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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

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

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Author(s):
Felisberto, M. L. [1] ; Passos, F. S. [1] ; Ferreira, A. S. [1] ; da Silva, M. A. A. [2] ; Cressoni, J. C. [1] ; Viswanathan, G. M. [3, 1, 4]
Total Authors: 6
Affiliation:
[1] Univ Fed Alagoas, Inst Fis, BR-57072970 Maceio, AL - Brazil
[2] Univ Sao Paulo, Dept Quim & Fis, FCFRP, BR-14040903 Ribeirao Preto, SP - Brazil
[3] Univ New Mexico, Dept Phys & Astron, Albuquerque, NM 87131 - USA
[4] Univ New Mexico, Consortium Amer Interdisciplinary Sci, Albuquerque, NM 87131 - USA
Total Affiliations: 4
Document type: Journal article
Source: European Physical Journal B; v. 72, n. 3, p. 427-433, DEC 2009.
Web of Science Citations: 3
Abstract

Random walks can undergo transitions from normal diffusion to anomalous diffusion as some relevant parameter varies, for instance the L,vy index in L,vy flights. Here we derive the Fokker-Planck equation for a two-parameter family of non-Markovian random walks with amnestically induced persistence. We investigate two distinct transitions: one order parameter quantifies log-periodicity and discrete scale invariance in the first moment of the propagator, whereas the second order parameter, known as the Hurst exponent, describes the growth of the second moment. We report numerical and analytical results for six critical exponents, which together completely characterize the properties of the transitions. We find that the critical exponents related to the diffusion-superdiffusion transition are identical in the positive feedback and negative feedback branches of the critical line, even though the former leads to classical superdiffusion whereas the latter gives rise to log-periodic superdiffusion. (AU)

FAPESP's process: 07/04220-4 - Diffusion and aggregation process in biological physics: prionic diseases and random walks with memory
Grantee:Marco Antonio Alves da Silva
Support Opportunities: Regular Research Grants