Abstract for the talk on 31.01.2023 (16:45 h)OS Analysis-Probability
Amit Acharya (Carnegie Mellon University)
An action functional for nonlinear dislocation dynamics
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.