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TMF, 2003, Volume 135, Number 2, Pages 338–352 (Mi tmf183)  

This article is cited in 21 scientific papers (total in 21 papers)

Wedge Dislocation in the Geometric Theory of Defects

M. O. Katanaev

Steklov Mathematical Institute, Russian Academy of Sciences

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


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English version:
Theoretical and Mathematical Physics, 2003, 135:2, 733–744

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Document Type: Article
Received: 20.05.2002
Revised: 02.09.2002

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
\by M.~O.~Katanaev
\paper Wedge Dislocation in the Geometric Theory of Defects
\jour TMF
\yr 2003
\vol 135
\issue 2
\pages 338--352
\jour Theoret. and Math. Phys.
\yr 2003
\vol 135
\issue 2
\pages 733--744

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    This publication is cited in the following articles:
    1. M. O. Katanaev, “One-Dimensional Topologically Nontrivial Solutions in the Skyrme Model”, Theoret. and Math. Phys., 138:2 (2004), 163–176  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. Carvalho AMD, Moraes F, Furtado C, “The self-energy of a charged particle in the presence of a topological defect distribution”, International Journal of Modern Physics A, 19:13 (2004), 2113–2122  crossref  mathscinet  adsnasa  isi  scopus  scopus
    3. M. O. Katanaev, “Geometric theory of defects”, Phys. Usp., 48:7 (2005), 675–701  mathnet  crossref  crossref  adsnasa  isi
    4. Marques, GD, “Quantum effects due to a magnetic flux associated to a topological defect”, International Journal of Modern Physics A, 20:26 (2005), 6051  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Furtado, C, “Aharonov-Bohm effect and disclinations in an elastic medium”, Modern Physics Letters A, 21:17 (2006), 1393  crossref  zmath  adsnasa  isi  elib  scopus  scopus
    6. de Berredo-Peixoto, G, “Inside the BTZ black hole”, Physical Review D, 75:2 (2007), 024004  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    7. Carvalho, J, “Self-interaction in the von Karman cosmic string street configuration”, European Physical Journal C, 58:2 (2008), 331  crossref  adsnasa  isi  scopus  scopus
    8. Netto, ALS, “Elastic Landau levels”, Journal of Physics-Condensed Matter, 20:12 (2008), 125209  crossref  adsnasa  isi  scopus  scopus
    9. de Berredo-Peixoto, G, “Tube dislocations in gravity”, Journal of Mathematical Physics, 50:4 (2009), 042501  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Carvalho, AMD, “TOPOLOGICAL DEFECT DISTRIBUTIONS AND THE SELF-ENERGY OF A CHARGED PARTICLE”, International Journal of Modern Physics D, 18:2 (2009), 237  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    11. de Berredo-Peixoto G., Katanaev M.O., Konstantinova E., Shapiro I.L., “Schrodinger equation in the space with cylindrical geometric defect and possible application to multi-wall nanotubes”, Nuovo Cimento Della Societa Italiana Di Fisica B-Basic Topics in Physics, 125:8 (2010), 915–931  isi
    12. Mesaros A., Sadri D., Zaanen J., “Parallel transport of electrons in graphene parallels gravity”, Physical Review B, 82:7 (2010), 073405  crossref  adsnasa  isi  elib  scopus  scopus
    13. Katanaev M.O., Mannanov I.G., “Wedge Dislocations, Three-Dimensional Gravity, and the Riemann–Hilbert Problem”, Phys. Part. Nuclei, 43:5 (2012), 639–643  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    14. Bohmer C.G., Obukhov Yu.N., “A Gauge-Theoretical Approach to Elasticity with Microrotations”, Proc. R. Soc. A-Math. Phys. Eng. Sci., 468:2141 (2012), 1391–1407  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    15. Boehmer C.G., Tamanini N., “Rotational Elasticity and Couplings To Linear Elasticity”, Math. Mech. Solids, 20:8 (2015), 959–974  crossref  mathscinet  zmath  isi  scopus  scopus
    16. Katanaev M.O., “Rotational Elastic Waves in Double Wall Tube”, Phys. Lett. A, 379:24-25 (2015), 1544–1548  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    17. Katanaev M.O., “Rotational Elastic Waves in a Cylindrical Waveguide With Wedge Dislocation”, J. Phys. A-Math. Theor., 49:8 (2016), 085202  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    18. 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  crossref  mathscinet  zmath  isi  scopus
    19. Katanaev M.O., “Chern–Simons Term in the Geometric Theory of Defects”, Phys. Rev. D, 96:8 (2017), 084054  crossref  isi  scopus  scopus
    20. M. O. Katanaev, “Chern–Simons action and disclinations”, Proc. Steklov Inst. Math., 301 (2018), 114–133  mathnet  crossref  crossref  isi  elib  elib
    21. 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  crossref  mathscinet  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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