Experimental realization of directed percolation criticality in turbulent liquid crystals

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 80, Issue 5, 2009, Pages

  Takeuchi, Kazumasa A ^a,b   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

ABSORBING STATE; CRITICAL BEHAVIOR; CRITICAL EXPONENT; DIRECTED PERCOLATION; ELECTROCONVECTION; EXPERIMENTAL TECHNIQUES; FIELD THEORETIC APPROACH; PULSE LASER; SCALING FUNCTIONS; SCALING RELATIONS; STATIC AND DYNAMIC; TURBULENT LIQUIDS; TURBULENT STATE; UNIVERSALITY CLASS;

CRYSTALS; DYNAMIC POSITIONING; LIQUID CRYSTALS; LIQUIDS; NEMATIC LIQUID CRYSTALS; PERCOLATION (SOLID STATE); PULSED LASER APPLICATIONS; SOLVENTS;

PHASE TRANSITIONS;

EID: 71449095379     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.051116     Document Type: Article

References (65)

1. H. Hinrichsen, Adv. Phys. 49, 815 (2000). 10.1080/00018730050198152
2. M. Henkel, H. Hinrichsen, and S. Lübeck, Non-Equilibrium Phase Transitions, Vol. I: Absorbing Phase Transitions (Springer, Dordrecht, 2008).
3. L. Baroni, R. Livi, and A. Torcini, Phys. Rev. E 63, 036226 (2001). 10.1103/PhysRevE.63.036226
4. V. Ahlers and A. Pikovsky, Phys. Rev. Lett. 88, 254101 (2002). 10.1103/PhysRevLett.88.254101
5. R. Dickman, M. A. Muñoz, A. Vespignani, and S. Zapperi, Braz. J. Phys. 30, 27 (2000).
6. Y. Pomeau, Physica D 23, 3 (1986). 10.1016/0167-2789(86)90104-1
7. S. V. Buldyrev, A. -L. Barabási, F. Caserta, S. Havlin, H. E. Stanley, and T. Vicsek, Phys. Rev. A 45, R8313 (1992). 10.1103/PhysRevA.45.R8313
8. F. Ginelli, V. Ahlers, R. Livi, D. Mukamel, A. Pikovsky, A. Politi, and A. Torcini, Phys. Rev. E 68, 065102 (R) (2003). 10.1103/PhysRevE.68.065102
9. H. K. Janssen, Z. Phys. B: Condens. Matter 42, 151 (1981). 10.1007/BF01319549
10. P. Grassberger, Z. Phys. B: Condens. Matter 47, 365 (1982). 10.1007/BF01313803
11. S. Ciliberto and P. Bigazzi, Phys. Rev. Lett. 60, 286 (1988). 10.1103/PhysRevLett.60.286
12. F. Daviaud, M. Bonetti, and M. Dubois, Phys. Rev. A 42, 3388 (1990). 10.1103/PhysRevA.42.3388
13. S. Michalland, M. Rabaud, and Y. Couder, Europhys. Lett. 22, 17 (1993). 10.1209/0295-5075/22/1/004
14. H. Willaime, O. Cardoso, and P. Tabeling, Phys. Rev. E 48, 288 (1993). 10.1103/PhysRevE.48.288
15. M. M. Degen, I. Mutabazi, and C. D. Andereck, Phys. Rev. E 53, 3495 (1996). 10.1103/PhysRevE.53.3495
16. P. W. Colovas and C. D. Andereck, Phys. Rev. E 55, 2736 (1997). 10.1103/PhysRevE.55.2736
17. H. Téphany, J. Nahmias, and J. A. M. S. Duarte, Physica A 242, 57 (1997). 10.1016/S0378-4371(97)00202-1
18. A. Daerr and S. Douady, Nature (London) 399, 241 (1999). 10.1038/20392
19. A. Cros and P. Le Gal, Phys. Fluids 14, 3755 (2002). 10.1063/1.1508796
20. P. Rupp, R. Richter, and I. Rehberg, Phys. Rev. E 67, 036209 (2003). 10.1103/PhysRevE.67.036209
21. V. Lepiller, A. Prigent, F. Dumouchel, and I. Mutabazi, Phys. Fluids 19, 054101 (2007). 10.1063/1.2721756
