Synchronization transitions in Josephson arrays: a puzzle and its resolution

Annalen der Physik (Leipzig)

Volumn 9, Issue 9, 2000, Pages 689-696

  Heath, Ted ^a,b   Wiesenfeld, K ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b GEORGIA TECH RESEARCH INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARRAYS; DEGREES OF FREEDOM (MECHANICS); DYNAMICS; FREQUENCIES; MAGNETIC HYSTERESIS; MATHEMATICAL MODELS; OSCILLATORS (ELECTRONIC); SYNCHRONIZATION;

AVERAGING METHOD; COLLECTIVE DYNAMICS; GLOBALLY COUPLED OSCILLATORS; PHASE MODEL; SYNCHRONIZATION TRANSITIONS;

JOSEPHSON JUNCTION DEVICES;

EID: 0033713992     PISSN: 00033804     EISSN: None     Source Type: Journal    
DOI: 10.1002/1521-3889(200010)9:9/10<689::AID-ANDP689>3.0.CO;2-7     Document Type: Article

References (32)

1. C. A. Hamilton, F. L. Lloyd, K. Chieh, and W.C. Goeke, IEEE Trans. Instrum. Meas. 38 (1989) 314; R. L. Steiner and B. F. Field, ibid. 38 (1989) 296; S. P. Benz, C. A. Hamilton, C. J. Burroughs, T. E. Harvey, and L. A. Christian, Appl. Phys. Lett. 71 (1997) 1866
2. C. A. Hamilton, F. L. Lloyd, K. Chieh, and W.C. Goeke, IEEE Trans. Instrum. Meas. 38 (1989) 314; R. L. Steiner and B. F. Field, ibid. 38 (1989) 296; S. P. Benz, C. A. Hamilton, C. J. Burroughs, T. E. Harvey, and L. A. Christian, Appl. Phys. Lett. 71 (1997) 1866
3. C. A. Hamilton, F. L. Lloyd, K. Chieh, and W.C. Goeke, IEEE Trans. Instrum. Meas. 38 (1989) 314; R. L. Steiner and B. F. Field, ibid. 38 (1989) 296; S. P. Benz, C. A. Hamilton, C. J. Burroughs, T. E. Harvey, and L. A. Christian, Appl. Phys. Lett. 71 (1997) 1866
4. A. K. Jain, K. K. Likharev, J. E. Lukens, and J. E. Sauvageau, Phys. Rep. 109 (1984) 310; S. Han, B. Bi, W. Zhang, and J. E. Lukens, Appl. Phys. Lett. 64 (1994) 1424; P. A. Booi and S. P. Benz, Appl. Phys. Lett. 6 (1996) 3799
5. A. K. Jain, K. K. Likharev, J. E. Lukens, and J. E. Sauvageau, Phys. Rep. 109 (1984) 310; S. Han, B. Bi, W. Zhang, and J. E. Lukens, Appl. Phys. Lett. 64 (1994) 1424; P. A. Booi and S. P. Benz, Appl. Phys. Lett. 6 (1996) 3799
6. A. K. Jain, K. K. Likharev, J. E. Lukens, and J. E. Sauvageau, Phys. Rep. 109 (1984) 310; S. Han, B. Bi, W. Zhang, and J. E. Lukens, Appl. Phys. Lett. 64 (1994) 1424; P. A. Booi and S. P. Benz, Appl. Phys. Lett. 6 (1996) 3799
7. S. Wahlstein, S. Rudner, and T. Claeson, J. Appl. Phys. 49 (1978) 4248; B. Yurke, M. L. Roukes, R. Movshovich, and N. Pargellis, Appl. Phys. Lett. 69 (1996) 3078
8. S. Wahlstein, S. Rudner, and T. Claeson, J. Appl. Phys. 49 (1978) 4248; B. Yurke, M. L. Roukes, R. Movshovich, and N. Pargellis, Appl. Phys. Lett. 69 (1996) 3078
9. I. B. Schwartz and K. Y. Tsang, Phys. Rev. Lett. 73 (1994) 2797; S. Watanabe and S. H. Strogatz, Physica D 74 (1994) 197; S. Watanabe, S. H. Strogatz, H. S. J. van der Zant, and T. P. Orlando, Phys. Rev. Lett. 74 (1995) 379; A. S. Landsberg, Y. Braiman, and K. Wiesenfeld, Phys. Rev. B 52 (1996) 15458
