale, and at a mesoscopic 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 dislocations orientation, these points may collide in finite time. 
Then we consider the Peierls-Nabarro model in any dimension and we identify at a large scale an evolution model for the dynamics of a density of dislocations. This model is a  macroscopic model for crystal  elasto-visco-plasticity. The results that will be presented have been obtained in some papers in collaboration with   E. Valdinoci.

Biography
Dr Stefania Patrizi is currently Postdoctoral research fellow at WIAS-Berlin since September 2013. Previously, she was at the Sapienza University in Rome, where she received a Ph.D in Mathematics in January 2010,  under the direction of Prof. I. Capuzzo Dolcetta and Prof. I. Birindelli. From 2010 to 2013, she was a Research Fellow in the Austin-Lisbon CoLab program. Her research is focused in the Analysis of Partial Differential Equations, with emphasis in eigenvalues problems for fully nonlinear operators, fractional operators, homogenization problems, free boundary problems.