Advertisement

Biophysics

, Volume 60, Issue 2, pp 317–330 | Cite as

Local fractal analysis of noise-like time series by the all-permutations method for 1–115 min periods

  • V. A. PanchelyugaEmail author
  • M. S. Panchelyuga
Complex Systems Biophysics
  • 18 Downloads

Abstract

The results of the analysis of a 329-per-day time series of the rate fluctuations of 239Pu alphadecay, which was obtained using the developed local fractal analysis of noise-like time series via the all-permutation method (APM) are presented. With the use of this method, a stable frequency structure is revealed in the time series. It is demonstrated that the found set of frequencies coincides with the Earth’s natural oscillations. Studies that analyze the time series of fluctuations in processes of different natures are briefly reviewed. It is shown that the periodicity values found in these works coincide with those that are observed in our experiments, thus indicating the universal nature of this phenomenon.

Keywords

fractal dimension time series noise local analysis of time series method of minimal cover 

Abbreviation

APM

All–permutations method

EFOs

Earth’s free oscillations

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    V. A. Panchelyuga and M.S. Panchelyuga, Biophysics (Moscow) 58 (2), 283 (2013).CrossRefGoogle Scholar
  2. 2.
    V. A. Panchelyuga and M. S. Panchelyuga, Giperkompl. Chisla Geom. Fiz. 11 (21), 107 (2014).Google Scholar
  3. 3.
    M. M. Dubovikov, N. V. Starchenko, and M. S. Dubovikov, Physica A 339, 591 (2004).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    M. M. Dubovikov, N. V. Starchenko, Usp. Fiz. Nauk 181 (7), 779 (2011).CrossRefGoogle Scholar
  5. 5.
    M. M. Dubovikov, A. V. Kryanev, N. V. Starchenko, Vestn. RUDN, Ser. Prikl. Komp. Mat. 3 (1), 30 (2004).Google Scholar
  6. 6.
    N. V. Starchenko, Candidate’s Dissertation in Mathematics and Physics, (Moscow, 2005).Google Scholar
  7. 7.
    S. E. Shnoll and V. A. Panchelyuga, Mir Izmerenii 6, 49 (2007).Google Scholar
  8. 8.
    S. E. Shnoll, V. A. Kolombet, E. V. Pozharskii, et al., Usp. Fiz. Nauk 168 (10), 1129 (1998).CrossRefGoogle Scholar
  9. 9.
    S. E. Shnoll, T. A. Zenchenko, K. I.Zenchenko, et al., Usp. Fiz. Nauk 170 (2), 214 (2000).CrossRefGoogle Scholar
  10. 10.
    V. A. Panchelyuga and S. E. Shnoll, Giperkompl. Chisla Geom. Fiz. 3 (6), 188 (2006).Google Scholar
  11. 11.
    V. A. Panchelyuga, V. A. Kolombet, M. S. Panchelyuga, and S. E. Shnoll, Giperkompl. Chisla Geom. Fiz. 3 (5), 116 (2006).Google Scholar
  12. 12.
    E. Rutherford, Radioactive Substances and Their Radiations (Cambridge Univ. Press, Cambridge, 1913).Google Scholar
  13. 13.
    S. E. Rutherford, J. Chadwick, and C. Ellis, Radiations from Radioactive Substances (Cambridge Univ. Press, 1930).zbMATHGoogle Scholar
  14. 14.
    J. H. Jenkins, E. Fischbach, J. B. Buncher, et al., arXiv:0808.3283v1 [astro-ph] 25 Aug 2008.Google Scholar
  15. 15.
    J. H. Jenkins, E. Fischbach, J. B. Buncher, et al., Astropart. Phys. 32, 42 (2009).ADSCrossRefGoogle Scholar
  16. 16.
    E. Fischbach, J. B. Buncher, J. T. Gruenwald, et al., Space Sci. Rev. 145, 285 (2009).ADSCrossRefGoogle Scholar
  17. 17.
    J. H. Jenkins and E. Fischbach, Astropart. Phys. 31, 407 (2009).ADSCrossRefGoogle Scholar
  18. 18.
    E. Fischbach, K. J. Chen, R. E. Gold, et al., Astrophys. Space Sci. 337, 39 (2012).ADSCrossRefGoogle Scholar
  19. 19.
    P. A. Sturrock, G. Steinitz, E. Fischbach, et al., Astropart, Phys. 36, 18 (2012).ADSCrossRefGoogle Scholar
  20. 20.
    D. E. Krause, B. A. Rogers, E. Fischbach, et al., Astropart. Phys. 36, 51 (2012).ADSCrossRefGoogle Scholar
  21. 21.
    J. H. Jenkins, K. R. Herminghuysen, Th. E. Blue, et al., Astropart. Phys. 37, 81 (2012).ADSCrossRefGoogle Scholar
  22. 22.
    P. A. Sturrock, L. Bertello, E. Fischbach, et al., Astropart. Phys. 42, 62 (2013).ADSCrossRefGoogle Scholar
  23. 23.
    P. A. Sturrock, A. G. Parkhomov, E. Fischbach, and J. H. Jenkins, Astropart. Phys. 35 (11), 755 (2012).ADSCrossRefGoogle Scholar
  24. 24.
    P. A. Sturrock, E. Fischbach, D. Javorsek II, et al., Astropart. Phys. 59, 47 (2014).ADSCrossRefGoogle Scholar
  25. 25.
    P. S. Cooper, Astropart. Phys. 31 (4), 267 (2009).ADSCrossRefGoogle Scholar
  26. 26.
    E. N. Alexeyev, V. V. Alekseenko, Ju. M. Gavriljuk, et al., Astropart. Phys. 46, 23 (2013).ADSCrossRefGoogle Scholar
  27. 27.
    K. Bikit, J. Nikolov, I. Bikit, et al., Astropart. Phys. 47, 38 (2013).ADSCrossRefGoogle Scholar
  28. 28.
    K. Kossert and O. J. Nahle, Astropart. Phys. 55, 33 (2014).ADSCrossRefGoogle Scholar
  29. 29.
    Yu. A. Baurov, Yu. G. Sobolev, Yu. V. Ryabov, and V. F. Kushniruk, Phys. Atom. Nucl. 70 (11), 1825 (2007).ADSCrossRefGoogle Scholar
  30. 30.
    D. P. Veprev and V. I. Muromtsev, Astropart. Phys. 36, 26 (2012).ADSCrossRefGoogle Scholar
  31. 31.
    E. M. Lin’kov, Seismic Phenomena (Leningr. Gos. Univ., Leningrad, 1987) [in Russian].Google Scholar
  32. 32.
    L. N. Petrova, Vulkanol. Seismol. 4–5, 116 (1999).Google Scholar
  33. 33.
    T. G. Masters and R. Widmer, in Free Oscillations: Frequencies and Attenuations, Ed. by T.J. Ahrens (American Geophysical Union, 1995), pp. 104–125.Google Scholar
  34. 34.
    R. Buland, J. Berger, and F. Gilbert, Nature 277 (5695), 358 (1979).ADSCrossRefGoogle Scholar
  35. 35.
    G. C. Brown and A. E. Mussett, The Inaccessible Earth (Allen & Unwin, 1982; Mir, Moscow, 1984).Google Scholar
  36. 36.
    L. N. Rykunov. O. B. Khavroshkin, and V. V. Tsyplakov, Dokl. Akad. Nauk SSSR 238 (2), 303 (1978).Google Scholar
  37. 37.
    Yu. V. Antonov, I. Yu. Antonova, A. K. Pybin, and G. G. Shchelochkov, Izv. Vuzov, Geol. Razvedka 6, 51 (2010).Google Scholar
  38. 38.
    K. Aki and P. G. Richards, Quantitative Seismology (Freeman, San Francisco, 1980; Mir, Moscow, 1982), Vol. 1.Google Scholar
  39. 39.
    Self-Oscillations of the Earth (Mir, Moscow, 1964) [in Russian].Google Scholar
  40. 40.
    E. M. Lin’kov, L. N. Petrova, N. G. Savina, and T. B. Yanovskaya, Dokl. Akad. Nauk SSSR 262 (2), 321 (1982).Google Scholar
  41. 41.
    L. N. Petrova, Biofizika 37 (3), 508 (1992).MathSciNetGoogle Scholar
  42. 42.
    L. M. Antonova and N. G. Savina, in Applications of Long-Base Laser Interferometers in Geophysics (Vladivostok, 1978) [in Russian].Google Scholar
  43. 43.
    O. B. Khavroshkin, Some Problems in Nonlinear Seismology (IOFZ RAN, Moscow, 1999) [in Russian].Google Scholar
  44. 44.
    E. M. Lin’kov and S. Ya Tipisev, in Dynamic Processes in Discrete Geophysical Systems (Vladivostok, 1986) [in Russian].Google Scholar
  45. 45.
    S. N. Shapovalov, E. S. Gorshkov, T. D. Borisova, V. V. Sokolovskii, and O. A. Troshichev, Biophysics (Moscow) 46 (5), 777 (2001).Google Scholar
  46. 46.
    N. V. Klochek, L. E. Palamarchuk, L. A. Plyusnina, and M. V. Nikonova, Biofizika 37 (4), 656 (1992).Google Scholar
  47. 47.
    N. V. Klochek, L. E. Palamarchuk, and M. V. Nikonova, Biofizika 40 (4), 889 (1995).Google Scholar
  48. 48.
    G. I. Dolgikh, U. Kh. Kopvillem, O. B. Khavroshkin, V. V. Tsyplakov, Available from VINITI, No. 3070–79 (Moscow, 1979).Google Scholar
  49. 49.
    E. S. Gorshkov, S. N. Shapovalov, V. V. Sokolovskii, and O. A. Troshichev, Biophysics (Moscow) 45 (5), 920 (2000).Google Scholar
  50. 50.
    N. V. Klochek and M. V. Nikonova, Studies on Geomagnetosm, Aeronomics, and Solar Physics (Nauka, Moscow, 1988) [ in Russian].Google Scholar
  51. 51.
    Qian-Shen Wang, Xin-she Yang, Chuan-zhen Wu, et al., Phys. Rev. D 62, 041101 (2000).ADSCrossRefGoogle Scholar
  52. 52.
    S. W. Zhou and B. J. Huang, Il Nuovo Cimento 15C (2), 133 (1992).ADSCrossRefGoogle Scholar
  53. 53.
    V. S. Kazachok, O. B. Khavroshkin, V. V. Tsyplakov, behavior of Atomic and Mechanical Oscillators during Solar Eclipse (VNIIMS, 1976) [in Russian].Google Scholar
  54. 54.
    O. B. Khavroshkin and V. V. Tsyplakov, Inzh. Fiz. 3, 25 (2014).Google Scholar
  55. 55.
    A. V. Bruns and V. M. Vladimirskii, Izv. Krymsk. Astrofiz. Observ. 102, 164 (2006).Google Scholar
  56. 56.
    V. M. Vladimirskii, Biofizika 37 (3), 500 (1992).Google Scholar
  57. 57.
    A. V. Drozdov and T. P. Nagorskaya, Biophysics (Moscow) 59 (6), 973 (2014). http://www.biophys.ru/archive/spb2013/proc-p19.pdfCrossRefGoogle Scholar
  58. 58.
    A. V. Drozdov, personal communication.Google Scholar
  59. 59.
    F. R. Chernikov, Biofizika 31 (4), 596 (1986).MathSciNetGoogle Scholar
  60. 60.
    F. R. Chernikov, Biofizika 35 (5), 711 (1990).MathSciNetGoogle Scholar
  61. 61.
    F. R. Chernikov, Biofizika 35 (5), 717 (1990).MathSciNetGoogle Scholar
  62. 62.
    V. V. Aleksandrov, The Ecological Role of Electromagnetism (Politekhn. Univ., St. Petersburg, 2006) [in Russian].Google Scholar
  63. 63.
    V. S. Martynyuk, Biophysics (Moscow) 48 (5), 747 (1998).MathSciNetGoogle Scholar
  64. 64.
    T. A. Zenchenko, A. A. Medvedeva, N. I. Khorseva, and T. K. Breus, Geofiz. Prots. Biosfera 12 (4), 73 (2013).Google Scholar
  65. 65.
    T. A. Zenchenko, P. M. Nagorskii, T. K. Breus, and S. V. Smirnov, in Abstr. IV Int. Conf. “Man and Electromagnetic Fields” (Sarov, 2013), p. 39.Google Scholar
  66. 66.
    T. A. Zenchenko, P. M. Nagorskii, T. K. Breus, S. V. Smirnov, in Abstr. X Int. Conf. “Space and Biosphere (Koktebel, the Crimea, 2013), p. 187.Google Scholar
  67. 67.
    T. A. Zenchenko, Effect of Space Weather in Human Health in Space and on the Earth, Proc. Int. Conf. (Moscow, 2012), pp. 120–121.Google Scholar
  68. 68.
    U. Kh. Kopvillem, R. Z. Sharipov, A. M. Zapol’skii, and N. A. Aisdaicher, Biofizika 37 (4), 643 (1992).Google Scholar
  69. 69.
    G. I. Bortnikova, Biofizika 37 (3), 533 (1992).Google Scholar
  70. 70.
    M. V. Fedorov, E. V. Deshcherevskaya, S. N. Shapovalov, E. S. Gorshkov, and O. A. Troshichev, Biophysics (Moscow) 46 (5), 753 (2001).Google Scholar
  71. 71.
    O. B. Khavroshkin and V. V. Tsyplakov, Inzh. Fiz. 8, 53 (2013).Google Scholar
  72. 72.
    O. Khavroshkin and V. Tsyplakov, Natural Sci. 3 (8), 733 (2011).CrossRefGoogle Scholar
  73. 73.
    O. B. Khavroshkin and V. V. Tsyplakov, Natural Sci. 5 (9), 1001 (2013).CrossRefGoogle Scholar
  74. 74.
    E. N. Avdonina and V. B. Lukyanov, Biofizika 40 (4), 876 (1995).Google Scholar
  75. 75.
    Yu. A. Baurov, N. A. Demchuk, A. Yu. Baurov, et al., Prikl. Fiz. 5, 12 (2011).Google Scholar
  76. 76.
    A. V. Shabel’nikov and K. G. Kir’yanov, Biophysics (Moscow) 43 (5), 829 (1998).Google Scholar
  77. 77.
    A. V. Shabel’nikov, Biofizika 37 (3), 572 (1992).Google Scholar
  78. 78.
    V. M. Vladimirskii, Biofizika 37 (3), 500 (1992).Google Scholar
  79. 79.
    V. M. Vladimirskii, Vestn. Kaluzhsk. Univ. 1, 25 (2007).Google Scholar
  80. 80.
    D. G. Pavlov, Giperkompl. Chisla Geom. Fiz. 1 (1), 5 (2004).Google Scholar
  81. 81.
    D. G. Pavlov, Giperkompl. Chisla Geom. Fiz. 1 (1), 20 (2004).Google Scholar
  82. 82.
    D. G. Pavlov, Giperkompl. Chisla Geom. Fiz. 1 (1), 33 (2004).Google Scholar
  83. 83.
    G. I. Garas’ko, Giperkompl. Chisla Geom. Fiz. 1 (1), 75 (2004).Google Scholar
  84. 84.
    S. V. Lebedev, Giperkompl. Chisla Geom. Fiz. 1 (1), 68 (2004).Google Scholar
  85. 85.
    S. V. Siparov, Giperkompl. Chisla Geom. Fiz. 2 (4), 51 (2005).Google Scholar
  86. 86.
    R. G. Zaripov, Giperkompl. Chisla Geom. Fiz. 3 (5), 27 (2006).Google Scholar
  87. 87.
    G. I. Garas’ko, A Primer in Finsler Geometry for Physicists (Tetru, Moscow, 2009) [in Russian].Google Scholar
  88. 88.
    D. G. Pavlov and S. S. Kokarev, Giperkompl. Chisla Geom. Fiz. 5 (10), 3 (2008).Google Scholar
  89. 89.
    D. G. Pavlov, Giperkompl. Chisla Geom. Fiz. 6 (13), 3 (2010).Google Scholar
  90. 90.
    D. G. Pavlov and S. S. Kokarev, Giperkompl. Chisla Geom. Fiz. 6 (13), 78 (2010).Google Scholar
  91. 91.
    D. G. Pavlov and S. S. Kokarev, Giperkompl. Chisla Geom. Fiz. 16 (2011).Google Scholar
  92. 92.
    D. G. Pavlov and S. S. Kokarev, Giperkompl. Chisla Geom. Fiz. 7 (14), 11 (2010).Google Scholar
  93. 93.
    S. S. Kokarev, Giperkompl. Chisla Geom. Fiz. 9 (17), 175 (2012).Google Scholar
  94. 94.
    D. G. Pavlov, S. S. Kokarev, M. S. Panchelyuga, and V. A. Panchelyuga, Bull. Transilv. Univ. Brasov, Ser. III: Math., Informatics, Phys. 5 (54), 53 (2012).MathSciNetGoogle Scholar
  95. 95.
    D. G. Pavlov, S. S. Kokarev, M. S. Panchelyuga, and V. A. Panchelyuga, Prostr. Vremya 10 (4), 50 (2012).Google Scholar
  96. 96.
    D. G. Pavlov, M. S. Panchelyuga, and V. A. Panchelyuga, Giperkompl. Chisla Geom. Fiz. 9 (17), 162 (2012).Google Scholar
  97. 97.
    D. G. Pavlov, M. S. Panchelyuga, and V. A. Panchelyuga, Metafizika 1, 151 (2014).Google Scholar
  98. 98.
    D. G. Pavlov, M. S. Panchelyuga, S. F. Chalkin, and V. A. Panchelyuga, Giperkompl. Chisla Geom. Fiz. 11 (21), 96 (2014).Google Scholar
  99. 99.
    H. Muller, Prog. Phys. 2, 72 (2009).Google Scholar
  100. 100.
    H. Muller, Prog. Phys. 1, 62 (2010).Google Scholar
  101. 101.
    H. Muller, Prog. Phys. 3, 61 (2010).Google Scholar
  102. 102.
    A. Ries and M. V. L. Fook, Prog. Phys. 1, 103 (2011).Google Scholar
  103. 103.
    V. A. Panchelyuga and M. S. Panchelyuga, Prog. Phys. 4, 48 (2012).Google Scholar

Copyright information

© Pleiades Publishing, Inc. 2015

Authors and Affiliations

  1. 1.Institute of Theoretical and Experimental BiophysicsPushchinoRussia

Personalised recommendations