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1988

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Reviews of topical problems


Defects in liquid crystals: homotopy theory and experimental studies

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The fundamental concepts of the homotopy theory of defects in liquid crystals and the results of experimental studies in this field are presented. The concepts of degeneracy space, homotopy groups, and topological charge, which are used for classifying the topologically stable inhomogeneous distributions in different liquid-crystalline phases are examined (uni and biaxial nematics, cholesterics, smectics, and columnar phases). Experimental data are given for the different mesophases on the structure and properties of dislocations, disclinations, point defects in the volume (hedgehogs) and on the surface of the medium (boojums), monopoles, domain formations, and solitons. Special attention is paid to the results of studies of defects in closed volumes (spherical drops, cylindrical capillaries), and to the connection between the topological charges of these defects and the character of the orientation of the molecules of the liquid crystal at the surface. A set of fundamentally new effects that can occur in studying the topological properties of defects in liquid crystals is discussed.

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Fulltext is also available at DOI: 10.1070/PU1988v031n03ABEH005710
PACS: 61.30.Jf, 61.30.Eb, 61.30.Gd, 64.70.Md (all)
DOI: 10.1070/PU1988v031n03ABEH005710
URL: https://ufn.ru/en/articles/1988/3/b/
Citation: Kurik M V, Lavrentovich O D "Defects in liquid crystals: homotopy theory and experimental studies" Sov. Phys. Usp. 31 196–224 (1988)
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Оригинал: Курик М В, Лаврентович О Д «Дефекты в жидких кристаллах: гомотопическая теория и экспериментальные исследования» УФН 154 381–431 (1988); DOI: 10.3367/UFNr.0154.198803b.0381

References (249) ↓ Cited by (197) Similar articles (20)

  1. G. Friedel and F. Grandjean Bull. Soc. Fr. Miner. Cryst. 33 409 (1910); G. Friedel Ann. Phys. (Paris) 18 273 (1922)
  2. P. Oswald C. R. Acad. Sci. Ser. II 292 149 (1981); P. Oswald J. Phys. Lett. (Paris) 42 L-171 (1981)
  3. Y. Bouligand Physics Of Defects eds. R. Balian, M. Kléman, J.-P. Poirier (North-Holland, Amsterdam, 1981) p. 665
  4. G. Toulouse Modern Trends In The Theory Of Condensed Matter (Springer-Verlag, Berlin, 1980) p. 188
  5. G. E. Volovik and V. P. Mineev Pis’ma Zh. Eksp. Teor. Fiz. 24 605 (1976); G. E. Volovik and V. P. Mineev JEPT Lett. 24 561 (1976)
  6. G. E. Volovik and V. P. Mineev Zh. Eksp. Teor. Fiz. 72 2256 (1977); G. E. Volovik and V. P. Mineev Sov. Phys. JETP 45 1186 (1977)
  7. G. E. Volovik and V. P. Mineev Ibid. 73 767 (1977); G. E. Volovik and V. P. Mineev Sov. Phys. JETP 46 401 (1977)
  8. G. Toulouse and M. Kléman J. Phys. Lett. (Paris) 37 L-149 (1976)
  9. M. Kléman, L. Michel, and G. Toulouse Ibid. 38 L-195 (1977); M. Kléman and L. Michel Phys. Rev. Lett. 40 1387 (1978)
  10. M. Kléman J. Phys. Lett. (Paris) 38 L-199 (1977)
  11. A. Saupe Mol. Crystl. Liq. Cryst. 21 211 (1973)
  12. V. P. Chechetkin Zh. Eksp. Teor. Fiz. 71 1463 (1976); V. P. Chechetkin Sov. Phys. JETP 44 766 (1976); D. Rogula Trends In Applications Of Pure Mathematics To Mechanics ed. G. Fichera (Pitman, New York, 1976) p. 311; S. Blaha Phys. Rev. Lett. 36 874 (1976)
  13. D. Finkelstein J. Math. Phys. 7 1218 (1966); Yu. S. Tyupkin, V. A. Fateev, and A. S. Shvarts Pis’ma Zh. Eksp. Teor. Fiz. 21 91 (1975); Yu. S. Tyupkin, V. A. Fateev, and A. S. Shvarts JETP Lett. 21 42 (1975); M. I. Monastyrski&ibreve; and A. M. Perelomov Ibid. 94 (1975); M. I. Monastyrski&ibreve; and A. M. Perelomov JETP Lett. 21 43
  14. G. Toulouse J. Phys. Lett. (Paris) 38 L-67 (1977)
  15. M. V. Kurik and O. D. Lavrentovich Priroda (No. 12) 55 (1986)
