Advances in Nonlinear Optics
Volume 2009 (2009), Article ID 926810, 9 pages
doi:10.1155/2009/926810
Research Article

Localized States in Bi-Pattern Systems

U. Bortolozzo,1 M. G. Clerc,2 F. Haudin,1 R. G. Rojas,3 and S. Residori1

1l'Institut Non Linéaire de Nice (INLN), Centre National de la Recherche Scientifique (CNRS), Université de Nice Sophia Antipolis, 1361 Route des Lucioles, 06560 Valbonne, France
2Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Blanco Encalada 2008, Santiago, Chile
3Instituto de Física, Pontificia Univesidad Católica de Valparaíso, Casilla 4059, Avenida Brasil 2950, Valparaíso, Chile

Received 4 February 2009; Accepted 7 May 2009

Academic Editor: M. Tlidi

Copyright © 2009 U. Bortolozzo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. C. Cross and P. C. Hohenberg, “Pattern formation outside of equilibrium,” Reviews of Modern Physics, vol. 65, no. 3, pp. 851–1112, 1993. View at Publisher · View at Google Scholar
  2. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering, Addison-Wesley, Reading, Mass, USA, 1994.
  3. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, New York, NY, USA, 2003.
  4. H. A. Eschenfelder, Magnetic Bubble Technology, Springer, Berlin, Germany, 1981.
  5. S. Pirkl, P. Ribière, and P. Oswald, “Forming process and stability of bubble domains in dielectrically positive cholesteric liquid crystals,” Liquid Crystals, vol. 13, no. 3, pp. 413–425, 1993. View at Publisher · View at Google Scholar
  6. Y. A. Astrov and Y. A. Logvin, “Formation of clusters of localized states in a gas discharge system via a self-completion scenario,” Physical Review Letters, vol. 79, no. 16, pp. 2983–2986, 1997. View at Publisher · View at Google Scholar
  7. K.-J. Lee, W. D. McCormick, J. E. Pearson, and H. L. Swinney, “Experimental observation of self-replicating spots in a reaction-diffusion system,” Nature, vol. 369, no. 6477, pp. 215–218, 1994. View at Publisher · View at Google Scholar
  8. W. S. Edwards and S. Fauve, “Patterns and quasi-patterns in the Faraday experiment,” Journal of Fluid Mechanics, vol. 278, pp. 123–148, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  9. P. B. Umbanhowar, F. Melo, and H. L. Swinney, “Localized excitations in a vertically vibrated granular layer,” Nature, vol. 382, no. 6594, pp. 793–796, 1996. View at Publisher · View at Google Scholar
  10. M. G. Clerc, P. Cordero, J. Dunstan, et al., “Liquid-solid-like transition in quasi-one-dimensional driven granular media,” Nature Physics, vol. 4, no. 3, pp. 249–254, 2008. View at Publisher · View at Google Scholar
  11. R. Heinrichs, G. Ahlers, and D. S. Cannell, “Traveling waves and spatial variation in the convection of a binary mixture,” Physical Review A, vol. 35, no. 6, pp. 2761–2764, 1987. View at Publisher · View at Google Scholar
  12. P. Kolodner, D. Bensimon, and C. M. Surko, “Traveling-wave convection in an annulus,” Physical Review Letters, vol. 60, no. 17, pp. 1723–1726, 1988. View at Publisher · View at Google Scholar
  13. D. W. Mc Laughlin, J. V. Moloney, and A. C. Newell, “Solitary waves as fixed points of infinite-dimensional maps in an optical bistable ring cavity,” Physical Review Letters, vol. 51, no. 2, pp. 75–78, 1983. View at Publisher · View at Google Scholar
  14. N. N. Rosanov and G. V. Khodova, “Autosolitons in bistable interferometers,” Optics and Spectroscopy, vol. 65, pp. 449–450, 1988.
  15. M. Tlidi, P. Mandel, and R. Lefever, “Localized structures and localized patterns in optical bistability,” Physical Review Letters, vol. 73, no. 5, pp. 640–643, 1994. View at Publisher · View at Google Scholar
  16. P. Coullet, C. Riera, and C. Tresser, “Stable static localized structures in one dimension,” Physical Review Letters, vol. 84, no. 14, pp. 3069–3072, 2000. View at Publisher · View at Google Scholar
  17. U. Bortolozzo, M. G. Clerc, and S. Residori, submitted to New Journal of Physics.
  18. U. Bortolozzo, M. G. Clerc, and S. Residori, “Local theory of the slanted homoclinic snaking bifurcation diagram,” Physical Review E, vol. 78, no. 3, Article ID 036214, 4 pages, 2008. View at Publisher · View at Google Scholar
  19. W. van Saarloos and P. C. Hohenberg, “Pulses and fronts in the complex Ginzburg-Landau equation near a subcritical bifurcation,” Physical Review Letters, vol. 64, no. 7, pp. 749–752, 1990. View at Publisher · View at Google Scholar
  20. U. Bortolozzo, R. G. Rojas, and S. Residori, “Spontaneous nucleation of localized peaks in a multistable nonlinear system,” Physical Review E, vol. 72, no. 4, Article ID 045201, 4 pages, 2005. View at Publisher · View at Google Scholar
