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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access February 26, 2011

Pattern selection processes and noise induced pattern-forming transitions in periodic systems with transient dynamics

Dmytro Kharchenko, Vasyl Kharchenko and Iryna Lysenko
From the journal Open Physics

Abstract

We apply the phase field crystal method for nonequilibrium patterning to stochastic systems with an external source in which transient dynamics is essential. Considering a prototype model for a one-component periodic system subjected to external influence kind of irradiation we study properties of pattern selection processes and external noise induced pattern-forming transitions. These processes are examined by means of the structure function dynamics analysis. Nonequilibrium pattern-forming transitions are analyzed numerically.

[1] G. Ahlers, D.S. Cannell, V. Steinberg, Phys. Rev. Lett. 54, 1373 (1985) http://dx.doi.org/10.1103/PhysRevLett.54.137310.1103/PhysRevLett.54.1373Search in Google Scholar PubMed

[2] C.W. Meyer, G. Ahlers, D.S. Cannell, Phys. Rev. A 44, 2514 (1991) http://dx.doi.org/10.1103/PhysRevA.44.251410.1103/PhysRevA.44.2514Search in Google Scholar PubMed

[3] S.W. Morris, E. Bodenshaltz, D.S. Cannell, A. Ahlers, Phys. Rev. Lett. 71, 2026 (1993) http://dx.doi.org/10.1103/PhysRevLett.71.202610.1103/PhysRevLett.71.2026Search in Google Scholar PubMed

[4] A.S. Mikhailov, K. Showalter, Phys. Rep. 425, 79 (2006) http://dx.doi.org/10.1016/j.physrep.2005.11.00310.1016/j.physrep.2005.11.003Search in Google Scholar

[5] H. Katsuragi, Europhys. Lett. 73, 793 (2006) http://dx.doi.org/10.1209/epl/i2005-10464-810.1209/epl/i2005-10464-8Search in Google Scholar

[6] F. Sagues, J.M. Sancho, J. Garcia-Ojalvo, Rev. Mod. Phys. 79, 829 (2007) http://dx.doi.org/10.1103/RevModPhys.79.82910.1103/RevModPhys.79.829Search in Google Scholar

[7] B. Lindner, J. Garcia-Ojalvo, A. Neiman, L. Shimansky-Geier, Phys. Rep. 392, 321 (2004) http://dx.doi.org/10.1016/j.physrep.2003.10.01510.1016/j.physrep.2003.10.015Search in Google Scholar

[8] G. Stegemann, A.G. Balanov, E. Schöll, Phys. Rev. E 71, 016221 (2005) http://dx.doi.org/10.1103/PhysRevE.71.01622110.1103/PhysRevE.71.016221Search in Google Scholar PubMed

[9] S.E. Mangioni, H.S. Wio, Phys. Rev. E 71, 056203 (2005) http://dx.doi.org/10.1103/PhysRevE.71.05620310.1103/PhysRevE.71.056203Search in Google Scholar PubMed

[10] D. Kharchenko, S.V. Kokhan, A.V. Dvornichenko, Physica D 238, 2251 (2009) http://dx.doi.org/10.1016/j.physd.2008.12.00510.1016/j.physd.2008.12.005Search in Google Scholar

[11] D.O. Kharchenko, S.V. Kokhan, A.V. Dvornichenko, Metallofiz. Nov. Tekh.+ 31, 23 (2009) Search in Google Scholar

[12] V. Kharchenko, Physica A 388, 268 (2009) http://dx.doi.org/10.1016/j.physa.2008.10.01610.1016/j.physa.2008.10.016Search in Google Scholar

[13] S.E. Mangioni, Physica A 389, 1799 (2010) http://dx.doi.org/10.1016/j.physa.2010.01.01110.1016/j.physa.2010.01.011Search in Google Scholar

[14] R.A. Enrique, P. Bellon, Phys. Rev. B 63, 134111 (2001) http://dx.doi.org/10.1103/PhysRevB.63.13411110.1103/PhysRevB.63.134111Search in Google Scholar

[15] J. Ye, P. Bellon, Phys. Rev. B 70, 094104 (2004) http://dx.doi.org/10.1103/PhysRevB.70.09410410.1103/PhysRevB.70.094104Search in Google Scholar

[16] J. Lian, W. Zhou, Q.M. Wei et al., Appl. Phys. Lett. 88, 093112 (2006) http://dx.doi.org/10.1063/1.218120310.1063/1.2181203Search in Google Scholar

