Skip to main content

Moment analysis and Zipf law

  • Conference paper
  • First Online:
Dynamics and Thermodynamics with Nuclear Degrees of Freedom
  • 578 Accesses

Abstract

The moment analysis method and nuclear Zipf’s law of fragment size distributions are reviewed to study nuclear disassembly. In this report, we present a compilation of both theoretical and experimental studies on moment analysis and Zipf law performed so far. The relationship of both methods to a possible critical behavior or phase transition of nuclear disassembly is discussed. In addition, scaled factorial moments and intermittency are reviewed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. C.A. Ogilvie et al., Phys. Rev. Lett. 67, 1214 (1991); M.B. Tsang et al., Phys. Rev. Lett. 71, 1502 (1993); Y.G. Ma, W.Q. Shen, Phys. Rev. C 51, 710 (1995).

    Article  ADS  Google Scholar 

  2. M.E. Fisher, Physics (N.Y.) 3, 255 (1967).

    Google Scholar 

  3. S. Albergo, S. Costa, E. Costanzo, A. Rubbino, Nuovo Cimento A 89, 1 (1985).

    Article  ADS  Google Scholar 

  4. J. Pochodzalla et al., Phys. Rev. Lett. 75, 1040 (1995).

    Article  ADS  Google Scholar 

  5. Y.G. Ma et al., Phys. Lett. B 390, 41 (1997).

    Article  ADS  Google Scholar 

  6. J.B. Natowitz et al., Phys. Rev. C 65, 034618 (2002).

    Article  ADS  Google Scholar 

  7. J.B. Natowitz, K. Hagel, Y.G. Ma, M. Murray, L. Qin, R. Wada, J. Wang, Phys. Rev. Lett. 89, 212701 (2002).

    Article  ADS  Google Scholar 

  8. W. Bauer, Phys. Rev. C 38, 1297 (1988).

    Article  ADS  Google Scholar 

  9. M.L. Gilkes et al., Phys. Rev. Lett. 73, 1590 (1994).

    Article  ADS  Google Scholar 

  10. M. D’Agostino et al., Nucl. Phys. A 650, 329 (1999).

    Article  ADS  Google Scholar 

  11. J.B. Elliott et al., Phys. Rev. C 55, 1319 (1997).

    Article  ADS  Google Scholar 

  12. J.B. Elliott et al., Phys. Rev. C 49, 3185 (1994).

    Article  ADS  Google Scholar 

  13. M. Kleine Berkenbusch, W. Bauer, K. Dillman, S. Pratt, L. Beaulieu, K. Kwiatkowski, T. Lefort, W.C. Hsi, V.E. Viola, S.J. Yennello, R.G. Korteling, H. Breuer, Phys. Rev. Lett. 88, 022701 (2002).

    Article  ADS  Google Scholar 

  14. NIMROD Collaboration (Y.G. Ma et al.), Phys. Rev. C 69, 031604(R) (2004); 71, 054606 (2005).

    Article  Google Scholar 

  15. J. Richert, P. Wagner, Phys. Rep. 350, 1 (2001).

    Article  MATH  ADS  Google Scholar 

  16. S. Das Gupta, A.Z. Mekjian, M.B. Tsang, Adv. Nucl. Phys. 26, 89 (2001).

    Article  Google Scholar 

  17. A. Bonasera, M. Bruno, P.F. Mastinu, C.O. Dorso, Riv. Nuovo Cimento 23, No. 2 (2000).

    Google Scholar 

  18. Ph. Chomaz, Proceedings of the International Nuclear Physics Conference INPC2001, Berkeley CA, USA, 2001, edited by E. Norman, L. Schroeder, G. Wozniak, AIP Conf. Proc., Vol. 610 (Melville, New York, 2002) p. 167.

    Chapter  Google Scholar 

  19. L.G. Moretto, J.B. Elliott, L. Phair, G.J. Wozniak, C.M. Mader, A. Chappars, in L. Schroeder, G. Wozniak, AIP Conf. Proc., Vol. 610 (Melville, New York, 2002) [18] p. 182.