10. I. B. Schwartz and K. Y. Tsang, Phys. Rev. Lett. 73 (1994) 2797; S. Watanabe and S. H. Strogatz, Physica D 74 (1994) 197; S. Watanabe, S. H. Strogatz, H. S. J. van der Zant, and T. P. Orlando, Phys. Rev. Lett. 74 (1995) 379; A. S. Landsberg, Y. Braiman, and K. Wiesenfeld, Phys. Rev. B 52 (1996) 15458
11. I. B. Schwartz and K. Y. Tsang, Phys. Rev. Lett. 73 (1994) 2797; S. Watanabe and S. H. Strogatz, Physica D 74 (1994) 197; S. Watanabe, S. H. Strogatz, H. S. J. van der Zant, and T. P. Orlando, Phys. Rev. Lett. 74 (1995) 379; A. S. Landsberg, Y. Braiman, and K. Wiesenfeld, Phys. Rev. B 52 (1996) 15458
12. I. B. Schwartz and K. Y. Tsang, Phys. Rev. Lett. 73 (1994) 2797; S. Watanabe and S. H. Strogatz, Physica D 74 (1994) 197; S. Watanabe, S. H. Strogatz, H. S. J. van der Zant, and T. P. Orlando, Phys. Rev. Lett. 74 (1995) 379; A. S. Landsberg, Y. Braiman, and K. Wiesenfeld, Phys. Rev. B 52 (1996) 15458
13. S. H. Strogatz and I. Stewart, Sci. Am. 269 (1993) 102; I. I. Blekhman, Synchronization in Science and Technology, ASME Press, New York 1988
14. S. H. Strogatz and I. Stewart, Sci. Am. 269 (1993) 102; I. I. Blekhman, Synchronization in Science and Technology, ASME Press, New York 1988
15. Y. Kuramoto, Lecture Notes in Physics 39 (1975) 420
16. K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. Lett. 76 (1996) 404; Phys. Rev. E 57 (1998) 1563
17. K. Wiesenfeld, P. Colet, and S. H. Strogatz, Phys. Rev. Lett. 76 (1996) 404; Phys. Rev. E 57 (1998) 1563
18. J. W. Swift, S. H. Strogatz, and K. Wiesenfeld, Physica D 55 (1992) 239
19. K. Wiesenfeld and J. W. Swift, Phys. Rev. E 51 (1995) 1020
20. H. Sakaguchi and Y. Kuramoto, Prog. Theor. Phys. 76 (1986) 576
21. P. Colet and K. Wiesenfeld, unpublished.
22. P. Hadley and M. R. Beasley, Appl. Phys. Lett. 50 (1987) 621
23. P. Ashwin and J. W. Swift, J. Nonlinear Sci. 2 (1992) 69
24. D. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, Oxford University Press, Oxford 1977
25. In the absence of disorder, the inphase state results are independent of N (for N > 2). For all practical purposes, the splay phase state results are also independent of N (for large N). Owing to this independence, for convenience we have integrated Eqs. (1), (2) with N = 3 instead of N = 100 as in Ref. [7].
26. L. Fabiny, P. Colet, and R. Roy, Phys. Rev. A 47 (1993) 4287; A. I. Khibnik, Y. Braiman, T. A. B. Kennedy, and K. Wiesenfeld, Physica D 111 (1998) 295
27. L. Fabiny, P. Colet, and R. Roy, Phys. Rev. A 47 (1993) 4287; A. I. Khibnik, Y. Braiman, T. A. B. Kennedy, and K. Wiesenfeld, Physica D 111 (1998) 295
28. S. S. Wang and H. G. Winful, Appl. Phys. Lett. 52 (1988) 1774; H. G. Winful, Phys. Rev. A 46 (1992) 6093
29. S. S. Wang and H. G. Winful, Appl. Phys. Lett. 52 (1988) 1774; H. G. Winful, Phys. Rev. A 46 (1992) 6093
30. R. A. York, IEEE Trans. Microwave Theory Tech. 41 (1993) 1799
31. N. Minorsky, Nonlinear Oscillations, van Nostrand, Princeton 1962
32. T. Heath and K. Wiesenfeld, unpublished.