  16. E. I. Kats and G. E. Volovik J. Phys. Lett. (Paris) 40 L-149 (1979); J.-M. Dreyfus and P. Pieranski J. Phys. (Paris) 42 459 (1981)
  17. R. I. Mints and E. V. Konenko Itogi Nauki I Tekhniki (Ser. Biofizika (Results of Science and Technology, Ser. Biophysics)) Vol. 13 (VINITI, M., 1982); Y. Bouligand Liquid-Crystalline Order In Polymers ed. A. Blumstein (Academic Press, N. Y., 1978); Russ. transl., Y. Bouligand Liquid-Crystalline Order In Polymers (Mir, M., 1981), see Ref. 3, p. 777; G. H. Brown and J. J. Wolken Liquid Crystals And Biological Structures (Academic Press, N. Y., 1979); Russ. Transl., G. H. Brown and J. J. Wolken Liquid Crystals And Biological Structures (Mir, M., 1982)
  18. R. Shanker J. Phys. (Paris) 38 1405 (1977)
  19. M. Kléman Ibid. 39 (Coll. C5) C5–23 (1978); M. Kléman J. Microsc. Spectrosc. Electron. 3 357 (1978)
  20. M. Kléman Points, Lines And Walls In Liquid Crystals, Magnetic Systems And Various Ordered Media (Wiley, N. Y., 1983)
  21. L. Michel Lect. Notes Phys. 79 247 (1978); L. Michel Rev. Mod. Phys. 52 617 (1980), see Ref. 3, p. 361
  22. N. D. Mermin J. Math. Phys. 19 1457 (1978); N. D. Mermin Rev. Mod. Phys. 51 591 (1979)
  23. V. Poenaru III-Condensed Matter eds. R. Balian, R. Maynard, G. Toulouse (North-Holland, Amsterdam, 1979) p. 264; V. Poenaru Lect. Notes Phys. 116 148 (1980)
  24. V. P. Mineev Sov. Sci. Rev. Sect. A ed. I. M. Khalatnikov (Chur, London); V. P. Mineev Sov. Sci. Rev. Sect. A Vol. Vol. 2 (Harwood Academic Publ., N. Y., 1980) p. 173
  25. J. Dzyaloshinskii see Ref. 3 p. 217
  26. H.-R. Trebin Adv. Phys. 31 195 (1982); H.-R. Trebin Adv. Phys. (MATCH No. 10) 211 (1981)
  27. O. D. Lavrentovich Ukr. Fiz. Zh. 31 551 (1986)
  28. S. S. Rozhkov Usp. Fiz. Nauk 149 259 (1986); S. S. Rozhkov Sov. Phys. Usp. 29 530 (1986)
  29. M. I. Monastyrski&ibreve; Priroda (No. 5) 55 (1979); G. E. Volovik and V. P. Mineev Physics And Topology (in Russian) (Znanie, M., 1980); V. P. Mineev Graphic Topology (in Russian) (Nauka, M.) p. 148; M. V. Kurik and O. D. Lavrentovich Znannya Ta Pratsya (No. 9) 4 (1983), (in Ukrainian)
  30. T. F. Rosenbaum and D. L. Stein Am. J. Phys. 49 128 (1981); W. F. Brinkham and P. E. Cladis Phys. Today 35 48 (1982)
  31. P. G. de Gennes The Physics Of Liquid Crystals (Clarendon Press, Oxford, 1974); Russ. Transl., P. G. de Gennes The Physics Of Liquid Crystals (Mir, M., 1977)
  32. S. Chandrasekhar Liquid Crystals (Cambridge University Press, N. Y., 1977); Russ. Transl., S. Chandrasekhar Liquid Crystals (Mir, M., 1980)
  33. L. M. Blinov Electro-optical And Magnetooptical Properties Of Liquid Crystals (Wiley, N. Y., 1984); Russ. original, L. M. Blinov Electro-optical And Magnetooptical Properties Of Liquid Crystals (Nauka, M., 1978)
  34. S. A. Pikin Structural Transformations In Liquid Crytals (in Russian) (Nauka, M., 1981)
  35. A. S. Sonin Introduction To The Physics Of Liquid Crystals (in Russian) (Nauka, M., 1983)
  36. D. Demus and L. Richter Textures Of Liquid Crystals (VEB Deutscher Verlag fur Grundstoffindustrie, Leipzig, 1980)
  37. V. A. Belyakov Liquid Crystals (in Russian) (Znanie, M., 1986)
  38. V. P. Mineyev and G. E. Volovik Phys. Rev. B 18 3197 (1978)
  39. D. Rüppel and E. Sackmann J. Phys. (Paris) 44 1025 (1983)
  40. E. Sackmann, D. Rüppel, and C. Gebhardt Liquid Crystals In One-and Two-Dimensional Order eds. W. Helfrich and G. Heppke (Springer-Verlag, Berlin, 1980) p. 309
  41. R. E. Stoiber and S. A. Morse Microscopic Identification Of Crystals (Ronald Press, N. Y., 1972); Russ. transl., R. E. Stoiber and S. A. Morse Microscopic Identification Of Crystals (Mir, M., 1974)
  42. S. Sakagami, A. Takase, M. Nakamizo, and H. Kakiyama Mol. Cryst. Liq. Cryst. 19 303 (1973)
  43. M. V. Kurik and O. D. Lavrentovich Ukr. Fiz. Zh. 28 452 (1983)
  44. G. Malet and J. C. Martin J. Phys. (Paris) 40 355 (1979)
  45. F. Scudieri Appl. Opt. 18 1455 (1979); F. Scudieri, M. Bertolotti, and A. Ferrari see Ref. 40 p. 90