    Chapter  Google Scholar 

  20. A. Kelic, J.B. Natowitz, K.-H. Schmidt, this topical issue.

    Google Scholar 

  21. V.E. Viola, R. Bougault, this topical issue.

    Google Scholar 

  22. B. Borderie, P. Désesquelles, this topical issue.

    Google Scholar 

  23. F. Gulminelli, M. D’Agostino, this topical issue.

    Google Scholar 

  24. O. Lopez, M.F. Rivet, this topical issue.

    Google Scholar 

  25. X. Campi, J. Phys. A 19, L 917 (1986).

    Article  ADS  Google Scholar 

  26. X. Campi, Phys. Lett. B 208, 351 (1988).

    Article  ADS  Google Scholar 

  27. W. Bauer et al., Phys. Lett. B 150, 53 (1985).

    Article  ADS  Google Scholar 

  28. W. Bauer et al., Nucl. Phys. A 452, 699 (1986).

    Article  ADS  Google Scholar 

  29. D. Stauffer, Introduction to Percolation Theory (Taylor and Francis, London, 1985).

    Book  MATH  Google Scholar 

  30. K. Binder, Monte Carlo Methods in Statistical Mechanics, 2nd ed. (Springer-Verlag, Berlin, 1986).

    Google Scholar 

  31. H.R. Jaqaman, D.H.E. Gross, Nucl. Phys. A 524, 321 (1991).

    Article  ADS  Google Scholar 

  32. N. Tan et al., Phys. Rev. B 29, 6354 (1984).

    Google Scholar 

  33. B.K. Srivastava et al., Phys. Rev. C 64, 041605 (2001); 65, 054617 (2002).

    Article  ADS  Google Scholar 

  34. R.P. Scharenberg et al., Phys. Rev. C 64, 054602 (2001).

    Article  ADS  Google Scholar 

  35. J.A. Hauger et al., Phys. Rev. C 57, 764 (1998).

    Article  ADS  Google Scholar 

  36. J.A. Hauger et al., Phys. Rev. C 62, 024616 (2000).

    Article  ADS  Google Scholar 

  37. D. Cussol et al., Nucl. Phys. A 561, 298 (1993).

    Article  ADS  Google Scholar 

  38. J. Lauret et al., Phys. Rev. C 62, R1051 (1998).

    Article  ADS  Google Scholar 

  39. W. Bauer, W.A. Friedman, Phys. Rev. Lett. 77, 767c (1995).

    Article  ADS  Google Scholar 

  40. M.L. Gilkes et al., Phys. Rev. Lett. 77, 768c (1995).

    Article  ADS  Google Scholar 

  41. J.B. Elliott et al., Phys. Rev. C 67, 024609 (2003).

    Article  ADS  Google Scholar 

  42. X. Campi, H. Krivine, Nucl. Phys. A 545, 161c (1992).

    Article  ADS  Google Scholar 

  43. X. Campi, H. Krivine, Z. Phys. A 344, 81 (1992).

    Article  ADS  Google Scholar 

  44. Y.G. Ma et al., Nucl. Phys. A 749, 106c (2005).

    Article  ADS  Google Scholar 

  45. C.O. Dorso, V.C. Latora, A. Bonasera, Phys. Rev. C 60, 034606 (1999).

    Article  ADS  Google Scholar 

  46. R. Botet, M. Ploszajczak, A. Chbihi, B. Borderie, D. Durand, J. Frankland, Phys. Rev. Lett. 86, 3514 (2001).

    Article  ADS  Google Scholar 

  47. Y.G. Ma, J. Phys. G 27, 2455 (2001).

    Article  ADS  Google Scholar 

  48. A. Bialas, R. Peschanski, Nucl. Phys. B 273, 703 (1986).

    Article  ADS  Google Scholar 

  49. B. Mandelbrot, J. Fluid Mech. 62, 331 (1974); U. Frisch, P. Sulem, M. Nelkin, J. Fluid Mech. 87, 719 (1978).

    Article  MATH  ADS  Google Scholar 

  50. Ya. B. Zeldovich et al., Sov. Phys. Usp. 30, 353 (1987).

    Article  MathSciNet  ADS  Google Scholar 

  51. G. Paladin, V. Vulpiani, Phys. Rep. 156, 147 (1987).

    Article  ADS  MathSciNet  Google Scholar 

  52. A. Bialias, R.C. Hwa, Phys. Lett. B 207, 59 (1988).

    Article  ADS  Google Scholar 

  53. R.C. Hwa, M.T. Nazirov, Phys. Rev. Lett. 69, 741 (1992).

    Article  ADS  Google Scholar 

  54. H. Satz, Nucl. Phys. B 326, 613 (1989).

    Article  ADS  MathSciNet  Google Scholar 

  55. M. Ploszajczak, A. Tucholski, Phys. Rev. Lett. 65, 1539 (1999).

    Article  ADS  Google Scholar 

  56. L. Phair et al., Phys. Rev. Lett. 79, 3538 (1996); Phys. Lett. B 291, 7 (1992).

    Article  ADS  Google Scholar 

  57. B. Elattari, J. Richert, P. Wagner, Phys. Rev. Lett. 69, 45 (1992); Nucl. Phys. A 560, 603 (1993).

    Article  ADS  Google Scholar 

  58. H.W. Barz et al., Phys. Rev. C 45, R2541 (1992).

    Article  ADS  Google Scholar 

  59. V. Latora, M. Belkacem, A. Bonesera, Phys. Rev. Lett. 73, 1765 (1994); M. Belkacem, V. Latora, A. Bonasera, Phys. Rev. C 52, 271 (1995).

