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Noise-induced threshold shift and pattern formation in electroconvection by controlling characteristic time scales

Department of Mechanical Information Science and Technology, Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, Fukuoka 820-8502, Japan

Phys. Rev. E 84, 025302(R) – Published 26 August, 2011

DOI: https://doi.org/10.1103/PhysRevE.84.025302

Abstract

We report external noise-induced threshold shift and pattern formation in ac-driven electroconvection (EC) in nematic liquid crystals. We investigate the noise intensity dependence of the threshold and determine the relationship $f_{c}^{*} = h f_{c d}^{a}$ (α ∼ 1.4, $h$ ∼ 0.1) between the characteristic cutoff frequency ( $f_{c}^{*}$ ) of the noise and the characteristic ac frequency ( $f_{c d}$ ) of EC. For $f_{c} > f_{c}^{*}$ , the noise contributes to stabilizing EC (i.e., upward threshold shift), whereas for $f_{c} < f_{c}^{*}$ , it contributes to destabilizing EC (i.e., downward threshold shift). For $f_{c} = f_{c}^{*}$ , the noise makes no contribution to the threshold shift. However, the characteristic wavelength of EC strongly depends on the noise intensity but not on $f_{c}$ .

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W. Horsthemke and R. Lefever, Noise-Induced Transitions (Springer, Berlin, 1984).
J. Garcia-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (Springer, New York, 1999).
R. Benzi, G. Parishi, A. Sutera, and A. Vulpiani, Tellus 34, 10 (1982).
F. Moss, D. Pierson, and D. O’Gorman, Int. J. Bifurcation Chaos Appl. Sci. Eng 4, 1383 (1994); L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998).
S. Kai, T. Kai, M. Takata, and K. Hirakawa, J. Phys. Soc. Jpn. 47, 1379 (1979); H. Brand and A. Schenzle, ibid. 48, 1382 (1980).
M. W. Evans, M. Ferrario, and P. Grigolini, Physica A 111, 255 (1982); N. Hashimoto, J. Phys. Soc. Jpn. 75, 084002 (2006).
J. M. R. Parrondo, C. van den Broeck, J. Buceta, and F. J. de la Rubia, Physica A 224, 153 (1996).
R. Kawai, X. Sailer, L. Schimansky-Geier, and C. Van den Broeck, Phys. Rev. E 69, 051104 (2004); F. Sagués, J. M. Sancho, and J. García-Ojalvo, Rev. Mod. Phys. 79, 829 (2007).
D. F. Russell, A. Tucker, B. A. Wettering, A. B. Neiman, L. A. Wilkens, and F. Moss, Fluctuation Noise Lett. 1, L71 (2001); J. J. Collins, T. T. Imhoff, and P. Grigg, Phys. Rev. E 56, 923 (1997).
L. B. Kish, Y. Li, J. L. Solis, W. H. Marlow, R. Vajtai, C. G. Granqvist, V. Lantto, J. M. Smulko, and G. Schmera, IEEE Sensors J. 5, 671 (2005).
R. J. Windle, S. A. Wood, N. Shanks, S. L. Lightman, and C. D. Ingram, Endocrinology, 139, 443 (1998).
U. Will and E. Berg, Neurosci. Lett. 424, 55 (2007).
T. Mori and S. Kai, Phys. Rev. Lett. 88, 218101 (2002).
See recent reviews and references therein, for example, T. John, U. Behn, J. Heuer, and R. Stannarius, Phys. Rev. E 71, 056307 (2005); A. Buka, N. Eber, W. Pesch, and L. Kramer, Phys. Rep. 448, 115 (2007).
R. Williams, J. Chem. Phys. 39, 384 (1963); E. F. Carr, Mol. Cryst. Liq. Cryst. 7, 256 (1969); W. Helfrich, J. Chem. Phys. 51, 4092 (1969).
T. Kawakubo, A. Yanagita, and S. Kabashima, J. Phys. Soc. Jpn. 50, 1451 (1981).
H. R. Brand, S. Kai, and S. Wakabayashi, Phys. Rev. Lett. 54, 555 (1985).
U. Behn and R. Müller, Phys. Lett. A 113, 85 (1985); R. Müller and U. Behn, Z. Phys. B 69, 185 (1987).
S. Kai, H. Fukunaga, and H. Brand, J. Phys. Soc. Jpn. 56, 3759 (1987); J. Stat. Phys. 54, 1133 (1989); S. Kai, M. Imasaki, S. Yamaguchi, and F. Sagues: Research of Pattern Formation, edited by R. Takaki (KTK, Tokyo, 1994), p. 343; A. Becker and L. Kramer, Phys. Rev. Lett. 73, 955 (1994); H. Amm, U. Behn, T. John, and R. Stannarius, Mol. Cryst. Liq. Cryst. 304, 525 (1997).
U. Behn, A. Lange, and T. John, Phys. Rev. E 58, 2047 (1998); T. John, R. Stannarius, and U. Behn, Phys. Rev. Lett. 83, 749 (1999); T. John, U. Behn, and R. Stannarius, Phys. Rev. E 65, 046229 (2002).
J.-H. Huh, J. Phys. Soc. Jpn. 76, 033001 (2007); J.-H. Huh and S. Kai, ibid. 77, 083601 (2008); 78, 043601 (2009); J.-H. Huh, A. Kuribayashi, and S. Kai, ibid. 78, 083601 (2009); Phys. Rev. E 80, 066304 (2009); J.-H. Huh, J. Phys. Soc. Jpn. 79, 123602 (2010).
D. Nozaki and Y. Yamamoto, Phys. Lett. A 243, 281 (1998).
U. Rascher and L. Nedbal, Curr. Opin. Plant Biol. 9, 671 (2006); C. Brunet and J. Lavaud, J. Plankton Res. 32, 1609 (2010).
A. Guderian, G. Dechert, K.-P. Zeyer, and F. W. Schneider, J. Phys. Chem. 100, 4437 (1996).
J.-H. Huh, Y. Hidaka, A. G. Rossberg, and S. Kai, Phys. Rev. E 61, 2769 (2000); J.-H. Huh, Y. Yusuf, Y. Hidaka, and S. Kai, ibid. 66, 031705 (2002).

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Noise-induced threshold shift and pattern formation in electroconvection by controlling characteristic time scales

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