M. O. Katanaev, “Wedge Dislocation in the Geometric Theory of Defects”, TMF, 135:2 (2003), 338–352; Theoret. and Math. Phys., 135:2 (2003), 733

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Teoreticheskaya i Matematicheskaya Fizika, 2003, Volume 135, Number 2, Pages 338–352
DOI: https://doi.org/10.4213/tmf183 (Mi tmf183)

This article is cited in 34 scientific papers (total in 34 papers)

Wedge Dislocation in the Geometric Theory of Defects

M. O. Katanaev

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (341 kB) Citations (34)

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DOI: https://doi.org/10.4213/tmf183

Abstract: We consider a wedge dislocation in the framework of elasticity theory and the geometric theory of defects. We show that the geometric theory quantitatively reproduces all the results of elasticity theory in the linear approximation. The coincidence is achieved by introducing a postulate that the vielbein satisfying the Einstein equations must also satisfy the gauge condition, which in the linear approximation leads to the elasticity equations for the displacement vector field. The gauge condition depends on the Poisson ratio, which can be experimentally measured. This indicates the existence of a privileged reference frame, which denies the relativity principle.

Keywords: dislocation, Riemann–Cartan geometry.

Received: 20.05.2002
Revised: 02.09.2002

English version:
Theoretical and Mathematical Physics, 2003, Volume 135, Issue 2, Pages 733–744
DOI: https://doi.org/10.1023/A:1023687003017

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: M. O. Katanaev, “Wedge Dislocation in the Geometric Theory of Defects”, TMF, 135:2 (2003), 338–352; Theoret. and Math. Phys., 135:2 (2003), 733–744

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf183

https://doi.org/10.4213/tmf183

https://www.mathnet.ru/eng/tmf/v135/i2/p338

This publication is cited in the following 34 articles:

F. L. Carneiro, B. C. C. Carneiro, D. L. Azevedo, S. C. Ulhoa, “On Nanocones as Gravitational Analog Systems”, Annalen der Physik, 2025
Takahiro Yajima, Hiroyuki Nagahama, “Geometric structures of micropolar continuum with elastic and plastic deformations based on generalized Finsler space”, Mathematics and Mechanics of Solids, 29:2 (2024), 327
N. Candemir, A.N. Özdemir, “Linear and nonlinear optical properties in a GaAs quantum dot with disclination under magnetic field and Aharonov-Bohm flux field”, Physics Letters A, 492 (2023), 129226
Mikhail O. Katanaev, Alexander V. Mark, “Combined Screw and Wedge Dislocations”, Universe, 9:12 (2023), 500–14
Nicolás Fernández, Pierre Pujol, Mario Solís, Teófilo Vargas, “Revisiting the electronic properties of disclinated graphene sheets”, Eur. Phys. J. B, 96:6 (2023)
A. V. Mark, “Cylindrical dislocation in a nonlinear elastic incompressible material”, J. Appl. Mech. Tech. Phys., 63:4 (2022), 702–710
A. Manapany, L. Moueddene, B. Berche, S. Fumeron, “Diffusion in the presence of a chiral topological defect”, Eur. Phys. J. B, 95:7 (2022)
M. O. Katanaev, “Disclinations in the Geometric Theory of Defects”, Proc. Steklov Inst. Math., 313 (2021), 78–98
Yajima T., Nagahama H., “Connection Structures of Topological Singularity in Micromechanics From a Viewpoint of Generalized Finsler Space”, Ann. Phys.-Berlin, 532:12 (2020), 2000306, 2000306
Zare S., Hassanabadi H., de Montigny M., “Duffin-Kemmer-Petiau Oscillator in the Presence of a Cosmic Screw Dislocation”, Int. J. Mod. Phys. A, 35:30 (2020), 2050195
Katanaev M.O., “The `T Hooft-Polyakov Monopole in the Geometric Theory of Defects”, Mod. Phys. Lett. B, 34:12 (2020), 2050126
Katanaev M.O. Volkov B.O., “Point Disclinations in the Chern-Simons Geometric Theory of Defects”, Mod. Phys. Lett. B, 34:1 (2020), 2150012
M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133
Yajima T., Yamasaki K., Nagahama H., “Non-Holonomic Geometric Structures of Rigid Body System in Riemann-Cartan Space”, J. Phys. Commun., 2:8 (2018), UNSP 085008
Katanaev M.O., “Chern–Simons Term in the Geometric Theory of Defects”, Phys. Rev. D, 96:8 (2017), 084054
Katanaev M.O., “Rotational Elastic Waves in a Cylindrical Waveguide With Wedge Dislocation”, J. Phys. A-Math. Theor., 49:8 (2016), 085202
Yajima T., Nagahama H., “Finsler geometry of topological singularities for multi-valued fields: Applications to continuum theory of defects”, Ann. Phys.-Berlin, 528:11-12 (2016), 845–851
Boehmer C.G., Tamanini N., “Rotational Elasticity and Couplings To Linear Elasticity”, Math. Mech. Solids, 20:8 (2015), 959–974
Katanaev M.O., “Rotational Elastic Waves in Double Wall Tube”, Phys. Lett. A, 379:24-25 (2015), 1544–1548
Katanaev M.O., Mannanov I.G., “Wedge Dislocations, Three-Dimensional Gravity, and the Riemann–Hilbert Problem”, Phys. Part. Nuclei, 43:5 (2012), 639–643

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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