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

• Authors: Dmytro Kharchenko , Vasyl Kharchenko , Iryna Lysenko
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

noise; spatial pattern; nonequilibrium transition; structure function

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2011
• Volume: 9
• Issue: 3
• Pages: 698-709

Dates

published

1 - 6 - 2011

online

26 - 2 - 2011

Contributors

author

Dmytro Kharchenko

• Institute of Applied Physics, Nat. Acad. of Sci. of Ukraine, 58 Petropavlovskaya St., 40030, Sumy, Ukraine

author

Vasyl Kharchenko

• Institute of Applied Physics, Nat. Acad. of Sci. of Ukraine, 58 Petropavlovskaya St., 40030, Sumy, Ukraine

author

Iryna Lysenko

• Institute of Applied Physics, Nat. Acad. of Sci. of Ukraine, 58 Petropavlovskaya St., 40030, Sumy, Ukraine

References

• [1] G. Ahlers, D.S. Cannell, V. Steinberg, Phys. Rev. Lett. 54, 1373 (1985) http://dx.doi.org/10.1103/PhysRevLett.54.1373[Crossref]
• [2] C.W. Meyer, G. Ahlers, D.S. Cannell, Phys. Rev. A 44, 2514 (1991) http://dx.doi.org/10.1103/PhysRevA.44.2514[Crossref]
• [3] S.W. Morris, E. Bodenshaltz, D.S. Cannell, A. Ahlers, Phys. Rev. Lett. 71, 2026 (1993) http://dx.doi.org/10.1103/PhysRevLett.71.2026[Crossref]
• [4] A.S. Mikhailov, K. Showalter, Phys. Rep. 425, 79 (2006) http://dx.doi.org/10.1016/j.physrep.2005.11.003[Crossref]
• [5] H. Katsuragi, Europhys. Lett. 73, 793 (2006) http://dx.doi.org/10.1209/epl/i2005-10464-8[Crossref]
• [6] F. Sagues, J.M. Sancho, J. Garcia-Ojalvo, Rev. Mod. Phys. 79, 829 (2007) http://dx.doi.org/10.1103/RevModPhys.79.829[Crossref]
• [7] B. Lindner, J. Garcia-Ojalvo, A. Neiman, L. Shimansky-Geier, Phys. Rep. 392, 321 (2004) http://dx.doi.org/10.1016/j.physrep.2003.10.015[Crossref]
• [8] G. Stegemann, A.G. Balanov, E. Schöll, Phys. Rev. E 71, 016221 (2005) http://dx.doi.org/10.1103/PhysRevE.71.016221[Crossref]
• [9] S.E. Mangioni, H.S. Wio, Phys. Rev. E 71, 056203 (2005) http://dx.doi.org/10.1103/PhysRevE.71.056203[Crossref]
• [10] D. Kharchenko, S.V. Kokhan, A.V. Dvornichenko, Physica D 238, 2251 (2009) http://dx.doi.org/10.1016/j.physd.2008.12.005[Crossref]
• [11] D.O. Kharchenko, S.V. Kokhan, A.V. Dvornichenko, Metallofiz. Nov. Tekh.+ 31, 23 (2009)
• [12] V. Kharchenko, Physica A 388, 268 (2009) http://dx.doi.org/10.1016/j.physa.2008.10.016[Crossref]
• [13] S.E. Mangioni, Physica A 389, 1799 (2010) http://dx.doi.org/10.1016/j.physa.2010.01.011[Crossref]
• [14] R.A. Enrique, P. Bellon, Phys. Rev. B 63, 134111 (2001) http://dx.doi.org/10.1103/PhysRevB.63.134111[Crossref]
• [15] J. Ye, P. Bellon, Phys. Rev. B 70, 094104 (2004) http://dx.doi.org/10.1103/PhysRevB.70.094104[Crossref]
• [16] J. Lian, W. Zhou, Q.M. Wei et al., Appl. Phys. Lett. 88, 093112 (2006) http://dx.doi.org/10.1063/1.2181203[Crossref]
• [17] R. Kree, T. Yasseri, A.K. Hartmann, Nucl. Instrum. Meth. B 267, 1407 (2009) http://dx.doi.org/10.1016/j.nimb.2009.01.064[Crossref]
• [18] K.R. Elder, M. Katakowski, M. Haataja, M. Grant, Phys. Rev. Lett. 88, 245701 (2002) http://dx.doi.org/10.1103/PhysRevLett.88.245701[Crossref]
• [19] A. Jaatinen, C.V. Achim, K.R. Elder et al., Phys. Rev. E 80, 031602 (2009) http://dx.doi.org/10.1103/PhysRevE.80.031602[Crossref]
• [20] J. Berry, M. Garnt, K.R. Elder, Phys. Rev. E 73, 031609 (2006) http://dx.doi.org/10.1103/PhysRevE.73.031609[Crossref]
• [21] J. Swift, P.C. Hohenberg, Phys. Rev. A 15, 319 (1977) http://dx.doi.org/10.1103/PhysRevA.15.319[Crossref]
• [22] P. Stefanovich, M. Haataja, N. Provatas, Phys. Rev. Lett. 96, 225504 (2006) http://dx.doi.org/10.1103/PhysRevLett.96.225504[Crossref]
