Geodesics around line defects in elastic solids

TL;DR

This paper derives exact geodesic solutions in an elastic medium with line defects, modeling particle motion around topological defects using a gravity-like geometric approach.

Contribution

It provides the first exact solutions for geodesics around a generic line defect, enhancing understanding of particle trajectories in defected elastic solids.

Findings

Exact geodesic solutions for dispiration defects

Unified treatment of screw dislocation and wedge disclination

Insights into particle motion in defected elastic media

Abstract

Topological defects in solids, usually described by complicated boundary conditions in elastic theory, may be described more simply as sources of a gravity- like deformation field in the geometric approach of Katanaev and Volovich. This way, the deformation field is described by non-Euclidean metric that incorporates the boundary imposed by the defects. A possible way of gaining some insight into the motion of particles in a medium with topological defects (e.g., electrons in a dislocated metal) is to look at the geodesics of the medium around the defect. In this work, we find the exact solution for the geodesic equation for elastic medium with a generic line defect, the dispiration, that can either be a screw dislocation or a wedge disclination for particular choices of its parameters.