  46. N. A. Clark and A. J. Hurd J. Phys. (Paris) 43 1159 (1982)
  47. S. T. Lagerwall and B. Stebler see Ref. 3 p. 757
  48. W. J. Benton and C. A. Miller Prog. Colloid Polymer Sci. 68 71 (1983)
  49. N. B. Baranova and B. Ya. Zel’dovich Pis’ma Zh. Eksp. Teor. Fiz. 32 636 (1980); N. B. Baranova and B. Ya. Zel’dovich JETP Lett. 32 622 (1980)
  50. L. K. Vistin and S. S. Yakovenko Kristallografiya 28 992 (1983); L. K. Vistin and S. S. Yakovenko Sov. Phys. Crystallogr. 28 587 (1983)
  51. G. Ryschenkow J. Phys. (Paris) 36 243 (1975)
  52. H. Miike, Y. Kuriyama, Y. Itou, H. Hashimoto, and Y. Ebina Phys. Rev. A 31 2756 (1985)
  53. J. Rault C. R. Acad. Sci. Ser. B 272 1275 (1971)
  54. P. Cladis, M. Kléman, and P. Pieransky Ibid. 273 275 (1971)
  55. D. Melzer, A. van Es, F. R. N. Nabarro, and E. Godinho Philos. Mag. Ser. A 44 835 (1981)
  56. D. Demus, P. Schiller, and N. K. Sharma Cryst. Res. Technol. 19 577 (1984)
  57. J. F. Goodman and J. S. Clunie Liquid Crystals And Plastic Crystals Vol. Vol. 2 eds. G. W. Gray and P. A. Winsor (Ellis Hordwood Chichester and Halsted Press, New York, 1974) p. 1
  58. M. Kléman, C. Colliex, and M. Veyssie Adv. Chem. Ser. 152 71 (1976)
  59. M. Kléman, C. E. Williams, M. J. Costello, and T. Gulik-Krzywicki Philos. Mag. 35 33 (1977)
  60. J. Van der Veen and H. B. Haanstra J. Phys. Lett. (Paris) 37 L-43 (1976)
  61. G. Kästner and Ch. Dietzsch Electron Microsc. 4 400 (1980)
  62. J. E. Zimmer and J. L. White Mol. Cryst. Liq. Cryst. 38 177 (1977); J. E. Zimmer and J. L. White Adv. Liq. Cryst. 5 157 (1982)
  63. S. Meiboom and M. Sammon Phys. Rev. A 29 2957 (1984); J. A. M. Zasadzinski, S. Meiboom, M. J. Sammon, and D. W. Berreman Phys. Rev. Lett. 57 364 (1986)
  64. E. S. Luk’yanchenko, V. A. Kozunov, and V. I. Grigos Usp. Khim. 54 214 (1985); F. Kan, G. Te&ibreve;lor, and G. Shonkhorn Proc. IEEE [Russ. Transl. 61 28 (1973)
  65. W. H. De Jeu Physical Properties Of Liquid-Crystalline Materials (Gordon and Breach, N. Y., 1976); Russ. Transl., W. H. De Jeu Physical Properties Of Liquid-Crystalline Materials (Mir, M., 1982); Zh. Kon’yar Orientation Of Nematic Liquid Crystals And Mixtures Of Them (in Russian) (Izd-vo "Universitetskoe," Minsk, 1986)
  66. C. Williams, P. Pieranski, and P. E. Cladis Phys. Rev. Lett. 29 90 (1972); C. Williams, P. E. Cladis, and M. Kléman Mol. Cryst. Liq. Cryst. 21 355 (1973)
  67. R. B. Meyer Philos. Mag. 27 405 (1973)
  68. C. Williams and Y. Bouligand J. Phys. (Paris) 35 589 (1974)
  69. P. E. Cladis Philos. Mag. 29 641 (1974)
  70. D. Melzer and F. R. N. Nabarro Ibid. 35 901 (1977)
  71. D. Melzer and F. R. N. Nabarro Ibid. 35 907 (1977)
  72. P. E. Cladis, A. E. White, and W. F. Brinkman J. Phys. (Paris) 40 325 (1979)
  73. M. V. Kurik Zh. Tekh. Fiz. 51 2385 (1981); M. V. Kurik Sov. Phys. Tekh. Phys. 26 1404 (1981)
  74. M. Kuzma and M.M. Labes Mol. Cryst. Liq. Cryst. 100 103 (1983)
  75. J. M. Di Meglio, M. Dvolaitzky, R. Ober, and C. Taupin J. Phys. Lett. (Paris) 44 L-229 (1983)
  76. C. Robinson Trans. Faraday Soc. 52 571 (1956); C. Robinson Tetrahedron 13 219 (1961)
  77. C. Robinson J. C. Ward, And R. B. Beevers, Discuss, Faraday Soc, No. 25 29 (1958)
  78. R. W. Filas J. Phys. (Paris) 39 49 (1978)
  79. M. Matsuo, F. Ozaki, Y. Konno, and T. Ogita J. Polym. Sci. Polym. Phys. Edn. 19 1531 (1981)
  80. D. Anguie, M. Oberlin, and P. Hyvernat Carbon 18 337 (1980); A. J. Perrota, R. M. Henry, J. D. Bacha, and E. W. Albaugh High Temp. High Press. 13 159 (1981); J. L. White, M. Buechler, and C. B. Ng Carbon 20 536 (1982); M. Buechler, C. B. Ng, and J. L. White Carbon 21 603 (1983); Honda, H Mol. Cryst. Liq. Cryst. 94 97 (1983); S. Higuchi, B. Otsuka, and M. Shiraishi J. Mater. Sci. 19 270 (1984); A. N. Chuvyrov and Yu. A. Lebedev Pis’ma Zh. Tekh. Fiz. 10 1439 (1984); A. N. Chuvyrov and Yu. A. Lebedev Sov. Tech. Phys. Lett. 10 608 (1984)
