Skip to main content
SpringerLink
Log in

Introduction to Pattern Formation in Nonequilibrium Systems

  • Chapter
Pattern Formation in Liquid Crystals

Part of the book series: Partially Ordered Systems ((PARTIAL.ORDERED))

  • 300 Accesses

Abstract

After a brief introduction into the subject a simple one-dimensional model is presented to illustrate typical features of pattern forming systems and to demonstrate the linear stability analysis. The special features of liquid crystals are outlined and two particular topics are discussed: transient patterns in the Freédericksz transition and patterns obtained in rotating magnetic and electric fields.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. C. Cross and P. C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).

    Article  ADS  Google Scholar 

  2. P. Hohenberg, L. Kramer, and H. Riecke, Physica D 15, 402 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  3. H. Riecke and L. Kramer, J. Chem. Phys. 83, 3941 (1985).

    Article  MathSciNet  ADS  Google Scholar 

  4. L. Kramer, E. Ben-Jacob, H. Brand, and M. Cross, Phys. Rev. Lett. 49, 1891 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  5. S. Rasenat, G. Hartung, B. Winkler, and I. Rehberg, Exp. in Fluids 7, 412 (1989).

    Article  ADS  Google Scholar 

  6. F. Lonberg and R. Meyer, Phys. Rev. Lett 55, 718 (1985).

    Article  ADS  Google Scholar 

  7. G. Barbero, E. Miraldi, and C. Oldano, Phys. Rev. A 38, 519 (1988).

    Article  ADS  Google Scholar 

  8. V. Chigrinov, V. Belyaev, S. Belyaev, and M. Grebenkin, Zh. Eksp. Teor. Fiz. 77, 2081 (1979).

    Google Scholar 

  9. U. Kini, J. Phys. (Paris) 48, 1187 (1979).

    Google Scholar 

  10. B. Frisken and P. Palffy-Muhoray, Phys. Rev. A 39, 1513 (1989).

    Article  ADS  Google Scholar 

  11. D. Allender, B. Frisken, and P. Palffy-Muhoray, Liq. Cryst. 5, 735 (1989).

    Article  Google Scholar 

  12. F. Lonberg, S. Fraden, A. Hurd, and R. Meyer, Phys. Rev. Lett. 52, 1903 (1984).

    Article  ADS  Google Scholar 

  13. G. Srajer, S. Fraden, and R. Meyer, Phys. Rev. A 39, 4828 (1989).

    Article  ADS  Google Scholar 

  14. M. Grigutsch, N. Klöpper, H. Schmiedel, and R. Stannarius, Phys. Rev. E 49, 5452 (1994).

    Article  ADS  Google Scholar 

  15. A. Rey and M. Denn, Liq. Cryst. 4, 409 (1989).

    Article  Google Scholar 

  16. E. Guyon, R. Meyer, and J. Salan, Mol. Cryst. Liq. Cryst. 54, 261 (1979).

    Article  Google Scholar 

  17. E. Carr, Mol. Cryst. Liq. Cryst. 34, 159 (1977).

    Article  Google Scholar 

  18. A. J. Hurd, S. Fraden, F. Lonberg, and R. B. Meyer, J. Phys. France 46, 905 (1985).

    Article  Google Scholar 

  19. S. Fraden, A. Hurd, R. Meyer, M. Cahoon, and D. Caspar, J. Phys. (Paris) Colloq. 46, C3–85 (1985).

    Article  Google Scholar 

  20. A. Buka, M. de la Torre Juarez, L. Kramer, and I. Rehberg, Phys. Rev. A 40, 7427 (1989).

    Article  ADS  Google Scholar 

  21. B.L. Winkler, H. Richter, I. Rehberg, W. Zimmermann, L. Kramer, and A. Buka, Phys. Rev. A 43, 1940(1991).

    Article  ADS  Google Scholar 

  22. A. Buka and L. Kramer, Phys. Rev. A 45, 5624 (1992).

    Article  ADS  Google Scholar 

  23. A. Buka and L. Kramer, J. Physique II 2, 315 (1992).

    Article  ADS  Google Scholar 

  24. A. Buka and L. Kramer, “Theory of transient patterns in the splay Freedericksz transition of nematics,” in Pattern Formation in Complex Dissipative Systems, edited by S. Kai, World Scientific, Kitakyushu, Japan (1991).

    Google Scholar 

  25. W. de Jeu and C. Gerritsma, J. Chem. Phys. 56, 4752 (1971).

    Article  Google Scholar 

  26. M. S. Miguel and F. Sagues, Phys. Rev. A 36, 1883 (1987).

    Article  ADS  Google Scholar 

  27. F. Sagues, F. Arias, and M. Miguel, Phys. Rev. A 37, 3601 (1988).

    Article  ADS  Google Scholar 

  28. F. Sagues, M. C. Torrent, F. Arias, and M. Miguel, Phys. Scr. 38, 418 (1988).

    Article  ADS  Google Scholar 

  29. F. Sagues and F. Arias, Phys. Rev. A 38, 5367 (1988).

    Article  ADS  Google Scholar 

  30. M. S. Miguel and F. Sagues, “Transient pattern dynamics: general concepts and the Freédericksz transition in nematics,” in Patterns, Defects ans Materials Instabilities, edited by D. Walgraef and N. Goniem, Kluwer Academic Dordrecht (1990). p. 35.

