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Advances in High Energy Physics
Volume 2016 (2016), Article ID 7287803, 9 pages
http://dx.doi.org/10.1155/2016/7287803
Research Article

Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

1Nuclear and Particle Physics Research Centre, Department of Physics, Jadavpur University, Kolkata 700032, India
2Department of Physics, New Alipore College, L Block, New Alipore, Kolkata 700053, India

Received 4 February 2016; Accepted 7 April 2016

Academic Editor: Ming Liu

Copyright © 2016 Gopa Bhoumik et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. B. B. Mandelbrot, The Fractal Geometry of Nature, Freeman, San Francisco, Calif, USA, 1999.
  2. S. Ahmad and M. A. Ahmad, “A comparative study of multifractal moments in relativistic heavy-ion collisions,” Journal of Physics G: Nuclear and Particle Physics, vol. 32, no. 9, pp. 1279–1293, 2006. View at Publisher · View at Google Scholar
  3. M. M. Khan, N. Ahmad, A. Kamal, A. A. Masoodi, and M. Irfan, “Correlation and fluctuations in relativistic nucleus-nucleus collisions,” Indian Journal of Physics, vol. 85, no. 1, pp. 189–193, 2011. View at Publisher · View at Google Scholar · View at Scopus
  4. G. Singh and P. L. Jain, “Multifractal analysis of 197Au collisions at 10.6A GeV,” Physical Review C, vol. 50, no. 5, pp. 2508–2515, 1994. View at Publisher · View at Google Scholar
  5. A. Bershadskii, “Multifractal critical chaos and intermittency in multiparticle production,” Journal of Physics G: Nuclear and Particle Physics, vol. 26, no. 7, pp. 1011–1015, 2000. View at Publisher · View at Google Scholar
  6. Z. Chen, P. Ch. Ivanov, K. Hu, and H. E. Stanley, “Effect of nonstationarities on detrended fluctuation analysis,” Physical Review E, vol. 65, no. 4, pp. 041107–041122, 2002. View at Publisher · View at Google Scholar
  7. S. V. Chekanov and V. I. Kuvshinov, “Multifractal multiplicity distribution in bunching parameter analysis,” Journal of Physics G: Nuclear and Particle Physics, vol. 22, no. 5, pp. 601–610, 1996. View at Publisher · View at Google Scholar
  8. A. Bialas, “Intermittency '90,” Nuclear Physics A, vol. 525, pp. 345–360, 1991. View at Publisher · View at Google Scholar · View at Scopus
  9. R. Peschanski, “Intermittency in particle collisions,” International Journal of Modern Physics A, vol. 6, no. 21, pp. 3681–3722, 1991. View at Publisher · View at Google Scholar
  10. E. A. De Wolf, I. M. Dremin, and W. Kittel, “Scaling laws for density correlations and fluctuations in multiparticle dynamics,” Physics Reports, vol. 270, no. 1-2, pp. 1–141, 1996. View at Publisher · View at Google Scholar
  11. P. Carruthers and M. Duong-Van, “Evidence for a common fractal dimension in multiparticle production,” Los Alamos Report LA-UR-83-2419, 1983. View at Google Scholar
  12. R. C. Hwa, “Fractal measures in multiparticle production,” Physical Review D, vol. 41, no. 5, pp. 1456–1462, 1990. View at Publisher · View at Google Scholar · View at Scopus
  13. R. C. Hwa and J. Pan, “Fractal behavior of multiplicity fluctuations in high-energy collisions,” Physical Review D, vol. 45, no. 5, pp. 1476–1483, 1992. View at Publisher · View at Google Scholar
  14. I. M. Dermin, “The fractal correlation measure for multiple production,” Modern Physics Letters A, vol. 3, no. 14, p. 1333, 1988. View at Publisher · View at Google Scholar
  15. P. Carruthers, “Fractal structures and correlations in hadronic multiparticle distributions,” International Journal of Modern Physics A, vol. 4, no. 20, pp. 5587–5614, 1989. View at Publisher · View at Google Scholar
  16. Ph. Brax and R. Peschanski, “Multifractal analysis of intermittency and phase transitions in multiparticle dynamics,” Nuclear Physics B, vol. 346, no. 1, pp. 65–83, 1990. View at Google Scholar
  17. F. Takagi, “Multifractal structure of multiplicity distributions in particle collisions at high energies,” Physical Review Letters, vol. 72, no. 1, pp. 32–35, 1994. View at Publisher · View at Google Scholar
  18. G. Paladin and A. Vulpiani, “Anomalous scaling laws in multifractal objects,” Physics Reports, vol. 156, no. 4, pp. 147–225, 1987. View at Publisher · View at Google Scholar
  19. P. Grassberger and I. Procaccia, “Dimensions and entropies of strange attractors from a fluctuating dynamics approach,” Physica D: Nonlinear Phenomena, vol. 13, no. 1-2, pp. 34–54, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  20. T. C. Halsey, M. H. Jensen, L. P. Kadanoff, I. Procaccia, and B. I. Shraiman, “Fractal measures and their singularities: the characterization of strange sets,” Physical Review A, vol. 33, no. 2, pp. 1141–1151, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  21. M. I. Haque, M. Tariq, and T. Hussain, “Presence of multifractality in high-energy nuclear collisions,” Journal of Modern Physics, vol. 5, no. 17, pp. 1889–1895, 2014. View at Google Scholar
  22. N. Ahmad, A. Kamal, M. M. Khan, Hushnud, and A. Tufail, “A study of multifractal spectra and renyi dimensions in 14.5A GeV/c 28Si-nucleus collisions,” Journal of Modern Physics, vol. 5, pp. 1288–1293, 2014. View at Publisher · View at Google Scholar
  23. D. Ghosh, A. Deb, R. Chattopadhyay et al., “Evidence of multifractal nature of target-evaporated slow particles produced in ultrarelativistic heavy ion interactions,” Physical Review C, vol. 58, no. 6, p. 3553, 1998. View at Publisher · View at Google Scholar
  24. C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, and A. L. Goldberger, “Mosaic organization of DNA nucleotides,” Physical Review E, vol. 49, no. 2, pp. 1685–1689, 1994. View at Publisher · View at Google Scholar
  25. J. W. Kantelhardt, D. Rybski, S. A. Zschiegner et al., “Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods,” Physica A: Statistical Mechanics and Its Applications, vol. 330, no. 1-2, pp. 240–245, 2003. View at Publisher · View at Google Scholar
  26. I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, Pa, USA, 1992.
  27. S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1999.
  28. P. Manimaran, P. K. Panigrahi, and J. C. Parikh, “Wavelet analysis and scaling properties of time series,” Physical Review E, vol. 72, Article ID 046120, 2005. View at Publisher · View at Google Scholar
  29. P. Manimaran, P. Anantha Lakshmi, and P. K. Panigrahi, “Spectral fluctuation characterization of random matrix ensembles through wavelets,” Journal of Physics A: Mathematical and General, vol. 39, no. 42, p. L599, 2006. View at Publisher · View at Google Scholar
  30. J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, and H. E. Stanley, “Multifractal detrended fluctuation analysis of nonstationary time series,” Physica A: Statistical Mechanics and its Applications, vol. 316, no. 1–4, pp. 87–114, 2002. View at Publisher · View at Google Scholar · View at Scopus
  31. M. S. Taqqu, V. Teverovsky, and W. Willinger, “Estimators for long-range dependence: an empirical study,” Fractals, vol. 3, no. 4, pp. 785–798, 1995. View at Publisher · View at Google Scholar
  32. J. P. Bouchaud, M. Potters, and M. Meyer, “Apparent multifractality in financial time series,” The European Physical Journal B, vol. 13, no. 3, pp. 595–599, 2000. View at Publisher · View at Google Scholar
  33. P. Mali and A. Mukhopadhyay, “Multifractal characterization of gold market: a multifractal detrended fluctuation analysis,” Physica A: Statistical Mechanics and Its Applications, vol. 413, pp. 361–372, 2014. View at Publisher · View at Google Scholar · View at Scopus
  34. Y. Yuan, X.-T. Zhuang, and X. Jin, “Measuring multifractality of stock price fluctuation using multifractal detrended fluctuation analysis,” Physica A: Statistical Mechanics and Its Applications, vol. 388, no. 11, pp. 2189–2197, 2009. View at Publisher · View at Google Scholar · View at Scopus
  35. Y. Wang, L. Liu, and R. Gu, “Analysis of efficiency for Shenzhen stock market based on multifractal detrended fluctuation analysis,” International Review of Financial Analysis, vol. 18, no. 5, pp. 271–276, 2009. View at Publisher · View at Google Scholar
  36. P. Norouzzadeh and B. Rahmani, “A multifractal detrended fluctuation description of Iranian rial-US dollar exchange rate,” Physica A: Statistical Mechanics and Its Applications, vol. 367, pp. 328–336, 2006. View at Publisher · View at Google Scholar · View at Scopus
  37. P. Zhou, F. Li, W.-Y. Liu, and M. Yang, World Congress on Medical Physics and Biomedical Engineering, Edited by S. I. Kim, T. S. Suh, Springer, Berlin, Germany, 2007.
  38. S. Dutta, D. Ghosh, and S. Chatterjee, “Multifractal detrended fluctuation analysis of human gait diseases,” Frontiers in Physiology, vol. 4, article 274, 2013. View at Publisher · View at Google Scholar
  39. P. Mali, “Multifractal characterization of global temperature anomalies,” Theoretical and Applied Climatology, vol. 121, no. 3-4, pp. 641–648, 2015. View at Publisher · View at Google Scholar
  40. R. B. de Benicio, T. Stošić, P. H. de Figueirêdo, and B. D. Stošić, “Multifractal behavior of wild-land and forest fire time series in Brazil,” Physica A: Statistical Mechanics and Its Applications, vol. 392, no. 24, pp. 6367–6374, 2013. View at Publisher · View at Google Scholar · View at Scopus
  41. J. W. Kantelhardt, A. Bunde, and L. Schweitzer, “Are the phases in the Anderson model long-range correlated?” Physica A, vol. 266, pp. 461–464, 1999. View at Publisher · View at Google Scholar
  42. N. Vandewalle, M. Ausloos, M. Houssa, P. W. Mertens, and M. M. Heyns, “Non-Gaussian behavior and anticorrelations in ultrathin gate oxides after soft breakdown,” Applied Physics Letters, vol. 74, no. 11, pp. 1579–1581, 1999. View at Publisher · View at Google Scholar
  43. Y. X. Zhang, W. Y. Qian, and C. B. Yang, “Multifractal structure of pseudorapidity and azimuthal distributions of the shower particles in Au + Au collisions at 200 A GeV,” International Journal of Modern Physics A, vol. 23, no. 18, p. 2809, 2008. View at Publisher · View at Google Scholar
  44. X. Wang and C. B. Yang, “Fractal properties of particles in phase space from URQMD model,” International Journal of Modern Physics E, vol. 22, no. 4, Article ID 1350021, 8 pages, 2013. View at Publisher · View at Google Scholar
