Lucia Scardia

 Title: Convergence of Interaction-driven Evolutions of Dislocations

 Abstract: It is well known that the plastic, or permanent, deformation 
           of a metal is caused by the movement of curve-like defects in its 
           crystal lattice. These defects are called dislocations. What is not 
           yet clear is how to use this microscale information to make theoretical 
           predictions at the continuum scale. Motivated by this, M.G. Mora, M.
           Peletier and I 
           considered a system of interacting dislocations and studied the
           convergence of the evolution of the corresponding empirical measures in the limit of
           many dislocations. In the continuum limit we obtained an evolution law for the 
           dislocation density. In this talk I will present this result and discuss
           its limitations and further extensions towards more realistic and complex
           systems.