    Google Scholar 

  31. A. Amengual, E. Hernández-García, and M. S. Miguel, Phys. Rev. E 47, 4151 (1993).

    Article  ADS  Google Scholar 

  32. R. Montagne, A. Amengual, E. Hernández-García, and M. S. Miguel, Phys. Rev. E 50, 377(1994).

    Article  MathSciNet  ADS  Google Scholar 

  33. M. S. Miguel, A. Amengual, and E. Hernândez-Garcia, Phase Transitions 48, 65 (1994).

    Article  Google Scholar 

  34. F. Brochard, L. Leger, and R. Meyer, J. Physique 36, C1–209 (1975).

    Google Scholar 

  35. K. Migler and R. B. Meyer, Phys. Rev. Lett. 66, 1485 (1991).

    Article  ADS  Google Scholar 

  36. K. Migler and R. B. Meyer, Phys. Rev. E 48, 1218 (1993).

    Article  ADS  Google Scholar 

  37. K. Migler and R. B. Meyer, Physica D 71, 412 (1994).

    Article  ADS  MATH  Google Scholar 

  38. J. Gilli, M. Morabito, and T. Frisch, J. Physique II 4, 319 (1994).

    Article  ADS  Google Scholar 

  39. T. Frisch, S. Rica, P. Coullet, and J. Gilli, Phys. Rev. Lett. 72, 1471 (1994).

    Article  ADS  Google Scholar 

  40. T. Frisch, Physica D 84, 601 (1995).

    Article  Google Scholar 

  41. S. Nasuno, N. Yoshimo, and S. Kai, Phys. Rev. E 51, 1598 (1995).

    Article  ADS  Google Scholar 

  42. I. S. Aranson, Phys. Rev. E 51, R3827 (1995).

    Article  MathSciNet  ADS  Google Scholar 

  43. E. Pashkowski, W. Stille, G. Strobl, and D. Talebi, (unpublished, 1995).

    Google Scholar 

  44. M. Grigutsch and R. Stannarius, (unpublished, 1995).

    Google Scholar 

  45. G. Ranganath, Mol. Cryst. Liq. Cryst. 154, 43 (1988).

    Article  Google Scholar 

  46. P. Coullet, J. Lega, B. Houchmanzadeh, and J. Lajzerowicz, Phys. Rev. Lett. 65, 11352 (1990).

    Article  ADS  Google Scholar 

  47. A. Mikhailov, Foundation of Synergetics I, Springer, Berlin (1994).

    Google Scholar 

  48. A. Hagberg and E. Meron, Chaos 4, 477 (1994).

    Article  ADS  Google Scholar 

  49. C. Elphick, A. Hagberg, and E. Meron, Phys. Rev. E 51, 3052 (1995).

    Article  ADS  Google Scholar 

  50. M. Büttiker and R. Landauer, Phys. Rev. A 23, 1397 (1981).

    Article  MathSciNet  ADS  Google Scholar 

  51. S. Burkov, V. Pokrovsy, and G. Uimin, Solid State Comm. 40, 363 (1981).

    Article  Google Scholar 

  52. T. Frisch and J. Gilli, J. Physique II 5, 561 (1995).

    Article  ADS  Google Scholar 

  53. P. Coullet and F. Plaza, Int. J. Bif Chaos 4, 1173 (1994).

    Article  MATH  Google Scholar 

  54. G. Hauk and H. Koswig, Ferroelectrics 122, 253 (1991).

    Article  Google Scholar 

  55. G. Hauk, H. Koswig, and U. Labes, in Modern Topics in Liquid Crystals, edited by A. Buka, World Scientific, Singapore (1993).

    Google Scholar 

  56. A. Kilian, H. Koswig, and A. Sonnet, Mol. Cryst. Liq. Cryst. 265, 321 (1995).

    Article  Google Scholar 

  57. P. Cladis, P. Finn, and H. Brand, Phys. Rev. Lett. 75, 1518 (1995).

    Article  ADS  Google Scholar 

  58. P. Cladis, Y. Couder, and H. Brand, Phys. Rev. Lett. 55, 2945 (1995).

    Article  ADS  Google Scholar 

  59. I. Mutabazi, P. Finn, J. Gleeson, J. Goodby, C. Andereck, and P. Cladis, Europhys. Lett. 19, 391 (1992).

    Article  ADS  Google Scholar 

  60. A. Chuvyrov, Sov. Phys. JETP 55, 451 (1982).

    Google Scholar 

  61. A. Chuvyrov, O. Scaldin, and V. Delev, Mol. Cryst. Liq. Cryst. 215, 187 (1992).

    Article  Google Scholar 

  62. A. Krekhov, L. Kramer, A. Buka, and A. Chuvyrov, J. Physique II 3, 1387 (1993).

    Article  ADS  Google Scholar 

  63. A. Krekhov and L. Kramer, J. Physique II 4, 677 (1994).

    Article  ADS  Google Scholar 

Download references

Authors
  1. Lorenz Kramer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Agnes Buka
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Institute for Solid-State Physics, Hungarian Academy of Sciences, POB. 49, H-1525, Budapest, Hungary

    Agnes Buka

  2. Institut fur Physik, Universitat Bayreuth, D-95440, Bayreuth, Germany

    Lorenz Kramer

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Kramer, L., Buka, A. (1996). Introduction to Pattern Formation in Nonequilibrium Systems. In: Buka, A., Kramer, L. (eds) Pattern Formation in Liquid Crystals. Partially Ordered Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3994-9_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3994-9_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8464-2

  • Online ISBN: 978-1-4612-3994-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation