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Mode-Locking in Driven Disordered Systems as a Boundary-Value Problem

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Abstract

We study mode-locking in disordered media as a boundary-value problem. Focusing on the simplest class of mode-locking models that consists of a single driven overdamped degree-of-freedom, we develop an analytical method to obtain the shape of the Arnol’d tongues in the regime of low AC-driving amplitude or high AC-driving frequency. The method is exact for a scalloped pinning potential and easily adapted to other pinning potentials. It is complementary to the analysis based on the well-known Shapiro’s argument that holds in the perturbative regime of large driving amplitudes or low driving frequency where the effect of pinning is weak.

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References

  1. Cross, F.R., Siggia, E.D.: Phys. Rev. E 72, 021910 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  2. Calabrese, R.L., de Schutter, E.: Trends Neurosci. 15, 439 (1992)

    Article  Google Scholar 

  3. Coombes, S., Bressloff, P.C.: Phys. Rev. E 60, 2086 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  4. Mureithi, N.W., Masaki, R., Kaneko, S., Nakamura, T.: J. Press. Vessel Technol. 363, 19 (1998)

    Google Scholar 

  5. Andreotti, B.: Phys. Rev. Lett. 93, 238001 (2004)

    Article  ADS  Google Scholar 

  6. Haus, H.A.: IEEE J. Sel. Top. Quantum. Electron. 6, 1173 (2000)

    Article  Google Scholar 

  7. Gat, O., Gordon, A., Fischer, B.: New J. Phys. 7, 151 (2005)

    Article  ADS  Google Scholar 

  8. Moores, J.D.: Opt. Lett. 26, 87 (2001)

    Article  ADS  Google Scholar 

  9. Das, S., Datta, S., Sahdev, D.: Phys. D 101, 333 (1997)

    Article  MATH  Google Scholar 

  10. Karapetrov, G., Fedor, J., Iavarone, M., Rosemann, D., Kwok, W.K.: Phys. Rev. Lett. 95, 167002 (2005)

    Article  ADS  Google Scholar 

  11. Kokubo, N., Besseling, R., Vinokur, V.M., Kes, P.H.: Phys. Rev. Lett. 88, 247004 (2002)

    Article  ADS  Google Scholar 

  12. Besseling, R., Benningshof, O., Kokubo, N., Kes, P.H.: Phys. C 408, 581 (2004)

    Article  ADS  Google Scholar 

  13. Lübbig, H., Luther, H.: Rev. Phys. Appl. 9, 29 (1974)

    Google Scholar 

  14. Grüner, G.: Rev. Mod. Phys. 60, 1129 (1988)

    Article  ADS  Google Scholar 

  15. Fukuyama, H., Lee, P.A.: Phys. Rev. B 17, 535 (1978)

    Article  ADS  Google Scholar 

  16. Lee, P.A., Rice, T.M.: Phys. Rev. B 19, 3970 (1979)

    Article  ADS  Google Scholar 

  17. Kolton, A.B., Dominguez, D., Gronbech-Jensen, N.: Phys. Rev. Lett. 86, 4112 (2001)

    Article  ADS  Google Scholar 

  18. Fisher, D.S.: Phys. Rev. Lett. 50, 1486 (1983)

    Article  ADS  Google Scholar 

  19. Fisher, D.S.: Phys. Rev. B 31, 1396 (1985)

    Article  ADS  Google Scholar 

  20. Alstrom, P., Ritala, R.K.: Phys. Rev. A 35, 300 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  21. Pradhan, G.R., Chatterjee, N., Gupte, N.: Phys. Rev. E 65, 046227 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  22. Waldrum, J.R., Wu, P.H.: J. Low Temp. Phys. 47, 363 (1982)

    Article  ADS  Google Scholar 

  23. Renne, M.J., Polder, D.J.: Rev. Phys. Appl. 9, 25 (1974)

    Google Scholar 

  24. Wiersig, J., Anh, K.H.: Phys. E 12, 256 (2002)

    Article  Google Scholar 

  25. Jensen, M.H., Bak, P., Bohr, T.: Phys. Rev. A 30, 1960 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  26. Halsey, T.C., Jensen, M.H., Kadanoff, L.P., Procaccia, I., Shraiman, B.I.: Phys. Rev. A 33, 1141 (1986)

    Article  MathSciNet  ADS  Google Scholar 

  27. Biham, O., Mukamel, D.: Phys. Rev. A 39, 5326 (1989)

    Article  ADS  Google Scholar 

  28. Wenzel, W., Biham, O., Jayaprakash, C.: Phys. Rev. A 43, 6550 (1991)

    Article  ADS  Google Scholar 

  29. Shapiro, S., Janus, A., Holly, S.: Rev. Mod. Phys. 36, 223 (1964)

    Article  ADS  Google Scholar 

  30. Thorne, R.E., Tucker, J.R., Bardeen, J., Brown, S.E., Gruner, G.: Phys. Rev. B 33, 7342 (1986)

    Article  ADS  Google Scholar 

  31. Azbel, M.Y., Bak, P.: Phys. Rev. B 30, 3722 (1984)

    Article  ADS  Google Scholar 

  32. MacKay, R.S.: J. Nonlinear Sci. 4, 301 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Northwestern University, Evanston, IL, 60208, USA

    William Kung

  2. Department of Physics, Syracuse University, Syracuse, NY, 13244, USA

    M. Cristina Marchetti

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  1. William Kung
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  2. M. Cristina Marchetti
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Correspondence to William Kung.

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Kung, W., Marchetti, M.C. Mode-Locking in Driven Disordered Systems as a Boundary-Value Problem. J Stat Phys 132, 945–955 (2008). https://doi.org/10.1007/s10955-008-9573-4

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  • DOI: https://doi.org/10.1007/s10955-008-9573-4

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