Back to Departmental Colloquium: Fall 2012
Departmental Colloquium
Date: Thursday, Nov 8, 2012
Time: 4:15PM
Location: JWB 335
Anna Vainchtein
University of Pittsburgh
Title |
From discrete to continuum: kinetic relations and beyond |
Abstract |
Propagation of phase boundaries, cracks and dislocations in crystal lattices is associated with energy dissipation that takes place in atomically sharp transition zones. Classical continuum theories represent these lattice defects as singularities, and the information about their kinetics is lost. This can lead to non-uniqueness of solutions of the associated initial value problem unless an additional constitutive function that relates the velocity of a moving defect to the driving force is specified. This kinetic relation can be extracted from the underlying discrete model by considering a traveling wave solution representing the moving defect. In this talk, I will illustrate this by considering some prototypical discrete systems with nonconvex interactions. I will then introduce a more general concept of kinetic equations that are nonlocal in time. |
Mathematical Biology