  21. Y. A. Logvin, B. Schäpers, and T. Ackemann, “Stationary and drifting localized structures near a multiple bifurcation point,” Physical Review E, vol. 61, no. 4, pp. 4622–4625, 2000. View at Publisher · View at Google Scholar
  22. D. Gomila and G.-L. Oppo, “Subcritical patterns and dissipative solitons due to intracavity photonic crystals,” Physical Review A, vol. 76, no. 4, Article ID 043823, 7 pages, 2007. View at Publisher · View at Google Scholar
  23. H. Arbell and J. Fineberg, “Temporally harmonic oscillons in Newtonian fluids,” Physical Review Letters, vol. 85, no. 4, pp. 756–759, 2000. View at Publisher · View at Google Scholar
  24. M. G. Clerc, E. Tirapegui, and M. Trejo, “Pattern formation and localized structures in monoatomic layer deposition,” The European Physical Journal, vol. 146, no. 1, pp. 407–425, 2007. View at Publisher · View at Google Scholar
  25. P. L. Ramazza, E. Benkler, U. Bortolozzo, S. Boccaletti, S. Ducci, and F. T. Arecchi, “Tailoring the profile and interactions of optical localized structures,” Physical Review E, vol. 65, no. 6, Article ID 066204, 4 pages, 2002. View at Publisher · View at Google Scholar
  26. U. Bortolozzo and S. Residori, “Storage of localized structure matrices in nematic liquid crystals,” Physical Review Letters, vol. 96, no. 3, Article ID 037801, 4 pages, 2006. View at Publisher · View at Google Scholar
  27. F. Pedaci, S. Barland, E. Caboche, et al., “All-optical delay line using semiconductor cavity solitons,” Applied Physics Letters, vol. 92, no. 1, Article ID 011101, 3 pages, 2008. View at Publisher · View at Google Scholar
  28. C. Cleff, B. Gütlich, and C. Denz, “Gradient induced motion control of drifting solitary structures in a nonlinear optical single feedback experiment,” Physical Review Letters, vol. 100, no. 23, Article ID 233902, 4 pages, 2008. View at Publisher · View at Google Scholar
  29. U. Bortolozzo, M. G. Clerc, C. Falcon, S. Residori, and R. G. Rojas, “Localized states in bistable pattern-forming systems,” Physical Review Letters, vol. 96, no. 21, Article ID 214501, 4 pages, 2006. View at Publisher · View at Google Scholar
  30. M. G. Clerc and C. Falcon, “Localized patterns and hole solutions in one-dimensional extended systems,” Physica A, vol. 356, no. 1, pp. 48–53, 2005. View at Publisher · View at Google Scholar
  31. D. Bensimon, B. I. Shraiman, and V. Croquette, “Nonadiabatic effects in convection,” Physical Review A, vol. 38, no. 10, pp. 5461–5464, 1988. View at Publisher · View at Google Scholar
  32. Y. Pomeau, “Front motion, metastability and subcritical bifurcations in hydrodynamics,” Physica D, vol. 23, no. 1–3, pp. 3–11, 1986. View at Publisher · View at Google Scholar
  33. S. Residori, “Patterns, fronts and structures in a liquid-crystal-light-valve with optical feedback,” Physics Reports, vol. 416, no. 5-6, pp. 201–272, 2005. View at Publisher · View at Google Scholar
  34. E. Pampaloni, S. Residori, and F. T. Arecchi, “Roll-hexagon transition in a Kerr-like experiment,” Europhysics Letters, vol. 24, no. 8, pp. 647–652, 1993. View at Publisher · View at Google Scholar
  35. L. Kramer and W. Pesch, “Electrohydrodynamic instabilities in nematic liquid crystals in pattern formation in liquid crystals,” in Pattern Formation in Liquid Crystals, A. Buka and L. Kramer, Eds., pp. 221–255, Springer, New York, NY, USA, 1996.
  36. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, Oxford Science, Clarendon Press, Oxford, UK, 2nd edition, 1993.
  37. M. G. Clerc, A. Petrossian, and S. Residori, “Bouncing localized structures in a liquid-crystal light-valve experiment,” Physical Review E, vol. 71, no. 1, Article ID 015205, 4 pages, 2005. View at Publisher · View at Google Scholar
  38. T. O. Carroll, “Liquid-crystal diffraction grating,” Journal of Applied Physics, vol. 43, no. 3, pp. 767–770, 1972. View at Publisher · View at Google Scholar
  39. S. Rasenat, G. Hartung, B. L. Winkler, and I. Rehberg, “The shadowgraph method in convection experiments,” Experiments in Fluids, vol. 7, no. 6, pp. 412–420, 1989. View at Publisher · View at Google Scholar
  40. M. Henriot, J. Burguete, and R. Ribotta, “Entrainment of a spatially extended nonlinear structure under selective forcing,” Physical Review Letters, vol. 91, no. 10, Article ID 104501, 4 pages, 2003. View at Publisher · View at Google Scholar
  41. P. Collet and J. P. Eckmann, Instabilities and Fronts in Extended Systems, Princeton University Press, Princeton, NJ, USA, 1990.
  42. K. Kawasaki and T. Ohta, “Kink dynamics in one-dimensional nonlinear systems,” Physica A, vol. 116, no. 3, pp. 573–593, 1982. View at Publisher · View at Google Scholar
  43. M. G. Clerc, S. Coulibaly, D. Escaff, C. Falcón, C. Fernandez, and R. G. Rojas, in preparation.