Geometric theory of defects

Physics-Uspekhi

Volumn 48, Issue 7, 2005, Pages 675-701

  Katanaev, M O ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; ELASTICITY; FREE ENERGY; GEOMETRY; PHONONS; SCATTERING; TENSORS; TORSIONAL STRESS; VECTORS;

DISCLINATION DEFECTS; FRANK AND BURGERS VECTORS; RIEMANN-CARTAN GEOMETRY; TORSION TESORS;

DEFECTS;

EID: 27844593406     PISSN: 10637869     EISSN: None     Source Type: Journal    
DOI: 10.1070/PU2005v048n07ABEH002027     Document Type: Article

References (108)

1. Kondo K, in Proc. of the 2nd Japan National Congress for Applied Mechanics, Tokyo, Japan, 1952 (Tokyo, 1952) p. 41
2. Nye J F Acta Metal. 1 153 (1953)
3. Bilby B A, Bullough R, Smith E Proc. R. Soc. London Ser. A231 263 (1955)
4. Kröner E Kontinuumstheorie der Versetzungen und Eigenspannungen (Berlin: Springer, 1958)
5. Sedov L I, Berditchevski V L, in Mechanics of Generalized Continua: Proc. of the IUTAM-Symp. on the Generalized Casserat Continuum Theory of Dislocations with Applications, Germany, 1967 (Ed. E Kröner) (Berlin: Springer-Verlag, 1968) p. 214
6. Kléman M, in Dislocations in Solids (Ed. F R N Nabarro) Vol. 5 (Amsterdam: North-Holland Publ. Co., 1980) p. 243
7. Kröner E, in Physics of Defects, Less Hauches, Session XXXV, 1980 (Eds R Balian, M Kléman, J-P Poirier) (Amsterdam: North-Holland Publ. Co., 1981) p. 282
8. Dzyaloshinskii I E, Volovick G E Ann. Phys. (New York) 125 67 (1980)
9. Kadić A, Edelen D G B A Gauge Theory of Dislocations and Disclinations (Berlin: Springer-Verlag, 1983) [Translated into Russian (Moscow: Mir, 1987)]
10. Kunin I A, Kunin B I, in Trends in Applications of Pure Mathematics to Mechanics (Lecture Notes in Physics, Vol. 249, Eds E Kröner, K Kirchgässner) (Berlin: Springer-Verlag, 1986) p. 246
11. Kleinert H Gauge Fields in Condensed Matter Vol. 2 (Singapore: World Scientific, 1990)
12. Hehl F W et al. Phys. Rep. 258 1 (1995)
13. Cartan E CR Acad. Sci. (Paris) 174 593 (1922)
14. [Translated into russian: in Al'bert Einstein i Teoriya Gravitatsii (Moscow: Mir, 1979) p. 535]
15. Malyshev C Ann. Phys. (New York) 286 249 (2000)
16. Lazar M Ann. Phys. (Leipzig) 9 461 (2000)
17. Lazar M J. Phys. A: Math. Gen. 35 1983 (2002)
18. Lazar M J. Phys. A: Math. Gen. 36 1415 (2003)
19. Frank F C Discuss. Faraday Soc. 25 19 (1958)
20. Dzyaloshinskii I E, Volovik G E J. Phys. (Paris) 39 693 (1978)
21. Hertz J A Phys. Rev. B 18 4875 (1978)
22. Rivier N, Duffy D M J. Phys. (Paris) 43 293 (1982)
23. Katanaev M O, Volovich IV Ann. Phys. (New York) 216 1 (1992)
24. Katanaev M O Teor. Mat. Fiz. 135 338 (2003)
25. [Theor. Math. Phys. 135 733 (2003)]
26. Katanaev M O Teor. Mat. Fiz. 138 193 (2004)
27. [Theor. Math. Phys. 138 163 (2004)]
28. Furtado C, Moraes F Phys. Lett. A 188 394 (1994)
29. Furtado C et al. Phys. Lett. A 195 90 (1994)
30. Moraes F Mod. Phys. Lett. A 10 2335 (1995)
31. Azevedo S, Moraes F Phys. Lett. A 246 374 (1998)
32. Balachandran A P et al. Int. J. Mod. Phys. A 13 841 (1998)
