Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile


Autoria(s): Borges, G. M.; Ferreira, A. S.; Silva, M. A. A. da; Cressoni, J. C.; Viswanathan, G. M.; Mariz, A. M.
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

10/10/2013

10/10/2013

2012

Resumo

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e. g., fractional Brownian motion, Levy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation sigma t which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

CNPq

CNPq

FAPEAL

FAPEAL

FAPESP

FAPESP [2011/13685-6, 2011/06757-0]

Identificador

EUROPEAN PHYSICAL JOURNAL B, NEW YORK, v. 85, n. 9, SEP, 2012

1434-6028

http://www.producao.usp.br/handle/BDPI/34100

10.1140/epjb/e2012-30378-5

http://dx.doi.org/10.1140/epjb/e2012-30378-5

Idioma(s)

eng

Publicador

SPRINGER

NEW YORK

Relação

EUROPEAN PHYSICAL JOURNAL B

Direitos

restrictedAccess

Copyright SPRINGER

Palavras-Chave #ANOMALOUS DIFFUSION #FRACTIONAL DYNAMICS #PHYSICS, CONDENSED MATTER
Tipo

article

original article

publishedVersion