  81. M. V. Kurik and O. D. Lavrentovich Mol. Cryst. Liq. Cryst. Lett. 72 239 (1982)
  82. J. R. Quigley and W. J. Benton Ibid. 42 43 (1977)
  83. S. Candau, P. le Roy, and F. Debeauvais Ibid. 23 283 (1973); P. le Roy, S. Candau, and F. Debeauvais C. R. Acad. Sci. Ser. B 274 419 (1972)
  84. M. Press and A. Arrott Phys. Rev. Lett. 33 403 (1974); M. Press and A. Arrott J. Phys. (Paris) 36 (Suppl. C1.) C1–177 (1975)
  85. C. P. Shillaber Photomicrography In Theory And Practice (Wiley, N. Y., 1944); Russ. Transl., C. P. Shillaber Photomicrography In Theory And Practice (IL, M., 1951)
  86. G. E. Volovik and O. D. Lavrentovich Zh. Eksp. Teor. Fiz. 85 1997 (1983); G. E. Volovik and O. D. Lavrentovich Sov. Phys. JETP 58 1159 (1983)
  87. B. J. Forrest and L. W. Reeves Chem. Rev. 81 1 (1981)
  88. A. A. Vedenov and E. B. Levchenko Usp. Fiz. Nauk 141 3 (1983); A. A. Vedenov and E. B. Levchenko Sov. Phys. Usp. 26 747 (1983)
  89. S. Chandrasekhar Indian J. Pure Appl. Phys. 19 769 (1981); S. Chandrasekhar Adv. Liq. Cryst. 5 47 (1982)
  90. A. A. Balinski&ibreve;, G. E. Volovik, and E. I. Kats Zh. Eksp. Teor. Fiz. 87 1305 (1984); A. A. Balinski&ibreve;, G. E. Volovik, and E. I. Kats Sov. Phys. JETP 60 748 (1984)
  91. F. C. Frank Trans. Faraday Soc. 25 19 (1958)
  92. R. B. Meyer Phys. Rev. Lett. 22 918 (1969)
  93. I. E. Dzyaloshinski&ibreve; Zh. Eksp. Teor. Fiz. 58 1443 (1970); I. E. Dzyaloshinski&ibreve; Sov. Phys. JETP 31 773 (1970)
  94. S. I. Anisimov and I. E. Dzyaloshinski&ibreve; Ibid. 63 1460 (1972); S. I. Anisimov and I. E. Dzyaloshinski&ibreve; Sov. Phys. JETP 36 774 (1972)
  95. P. E. Cladis and M. Kléman J. Phys. (Paris) 33 591 (1972)
  96. J. Nehring and A. Saupe J. Chem. Soc. Faraday Trans. Ser. II 68 1 (1972)
  97. J. Nehring Phys. Rev. A 7 1737 (1973)
  98. M. Kléman Adv. Liq. Cryst. 1 267 (1975)
  99. G. S. Ranganath Mol. Cryst. Liq. Cryst. 97 77 (1983)
  100. D. J. Graziano and M. R. Mackley Ibid. 106 103 (1984)
  101. N. V. Madhusudana and R. Pratibha Ibid. 103 31 (1983); N. V. Madhusudana and R. Pratibha Curr. Sci. 51 877 (1982)
  102. I. F. Lyuksyutov Zh. Eksp. Teor. Fiz. 75 358 (1978); I. F. Lyuksyutov Sov. Phys. JETP 48 178 (1978)
  103. F. M. Aliev Pis’ma Zh. Eksp. Teor. Fiz. 41 254 (1985); F. M. Aliev JETP Lett. 41 310 (1985)
  104. Dzh. Ériksen Studies On The Mechanics Of Continuous Media (Russ. Transl. (Mir, M., 1977)
  105. H. Imura and K. Okano Phys. Lett. A 42 405 (1973)
  106. Y. Bouligand, P. E. Cladis, L. Liébert, and P. Strzelecki Mol. Cryst. Liq. Cryst. 25 233 (1974); B. Fayolle, C. Noel, and J. Billard J. Phys. (Paris) 40 (Coll. C3) C3–485 (1979)
  107. M. Kléman, L. Liébert, and P. Strzelecki Polymer 24 295 (1983)
  108. B. Millaud, A. Thierry, and A. Skoulios J. Phys. (Paris) 39 1109 (1978); B. Millaud, A. Thierry, and A. Skoulios J. Phys. Lett. (Paris) 40 L-607 (1979)
  109. Nguyen Huu Tinh, H. Gasparoux, and C. Destrade Mol. Cryst. Liq. Cryst. 68 101 (1981)
  110. A. Saupe, P. Boonbrahm, and L. J. Yu J. Chim. Phys. Phys.-Chim. Biol. 80 3 (1983)
  111. E. D. Belotski&ibreve;, B. I. Lev, and P. M. Tomchuk Ukr. Fiz. Zh. 26 625 (1981); E. D. Belotski&ibreve;, B. I. Lev, and P. M. Tomchuk Pis’ma Zh. Eksp. Teor. Fiz. 31 573 (1980); E. D. Belotski&ibreve;, B. I. Lev, and P. M. Tomchuk JETP Lett. 31 539 (1980)
  112. O. D. Lavrentovich and E. M. Terent’ev Zh. Eksp. Teor. Fiz. 91 2084 (1986); O. D. Lavrentovich and E. M. Terent’ev Sov. Phys. JETP 64 1237 (1986)
  113. Oeuvres de Henri Poincaré Sur Les Courbes Définies Par Les équations Différentielles, Tomel. (1951) p. 3–222; Oeuvres de Henri Poincaré Sur Les Courbes Définies Par Les équations Différentielles, Tomel. (Gauthier-Villars, Paris, 1951); Russ. transl., Oeuvres de Henri Poincaré Sur Les Courbes Définies Par Les équations Différentielles, Tomel. (OGIZ, M., L., 1947)
  114. F. R. N. Nabarro J. Phys. (Paris) 33 1089 (1972)
  115. S. Ostlund Phys. Rev. B 24 485 (1981)
  116. A. T. Garel J. Phys. (Paris) 39 225 (1978)
  117. N. D. Mermin Quantum Fluids And Solids (eds. S. B. Trickey, E. D. Adams, and J. W. Dufty (Plenum Press, N. Y., 1978) p. 3; Russ. transl., N. D. Mermin Quantum Fluids And Solids (Mir, M., 1979) p. 9
  118. G. E. Volovik Usp. Fiz. Nauk 143 73 (1984); G. E. Volovik Sov. Phys. Usp. 27 363 (1984)
  119. R. B. Meyer Mol. Cryst. Liq. Cryst. 16 355 (1972)
  120. N. V. Madhusudana and K. R. Sumathy Ibid. 92 193 (1983)
  121. P. Pieranski, E. Dubois-Violette, and E. Guyon Phys. Rev. Lett. 30 736 (1973)
  122. A. S. Sonin, A. N. Chuvyrov, A. S. Sobachkin, and V. A. Ovchinnikov Fiz. Tverd. Tela (Leningrad) 18 3099 (1976); A. S. Sonin, A. N. Chuvyrov, A. S. Sobachkin, and V. A. Ovchinnikov Sov. Phys. Solid State 18 1805 (1976)
  123. D. L. Stein, R. D. Pisarski, and P. W. Anderson Phys. Rev. Lett. 40 1269 (1978)
  124. K. Ro&ibreve;ciszewski Acta Phys. Polon. Ser. A 57 927 (1980)
  125. G. E. Volovik Pis’ma Zh. Eksp. Teor. Fiz. 28 65 (1978); G. E. Volovik JETP Lett. 28 59 (1978)
  126. N. V. Madhusudana and K. R. Sumathy Mol. Cryst. Liq. Cryst. Lett. 92 179 (1983)
  127. D. L. Stein Phys. Rev. A 19 1708 (1979)
  128. R. D. Williams Preprint RAL No. 85–062 (1985), July
  129. C. Williams, V. Vitek, and M. Kléman Solid State Commun. 12 581 (1973)
  130. R. B. Meyer Ibid. 585
  131. M. Kléman and C. Williams Philos. Mag. 28 725 (1973)
  132. V. Vitek and M. Kléman J. Phys. (Paris) 36 59 (1975)
  133. G. Porte Ibid. 38 509 (1977)
  134. G. S. Ranganath Ibid. 40 (Coll. C3) C3–87 (1979)
  135. L. Lejcek Czech, J. Phys. Ser. B 33 447 (1983)
  136. S. Faetti and V. Palleschi J. Phys. (Paris) 46 415 (1985)
  137. W. Helfrich Phys. Rev. Lett. 21 1518 (1968); P. G. De Gennes J. Phys. (Paris) 32 789 (1971)
  138. F. Brochard Ibid. 33 607 (1972)
  139. L. Léger Solid State Commun. 10 697 (1972); L. Léger Ibid 11 1499 (1972); L. Léger Mol. Cryst. Liq. Cryst. 24 33 (1973)
  140. G. Heppke and F. Schneider Z. Naturforsch. Teil A 28 1044 (1973)
  141. A. M. Figueiredo Neto, Ph. Martinot-Lagarde, and G. Durand J. Phys. Lett. (Paris) 45 L-793 (1984)
  142. L. Liebert and A. M. Figueiredo Neto Ibid. L-173
  143. V. G. Chigrinov Kristallografiya 27 404 (1982); V. G. Chigrinov Sov. Phys. Crytallogr. 27 245 (1982)
  144. A. N. Chuvyrov Ibid. 19 297 (1974); A. N. Chuvyrov Sov. Phys. Crystallogr. 19 180 (1974); W. H. De Jeu, C. J. Gerritsma, and Th. W. Lathouwers Chem. Phys. Lett. 14 503 (1972); A. Stieb, G. Baur, and G. Meier J. Phys. (Paris) 36 (Coll. C1) C1–185 (1975); A. Rapini, L. Léger, and A. Martinet Ibid. C1–189
  145. I. A. Ovid’ko Zh. Eksp. Teor. Fiz. 89 1301 (1985); I. A. Ovid’ko Sov. Phys. JETP 62 753 (1985)
  146. R. D. Pisarski and D. L. Stein J. Phys. (Paris) 41 345 (1980)
  147. M. Yamashita, H. Kimura, and H. Nakano Mol. Cryst. Liq. Cryst. 68 79 (1981)
  148. Y. Bouligand J. Phys. (Paris) 35 959 (1974)
  149. Y. Bouligand, B. Derrida, V. Poénaru, Y. Pomeau, and G. Toulouse Ibid. 39 863 (1978)
  150. L. J. Yu and A. Saupe Phys. Rev. Lett. 45 1000 (1980)
  151. R. Bartolino, T. Chiaranza, M. Meuti, and R. Compagnoni Phys. Rev. A 26 1116 (1982)
  152. Y. Galerne and L. Liébert Phys. Rev. Lett. 55 2449 (1985)
  153. V. Poenaru and G. Toulouse J. Phys. (Paris) 38 887 (1977)
  154. K. Jänich and H.-R. Trebin see Ref. 3 p. 421
  155. M. I. Monastyrsky and V. S. Retakh Commun. Math. Phys. 103 445 (1986)
  156. M. Kléman and L. Michel J. Phys. Lett. (Paris) 39 L-29 (1978)
  157. M. V. Kurik and O. D. Lavrentovich Zh. Eksp. Teor. Fiz. 85 511 (1983); M. V. Kurik and O. D. Lavrentovich Sov. Phys. JETP 58 299 (1983)
  158. V. P. Mineyev Preprint of Inst. of Solid State Phys. (USSR Acad. of Sci., Chernogolovka, 1979)
  159. M. Kléman and J. Friedel J. Phys. (Paris) 30 (Coll. C4) C4–43 (1969)
  160. R. Cano Bull. Soc. Fr. Minér. Cryst. 90 333 (1967); Orsay Group on Liquid Crystals Phys. Lett. A 28 687 (1969); Orsay Group on Liquid Crystals J. Phys. (Paris) 30 (Coll. C4) C4–38 (1969)