33. Furtado C, Moraes F Europhys. Lett. 45 279 (1999)
34. Bausch R, Schmitz R, Turski L A Phys. Rev. Lett. 80 2257 (1998)
35. Bausch R, Schmitz R, Turski L A Ann. Phys. (Leipzig) 8 181 (1999)
36. Furtado C, Moraes F J. Phys. A: Math. Gen. 33 5513 (2000)
37. Azevedo S, Moraes F J. Phys.: Condens. Matter 12 7421 (2000)
38. Azevedo S, Pereira J Phys. Lett. A 275 463 (2000)
39. Furtado C, Bezerra V B, Moraes F Europhys. Lett. 52 1 (2000)
40. de Lima Ribeiro C A, Furtado C, Moraes F Phys. Lett. A 288 329 (2001)
41. Vieira S R, Azevedo S Phys. Lett. A 288 29 (2001)
42. Azevedo S J. Phys. A: Math. Gen. 34 6081 (2001)
43. Furtado C, Bezerra V B, Moraes F Phys. Lett. A 289 160 (2001)
44. Marques G de A et al. J. Phys. A: Math. Gen. 34 5945 (2001)
45. Furtado C, de Lima Ribeiro C A, Azevedo S Phys. Lett. A 296 171 (2002)
46. Azevedo S Phys. Lett. A 293 283 (2002)
47. Azevedo S Int. J. Quantum Chem. 90 1596 (2002)
48. Azevedo S Mod. Phys. Lett. A 17 1263 (2002)
49. Azevedo S Phys. Lett. A 307 65 (2003)
50. Barbosa A de S, Bezerra de Mello E R, Bezerra V B Int. J. Mod. Phys. A 14 3565 (1999)
51. Azevedo S, Furtado C, Moraes F Phys. Status Solidi B 207 387 (1998)
52. Moraes F Phys. Lett. A 204 399 (1995)
53. Bezerra de Mello E R, Bezerra V B, Grats Yu V Class. Quantum Grav. 15 1915 (1998)
54. Azevedo S Phys. Lett. A 288 33 (2001)
55. Furtado C, Bezerra V B, Moraes F Mod. Phys. Lett. A 15 253 (2000)
56. Tanaka I Phys. Lett. A 277 262 (2000)
57. De Lorenci V A, Moreira E S (Jr) Phys. Rev. D 65 085013 (2002)
58. Azevedo S, Moraes F Phys. Lett. A 267 208 (2000)
59. Miranda J A, Moraes F J. Phys. A: Math. Gen. 36 863 (2003)
60. Moraes F Phys. Lett. A 214 189 (1996)
61. de Padua A, Parisio-Filho F, Moraes F Phys. Lett. A 238 153 (1998)
62. Katanaev M O, Volovich IV Ann. Phys. (New York) 271 203 (1999)
63. Miri M F, Rivier N J. Phys. A : Math. Gen. 35 1727 (2002)
64. Landau L D, Lifshits E M Teoriya Uprugosti (Theory of Elasticity) (Moscow: Nauka, 1987) [Translated into English (Oxford: Pergamon Press, 1986)]
65. Kosevich A M Fizicheskaya Mekhanika Real'nykh Kristallov (Physical Mechanics of Real Crystals) (Kiev: Naukova Dumka, 1981)
66. Verçin A Int. J. Theor. Phys. 29 (1) 7 (1990)
67. Zakharov V E et al. Teoriya Solitonov: Metod Obratnoi Zadachi (The Inverse Scattering Method) (Eds S P Novikov et al.) (Moscow: Nauka, 1980) [Translated into English (New York: Plenum, 1984)]
68. Rajaraman R Solitons and Instantons: an Introduction to Solitons and Instantons in Quantum Field Theory (Amsterdam: North-Holland Publ. Co., 1982) [Translated into Russian (Moscow: Mir, 1985)]
69. Takhtadzhyan L A, Faddeev L D Gamil'tonov Podkhod v Teorii Solitonov (The Hamiltonian Methods in the Theory of Solitons) (Moscow: Nauka, 1986)
70. [Translated into English: Faddeev L D, Takhtajan L A Hamiltonian Methods in the Theory of solitons (Berlin: Springer-Verlag, 1987)]
71. Zakrzewski W J Low-Dimensional Sigma Models (Bristol: A. Hilger, 1989)
