Zusammenfassung für den Vortrag am 31.01.2023 (16:45 Uhr)

Oberseminar ANALYSIS - PROBABILITY

Amit Acharya (Carnegie Mellon University)
An action functional for nonlinear dislocation dynamics
31.01.2023, 16:45 Uhr, MPI für Mathematik in den Naturwissenschaften Leipzig, E1 05 (Leibniz-Saal)

Dislocations are the physical defects whose motion and interaction are responsible for the plasticity of crystalline solids. The physics can be characterized by a system of nonlinear PDE which does not naturally arise from a variational principle. With a view towards an eventual path integral formulation to understand statistical properties, we describe a first step related to the development of a family of dual variational principles for this primal system with the property that the Euler-Lagrange equations of each of its members is the primal system in a well-defined sense. We illustrate the main idea of the scheme and its viability by applying it to compute approximate solutions to the linear heat, and first-order, scalar wave equations, and 1-d, nonconvex elastostatics. This is joint work with Udit Kouskiya and Siddharth Singh.

 

25.01.2023, 09:30