  45. P. Mali, S. Sarkar, S. Ghosh, A. Mukhopadhyay, and G. Singh, “Multifractal detrended fluctuation analysis of particle density fluctuations in high-energy nuclear collisions,” Physica A: Statistical Mechanics and Its Applications, vol. 424, pp. 25–33, 2015. View at Publisher · View at Google Scholar · View at Scopus
  46. D. Ghosh, P. Ghosh, A. Ghosh, and J. Roy, “Intermittency and fragmentation of target residue in high-energy nuclear interactions,” Physical Review C, vol. 49, no. 4, pp. R1747–R1750, 1994. View at Publisher · View at Google Scholar · View at Scopus
  47. D. Ghosh, A. Mukhopadhyay, A. Ghosh, and J. Roy, “Zonal poissonian pion multiplicity in central 24Mg-AgBr collisions at dubna energy,” Modern Physics Letters A, vol. 4, no. 13, pp. 1197–1202, 1989. View at Publisher · View at Google Scholar
  48. D. Ghosh, J. Roy, and R. Sengupta, “Study of multiparticle production in the interaction of 12C with photoemulsion nuclei at 4.5 GeV/c per nucleon,” Nuclear Physics A, vol. 468, no. 3-4, pp. 719–738, 1987. View at Publisher · View at Google Scholar
  49. K. Sengupta, P. L. Jain, G. Singh, and S. N. Kim, “Intermittency in multiparticle production at ultra-relativistic heavy ion collisions,” Physics Letters B, vol. 236, no. 2, pp. 219–223, 1990. View at Publisher · View at Google Scholar
  50. C. F. Powell et al., Pergamon, Oxford, UK, pp. 450–464, 1959.
  51. D. Ghosh, P. Ghosh, A. Ghosh, and J. Roy, “Nonstatistical fluctuations in fragmentation of target nuclei in high energy nuclear interactions,” Journal of Physics G: Nuclear and Particle Physics, vol. 20, no. 7, article 1077, 1994. View at Publisher · View at Google Scholar
  52. D. Ghosh, B. Biswas, A. Deb, and J. Roy, “Evidence of scaling of void probability in nucleus-nucleus interactions at few GeV energy,” Physical Review C, vol. 56, no. 5, pp. 2879–2881, 1997. View at Publisher · View at Google Scholar
  53. D. Ghosh, A. K. Jafry, A. Deb, S. Sarkar, R. Chattopadhyay, and S. Das, “Multidimensional intermittency analysis in ultrarelativistic heavy ion interaction,” Physical Review C, vol. 59, no. 4, p. 2286, 1999. View at Publisher · View at Google Scholar
  54. D. Ghosh, M. Lahiri, A. Deb et al., “Factorial correlator study in 32Ag/Br interaction at 200A GeV,” Physical Review C, vol. 52, no. 4, p. 2092, 1995. View at Publisher · View at Google Scholar
  55. J. Feder, Fractals, Plenum Press, New York, NY, USA, 1988.
  56. H.-O. Peitgen, H. Jürgens, and D. Saupe, Chaos and Fractals, Appendix B, Springer, New York, NY, USA, 1992.
  57. Y. Ashkenazy, D. R. Baker, H. Gildor, and S. Havlin, “Nonlinearity and multifractality of climate change in the past 420,000 years,” Geophysical Research Letters, vol. 30, no. 22, p. 2146, 2003. View at Publisher · View at Google Scholar
  58. Y. U. Shimizu, S. Thurner, and K. Ehrenberger, “Multifractal spectra as a measure of complexity in human posture,” Fractals, vol. 10, no. 1, pp. 103–116, 2002. View at Publisher · View at Google Scholar · View at Scopus
  59. L. Telesca, M. Balasco, G. Colangelo, V. Lapenna, and M. Macchiato, “Investigating the multifractal properties of geoelectrical signals measured in southern Italy,” Physics and Chemistry of the Earth, vol. 29, no. 4–9, pp. 295–303, 2004. View at Publisher · View at Google Scholar · View at Scopus
  60. C. Barman, H. Chaudhuri, A. Deb, D. Ghose, and B. Sinha, “The essence of multifractal detrended fluctuation technique to explore the dynamics of soil radon precursor for earthquakes,” Natural Hazards, vol. 78, no. 2, pp. 855–877, 2015. View at Publisher · View at Google Scholar