72. Rybakov Yu P, Sanyuk V I Mnogomernye Solitony (Multidimensional Solitons) (Moscow: Izd. RUDN, 2001)
73. Skyrme T H R Proc. R. Soc. London Ser. A 260 127 (1961)
74. Landau L D, Lifshits E M Elektrodinamika Sploshnykh Sred (Electrodynamics of Continuous Media) (Moscow: Nauka, 1982) [Translated into English (Oxford: Pergamon Press, 1984)]
75. Faddeev L D "Nelokal'nye, nelineinye i nerenormiruemye teorii polya" ("In search of multidimensional solitons. Nonlocal, nonlinear, and nonrenormalizable field theories"), Preprint D2-9788 (Dubna: Joint Institute Nucl. Res., 1977) p. 207
76. Cosserat E, Cosserat F Théorie des Corps Déformables (Paris: A. Hermann, 1909)
77. Nowacki W Theory of Asymmetric Elasticity (Oxford: Pergamon Press, 1986)
78. Sandru N Int. J. Eng. Sci. 4 81 (1966)
79. Staruszkiewicz A Acta Phys. Polon. 24 735 (1963)
80. Clemént G Nucl. Phys. B 114 437 (1976)
81. Deser S, Jackiw R, 't Hooft G Ann. Phys. 152 220 (1984)
82. Holz A Class. Quantum Grav. 5 1259 (1988)
83. Kohler C Class. Quantum Grav. 12 L11 (1995)
84. Kohler C Class. Quantum Grav. 12 2977 (1995)
85. Landau L D, Lifshitz E M Teoriya Polya (The Classical Theory of Fields) (Moscow: Nauka, 1988) [Translated into English (Oxford: Pergamon Press, 1983)]
86. Guillemin V, Sternberg S Geometric Asymptotics (Providence, RI: American Mathematical Society, 1977) [Translated into Russian (Moscow: Mir, 1981)]
87. Jahnke E, Emde F, Lösch F Tafeln Höherer Funktionen (Stuttgart: Teubner, 1960) [Translated into Russian (Moscow: Nauka, 1977)]
88. Aharonov Y, Bohm D Phys. Rev. 115 485 (1959)
89. Feinberg E L Usp. Fiz. Nauk 78 (1) 53 (1962)
90. [Sov. Phys. Usp. 5 753 (1963)]
91. Skarzhinskii V D Tr. Fiz. Inst. Akad. Nauk SSSR 167 139 (1986)
92. Katanaev M O J. Math. Phys. 38 946 (1997)
93. Volovich I V, Katanaev M O Pis'ma Zh. Eksp. Teor. Fiz. 43 212 (1986)
94. [JETP Lett. 43 267 (1986)]
95. Katanayev M O, Volovich I V Phys. Lett. B 175 413 (1986)
96. Katanaev M O, Volovich I V Ann. Phys. (New York) 197 1 (1990)
97. Katanaev M O Dokl. Akad. Nauk SSSR 309 591 (1989)
98. [Sov. Phys. Dokl. 34 982 (1989)]
99. Katanaev M O J. Math. Phys. 31 882 (1990)
100. Katanaev M O J. Math. Phys. 32 2483 (1991)
101. Katanaev M O J. Math. Phys. 34 700 (1993)
102. Vilenkin A, Shellard EPS Cosmic Strings and Other Topological Defects (Cambridge: Cambridge Univ. Press, 1994)
103. Hindmarsh M B, Kibble T W B Rep. Prog. Phys. 58 477 (1995)
104. Dubrovin B A, Novikov S P, Fomenko A T Sovremennaya Geometriya. Melody i Prilozheniya (Modern Geometry: Methods and Applications) 4th ed. (Moscow: Editorial URSS, 1998) [Translated into English: 2nd ed. (New York: Springer-Verlag, 1992)]
105. Weyl H Berl. Ber. 465 (1918)
106. [Translated into Russian: in Al'bert Einstein i Teoriya Gravitatsii (Moscow: Mir, 1979) p. 513]
107. Wolf J A Spaces of Constant Curvature (Boston: Publish or Perish, 1974) [Translated into Russian (Moscow: Nauka, 1982)]
108. Chern S S, Chen W H, Lam K S Lectures on Differential Geometry (Singapore: World Scientific, 1999)