Defining Creation in 1D Dislocation Dynamics

: A study in theory and simulation of the extension of 1D discrete dislocation dynamics models with creation

Abstract

We consider an interacting particle system with singular interaction, describing the dynamics of finite numbers of (charged) dislocations in one-dimensional space, including annihilation. In this thesis, we formalise several possible methods for introducing creation into the formal description of such a system. This results in three definitions of solution concepts to these systems, for one of which we prove uniqueness and other properties. Moreover, we describe a framework in which long-range effects of different creation methods can be compared, and draw conclusions on the effect of our developed creation methods. In addition, we describe basic numerical simulation of the developed system, which is non-trivial (even with automatic ODE-solvers) due to the intricacies of creation.

Date of Award	12 Sept 2022
Original language	English
Supervisor	Mark A. Peletier (Supervisor 1)