22. C. Pirat, A. Naso, J.-L. Meunier, P. Maïssa, and C. Mathis, Phys. Rev. Lett. 94, 134502 (2005). 10.1103/PhysRevLett.94.134502
23. H. Hinrichsen, A. Jiménez-Dalmaroni, Y. Rozov, and E. Domany, Phys. Rev. Lett. 83, 4999 (1999). 10.1103/PhysRevLett.83.4999
24. I. Jensen, J. Phys. A 32, 5233 (1999). 10.1088/0305-4470/32/28/304
25. P. Grassberger and Y. C. Zhang, Physica A 224, 169 (1996). 10.1016/0378-4371(95)00321-5
26. C. A. Voigt and R. M. Ziff, Phys. Rev. E 56, R6241 (1997). 10.1103/PhysRevE.56.R6241
27. Scaling relations used for μ and μ[Eq.4] may be slightly violated in the order of 10-2 due to some intermittency effects in DP.
28. P. Grassberger, in Nonlinearities in Complex Systems, edited by, S. Puri, and, S. Dattagupta, (Narosa, New Delhi, 1997), p. 61.
29. K. A. Takeuchi, M. Kuroda, H. Chaté, and M. Sano, Phys. Rev. Lett. 99, 234503 (2007). 10.1103/PhysRevLett.99.234503
30. E. Dubois-Violette, P. G. de Gennes, and O. Parodi, J. Phys. (Paris) 32, 305 (1971). 10.1051/jphys:01971003204030500
31. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford University Press, Oxford, 1993).
32. S. Kai, W. Zimmermann, M. Andoh, and N. Chizumi, J. Phys. Soc. Jpn. 58, 3449 (1989) 10.1143/JPSJ.58.3449
33. S. Kai, W. Zimmermann, M. Andoh, and N. Chizumi, Phys. Rev. Lett. 64, 1111 (1990). 10.1103/PhysRevLett.64.1111
34. J. Nehring, Phys. Rev. A 7, 1737 (1973). Note that topological defects observed there are obtained by switching off the applied voltage from DSM2 (see also Ref.). 10.1103/PhysRevA.7.1737
35. See the supplementary material to Ref., EPAPS Document No. E-PRLTAO-99-056749, for movies S1 and S2. This material may be accessed from the reference section of the online article, or via the EPAPS homepage http://www.aip.org/pubservs/epaps.html.
36. The deviation from criticality is measured in terms of V2 instead of V by convention since the dielectric torque that drives the electroconvection is proportional to V2. The results do not change if ρ̄ ∼ (V- Vc) β is used.
37. Confidence intervals of the critical exponents given in the present paper are determined as follows. (a) For values estimated from a finite number of independent data points [Eqs.], 95% confidence intervals in the sense of student's t are provided. (b) For values estimated from a continuous curve [Eqs.], range of fitting is varied within reasonable regions, and both the dependence on fitting regions and the confidence interval from each fitting are incorporated in the final estimate of error. When the threshold is simultaneously determined [Eqs.], uncertainty in the estimate of the threshold is also considered. (c) For values determined from data collapsing [Eq.], we provide the range of values of the exponent with which no systematic shift in data collapsing is seen. (d) For values derived from an equation, the range of error is estimated by the law of propagation of error. (e) For values cited from literature, we simply borrow the range of errors provided by the corresponding authors.
