메뉴 건너뛰기




Volumn 369, Issue 1, 2006, Pages 29-70

Theoretical studies of self-organized criticality

Author keywords

Abelian; Avalanches; Dissipation; River networks; Sandpile; Self organized criticality

Indexed keywords

ALGEBRA; AVALANCHES (SNOWSLIDES); CRYSTAL LATTICES; ENERGY DISSIPATION; PROBLEM SOLVING; STATISTICAL METHODS;

EID: 33745657432     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2006.04.004     Document Type: Article
Times cited : (283)

References (131)
  • 1
    • 33745675668 scopus 로고    scopus 로고
    • Available at arXiv.org/abs/cond-mat/9909009.
  • 3
    • 0000231046 scopus 로고    scopus 로고
    • A good introduction to various scaling laws in river-networks and references to earlier literature may be found in P.S. Dodds, D.H. Rothman, Phys. Rev. E 59 (1999) 4865
  • 4
    • 18644386664 scopus 로고    scopus 로고
    • P.S. Dodds, D.H. Rothman, Phys. Rev. E 63 (2001) 016115
  • 5
    • 18644367909 scopus 로고    scopus 로고
    • P.S. Dodds, D.H. Rothman, Phys. Rev. E 016116 (2001); P.S. Dodds, D.H. Rothman, Phys. Rev. E 016117 (2001). See also F. Colaiori, A. Flammini, A. Maritan, J.R. Banavar, Phys. Rev. Lett. 78 (1997) 4522
  • 6
    • 0035535089 scopus 로고    scopus 로고
    • J.R. Banavar, F. Colaiori, A. Flammini, A. Rinaldo, J. Stat. Phys. (2001) 1.
  • 12
    • 0002622074 scopus 로고    scopus 로고
    • The actual behavior of real sand is more complicated than this rather idealized description. Our concern here is to provide a physical motivation for the mathematical model. For a recent discussion of more realistic models of granular media, see H.J. Herrmann, Physica A 263 (1999) 51.
  • 13
    • 0003432181 scopus 로고    scopus 로고
    • Oxford University Press, Oxford
    • Bak P. How Nature Works (1997), Oxford University Press, Oxford
    • (1997) How Nature Works
    • Bak, P.1
  • 18
    • 33745677194 scopus 로고    scopus 로고
    • F. Redig, Les Houches Lectures, preprint, 2005.
  • 23
    • 33745676759 scopus 로고    scopus 로고
    • Models of this type were studied earlier by R. Burridge, L. Knopoff, Bull. Seismol. Soc. Am. 57 (1967) 341
  • 31
    • 33745667731 scopus 로고    scopus 로고
    • 2, which is actually an optimal bound.
  • 36
    • 33745669880 scopus 로고    scopus 로고
    • "My name means the shape I am- and a good handsome shape it is too. With a name like yours, you might be any shape, almost."- Humpty Dumpty to Alice in Through the Looking Glass by Lewis Carroll.
  • 43
    • 21144462565 scopus 로고    scopus 로고
    • This procedure is equivalent to the script test first proposed in Speer E. R., J. Phys. A 71 (1993) 61.
  • 48
    • 0042492825 scopus 로고    scopus 로고
    • For a recent treatment of this classical result, see F.Y. Wu, Rev. Mod. Phys. 54 (1982) 235.
  • 51
    • 0003780715 scopus 로고
    • Addison-Wesley, Reading, MA
    • Harary F. Graph Theory (1990), Addison-Wesley, Reading, MA
    • (1990) Graph Theory
    • Harary, F.1
  • 73
    • 0012523712 scopus 로고    scopus 로고
    • See also V.B. Priezzhev, Physica Scripta T49B (1993) 663.
  • 74
    • 33745661187 scopus 로고    scopus 로고
    • P. Grassberger, private communication.
  • 87
    • 0035335031 scopus 로고    scopus 로고
    • [cond-mat 0012102]
    • Agrawal H., and Dhar D. Phys. Rev. E 63 (2001) 056115 [cond-mat 0012102]
    • (2001) Phys. Rev. E , vol.63 , pp. 056115
    • Agrawal, H.1    Dhar, D.2
  • 88
  • 104
    • 33745655791 scopus 로고    scopus 로고
    • L. Laurson, M.J. Alava, S. Zapperi, J. Stat. Mech.; Theo. Exp. (2005) L11001.
  • 105
  • 108
    • 33745678706 scopus 로고    scopus 로고
    • P. Pradhan, D. Dhar, to appear in Phys. Rev. E (2006) [cond-mat/051127].
  • 109
    • 33745642087 scopus 로고    scopus 로고
    • M. Baiesi, C. Maes, preprint 2005 [cond-mat/0505274].
  • 118
    • 0009672256 scopus 로고    scopus 로고
    • [math-ph/0011042]
    • Kenyon R. Act. Math. 185 (2000) 239 [math-ph/0011042]
    • (2000) Act. Math. , vol.185 , pp. 239
    • Kenyon, R.1
  • 127
    • 0032629418 scopus 로고    scopus 로고
    • [cond-mat 9902137]
    • Dhar D. Physica A 270 (1999) 69 [cond-mat 9902137]
    • (1999) Physica A , vol.270 , pp. 69
    • Dhar, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.