• [23] W. Horsthemke, R. Lefever, Noise-Induced Transitions (Springer-Verlag, Berlin, 1984)
• [24] K.R. Elder, J. Vinals, M. Grant, Phys. Rev. Lett. 68, 3024 (1992) http://dx.doi.org/10.1103/PhysRevLett.68.3024[Crossref]
• [25] J. Garcia-Ojalvo, A. Hernandez-Machado, J.M. Sancho, Phys. Rev. Lett. 71, 1542 (1993) http://dx.doi.org/10.1103/PhysRevLett.71.1542[Crossref]
• [26] J. Garcia-Ojalvo, J.M. Sancho, Int. J. Bifurcat. Chaos 4, 1337 (1994) http://dx.doi.org/10.1142/S0218127494001039[Crossref]
• [27] J. Garcia-Ojalvo, J.M. Sancho, Phys. Rev. E 53, 5680 (1996) http://dx.doi.org/10.1103/PhysRevE.53.5680[Crossref]
• [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)00350-9[Crossref]
• [29] A.A. Zaikin, L. Shimansky-Geier, Phys. Rev. E 58, 4355 (1998) http://dx.doi.org/10.1103/PhysRevE.58.4355[Crossref]
• [30] K. Wood, J. Buceta, K. Lindenberg, Phys. Rev. E 73, 022101 (2006) http://dx.doi.org/10.1103/PhysRevE.73.022101[Crossref]
• [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.81.011121[Crossref]
• [32] G. Martin, Phys. Rev. B 30, 1424 (1984) http://dx.doi.org/10.1103/PhysRevB.30.1424[Crossref]
• [33] R. Enrique, P. Bellon, Phys. Rev. Lett. 84, 2885 (2000) http://dx.doi.org/10.1103/PhysRevLett.84.2885[Crossref]
• [34] R. Enrique, P. Bellon, Phys. Rev. B 70, 224106 (2004) http://dx.doi.org/10.1103/PhysRevB.70.224106[Crossref]
• [35] C.W. Gardiner, Handbook of Stochastic Methods (Springer-Verlag, Berlin, Heidelberg, New-York, Tokyo, 1985)
• [36] V.I. Dubinko, A.V. Tur, V.V. Yanovsky, Radiat. Eff. Defect. S. 112, 233 (1990) http://dx.doi.org/10.1080/10420159008213049[Crossref]
• [37] D. Jou, J. Casas-Vazquez, G. Lebon, Extended Irreversible Thermodynamics, 4th ed. (Springer, Berlin, 2010) http://dx.doi.org/10.1007/978-90-481-3074-0[Crossref]
• [38] D.O. Kharchenko, A.V. Dvornichenko, Physica A 387, 5342 (2008) http://dx.doi.org/10.1016/j.physa.2008.05.041[Crossref]
• [39] P.K. Galenko, D. Kharchenko, I. Lysenko, Physica A 389, 3443 (2010) http://dx.doi.org/10.1016/j.physa.2010.05.002[Crossref]
• [40] L.D. Landau, E.M. Lifshitz, Statistical Physics, Part I, Vol.5, 3rd ed. (Butterworth-Heinemann, Oxford, 1980)
• [41] J. Garcia-Ojalvo, J.M. Sancho, Noise in Spatially Extended Systems (Springer, New York, 1999) http://dx.doi.org/10.1007/978-1-4612-1536-3[Crossref]
• [42] P. Galenko, D. Jou, Phys. Rev. E 71, 046125 (2005) http://dx.doi.org/10.1103/PhysRevE.71.046125[Crossref]
• [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.2009.03.091[Crossref]
• [44] D. Kharchenko, I. Lysenko, S. Kokhan, Eur. Phys. J. B, DOI:10.1140/epjb/e2010-00172-8 [Crossref]
• [45] D. Kharchenko, I. Lysenko, V. Kharchenko, Physica A 389, 3356 (2010) http://dx.doi.org/10.1016/j.physa.2010.04.027[Crossref]
• [46] K.R. Elder, M. Grant, Phys. Rev. E 70, 051605 (2004) http://dx.doi.org/10.1103/PhysRevE.70.051605[Crossref]
• [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.75.064107[Crossref]
• [48] J. Berry, K.R. Elder, M. Grant, Phys. Rev. E 77, 061506 (2008) http://dx.doi.org/10.1103/PhysRevE.77.061506[Crossref]
• [49] P. Galenko, D. Danilov, V. Lebedev, Phys. Rev. E 79, 051110 (2009) http://dx.doi.org/10.1103/PhysRevE.79.051110[Crossref]
• [50] N. Lecoq, H. Zapolsky, P. Galenko, Eur. Phys. J.-Spec. Top. 177, 165 (2009) http://dx.doi.org/10.1140/epjst/e2009-01173-8[Crossref]
• [51] E.A. Novikov, Sov. Phys. JETP-USSR 20, 1290 (1965)
• [52] P. Galenko, V. Lebedev, Int. J. Thermodyn. 11, 21 (2008)
• [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

Identifiers

DOI

10.2478/s11534-010-0076-y