    Article  ADS  Google Scholar 

  60. X. Campi, H. Krivine, Nucl. Phys. A 589, 505 (1995).

    Article  ADS  Google Scholar 

  61. P.F. Mastinu et al., Phys. Rev. Lett. 76, 2646 (1996).

    Article  ADS  Google Scholar 

  62. Y.G. Ma, unpublished.

    Google Scholar 

  63. Y.G. Ma et al., Phys. Rev. C 60, 024607 (1999).

    Article  ADS  Google Scholar 

  64. Y.G. Ma, Phys. Rev. Lett. 83, 3617 (1999).

    Article  ADS  Google Scholar 

  65. Y.G. Ma, Eur. Phys. J. A 6, 367 (1999)

    Article  ADS  Google Scholar 

  66. G.K. Zipf, Human Behavior and the Principle of Least Effort (Addisson-Wesley Press, Cambridge, MA, 1949).

    Google Scholar 

  67. D.L. Turcotte, Rep. Prog. Phys. 62, 1377 (1999).

    Article  ADS  Google Scholar 

  68. M. Watanabe, Phys. Rev. E 53, 4187 (1996).

    Article  ADS  Google Scholar 

  69. T.D. Lee, C.N. Yang, Phys. Rev. 87, 410 (1952).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  70. T.S. Biro et al., Nucl. Phys. A 459, 692 (1986); S.K. Samaddar, J. Richert, Phys. Lett. B 218, 381 (1989); Z. Phys. A 332, 443 (1989); J.M. Carmona et al., Nucl. Phys. A 643, 115 (1998).

    Article  ADS  Google Scholar 

  71. X. Campi, H. Krivine, Nucl. Phys. A 620, 46 (1997).

    Article  ADS  Google Scholar 

  72. J. Pan, S. Das Gupta, Phys. Rev. C 53, 1319 (1996).

    Article  ADS  Google Scholar 

  73. W.F.J. Müller, Phys. Rev. C 56, 2873 (1997).

    Article  ADS  Google Scholar 

  74. J. Pan, S. Das Gupta, Phys. Lett. B 344, 29 (1995); Phys. Rev. C 51, 1384 (1995); Phys. Rev. Lett. 80, 1182 (1998); S. Das Gupta et al., Nucl. Phys. A 621, 897 (1997).

    Article  ADS  Google Scholar 

  75. J. Pan, S. Das Gupta, Phys. Rev. C 57, 1839 (1998).

    Article  ADS  Google Scholar 

  76. F. Gulminelli, Ph. Chomaz, Phys. Rev. Lett. 82, 1402 (1999).

    Article  ADS  Google Scholar 

  77. S. Ray et al., Phys. Lett. B 392, 7 (1997).

    Article  ADS  Google Scholar 

  78. A. Coniglio, E. Klein, J. Phys. A 13, 2775 (1980).

    Article  ADS  Google Scholar 

  79. G.F. Bertsch, P.J. Siemens, Phys. Lett. B 126, 9 (1983).

    Article  ADS  Google Scholar 

  80. L.G. Moretto et al., Phys. Rev. Lett. 77, 2634 (1996).

    Article  ADS  Google Scholar 

  81. L. Beaulieu et al., Phys. Rev. Lett. 84, 5971 (2000).

    Article  ADS  Google Scholar 

  82. M. Colonna et al., Phys. Rev. Lett. 88, 122701 (2002).

    Article  ADS  Google Scholar 

  83. B. Borderie et al., Phys. Rev. Lett. 86, 003252 (2001).

    Article  ADS  Google Scholar 

  84. A. Dabrowska, M. Szarska, A. Trzupek, W. Wolter, B. Bosiek, Acta Phys. Pol. B 32, 3099 (2001).

    Google Scholar 

  85. A. Dabrowska, M. Szarska, A. Trzupek, W. Wolter, B. Bosiek, Acta Phys. Pol. B 35, 2109 (2004).

    ADS  Google Scholar 

  86. X. Campi, H. Krivine, Phys. Rev. C 72, 057602 (2005).

    Article  ADS  Google Scholar 

  87. N. Sator, Phys. Rep. 376, 1 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  88. W. Bauer, B. Alleman, S. Pratt, nucl-th/0512101.

    Google Scholar 

  89. B. Mandelbrot, An informational theory of the statistical structure of language, in Communication Theory, edited by W. Jackson (Betterworths, 1953).

    Google Scholar 

  90. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, 1982)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Società Italiana di Fisica / Springer-Verlag

About this paper

Cite this paper

Ma, Y.G. (2006). Moment analysis and Zipf law. In: Chomaz, P., Gulminelli, F., Trautmann, W., Yennello, S.J. (eds) Dynamics and Thermodynamics with Nuclear Degrees of Freedom. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46496-9_18

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-46496-9_18

  • Received:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-46494-5

  • Online ISBN: 978-3-540-46496-9

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics