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

Autor(es)

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]}

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: European Physical Journal B; v. 72, n. 3, p. 427-433, DEC 2009.
• Citações Web of Science: 3

Resumo

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)

• Processo FAPESP: 07/04220-4 - Processo de difusão e agregação em física biológica: doenças priônicas e passeios aleatórios com memória
• Beneficiário: Marco Antonio Alves da Silva
• Linha de fomento: Auxílio à Pesquisa - Regular