  161. Y. Bouligand and M. Kléman J. Phys. (Paris) 31 1041 (1970)
  162. Y. Bouligand Ibid. 33 715 (1972); Y. Bouligand Ibid 34 603, 1011 (1973); Y. Bouligand Ibid 35 215 (1974)
  163. J. Rault Solid State Commun. 9 1965 (1971)
  164. J. Rault Mol. Cryst. Liq. Cryst. 16 143 (1972)
  165. J. Rault J. Phys. (Paris) 33 383 (1972)
  166. J. Rault Philos. Mag. 28 11 (1973)
  167. J. Rault Ibid. 29 621 (1974)
  168. G. Malet, J. Marignan, and O. Parodi J. Phys. Lett. (Paris) 36 L-317 (1975); G. Malet, J. Marignan, and O. Parodi J. Phys. (Paris) 37 865 (1976); M. De Zwart Ibid. 423; M. J. Press and A. S. Arrott Ibid. 39 750 (1978); A. E. Stieb Ibid. 40 (Coll. C3) C3–94 (1979); T. Kohno, H. Miike, and Y. J. Ebina J. Phys. Soc. Jpn. 44 1678 (1978); N. Nawa and K. Nakamura Jpn. J. Appl. Phys. 18 2041 (1979); O. Parodi, G. Durand, G. Malet, and J. Marignan J. Phys. Lett. (Paris) 43 L-727 (1982)
  169. S. V. Belyaev and L. M. Blinov Zh. Eksp. Teor. Fiz. 70 184 (1976); S. V. Belyaev and L. M. Blinov Sov. Phys. JETP 43 96 (1976); V. G. Chigrinov, V. V. Belyaev, S. V. Belyaev, and M. F. Grebenkin Ibid. 77 2081 (1979); V. G. Chigrinov, V. V. Belyaev, S. V. Belyaev, and M. F. Grebenkin Sov. Phys. JETP 50 994 (1979); R. I. Mints, E. V. Kononenko, and E. G. Aksel’rod Ibid. 80 1122 (1981); R. I. Mints, E. V. Kononenko, and E. G. Aksel’rod Sov. Phys. JETP 53 574 (1981); R. I. Mints, E. V. Kononenko, and E. G. Aksel’rod Kristallografiya 25 989 (1980); R. I. Mints, E. V. Kononenko, and E. G. Aksel’rod Sov. Phys. Crystallogr. 25 567 (1980)
  170. M. V. Kurik and O. D. Lavrentovich Pis’ma Zh. Eksp. Teor. Fiz. 33 545 (1981); M. V. Kurik and O. D. Lavrentovich JETP Lett. 33 528 (1981)
  171. A. G. Kleopov, M. V. Kurik, O. D. Lavrentovich, and V. G. Tishchenko Zh. Fiz. Khim. 56 2422 (1982); A. G. Kleopov, M. V. Kurik, O. D. Lavrentovich, and V. G. Tishchenko Russ. J. Phys. Chem. 56 1485 (1982)
  172. P. G. De Gennes C. R. Acad. Sci. Ser. B 266 571 (1968); T. J. Scheffer Phys. Rev. A 5 1327 (1972); G. S. Ranganath Mol. Cryst. Liq. Cryst. 94 285 (1983)
  173. F. Livolant Eur. J. Cell Biol. 33 300 (1984)
  174. Y. Bouligand J. Phys. (Paris) 36 (Coll. C1) C1–331 (1975); Y. Bouligand and F. Livolant Ibid. 45 1899 (1984); M. Kléman Ibid. 46 1193 (1985)
  175. O. D. Lavrentovich and Yu. A. Nastishin Pis’ma Zh. Eksp. Teor. Fiz. 40 242 (1984); O. D. Lavrentovich and Yu. A. Nastishin JETP Lett. 40 1015 (1984)
  176. P.-P. Grassé, A. Hollande, J. Cachon, and H. Cachon-Eujumet C. R. Acad. Sci. 260 6975 (1965)
  177. W. Haas and J. Adams Appl. Phys. Lett. 25 263, 535 (1974); M. Kawashi, O. Kogure, and Y. Kato Jpn. J. Appl. Phys. 13 1457 (1974); M. Kawachi and M. Kogure Ibid. 15 1557 (1976); N. Nava and K. Nakamura Ibid. 17 219 (1977); V. Bhide, S. Chandra, S. Jain, and R. Medhekar J. Appl. Phys. 47 120 (1976); J. Wahl J. Phys. (Paris) 40 (Coll. C3) C3–98 (1979)
  178. L. V. Volod’ko, A. Z. Abdulin, N. R. Posledovich, and N. P. Shchors Optical Methods of Processing Results (in Russian) (Nauka i Tekhnika, Minsk, 1978); D. F. Aliev, V. N. Chirkov, and A. Kh. Ze&ibreve;nally Kristallografiya 24 118 (1979); D. F. Aliev, V. N. Chirkov, and A. Kh. Ze&ibreve;nally Sov. Phys. Crystallogr. 24 65 (1979)
  179. A. E. Stieb J. Phys. (Paris) 41 961 (1980)
  180. B. Kerllenevich and A. Coche Mol. Cryst. Liq. Cryst. 68 47 (1981)
  181. T. Akahane and T. Tako Jpn. J. Appl. Phys. 15 1559 (1976); T. Akahane and T. Tako Mol. Cryst. Liq. Cryst. 38 251 (1977)
  182. P. Cladis and M. Kléman Ibid. 16 1 (1972)
  183. S. Hirata, T. Akahane, and T. Tako Ibid. 75 47 (1981)
  184. V. A. Belyakov and V. E. Dmitrienko Usp. Fiz. Nauk 146 369 (1985); V. A. Belyakov and V. E. Dmitrienko Sov. Phys. Usp. 28 535 (1985)
  185. P. Pieranski, R. Barbet-Massin, and P. Cladis Phys. Rev. A 31 3912 (1985)
  186. Y. Bouligand and M. Kléman J. Phys. (Paris) 40 79 (1979)
  187. R. Kutka and H. R. Trebin J. Phys. Lett. (Paris) 45 1119 (1984)
  188. C. E. Williams and M. Kléman Ibid. 35 L-33 (1974); M. Steers, M. Kléman, and C. Williams Ibid. L-21
  189. C. E. Williams and M. Kléman Ibid. 36 (Coll. C1) C1–315 (1975)
  190. S. A. Asher and P. S. Pershan Biophys. J. 27 393 (1979)
  191. J. Rault C. R. Acad. Sci. Ser. B 280 417 (1975); P. S. Pershan and J. Prost J. Appl. Phys. 46 2343 (1975); M. B. Schneider and W. W. Webb J. Phys. (Paris) 45 273 (1984)
  192. F. Candau, F. Ballet, F. Debeauvais, and J.-C. Wittmann J. Colloid Interface Sci. 87 356 (1982)
  193. R. B. Meyer, B. Stebler, and S. T. Lagerwall Phys. Rev. Lett. 41 1393 (1978); S. T. Lagerwall, R. B. Meyer, and B. Stebler Ann. Phys. (N.Y.) 3 249 (1978); S. T. Lagerwall, and B. Stebler Phys. Bull. 31 349 (1980)
  194. W. K. Chan and W. W. Webb Phys. Rev. Lett. 46 603 (1981); W. K. Chan and W. W. Webb J. Phys. (Paris) 42 1007 (1981)
  195. P. Oswald C. R. Acad. Sci. Ser. II 296 1385 (1983)
  196. P. Oswald and M. Allain J. Phys. (Paris) 46 831 (1985)
  197. M. Allain Ibid. 225
  198. C. E. Williams and M. Kléman Philos. Mag. 33 213 (1976)
  199. C. Williams J. Phys. (Paris) 39 (Coll. C2) C2–48 (1978); Thesis (Orsay, 1976)
  200. L. Bourdon Thesis (Paris, 1980)
  201. P. G. De Gennes C. R. Acad. Sci. Ser. B 275 939 (1972); P. S. Pershan J. Appl. Phys. 45 1590 (1974); M. Kléman J. Phys. (Paris) 35 595 (1974); M. Kléman J. Phys. Lett. (Paris) 37 L-93 (1976); M. Kléman Philos. Mag. 34 79 (1976)
  202. E. B. Loginov and E. M. Terent’ev Kristallografiya 30 10 (1985); E. B. Loginov and E. M. Terent’ev Sov. Phys. Crystallogr. 30 4 (1985)
  203. P. G. De Gennes Solid State Commun. 10 753 (1972); P. G. De Gennes Mol. Cryst. Liq. Cryst. 21 49 (1973)
  204. P. B. Vigman and V. M. Filev Zh. Eksp. Teor. Fiz. 69 1466 (1975); P. B. Vigman and V. M. Filev Sov. Phys. JETP 42 747 (1975); V. M. Filev Ibid. 74 1899 (1978); V. M. Filev Sov. Phys. JETP 47 989 (1978)
  205. P. E. Cladis and S. Torza J. Appl. Phys. 46 584 (1975); N. V. Madhusudana and B. S. Srikanta Mol. Cryst. Liq. Cryst. 99 375 (1983)
  206. M. V. Kurik and A. A. Rudenko Pis’ma Zh. Tekh. Fiz. 4 480 (1978); M. V. Kurik and A. A. Rudenko Sov. Tech. Phys. Lett. 4 194 (1978); M. V. Kurik and A. A. Rudenko Ukr. Fiz. Zh. 24 31 (1979)
  207. Y. Galerne J. Phys. Lett. (Paris) 40 L-73 (1979)
  208. P. E. Cladis and A. E. White J. Appl. Phys. 47 1256 (1977)
  209. P. E. Cladis J. Phys. (Paris) 37 (Coll. C3) C3–137 (1976); P. G. De Gennes and P. Pincus Ibid. 1359
  210. M. Lefevre, J.-L. Martinand, G. Durand, and M. Veyssie C. R. Acad. Sci. Ser. B 273 403 (1974); R. Bartolino and G. Durand Ann. Phys. (N.Y.) 3 257 (1978); M. Kléman Ibid. 263; M. Kléman and L. Lejcek Philos. Mag. 42 671 (1980)
  211. H. P. Hinov and M. Petrov Mol. Cryst. Liq. Cryst. 100 223 (1983)
  212. H. Arnold, D. Demus, and H. Sackmann Z. Phys. Chem. 222 15 (1963); D. Demus Krist. Und Techn. 10 933 (1975)
  213. C. Allet, M. Kléman, and P. Vidal J. Phys. (Paris) 39 181 (1978)
  214. H. P. Hinov J. Phys. Lett. (Paris) 45 L-185 (1984); H. P. Hinov Dokl. Bolg. Akad. Nauk 36 611 (1983)
  215. L. Lejcek Czech. J. Phys. Ser. B 34 563 (1984); L. Lejcek Ibid 35 726 (1985)
  216. M. Brunet and C. Williams Ann. Phys. (N.Y.) 3 237 (1978)
  217. V. Janovec Phys. Lett. A 99 384 (1983)
  218. M. Glogarova, L. Lejcek, J. Pavel, V. Janovec, and J. Fousek Mol. Cryst. Liq. Cryst. 91 309 (1983); J. Fousek and M. Glogarova Ferroelectrics 58 71 (1984); J. Pavel J. Phys. (Paris) 45 137 (1984); M. Glogarova and J. Pavel Ibid. 143; L. Lejcek Czech. J. Phys. Ser. B 35 655 (1985)
  219. M. Brunet and O. Parodi J. Phys. (Paris) 43 515 (1982)
  220. M. Yamashita J. Phys. Soc. Jpn. 52 3735 (1983); M. Yamashita Ferroelectrics 58 149 (1984)
  221. J. P. Sethna and M. Kléman Phys. Rev. A 26 3037 (1982)
  222. H.-R. Trebin and R. Kutka J. Phys. Lett. (Paris) 42 L-421 (1981)
  223. Y. Bouligand J. Phys. (Paris) 33 525, 715 (1972)
