Space-time evolution of Volterra disclinations

TL;DR

This paper investigates the space-time evolution of wedge disclinations in finite particle systems within a circular domain, providing existence theorems and numerical solutions for different motion scenarios.

Contribution

It introduces a mathematical framework with existence theorems for disclination trajectories, considering isotropic and crystalline media, and demonstrates these with numerical examples.

Findings

Existence theorems for disclination trajectories

Numerical solutions illustrating various configurations

Analysis of dynamics in isotropic and crystalline media

Abstract

The dynamics of a system of particles subject to a 4th order potential field modeling the space-time evolution of wedge disclinations is studied, focusing on finite systems of disclinations within a circular domain. Existence theorems for the trajectories of these disclinations are presented, considering both the dynamics without predefined preferred directions of motion in an isotropic medium and the dynamics in which the disclinations move parallel to predefined directions, modeling a crystalline material. The analysis is illustrated with a number of numerical solutions to demonstrate various relevant configurations.