Discrete-to-continuum limits of edge dislocations in 2D
Date
Thursday, March 2, 2017 16:00 - 18:00
Speaker
Patrick van Meurs (Kanazawa University, Japan)
Location
Seminar room Big Ground floor / Office Bldg West (I21.EG.101)
Series
Seminar/Talk
Tags
Mathematics and CS Seminar
Host
Jan Maas
Contact
The starting point is a 2D model for the dynamics of n dislocations, which are modelled as point particles with a positive or negative 'charge'. In the celebrated engineering paper by Groma and Balogh in 1999, the limit passage 
of these dislocation dynamics is performed in a statistical mechanics framework, which relies on a phenomenological closure assumption. In my talk, I present how to pass rigorously to the limit by using the theory of Wasserstein gradient ows and using advanced functional analysis on the weak form of the evolution equation. Interestingly, our conclusion for the limiting dynamics of the dislocation density differs from the conclusion in the paper by Groma and Balogh.