- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Sine-Gordon ratchets with general periodic, additive, and parametric driving forces

Elías Zamora-Sillero1,*, Niurka R. Quintero1,†, and Franz G. Mertens2,‡

  • 1Departamento de Física Aplicada I, E. U. P., Universidad de Sevilla, Virgen de África 7, 41011 Sevilla, Spain
  • 2Physikalisches Institut, Universität Bayreuth, D-85440, Germany

  • *ezamora80@us.es
  • †niurka@us.es
  • ‡franz.mertens@uni-bayreuth.de
PDF

Phys. Rev. E 76, 066601 – Published 6 December, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.066601

Abstract

We study the soliton ratchets in the damped sine-Gordon equation with periodic nonsinusoidal, additive, and parametric driving forces. By means of symmetry analysis of this system we show that the net motion of the kink is not possible if the frequencies of both forces satisfy a certain relationship. Using a collective coordinate theory with two degrees of freedom, we show that the ratchet motion of kinks appears as a consequence of a resonance between the oscillations of the momentum and the width of the kink. We show that the equations of motion that fulfill these collective coordinates follow from the corresponding symmetry properties of the original systems. As a further application of the collective coordinate technique we obtain another relationship between the frequencies of the parametric and additive drivers that suppresses the ratchetlike motion of the kink. We check all these results by means of numerical simulations of the original system and the numerical solutions of the collective coordinate equations.

View figure in article

Article Text

References (40)

