Alzheimer random walk model: Two previously overlooked diffusion regimes
Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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Data(s) |
05/11/2013
05/11/2013
2012
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Resumo |
A non-Markovian one-dimensional random walk model is studied with emphasis on the phase-diagram, showing all the diffusion regimes, along with the exactly determined critical lines. The model, known as the Alzheimer walk, is endowed with memory-controlled diffusion, responsible for the model's long-range correlations, and is characterized by a rich variety of diffusive regimes. The importance of this model is that superdiffusion arises due not to memory per se, but rather also due to loss of memory. The recently reported numerically and analytically estimated values for the Hurst exponent are hereby reviewed. We report the finding of two, previously overlooked, phases, namely, evanescent log-periodic diffusion and log-periodic diffusion with escape, both with Hurst exponent H = 1/2. In the former, the log-periodicity gets damped, whereas in the latter the first moment diverges. These phases further enrich the already intricate phase diagram. The results are discussed in the context of phase transitions, aging phenomena, and symmetry breaking. FAPESP FAPESP [2011/13685-6, 2011/06757-0] CNPq CNPq |
Identificador |
PHYSICAL REVIEW E, COLLEGE PK, v. 86, n. 4, supl. 1, Part 1, pp. 1439-1445, OCT 2, 2012 1539-3755 http://www.producao.usp.br/handle/BDPI/40901 10.1103/PhysRevE.86.042101 |
Idioma(s) |
eng |
Publicador |
AMER PHYSICAL SOC COLLEGE PK |
Relação |
PHYSICAL REVIEW E |
Direitos |
openAccess Copyright AMER PHYSICAL SOC |
Palavras-Chave | #DISCRETE-SCALE-INVARIANCE #FRACTIONAL DYNAMICS #DIMENSIONS #PHYSICS, FLUIDS & PLASMAS #PHYSICS, MATHEMATICAL |
Tipo |
article original article publishedVersion |