Scattering on Dislocations and Cosmic Strings in the Geometric Theory of Defects

Abstract

We consider scattering of elastic waves on parallel wedge dislocations in the geometric theory of defects or, equivalently, scattering of point particles and light rays on cosmic strings. Dislocations are described as torsion singularities located on parallel lines, and trajectories of phonons are assumed to be the corresponding extremals. Extremals are found for arbitrary distribution of the dislocations in the monopole, dipole, and quadrupole approximation and the scattering angle is obtained. Examples of continuous distribution of wedge and edge dislocations are considered. We have found that for deficit angles close to -2πa star located behind a cosmic string may have any even number of images, 2,4,6,... The close relationship between dislocations and conformal maps is elucidated in detail.

30 pages, 14 figures, minor changes

References in corpus (2)

• Geodesics around line defects in elastic solids
• Simulation of Quantum Field Theory and Gravity in Superfluid He-3

Cited by in corpus (23)

• Landau Levels in the Presence of Topological Defects
• An elastoplastic theory of dislocations as a physical field theory with torsion
• The Dislocation Stress Functions From the Double Curl T(3)-Gauge Equation: Linearity and a Look Beyond
• Gravity of Monopole and String and Gravitational Constant in 3He-A
• Deformations of the spin currents by topological screw dislocation and cosmic dispiration
• Propagation of acoustic waves in a von-Kármán vortex street like configuration of disclinations
• Geometrical optics limit of phonon transport in a channel of disclinations
• Noninertial effects on nonrelativistic topological quantum scattering
• Influences of Topological Defect on Spin Hall Effect
• Volume elements and torsion
• Tube dislocations in gravity
• Geometric theory of topological defects: methodological developments and new trends
• Disclinations in the geometric theory of defects
• The Einsteinian T(3)-Gauge Approach and the Stress Tensor of the Screw Dislocation in the Second Order: Avoiding the Cut-off at the Core
• The 't Hooft-Polyakov monopole in the geometric theory of defects
• Hall conductivity in the cosmic defect and dislocation space-time
• Chern--Simons term in the geometric theory of defects
• Inside the BTZ black hole
• Point disclinations in the Chern-Simons geometric theory of defects
• Torsional Elastic Waves in Cylindrical Waveguide with Wedge Dislocation
• Torsional Elastic Waves in Double Wall Tube
• Gauge parameterization of the $n$-field
• Trajectories in a space with a spherically symmetric dislocation