  1. J. Maddox, Nature (London) 369, 181 (1994); M. O. Magnasco, Phys. Rev. Lett. 71, 1477 (1993); see also Ratchets and Brownian Motors: Basics, Experiments and Applications, edited by H. Linke, special issue of Appl. Phys. A 75 (2002).
  2. I. Zapata, R. Bartussek, F. Sols, and P. Hänggi, Phys. Rev. Lett. 77, 2292 (1996).
  3. G. Carapella and G. Costabile, Phys. Rev. Lett. 87, 077002 (2001).
  4. F. Falo, P. J. Martínez, J. J. Mazo, and S. Cilla, Europhys. Lett. 45, 700 (1999); E. Trías, J. J. Mazo, F. Falo, and T. P. Orlando, Phys. Rev. E 61, 2257 (2000).
  5. A. V. Ustinov, C. Coqui, A. Kemp, Y. Zolotaryuk, and M. Salerno, Phys. Rev. Lett. 93, 087001 (2004).
  6. E. Goldobin, A. Sterck, and D. Koelle, Phys. Rev. E 63, 031111 (2001); for the experiments see M. Beck, E. Goldobin, M. Neuhaus, M. Siegel, R. Kleiner, and D. Koelle, Phys. Rev. Lett. 95, 090603 (2005).
  7. J. E. Villegas, S. Savelev, F. Nori, E. M. González, J. V. Anguita, R. García, and J. L. Vicent, Science 302, 1188 (2003).
  8. M. Schiavoni, L. Sánchez-Palencia, F. Renzoni, and G. Grynberg, Phys. Rev. Lett. 90, 094101 (2003); R. Gommers, S. Bergamini, and F. Renzoni, ibid. 95, 073003 (2005).
  9. P. Hänggi, F. Marchesoni, and F. Nori, Ann. Phys. 14, 51 (2005).
  10. P. Reimann and P. Häggi, Appl. Phys. A 75, 169 (2002).
  11. P. Hänggi and R. Bartussek, Nonlinear Physics of Complex System-Current Status and Future Trends, edited by J. Parisi , Lecture Notes in Physics Vol. 746 (Springer, Berlin, 1996), p. 476.
  12. R. D. Astumian and P. Hänggi, Phys. Today 55(11), 33 (2002).
  13. P. Reimann, Phys. Rep. 361, 57 (2002).
  14. Z. Farkas, P. Tegzes, A. Vukics, and T. Vicsek, Phys. Rev. E 60, 7022 (1999).
  15. L. Morales-Molina, F. G. Mertens, and A. Sánchez, Eur. Phys. J. B 37, 79 (2003); Phys. Rev. E 72, 016612 (2005).
  16. A. Ajdari, D. Mukamel, L. Peliti, and J. Prost, J. Phys. I 4, 1551 (1994).
  17. S. Flach, O. Yevtushenko, and Y. Zolotaryuk, Phys. Rev. Lett. 84, 2358 (2000).
  18. M. Salerno and Yaroslav Zolotaryuk, Phys. Rev. E 65, 056603 (2002).
  19. G. Costantini, F. Marchesoni, and M. Borromeo, Phys. Rev. E 65, 051103 (2002).
  20. L. Morales-Molina, N. R. Quintero, F. G. Mertens, and A. Sánchez, Phys. Rev. Lett. 91, 234102 (2003).
  21. A. Sánchez, L. Morales-Molina, F. G. Mertens, N. R. Quintero, J. Buceta, and K. Lindenberg, Fluct. Noise Lett. 4, L571 (2004).
  22. Mario Salerno and Niurka R. Quintero, Phys. Rev. E 65 025602(R) (2002).
  23. R. Gommers, P. Douglas, S. Bergamini, M. Goonasekera, P. H. Jones, and F. Renzoni, Phys. Rev. Lett. 94, 143001 (2005).
  24. R. Gommers, S. Denisov, and F. Renzoni, Phys. Rev. Lett. 96, 240604 (2006).
  25. S. Savel’ev, F. Marchesoni, P. Hänggi, and F. Nori, Europhys. Lett. 67, 179 (2004); Phys. Rev. E 70, 066109 (2004); M. Borromeo, P. Hänggi, and F. Marchesoni, J. Phys.: Condens. Matter 17, S3709 (2005).
  26. L. Morales-Molina, F. G. Mertens, and A. Sánchez, Phys. Rev. E 73, 046605 (2006).
  27. E. Zamora-Sillero, N. R. Quintero, and F. G. Mertens, Phys. Rev. E 74, 046607 (2006).
  28. S. Flach, Y. Zolotaryuk, A. E. Miroshnichenko, and M. V. Fistul, Phys. Rev. Lett. 88, 184101 (2002).
  29. A. L. Sukstanskii and K. I. Primak, Phys. Rev. Lett. 75, 3029 (1995); Yu. S. Kivshar and A. Sánchez, ibid. 77, 582 (1996).
  30. Ri. Chacón and N. R. Quintero, BioSystems 88, 308 (2007); see also F. G. Mertens, L. Morales-Molina, A. R. Bishop, A. Sánchez, and P. Müller, Phys. Rev. E 74, 066602 (2006).
  31. Bernardo Sánchez-Rey et al. (private communication).
  32. M. J. Rice and E. J. Mele, Solid State Commun. 35, 487 (1980).
  33. A. Sánchez and A. R. Bishop, SIAM Rev. 40, 579 (1998).
  34. N. R. Quintero and E. Zamora-Sillero, Physica D 197, 63 (2004); see also S. Cuenda and A. Sánchez, Chaos 15, 023502 (2005); J. Francisco Cao, E. Zamora-Sillero, and N. R. Quintero, Phys. Rev. E 73, 056603 (2006).
  35. N. R. Quintero, A. Sánchez, and F. G. Mertens, Phys. Rev. E 62, R60 (2000).
  36. N. R. Quintero and P. G. Kevrekidis, Phys. Rev. E 64, 056608 (2001).
  37. L. Morales-Molina, N. R. Quintero, A. Sánchez, and F. G. Mertens, Chaos 16, 013117 (2006).
  38. N. R. Quintero, A. Sánchez, and F. G. Mertens, Phys. Rev. E 64, 046601 (2001).
  39. N. R. Quintero, B. Sánchez-Rey, and M. Salerno, Phys. Rev. E 72, 016610 (2005).
  40. A. V. Ustinov, Phys. Lett. A 136, 155 (1989).

Outline

Information

Phys. Rev. E 76, 066601– Published 6 December, 2007
  • Received 3 July 2007

© 2007 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation