Sudden onset of log-periodicity and superdiffusion in non-Markovian random walks with amnestically induced persistence: Exact results

European Physical Journal B

Volumn 72, Issue 3, 2009, Pages 427-433

  Felisberto, M L ^a   Passos, F S ^a   Ferreira, A S ^a   Da Silva, M A A ^b   Cressoni, J C ^a   Viswanathan, G M ^a,c  

^a FEDERAL UNIVERSITY OF ALAGOAS   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL RESULTS; ANOMALOUS DIFFUSION; CLASSICAL SUPERDIFFUSION; CRITICAL EXPONENT; CRITICAL LINES; DISCRETE SCALE INVARIANCES; EXACT RESULTS; FIRST MOMENTS; HURST EXPONENTS; LOG-PERIODICITY; NEGATIVE FEEDBACK; NON-MARKOVIAN; ORDER PARAMETER; POSITIVE FEEDBACK; RANDOM WALK; SECOND MOMENTS; SECOND ORDERS; SUPERDIFFUSION;

DIFFUSION; FOKKER PLANCK EQUATION; INVARIANCE;

FEEDBACK;

EID: 72449182602     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2009-00361-6     Document Type: Article

References (30)

1. A. Einstein 1905 Annalen der Physik 17 549 10.1002/andp.19053220806 1905AnP....17..549E
2. L. Bachelier 1900 Annales Scientifiques de l'École Normale Superieure 17 21 1508978
3. R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics (Cambridge Univ. Press, Cambridge, 2000)
4. G.M. Schütz S. Trimper 2004 Phys. Rev. E 70 045101 10.1103/PhysRevE.70.045101 2004PhRvE..70d5101S
5. M.A.A. da Silva J.C. Cressoni G.M. Viswanathan 2006 Physica A 364 70 10.1016/j.physa.2005.08.066 2006PhyA..364...70D
6. J.C. Cressoni M.A.A. da Silva G.M. Viswanathan 2007 Phys. Rev. Lett. 98 070603 10.1103/PhysRevLett.98.070603 2284039 2007PhRvL..98g0603C
7. M.A.A. da Silva G.M. Viswanathan A.S. Ferreira J.C. Cressoni 2008 Phys. Rev. E 77 040101 10.1103/PhysRevE.77.040101
8. V.M. Kenkre, Analytic Formulation, Exact Solutions, and Generalizations of the Elephant and the Alzheimer Random Walks, e-print arXiv: 0708.0034v2 (2007)
9. V.M. Kenkre R.S. Knox 1974 Phys. Rev. B 9 5279 10.1103/PhysRevB.9.5279 1974PhRvB...9.5279K
10. V.M. Kenkre, in Statistical Mechanics and Statistical Methods in Theory and Application, edited by Landman U. (Plenum, New York, 1977)
11. B.D. Hughes M.F. Shlesinger E.W. Montroll 1981 Proc. Nat. Acad. Sci. 78 3287 0461.60085 10.1073/pnas.78.6.3287 619826 1981PNAS...78.3287H
12. M.F. Shlesinger 1979 Solid State Comm. 32 1207 10.1016/0038-1098(79) 90867-6 1979SSCom..32.1207S
13. R. Metzler J. Klafter 2000 Phys. Rep. 339 1 0984.82032 10.1016/S0370-1573(00)00070-3 1809268 2000PhR...339....1M
14. M.F. Shlesinger, G.M. Zaslavsky, U. Frisch, Lévy flights and related topics in physics (Springer, Berlin, 1995)
15. E. Barkai, R. Metzler, J. Klafter, Phys. Rev. E 61 (2000)
16. I.M. Sokolov 2000 Phys. Rev. E 63 011104 10.1103/PhysRevE.63.011104 2001PhRvE..63a1104S
17. G. Radons, R. Klages, I.M. Sokolov, Anomalous Transport (Wiley-VCH, Berlin, 2008)
18. H.E. Hurst, R.P. Black, Y.M. Simaika, Long-Term Storage: An Experimental Study (Constable, London, 1965)
19. B.B. Mandelbrot, The Fractal Geometry of Nature (Freeman W.H. and Co, New York, 1982)
20. A. Bunde, S. Havlin, Fractals and Disordered Systems (Springer, Berlin, 19910)
21. J.W. Bruce, D.D. William, The Lure of Modern Science: Fractal Thinking (World Scientific, Singapore, 1995)
22. J. Feder, Fractals (Plenum Press, New York, 1988)
23. A.L. Barabási, H.E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, Cambridge, 1995)
24. J.W. Kantelhardt S.A. Zschiegner E. Koscielny-Bunde S. Havlin A. Bunde H.E. Stanley 2002 Physica A 316 87 1001.62029 10.1016/S0378-4371(02)01383-3 2002PhyA..316...87K
25. H.E. Stanley 1999 Rev. Mod. Phys. 71 S358 10.1103/RevModPhys.71.S358
26. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, New York, 19710)
27. A.L. Barabási 1999 Science 286 509 10.1126/science.286.5439.509 2091634
28. P.C. Ivanov M.G. Rosenblum C.-K. Peng H.E. Stanley A.L. Goldberger 1996 Nature 383 323 10.1038/383323a0 1996Natur.383..323I
29. D. Sornette 2002 Proc. Nat. Acad. Sci. 99 2522 10.1073/pnas.022581999 2002PNAS...99.2522S
30. D. Sornette 1998 Phys. Rep. 297 239 10.1016/S0370-1573(97)00076-8 1710267