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UFN, 2005, Volume 175, Number 7, Pages 705–733 (Mi ufn198)  

This article is cited in 60 scientific papers (total in 60 papers)


Geometric theory of defects

M. O. Katanaev

V. A. Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: A description of dislocation and disclination defects in terms of the Riemann – Cartan geometry is given, with the curvature and torsion tensors interpreted as the surface densities of the Frank and Burgers vectors, respectively. A new free-energy expression describing the static distribution of defects is presented and equations of nonlinear elasticity theory are used to specify the coordinate system. Application of the Lorentz gauge leads to equations for the principal chiral SO(3) field. In the defect-free case, the geometric model reduces to elasticity theory for the displacement vector field and to a principal chiral SO(3)-field model for the spin structure. As illustrated by the example of a wedge dislocation, elasticity theory reproduces only the linear approximation of the geometric theory of defects. It is shown that the equations of asymmetric elasticity theory for Cosserat media can also be naturally incorporated into the geometric theory as gauge conditions. As an application of the theory, phonon scattering on a wedge dislocation is considered. The energy spectrum of impurities in the field of a wedge dislocation is also discussed.


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Physics–Uspekhi, 2005, 48:7, 675–701

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Document Type: Article
PACS: 02.40.-k, 46.05.+b, 61.72.Lk, 63.20.Mt
Received: July 21, 2004
Revised: March 31, 2005

Citation: M. O. Katanaev, “Geometric theory of defects”, UFN, 175:7 (2005), 705–733; Phys. Usp., 48:7 (2005), 675–701

Citation in format AMSBIB
\by M.~O.~Katanaev
\paper Geometric theory of defects
\jour UFN
\yr 2005
\vol 175
\issue 7
\pages 705--733
\jour Phys. Usp.
\yr 2005
\vol 48
\issue 7
\pages 675--701

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    1. E. S. Moreira, E. S. Oliveira, “Specific heat of a particle on the cone”, Phys Rev A, 73:5 (2006), 052105  crossref  mathscinet  adsnasa  isi  elib  scopus
    2. C Malyshev, “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”, J Phys A Math Theor, 40:34 (2007), 10657  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. G. de Berredo-Peixoto, “Inside the BTZ black hole”, Phys Rev D, 75:2 (2007), 024004  crossref  mathscinet  adsnasa  isi  elib  scopus
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    5. Mathy, CJM, “Nematic phases and the breaking of double symmetries”, Annals of Physics, 322:3 (2007), 709  crossref  mathscinet  zmath  adsnasa  isi  scopus
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    8. Baranov, SA, “Microkinetic Model of Nucleation and Its Application in Electrochemistry”, Surface Engineering and Applied Electrochemistry, 44:2 (2008), 98  crossref  isi  scopus
    9. Tartaglia, A, “A darkless space-time”, International Journal of Modern Physics D, 17:2 (2008), 275  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. G. de Berredo-Peixoto, M. O. Katanaev, “Tube dislocations in gravity”, J Math Phys (N Y ), 50:4 (2009), 042501  crossref  mathscinet  zmath  adsnasa  isi  scopus
    11. Markus Lazar, Friedrich W. Hehl, “Cartan’s Spiral Staircase in Physics and, in Particular, in the Gauge Theory of Dislocations”, Found Phys, 2010  crossref  mathscinet  isi  scopus
    12. 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
    13. Pereira E., Moraes F., “Diffraction of light by topological defects in liquid crystals”, Liquid Crystals, 38:3 (2011), 295–302  crossref  isi  elib  scopus
    14. Andrew Randono, Taylor Hughes, “Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter”, Phys. Rev. Lett, 106:16 (2011)  crossref  zmath  isi  scopus
    15. Y M Cho, D G Pak, “Vacuum tunneling in gravity”, Class. Quantum Grav, 28:15 (2011), 155008  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    16. C. Filgueiras, B.F. de Oliveira, “Electron on a cylinder with topological defects in a homogeneous magnetic field”, Ann. Phys, 2011, n/a  crossref  isi  scopus
    17. V. Kobelev, “On the Lagrangian and instability of medium with defects”, Meccanica, 2011  crossref  mathscinet  zmath  isi  scopus
    18. C. G. Bohmer, Y. N. Obukhov, “A gauge-theoretical approach to elasticity with microrotations”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2012  crossref  mathscinet  isi  scopus
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    21. M. O. Katanaev, I. G. Mannanov, “Wedge dislocations, three-dimensional gravity, and the Riemann–Hilbert problem”, Phys. Part. Nuclei, 43:5 (2012), 639  crossref  mathscinet  adsnasa  isi  elib  scopus
    22. A.A. Lima, C. Filgueiras, “Integer quantum Hall effect on an interface with disclinations”, Eur. Phys. J. B, 85:12 (2012)  crossref  zmath  isi
    23. S. Fumeron, E. Pereira, F. Moraes, “Modeling heat conduction in the presence of a dislocation”, International Journal of Thermal Sciences, 2013  crossref  isi  scopus
    24. Kamilla V. R. A. Silva, Cesar F. Freitas, Cleverson Filgueiras, “Geometry-induced quantum dots on surfaces with Gaussian bumps”, Eur. Phys. J. B, 86:4 (2013)  crossref  mathscinet  isi  scopus
    25. Reza Torabi, Zahra Rezaei, “The effect of Dirac phase on acoustic vortex in media with screw dislocation”, Physics Letters A, 2013  crossref  mathscinet  isi  scopus
    26. André G. Lima, Armelle Poux, Denise Assafrão, Cleverson Filgueiras, “Screw dislocation-induced influence of transverse modes on Hall conductivity”, Eur. Phys. J. B, 86:11 (2013)  crossref  isi
    27. Andrade A.F., de Berredo-Peixoto G., “Geodesics in a Space with a Spherically Symmetric Dislocation”, Gravit. Cosmol., 19:1 (2013), 29–34  crossref  mathscinet  zmath  adsnasa  isi  scopus
    28. S.A. Lychev, A.V. Manzhirov, “The mathematical theory of growing bodies. Finite deformations”, Journal of Applied Mathematics and Mechanics, 2013  crossref  mathscinet  isi  scopus
    29. S. Fumeron, E. Pereira, F. Moraes, “Principles of thermal design with nematic liquid crystals”, Phys. Rev. E, 89:2 (2014)  crossref  isi  elib  scopus
    30. J.R.. F. Lima, Júlio Brandão, Már.M.. Cunha, F. Moraes, “Effects of rotation in the energy spectrum of C60”, Eur. Phys. J. D, 68:4 (2014)  crossref  isi  scopus
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    35. J. Math. Sci. (N. Y.), 213:5 (2016), 750–755  mathnet  crossref  mathscinet
    36. Shi L., Li H., Xie Ch., Zhang Y., “Omnidirectional Diffraction Control With Rotational Topological Defects”, Opt. Express, 23:20 (2015), 25773–25782  crossref  isi  elib  scopus
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    41. 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
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    44. Lima A.A., Filgueiras C., Moraes F., “Torsion Effects on Condensed Matter: Like a Magnetic Field But Not So Much”, Eur. Phys. J. B, 90:2 (2017), 32  crossref  isi  scopus
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