Next Article in Journal
Trapezoid Orthogonality in Complex Normed Linear Spaces
Previous Article in Journal
RMPT: Reinforced Memory-Driven Pure Transformer for Automatic Chest X-Ray Report Generation
Previous Article in Special Issue
In-Plane Vibrations of Elastic Lattice Plates and Their Continuous Approximations
 
 
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Line Defects in One-Dimensional Hexagonal Quasicrystals

Institute for Mechanics, Technical University of Darmstadt, D-64287 Darmstadt, Germany
Mathematics 2025, 13(9), 1493; https://doi.org/10.3390/math13091493
Submission received: 7 March 2025 / Revised: 8 April 2025 / Accepted: 17 April 2025 / Published: 30 April 2025
(This article belongs to the Special Issue Multiscale Mathematical Modeling)

Abstract

Using the eight-dimensional framework of the integral formalism of one-dimensional quasicrystals, the analytical expressions for the displacement fields and stress functions of line defects, which are dislocations and line forces, in one-dimensional hexagonal quasicrystals of Laue class 10 are derived. The self-energy of a straight dislocation, the self-energy of a line force, the Peach–Koehler force between two straight dislocations, and the Cherepanov force between two straight line forces in one-dimensional hexagonal quasicrystals of Laue class 10 are calculated. In addition, the two-dimensional Green tensor of one-dimensional hexagonal quasicrystals of Laue class 10 is given within the framework of the integral formalism.
Keywords: line defects; dislocations; line forces; anisotropic elasticity; integral formalism; Stroh formalism; quasicrystals line defects; dislocations; line forces; anisotropic elasticity; integral formalism; Stroh formalism; quasicrystals

Share and Cite

MDPI and ACS Style

Lazar, M. Line Defects in One-Dimensional Hexagonal Quasicrystals. Mathematics 2025, 13, 1493. https://doi.org/10.3390/math13091493

AMA Style

Lazar M. Line Defects in One-Dimensional Hexagonal Quasicrystals. Mathematics. 2025; 13(9):1493. https://doi.org/10.3390/math13091493

Chicago/Turabian Style

Lazar, Markus. 2025. "Line Defects in One-Dimensional Hexagonal Quasicrystals" Mathematics 13, no. 9: 1493. https://doi.org/10.3390/math13091493

APA Style

Lazar, M. (2025). Line Defects in One-Dimensional Hexagonal Quasicrystals. Mathematics, 13(9), 1493. https://doi.org/10.3390/math13091493

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop