Self-Organization of Condensed Matter in Fluctuating Environment

D. O. Kharchenko

Sumy State University, 2 Rymsky-Korsakov Str., UA-40007 Sumy, Ukraine

Received: 06.04.2004. Download: PDF

A synergetic conception of plastic deformation is presented allowing for the defects’ interplay resulting in a phase transition. A qualitative-reconstruction pattern of imperfect condensed-matter structure in the presence of fluctuations in both 0-dimensional and distributed (extended) systems is considered. As shown, the system undergoes the reversible phase transitions under the increasing intensity of fluctuations, diffusion constituent and deformation-type external parameters. Within the framework of the synergetic approach based on the Lorenz system, a pattern of explosive crystallization is shown to be scripting the same way as the avalanches formation. The relationships are set between the exponent of a size distribution of avalanches, the fractal dimension of a phase space, characteristics of noise, the number of governing equations, the dynamical exponent, and the non-additivity parameter. As shown, the regime of self-organized criticality is associated with an anomalous diffusion processes.

Keywords: noise-induced phase transitions, order parameter, self-organized criticality, fractal dimension, anomalous diffusion.

PACS: 05.40.Ca, 05.45.Df, 05.65.+b, 05.70.Fh, 45.70.Ht, 64.60.Ak

DOI: https://doi.org/10.15407/ufm.06.01.001

Citation: D. O. Kharchenko, Self-Organization of Condensed Matter in Fluctuating Environment, Usp. Fiz. Met., 6, No. 1: 1—54 (2005), doi: 10.15407/ufm.06.01.001