38. G. Strangi, C. Versace, N. Scaramuzza, D. E. Lucchetta, V. Carbone, and R. Bartolino, Phys. Rev. E 59, 5523 (1999). 10.1103/PhysRevE.59.5523
39. T. Nagaya, T. Takeda, and H. Orihara, J. Phys. Soc. Jpn. 68, 3848 (1999). 10.1143/JPSJ.68.3848
40. This correction was not made in Ref.. Although algebraic decays in the distributions are not much influenced, this correction is significant to have exponential decays in sufficiently large scales to estimate the correlation length and time.
41. B. Hede, J. Kertész, and T. Vicsek, J. Stat. Phys. 64, 829 (1991). 10.1007/BF01048318
42. M. Henkel and R. Peschanski, Nucl. Phys. B 390, 637 (1993). 10.1016/0550-3213(93)90492-8
43. T. E. Harris, Ann. Probab. 2, 969 (1974). 10.1214/aop/1176996493
44. Note that parallel and perpendicular directions (x and y in our notation) in the second reference in Ref. are opposite.
45. M. Henkel, J. Phys.: Condens. Matter 19, 065101 (2007). 10.1088/0953-8984/19/6/065101
46. F. Baumann and A. Gambassi, J. Stat. Mech.: Theory Exp. (2007), P01002. 10.1088/1742-5468/2007/01/P01002
47. S. N. Majumdar, Curr. Sci. 77, 370 (1999), and references therein.
48. H. Hinrichsen and H. M. Koduvely, Eur. Phys. J. B 5, 257 (1998). 10.1007/s100510050443
49. E. V. Albano and M. A. Muñoz, Phys. Rev. E 63, 031104 (2001). 10.1103/PhysRevE.63.031104
50. G. I. Menon, S. Sinha, and P. Ray, Europhys. Lett. 61, 27 (2003). 10.1209/epl/i2003-00240-x
51. J. Fuchs, J. Schelter, F. Ginelli, and H. Hinrichsen, J. Stat. Mech.: Theory Exp. (2008), P04015. 10.1088/1742-5468/2008/04/P04015
52. P. Grassberger, J. Stat. Mech.: Theory Exp. (2009), P08021. 10.1088/1742-5468/2009/08/P08021
53. K. A. Takeuchi, Phys. Rev. E 77, 030103 (R) (2008). 10.1103/PhysRevE.77. 030103
54. M. Mizuno and T. Shinoda, Mol. Cryst. Liq. Cryst. 41, 155 (1978). 10.1080/00268947808070290
55. M. Mizuno and T. Shinoda, Mol. Cryst. Liq. Cryst. 69, 103 (1981). 10.1080/00268948108072691
56. J. Hooyberghs, F. Iglói, and C. Vanderzande, Phys. Rev. Lett. 90, 100601 (2003). 10.1103/PhysRevLett.90.100601
57. J. A. Hoyos, Phys. Rev. E 78, 032101 (2008). 10.1103/PhysRevE.78.032101
58. T. Vojta and M. Dickison, Phys. Rev. E 72, 036126 (2005) 10.1103/PhysRevE.72.036126
59. T. Vojta, A. Farquhar, and J. Mast, Phys. Rev. E 79, 011111 (2009). 10.1103/PhysRevE.79.011111
60. C. J. Neugebauer, S. V. Fallert, and S. N. Taraskin, Phys. Rev. E 74, 040101 (R) (2006) 10.1103/PhysRevE.74.040101
61. S. V. Fallert and S. N. Taraskin, Phys. Rev. E 79, 042105 (2009). 10.1103/PhysRevE.79.042105
62. H. Chaté and P. Manneville, Physica D 32, 409 (1988). 10.1016/0167-2789(88)90065-6
63. H. Chaté (unpublished).
64. L. Corté, P. M. Chaikin, J. P. Gollub, and D. J. Pine, Nat. Phys. 4, 420 (2008). 10.1038/nphys891
65. N. Mangan, C. Reichhardt, and C. J. Olson Reichhardt, Phys. Rev. Lett. 100, 187002 (2008). 10.1103/PhysRevLett.100.187002