  224. D. Hilbert and S. Cohn-Vossen Geometry And The Imagination (Chelsea Publishing, N. Y., 1952); Russ. Transl., D. Hilbert and S. Cohn-Vossen Geometry And The Imagination (Nauka, M., 1981)
  225. N. H. Hartshorne and A. Stuart Crystals And The Polarizing Microscope (Arnold, London, 1970); M. Delaye et al Phys. Lett. A 44 139 (1973); N. A. Clark and R. B. Meyer Appl. Phys. Lett. 22 403 (1973); M. Hareng, S. Le Berre, and J. J. Metzger Ibid. 27 575 (1975); C. E. Williams Philos. Mag. 32 313 (1975); F. Scudieri Ann. Phys. (N.Y.) 3 311 (1978); J. Marignan, G. Malet, and O. Parodi Ibid. 221; J. Marignan and O. Parodi J. Phys. (Paris) 40 (Coll. C3) C3–78 (1979); J. Marignan and O. Parodi Ibid 44 665 (1983); H. P. Hinov, N. Shonova, and K. Avramova Mol. Cryst. Liq. Cryst. 97 297 (1983); M. Fernandes Atti Fondaz. G. Ronchi 38 112 (1983)
  226. P. V. Adomenas, L. K. Vistin’, A. N. Mesropyan, A. A. Tubelite, I. G. Chistyakov, S. P. Chumakova, V. M. É&ibreve;genbrot, and S. S. Yakovenko Zh. Eksp. Teor. Fiz. 73 1903 (1977); P. V. Adomenas, L. K. Vistin’, A. N. Mesropyan, A. A. Tubelite, I. G. Chistyakov, S. P. Chumakova, V. M. É&ibreve;genbrot, and S. S. Yakovenko Sov. Phys. JETP 46 999 (1977); A. N. Nesrullaev and A. S. Sonin Zh. Fiz. Khim. 53 2481 (1979); A. N. Nesrullaev and A. S. Sonin Russ. J. Phys. Chem. 53 1416 (1979)
  227. A. Perez, M. Brunet, and O. Parodi J. Phys. Lett. (Paris) 39 L-353 (1978)
  228. L. Bourdon, J. Sommeria, and M. Kléman J. Phys. (Paris) 43 77 (1982)
  229. Ch. S. Rosenblatt, R. Pindak, N. A. Clark, and R. B. Meyer Ibid. 38 1105 (1977); P. Oswald, J. Behar, and M. Kléman Philos. Mag. Ser. A 46 899 (1982)
  230. S. A. Asher and P. S. Pershan J. Phys. (Paris) 40 161 (1979); W. J. Benton, E. W. Toor, C. A. Miller, and T. Fort, Jr Ibid. 107
  231. A. Perez and J. E. Proust J. Phys. Lett. (Paris) 38 L-l, 17 (1977); S. Le Berre and M. Hareng Ann. Phys. (N.Y.) 3 327 (1978); H. P. Hinov J. Phys. (Paris) 42 307 (1981); N. J. Chou, S. W. Depp, J. M. Eldrige, M. H. Lee, G. J. Sprokel, A. Juliana, and J. Brown J. Appl. Phys. 54 1827 (1983)
  232. A. Perez, M. Bruent, and O. Parodi J. Phys. (Paris) 42 1559 (1981)
  233. J. A. Geurst Phys. Lett. A 34 283 (1971); M. Kléman and O. Parodi J. Phys. (Paris) 36 671 (1975); M. Kléman Proc. R. Soc. London Ser. A 347 387 (1976)
  234. M. Kléman J. Phys. (Paris) 38 1511 (1977)
  235. R. Bidaux, N. Boccara, G. Sarma, L. de Seze, P. G. De Gennes, and O. Parodi Ibid. 34 661 (1973)
  236. O. D. Lavrentovich Zh. Eksp. Teor. Fiz. 91 1666 (1986); O. D. Lavrentovich Sov. Phys. JETP 64 984 (1986)
  237. P. A. M. Dirac Proc. R. Soc. London Ser. A 133 60 (1931)
  238. B. Cabrera Phys. Rev. Lett. 48 1387 (1982); B. Cabrera, M. Taber, B. Gardner, and J. Bour Ibid. 51 1933 (1983)
  239. G. E. Volovik Pis’ma Zh. Eksp. Teor. Fiz. 29 357 (1979); G. E. Volovik JETP Lett. 29 322 (1979)
  240. M. V. Kurik and O. D. Lavrentovich Ibid. 35 362 (1982); M. V. Kurik and O. D. Lavrentovich JETP Lett. 35 444 (1982)
  241. O. D. Lavrentovich Ibid. 43 297 (1986); O. D. Lavrentovich JETP Lett. 43 382 (1986)
  242. E. I. Kats Usp. Fiz. Nauk 142 99 (1984); E. I. Kats Sov. Phys. Usp. 27 42 (1984)
  243. J. M. F. Gunn and K. B. Ma J. Phys. C 13 963 (1980); K. B. Ma and J. M. F. Gunn Prog. Cryst. Growth Charact. 3 273 (1981)
  244. P. Oswald J. Phys. Lett. (Paris) 45 L-1037 (1984); P. Oswald J. Phys. (Paris) 46 1255 (1985)
  245. Y. Bouligand Ibid. 41 1297, 1307 (1980)
  246. M. Kléman and P. Oswald Ibid. 43 655 (1982)
  247. M. Kléman Ibid. 41 737 (1980)
  248. S. Chandrasekhar, B. K. Sadashiva, K. A. Suresh, N. V. Madhusudana, S. Kumar, R. Shashidhar, and G. Ventakesh Ibid. 40 (Coll. C3) C3–120 (1979); P. Oswald and M. Kléman Ibid. 42 1461 (1981); M. Cagnon, M. Gharbia, and G. Durand Phys. Rev. Lett. 53 938 (1984)
  249. M. B. L. Santos and G. Durand J. Phys. Lett. (Paris) 44 L-195 (1983)
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