References (63)  
  1. G. Nicolis and I. Prigogine, Self-Organization in Nonequilibrium Systems (New York, London, Sydney, Toronto: A Wiley-Interscience Publ., John Wiley & Sons: 1977).
  2. H. Haken, Synergetics—An Introduction (Berlin, Heidelberg, New York: Springer-Verlag: 1983). Crossref
  3. C. W. Gardiner, Handbook of Stochastic Methods (Berlin: Springer-Verlag: 1983). Crossref
  4. W. Horsthemke and R. Lefever, Noise-Induced Transitions (Berlin: Springer-Verlag: 1984).
  5. J. Garcia-Ojalvo and J. M. Sancho, Noise in Spatially Extended Systems (New York: Springer-Verlag: 1999). Crossref
  6. P. Bak, How Nature Works: the Science of Self-Organized Criticality (Oxford: Oxford University Press: 1997).
  7. H. J. Jensen, Self-Organized Criticality. Emergent Complex Behaviour in Physical and Biological Systems. Cambridge Lecture Notes in Physics (Cambridge: Cambridge University Press: 1998). Crossref
  8. J. Feder, Fractals (New York: Plenum: 1989).
  9. Applications of Fractional Calculus in Physics (Ed. R. Hilfer) (Singapore: World Scientific: 2000).
  10. V. V. Rubin, Bol'shie Plasticheskie Deformatsii i Razrushenie Metallov (Large Plastic Deformations and Failure of Metals) (Moscow: Metallurgiya: 1985) (in Russian).
  11. V. E. Panin, V. A. Likhachyov, and Yu. V. Grinyayev, Strukturnyye Urovni Deformatsii Tvyordykh Tel (Structural Levels of Deformation of Condensed Matter) (Novosibirsk: Nauka: 1985) (in Russian).
  12. V. P. Skripov and V. P. Koverda, Spontannaya Kristallizatsiya Pereokhlazhdyonnykh Zhydkostej (Spontaneous Crystallization of Supercooled Liquids) (Moscow: Nauka: 1984) (in Russian).
  13. S. F. Edwards and R. B. S. Oakeshott, Physica A, 157: 1080 (1989). Crossref
  14. S. F. Edwards, Granular Matter: An Interdisciplinary Approach (Ed. A. Metha) (New York: Springer-Verlag: 1994).
  15. C. Tsallis, Lecture Notes in Physics (Eds. S. Abe and Y. Okamoto) (Heidelberg: Springer-Verlag: 2001).
  16. G. M. Zaslavsky, Chaos, 4: 25 (1994); idem, Physica D, 76: 110 (1994); https://doi.org/10.1016/0167-2789(94)90254-2
  17. A. Damask and J. Diens, Point Defects in Metals (New York: Gordon and Breach: 1963).
  18. J. Friedel, Dislocations (Oxford, London, Edinburg, NewYork, Paris, Frankfurt: Pergamon Press: 1964).
  19. J. D. Vishnyakov, Defekty Upakovki v Kristallicheskoj Strukture (Defects of Packing in Crystal Structure) (Moscow: Metallurgiya: 1970) (in Russian).
  20. J. P. Hirth and J. Lothe, Theory of Dislocations (New York: McGraw-Hill: 1968).
  21. B. I. Smirnov, Dislokatsionnaya Struktura i Uprochnenie Kristallov (Dislocation Structure and Strengthening) (Leningrad: Nauka: 1981) (in Russian).
  22. V. I. Vladimirov and A. E. Romanov, Disklinatsii v Kristallakh (Disclinations in Crystals) (Leningrad: Nauka: 1986) (in Russian).
  23. R. de Witt, Continual Theory of Disclinations. (Moscow: Mir Publishers: 1977) (Russian translation).
  24. A. I. Olemskoi, Physics Reviews (Ed. I. M. Khalatnikov) (London: Gordon & Breach: 1996), vol. 18, Part 1, p. 1.
  25. A. I. Olemskoi and A. V. Khomenko, Usp. Fiz. Met., 2: 189 (2001). Crossref
  26. S. E. Mangioni, R. R. Deza, R. Toral, and H. S. Wio, Phys. Rev. E, 61: 223, (2000). Crossref
  27. P. Jung and P. Hänggi, Phys. Rev. A, 35: 4467 (1987); F. Castro, H. S. Wio, and G. Abramson, Phys. Rev. E, 52: 159 (1995) Crossref
  28. D. O. Kharchenko and I. A. Knyaz', Mettallofiz. Noveishie Tekhnol., 24, No. 3: 389 (2002).
  29. E. A. Novikov, JETP, 47: 1919 (1964).
  30. M. A. Munoz, Phys. Rev. E, 57: 1377 (1998). Crossref
  31. A. I. Olemskoi and D. O. Kharchenko, Met. Phys. Adv. Tech., 16: 841 (1996).
  32. A. I. Olemskoi and D. O. Kharchenko, Physics of Solid State, 42: 520 (2000). Crossref
  33. D. O. Kharchenko, Physica A, 308: 101 (2002). Crossref
  34. D. O. Kharchenko and I. A. Knyaz', Eur. Phys. J. B, 32: 375 (2003). Crossref
  35. N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Amsterdam: North Holland: 1992).
  36. V. E. Shapiro, Phys. Rev. E, 48: 109 (1993). Crossref
  37. H. Risken, The Fokker–Planck Equation (Berlin: Springer Verlag: 1989).
  38. S. F. Edwards and D. R. Wilkinson, Proc. Roy. Soc. A, 381: 17 (1982). Crossref
  39. A. Mehta and G. C. Barker, Rep. Prog. Phys., 57: 383 (1994). Crossref
  40. J. -P. Bouchaud, M. E. Cates, J. R. Prakash, and S. F. Edwards, J. Phys. I (France), 4: 1383 (1994). Crossref
  41. K. P. Hadeler and C. Kuttler, Granular Matter, 2: 9 (1999). Crossref
  42. P. Bak and K. Sneppen, Phys. Rev. Lett., 71: 4083 (1993). Crossref
  43. A. I. Olemskoi, A. V. Khomenko, and V. P. Koverda, Physica A, 284: 79 (2002). Crossref
  44. L. Pietronero, A. Vespignani, and S. Zapperi, Phys. Rev. Lett., 72: 1690 (1994); idem, Phys. Rev. E, 51: 1711 (1995).
  45. V. P. Koverda and V. P. Skripov, Rasplavy, 1, No. 4: 3 (1987) (in Russian).
  46. N. M. Bogdanov, V. P. Koverda, V. N. Skokov, V. P. Skripov, and A. A. Dik, Kristallografiya, 33, No. 5: 1251 (1988) (in Russian).
  47. D. A. Kurtze, Phys. Rev. B, 34: 1770 (1986). Crossref
  48. V. P. Koverda, Zh. Tekhn. Fiz., 64, No. 3: 62 (1994) (in Russian).
  49. A. I. Olemskoi, A. V. Khomenko, and D. O. Kharchenko, Physica A, 323: 263 (2003). Crossref
  50. A. Vespignani and S. Zapperi, Phys. Rev. Lett., 78: 4793 (1997); idem, Phys. Rev. E, 57: 6345 (1998). Crossref
  51. A. I. Olemskoi and A. V. Khomenko, JETP, 83: 1180 (1996).
  52. A. I. Olemskoi, Physics—Uspekhi, 41: 269 (1998). Crossref
  53. D. O. Kharchenko, Fluct. and Noise Lett., 2, No. 4: L287 (2002). Crossref
  54. A. Chessa, E. Marinari, A. Vespignani, and S. Zapperi, Phys. Rev. E, 57: R6241 (1998). Crossref
  55. L. Gil and D. Sornette, Phys. Rev. Lett., 76: 3991 (1996). Crossref
  56. A. Vespignani, R. Dickman, M. A. Mu-oz, and S. Zapperi, Phys. Rev. Lett., 81: 5676 (1998); idem, Phys. Rev. E, 62: 4564 (2000). Crossref
  57. A. I. Olemskoi, JETP Let., 71: 285 (2000). Crossref
  58. A. I. Olemskoi and D. O. Kharchenko, Physica A, 293: 178 (2001). Crossref
  59. D. O. Kharchenko and S. V. Kohan, Eur. Phys. J. B, 29: 97 (2002). Crossref
  60. J. -P. Bouchaud and A. Georges, Phys. Rep., 195: 127 (1991). Crossref
  61. H. C. Fogedby, Phys. Rev. E, 58: 160 (1998). Crossref
  62. D. H. Zanette and P. A. Alemany, Phys. Rev. Lett., 75: 366 (1995). Crossref
  63. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional Integrals and Derivatives—Theory and Applications (New York: Gordon and Breach: 1993).
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  1. D. O. Kharchenko, P. K. Galenko and V. G. Lebedev, Usp. Fiz. Met. 10, 27 (2009).