Directed percolation criticality in turbulent liquid crystals

Physical Review Letters

Volumn 99, Issue 23, 2007, Pages

  Takeuchi, Kazumasa A ^a   Kuroda, Masafumi ^a   Chaté, Hugues ^b   Sano, Masaki ^a  

^a UNIVERSITY OF TOKYO   (Japan)

^b SERVICE DE PHYSIQUE DE L ETAT CONDENSÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ABSORPTION; ELECTROHYDRODYNAMICS; PERCOLATION (SOLID STATE); PHASE TRANSITIONS;

DIRECTED PERCOLATION CRITICALITY; SPATIOTEMPORAL INTERMITTENCY; TURBULENT LIQUID CRYSTALS;

NEMATIC LIQUID CRYSTALS;

EID: 36849054725     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.99.234503     Document Type: Article

References (29)

1. H. Hinrichsen, Adv. Phys. 49, 815 (2000). ADPHAH 0001-8732 10.1080/00018730050198152
2. V. Ahlers and A. Pikovsky, Phys. Rev. Lett. 88, 254101 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.88.254101
3. R. Dickman, M.A. Muñoz, A. Vespignani, and S. Zapperi, Braz. J. Phys. 30, 27 (2000). BJPHE6 0103-9733
4. F. Ginelli, Phys. Rev. E 68, 065102(R) (2003). PLEEE8 1063-651X 10.1103/PhysRevE.68.065102
5. H.K. Janssen, Z. Phys. B ZPCMDN 0722-3277 42, 151 (1981). 10.1007/BF01319549
6. P. Grassberger, Z. Phys. B ZPCMDN 0722-3277 47, 365 (1982). 10.1007/BF01313803
7. S. Ciliberto and P. Bigazzi, Phys. Rev. Lett. 60, 286 (1988); PRLTAO 0031-9007 10.1103/PhysRevLett.60.286
8. F. Daviaud, M. Bonetti, and M. Dubois, Phys. Rev. A 42, 3388 (1990); PLRAAN 1050-2947 10.1103/PhysRevA.42.3388
9. S.V. Buldyrev, Phys. Rev. A 45, R8313 (1992); PLRAAN 1050-2947 10.1103/PhysRevA.45.R8313
10. S. Michalland, M. Rabaud, and Y. Couder, Europhys. Lett. 22, 17 (1993); EULEEJ 0295-5075 10.1209/0295-5075/22/1/004
11. H. Willaime, O. Cardoso, and P. Tabeling, Phys. Rev. E 48, 288 (1993); PLEEE8 1063-651X 10.1103/PhysRevE.48.288
12. M.M. Degen, I. Mutabazi, and C.D. Andereck, Phys. Rev. E 53, 3495 (1996); PLEEE8 1063-651X 10.1103/PhysRevE.53.3495
13. P.W. Colovas and C.D. Andereck, Phys. Rev. E 55, 2736 (1997); PLEEE8 1063-651X 10.1103/PhysRevE.55.2736
14. H. Téphany, J. Nahmias, and J.A.M.S. Duarte, Physica (Amsterdam) 242A, 57 (1997); PHYADX 0378-4371 10.1016/S0378-4371(97)00202-1
15. A. Daerr and S. Douady, Nature (London) NATUAS 0028-0836 399, 241 (1999); 10.1038/20392
16. P. Rupp, R. Richter, and I. Rehberg, Phys. Rev. E 67, 036209 (2003); PLEEE8 1063-651X 10.1103/PhysRevE.67.036209
17. C. Pirat, A. Naso, J.-L. Meunier, P. Maïssa, and C. Mathis, Phys. Rev. Lett. 94, 134502 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.94.134502
18. See EPAPS Document No. E-PRLTAO-99-056749 for the binarization algorithm, Movies S1 and S2, and Table S1. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
19. P. Grassberger, in Nonlinearities in Complex Systems, edited by, S. Puri, and, S. Dattagupta, (Narosa, New Delhi, 1997), p. 61;
20. H. Hinrichsen, Braz. J. Phys. 30, 69 (2000). BJPHE6 0103-9733 10.1590/S0103-97332000000100007
21. J. Hooyberghs, F. Iglói, and C. Vanderzande, Phys. Rev. Lett. 90, 100601 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.90.100601
22. P.G. de Gennes and J. Prost, The Physics of Liquid Crystals (Oxford University Press, Oxford, 1993), 2nd ed.
23. S. Kai, W. Zimmermann, M. Andoh, and N. Chizumi, J. Phys. Soc. Jpn. 58, 3449 (1989); JUPSAU 0031-9015 10.1143/JPSJ.58.3449
24. S. Kai W. Zimmermann M. Andoh N. Chizumi Phys. Rev. Lett. 64, 1111 (1990). PRLTAO 0031-9007 10.1103/PhysRevLett.64.1111
25. Y. Pomeau, Physica (Amsterdam) 23D, 3 (1986). PDNPDT 0167-2789 10.1016/0167-2789(86)90104-1
26. P. Grassberger and Y.C. Zhang, Physica (Amsterdam) 224A, 169 (1996); PHYADX 0378-4371 10.1016/0378-4371(95)00321-5
27. C.A. Voigt and R.M. Ziff, Phys. Rev. E 56, R6241 (1997); PLEEE8 1063-651X 10.1103/PhysRevE.56.R6241
28. for a useful list of the exponents, see M.A. Muñoz, R. Dickman, A. Vespignani, and S. Zapperi, Phys. Rev. E 59, 6175 (1999). PLEEE8 1063-651X 10.1103/PhysRevE.59.6175
29. Kai et al. reported hysteresis of the DSM1-DSM2 transition showing algebraic dependence on the ramp rate of V. This may seem in contradiction with the DP framework, but this scaling of hysteresis loops turns out to be one aspect of DP criticality under the presence of a tiny residual probability for spontaneous nucleation of DSM2 patches. This is detailed in K.A. Takeuchi, arXiv:0706.4152.