[17] R. Kree, T. Yasseri, A.K. Hartmann, Nucl. Instrum. Meth. B 267, 1407 (2009) http://dx.doi.org/10.1016/j.nimb.2009.01.06410.1016/j.nimb.2009.01.064Search in Google Scholar

[18] K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. Lett. 88, 245701 (2002) http://dx.doi.org/10.1103/PhysRevLett.88.24570110.1103/PhysRevLett.88.245701Search in Google Scholar PubMed

[19] A. Jaatinen, C.V. Achim, K.R. Elder et al., Phys. Rev. E 80, 031602 (2009) http://dx.doi.org/10.1103/PhysRevE.80.03160210.1103/PhysRevE.80.031602Search in Google Scholar PubMed

[20] J. Berry, M. Garnt, K.R. Elder, Phys. Rev. E 73, 031609 (2006) http://dx.doi.org/10.1103/PhysRevE.73.03160910.1103/PhysRevE.73.031609Search in Google Scholar PubMed

[21] J. Swift, P.C. Hohenberg, Phys. Rev. A 15, 319 (1977) http://dx.doi.org/10.1103/PhysRevA.15.31910.1103/PhysRevA.15.319Search in Google Scholar

[22] P. Stefanovich, M. Haataja, N. Provatas, Phys. Rev. Lett. 96, 225504 (2006) http://dx.doi.org/10.1103/PhysRevLett.96.22550410.1103/PhysRevLett.96.225504Search in Google Scholar

[23] W. Horsthemke, R. Lefever, Noise-Induced Transitions (Springer-Verlag, Berlin, 1984) 10.1007/978-3-642-70196-2_23Search in Google Scholar

[24] K.R. Elder, J. Vinals, M. Grant, Phys. Rev. Lett. 68, 3024 (1992) http://dx.doi.org/10.1103/PhysRevLett.68.302410.1103/PhysRevLett.68.3024Search in Google Scholar

[25] J. Garcia-Ojalvo, A. Hernandez-Machado, J.M. Sancho, Phys. Rev. Lett. 71, 1542 (1993) http://dx.doi.org/10.1103/PhysRevLett.71.154210.1103/PhysRevLett.71.1542Search in Google Scholar

[26] J. Garcia-Ojalvo, J.M. Sancho, Int. J. Bifurcat. Chaos 4, 1337 (1994) http://dx.doi.org/10.1142/S021812749400103910.1142/S0218127494001039Search in Google Scholar

[27] J. Garcia-Ojalvo, J.M. Sancho, Phys. Rev. E 53, 5680 (1996) http://dx.doi.org/10.1103/PhysRevE.53.568010.1103/PhysRevE.53.5680Search in Google Scholar

[28] J.M.R. Parrondo, C. Van der Broeck, J. Buceta et al., Physica A 224, 153 (1996) http://dx.doi.org/10.1016/0378-4371(95)00350-910.1016/0378-4371(95)00350-9Search in Google Scholar

[29] A.A. Zaikin, L. Shimansky-Geier, Phys. Rev. E 58, 4355 (1998) http://dx.doi.org/10.1103/PhysRevE.58.435510.1103/PhysRevE.58.4355Search in Google Scholar

[30] K. Wood, J. Buceta, K. Lindenberg, Phys. Rev. E 73, 022101 (2006) http://dx.doi.org/10.1103/PhysRevE.73.02210110.1103/PhysRevE.73.022101Search in Google Scholar PubMed

[31] J.A.P. Ramos, E. Granato, S.C. Ying et al., Phys. Rev. E 81, 011121 (2010) http://dx.doi.org/10.1103/PhysRevE.81.01112110.1103/PhysRevE.81.011121Search in Google Scholar PubMed

[32] G. Martin, Phys. Rev. B 30, 1424 (1984) http://dx.doi.org/10.1103/PhysRevB.30.142410.1103/PhysRevB.30.1424Search in Google Scholar

[33] R. Enrique, P. Bellon, Phys. Rev. Lett. 84, 2885 (2000) http://dx.doi.org/10.1103/PhysRevLett.84.288510.1103/PhysRevLett.84.2885Search in Google Scholar PubMed

[34] R. Enrique, P. Bellon, Phys. Rev. B 70, 224106 (2004) http://dx.doi.org/10.1103/PhysRevB.70.22410610.1103/PhysRevB.70.224106Search in Google Scholar

[35] C.W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, Heidelberg, New-York, Tokyo, 1985) Search in Google Scholar

[36] V.I. Dubinko, A.V. Tur, V.V. Yanovsky, Radiat. Eff. Defect. S. 112, 233 (1990) http://dx.doi.org/10.1080/1042015900821304910.1080/10420159008213049Search in Google Scholar

[37] D. Jou, J. Casas-Vazquez, G. Lebon, Extended Irreversible Thermodynamics, 4th ed. (Springer, Berlin, 2010) http://dx.doi.org/10.1007/978-90-481-3074-010.1007/978-90-481-3074-0Search in Google Scholar

[38] D.O. Kharchenko, A.V. Dvornichenko, Physica A 387, 5342 (2008) http://dx.doi.org/10.1016/j.physa.2008.05.04110.1016/j.physa.2008.05.041Search in Google Scholar

[39] P.K. Galenko, D. Kharchenko, I. Lysenko, Physica A 389, 3443 (2010) http://dx.doi.org/10.1016/j.physa.2010.05.00210.1016/j.physa.2010.05.002Search in Google Scholar

[40] L.D. Landau, E.M. Lifshitz, Statistical Physics, Part I, Vol.5, 3rd ed. (Butterworth-Heinemann, Oxford, 1980) Search in Google Scholar

[41] J. Garcia-Ojalvo, J.M. Sancho, Noise in Spatially Extended Systems (Springer, New York, 1999) http://dx.doi.org/10.1007/978-1-4612-1536-310.1007/978-1-4612-1536-3Search in Google Scholar

[42] P. Galenko, D. Jou, Phys. Rev. E 71, 046125 (2005) http://dx.doi.org/10.1103/PhysRevE.71.04612510.1103/PhysRevE.71.046125Search in Google Scholar PubMed

[43] A.A. Ponomarov, V.I. Miroshnichenko, A.G. Ponomarev, Nucl. Instrum. Meth. B 267, 2041 (2009) http://dx.doi.org/10.1016/j.nimb.2009.03.09110.1016/j.nimb.2009.03.091Search in Google Scholar

[44] D. Kharchenko, I. Lysenko, S. Kokhan, Eur. Phys. J. B, DOI:10.1140/epjb/e2010-00172-8 10.1140/epjb/e2010-00172-8Search in Google Scholar

[45] D. Kharchenko, I. Lysenko, V. Kharchenko, Physica A 389, 3356 (2010) http://dx.doi.org/10.1016/j.physa.2010.04.02710.1016/j.physa.2010.04.027Search in Google Scholar

[46] K.R. Elder, M. Grant, Phys. Rev. E 70, 051605 (2004) http://dx.doi.org/10.1103/PhysRevE.70.05160510.1103/PhysRevE.70.051605Search in Google Scholar PubMed

[47] K.R. Elder, N. Provatas, J. Berry, P. Stefanovich, M. Grant, Phys. Rev. B 75, 064107 (2007) http://dx.doi.org/10.1103/PhysRevB.75.06410710.1103/PhysRevB.75.064107Search in Google Scholar

[48] J. Berry, K.R. Elder, M. Grant, Phys. Rev. E 77, 061506 (2008) http://dx.doi.org/10.1103/PhysRevE.77.06150610.1103/PhysRevE.77.061506Search in Google Scholar PubMed

[49] P. Galenko, D. Danilov, V. Lebedev, Phys. Rev. E 79, 051110 (2009) http://dx.doi.org/10.1103/PhysRevE.79.05111010.1103/PhysRevE.79.051110Search in Google Scholar PubMed

[50] N. Lecoq, H. Zapolsky, P. Galenko, Eur. Phys. J.-Spec. Top. 177, 165 (2009) http://dx.doi.org/10.1140/epjst/e2009-01173-810.1140/epjst/e2009-01173-8Search in Google Scholar

[51] E.A. Novikov, Sov. Phys. JETP-USSR 20, 1290 (1965) Search in Google Scholar

[52] P. Galenko, V. Lebedev, Int. J. Thermodyn. 11, 21 (2008) Search in Google Scholar

[53] W. Jager, P. Ehrhart, W.W. Schilling, In: G. Martin, L.P. Kubin (Eds.), Nonlinear Phenomena in Material Science (Trans Tech. Aedermannsdorf, Switzerland, 1998) 279 Search in Google Scholar

Published Online: 2011-2-26
Published in Print: 2011-6-1

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