Editorial Office:
Management:
R. S. Oyarzabal
Technical Support:
D. H. Diaz
M. A. Gomez
W. Abrahão
G. Oliveira
Publisher by Knobook Pub
doi: 10.6062/jcis.2008.01.02.0012(Free PDF)
Guilherme R. Rezende, Luciano C. Lapas and Fernando A. Oliveira
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known better. In this paper, we discuss how simple ideas of diffusion can be used to deal with the description of most complex structure.
Anomalous diffusion, non-exponential behavior, ergodicity.
[1] PINCUS SM. 1991. Proc. Nati. Acad. Sci. USA, 88: 2297.
[2] ROSA RR, SHARMA AA & VALDIVIA JA. 1999. Int. J. Mod. Phys. C, 10: 147. 10.1142/S0129183199000103
[3] KUBO R, TODA M & HASHITSUME N. 1991. Statistical Physics II, (Springer, Berlin).
[4] CROSS MC & HOHENBERG PC. 1993. Rev. Mod. Phys. 65: 851. 10.1103/RevModPhys.65.851
[5] FUENTES MA, KUPERMAN MN & KENKRE VM. 2003. Phys. Rev. Lett., 91: 158104. 10.1103/PhysRevLett.91.158104
[6] GIUGGIOLI L & KENKRE VM. 2003. Physica D, 183: 245. doi:10.1016/S0167-2789(03)00176-3
[7] DA CUNHA JAR, PENNA ALA, VAINSTEIN MH, MORGADO R & OLIVEIRA FA. 2009. Phys. Lett. A, 373: 661. 10.1016/j.physleta.2008.12.034
[8] DA CUNHA JAR, PENNA ALA & OLIVEIRA FA, this section.
[9] COSTA IVL, MORGADO R, LIMA MVBT & OLIVEIRA FA. 2003. Europhys. Lett., 63: 173. 10.1209/epl/i2003-00514-3
[10] LAPAS LC, COSTA IVL, VAINSTEIN MH & OLIVEIRA FA. 2007. Europhys. Lett., 77: 37004. 10.1209/0295-5075/77/37004
[11] LEE MH. 2007. Phys. Rev. Lett., 98: 190601. 10.1103/PhysRevLett.98.190601
[12] KHINCHIN AY. 1949. Mathematical Foundations of Statistical Mechanics. (Dover, New York).
[13] BOLTZMANN L. 1974. On the Development of the Methods of Theoretical Physics in Recent Times. In: Theoretical Physics and Philosophical Problems: Selected Writings, (Kluwer Academic Publishers).
[14] LEE MH. 2001. Phys. Rev. Lett., 87: 250601. 10.1103/PhysRevLett.87.250601
[15] OLIVEIRA FA. 1981. Sol. Stat. Comm., 40: 859. doi:10.1016/0038-1098(81)90171-X
[16] KRAMERS HA. 1940. Physica, 7: 284. doi:10.1016/S0031-8914(40)90098-2
[17] HANGGI P, TALKNER P & BORKOVEC M. 1990. Rev. Mod. Phys., š 62: 251. 10.1103/RevModPhys.62.251
[18] OLIVEIRA FA. 1998. Physica A, 257: 128. doi:10.1016/S0378-4371(98)00134-4
[19] ASTUMIAN RD & HANGGI P. 2002. Physics Today, 55: 33. š doi:10.1063/1.1535005
[20] MORGADO R, OLIVEIRA FA, BATROUNI GG & HANSEN A. 2002. Phys. Rev. Lett., 89: 100601. 10.1103/PhysRevLett.89.100601
[21] BULASHENKO OM & RUBI JM. 2002. Phys. Rev. Lett., 66: 045310. 10.1103/PhysRevB.66.045310
[22] BAO JD & ZHUO YZ. 2003. Phys. Rev. Lett., 91: 138104. 10.1103/PhysRevLett.91.138104
[23] BUDINI AA & CACERES M. 2004. J. Phys. A: Math. Gen., 37: 5959. doi: 10.1088/0305-4470/37/23/002
[24] DOREA CCY & MEDINO AV. 2006. J. Stat. Phys., 123: 685. DOI: 10.1007/s10955-006-9074-2
[25] BAO JD, ZHUO YZ, OLIVEIRA FA & HANGGI P. 2006. Phys. Rev. E, š 74: 061111.
[26] MORI H. 1965. Prog. Theor. Phys., 33: 423.
[27] KUBO R. 1966. Rep. Prog. Phys., 29: 255.
[28] KAUZMANN W. 1948. Chem. Rev., 43: 219.
[29] PEREZ-MADRID A, REGUERA D & RUB Ž Ž I JM. 2003. Physica A, 329: 357.
[30] LAPAS LC, MORGADO R, VAINSTEIN MH, RUBÍ JM & OLIVEIRA FA. 2008. Phys. Rev. Lett., 101: 230602.
[31] HELLEMAN RHG. 1980. Fundamental Problems in Statistical Mechanics, volume 5, (North-Holland, Amsterdam).
[32] KOU SC & XIE XS. 2004. Phys. Rev. Lett., 93: 180603.
[33] DUA A & ADHIKARI R. 2008. arXiv:0810.2232v1.
[34] LEE MH. 1983. Phys. Rev. Lett., 51: 1227.
[35] GLUSKIN E. 2003. Eur. J. Phys., 24: 591.
[36] SHLESINGER MF, ZASLAVSKY GM & KLAFTER J. 1993. Nature, 363: 31.
[37] ZASLAVSKY GM. 2003. Phys. Rep., 371: 461.
[38] RICCI-TERSENGHI F, STARIOLO DA & ARENZON JJ. 2000. Phys. Rev. Lett., 84: 4473.
[39] HENTSCHEL HGE, ILYIN V, MAKEDONSKA N, PROCACCIA I & SCHUPPER N. 2007. Phys. Rev. E, 75: R050404.
[40] METZLER R & KLAFTER J. 2000. Phys. Rep., 339: 1.
[41] METZLER R & KLAFTER J. 2004. J. Phys. A: Math. Gen., 37: 161.
[42] SANTAMARŽ IA-HOLEK I, REGUERA D & RUBŽ I JM. 2001. Phys. Rev. E, 63: 051106.
[43] RUBI JM & KJELSTRUP S. 2003. J. Phys. Chem. B, 107: 13471.
[44] VAINSTEIN MH, COSTA IVL & OLIVEIRA FA. 2006. Lect. Not. Phys., 688: 159.
[45] VAINSTEIN MH, COSTA IVL, MORGADO R & OLIVEIRA FA. 2006. Europhys. Lett., 73: 726.
[46] HELENIUS J, BROUHARD G, KALAIDZIDIS Y, DIEZ S & HOWARD J. 2006. Nature, 441: 115.
[47] FARETTA MR & BASSETTI B. 1998. Europhys. Lett., 41: 689.
[48] RUBŽ I JM & PEREZ-VICENTE C (Eds.). 1997. Complex behaviour of glassy systems. (Springer, Berlin).
[49] FRAUENFELDER H, SLIGAR SG & WOLYNES PG. 1991. Science, 254: 1598.
[50] ONUCHIC JN, LUTHEY-SCHULTEN Z & WOLYNES PG. 1997. Ann. Rev. Phys. Chem., 48: 545.
[51] KAFRI Y, LUBENSKY DK & NELSON DR. 2005. Phys. Rev. E, 71: 041906.