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Previous issue date: 2014-09-12 / Os modelos de caminhada aleat?ria com correla??o temporal (ou seja, mem?ria)
t?m despertado o interesse para o estudo sobre difus?o an?mala. A caminhada aleat?ria e
suas generaliza??es v?m ocupando um lugar de destaque na caracteriza??o de fen?menos
f?sicos, qu?micos e biol?gicos. A correla??o temporal ? um fator necess?rio neste modelos
para provocar difus?o an?mala. Os modelos que apresentam correla??es temporais de
longo-alcance s?o denominados genuinamente de n?o-Markovianos, caso contr?rio, de
curto-alcance, Markovianos. Dentro deste contexto, fizemos uma revis?o dos modelos j?
existentes que apresentam correla??o temporal, isto ?, mem?ria total, modelo de caminhada
do elefante, ou mem?ria parcial, modelo de caminhada com alzheimer e o modelo
com mem?ria com perfil gaussiano. Percebe-se que esses modelos apresentaram superdifus?o,
expoente de Hurst (H > 1/2). Estudamos neste trabalho um modelo de caminhada
aleat?ria superdifusivo com mem?ria exponencialmente decrescente. Esse parece
ser um resultado contradit?rio, uma vez que, ? bem conhecido que a caminhada aleat?-
ria com correla??es que decaem exponencialmente pode ser aproximada arbitrariamente
bem por um processo Markoviano e que o teorema do limite central pro?be superdifus?o
quando a vari?ncia do tamanho dos passos for finita. Nossa proposta para resolver
o aparente paradoxo parte do princ?pio de que o modelo exponencial seja genuinamente
n?o-Markoviano, devido a constante de decaimento da exponencial ser dependente de
tempo. Finalmente, discutimos ideias para futuras investiga??es. / The random walk models with temporal correlation (i.e. memory) are of interest
in the study of anomalous diffusion phenomena. The random walk and its generalizations
are of prominent place in the characterization of various physical, chemical and biological
phenomena. The temporal correlation is an essential feature in anomalous diffusion models.
These temporal long-range correlation models can be called non-Markovian models,
otherwise, the short-range time correlation counterparts are Markovian ones. Within this
context, we reviewed the existing models with temporal correlation, i.e. entire memory,
the elephant walk model, or partial memory, alzheimer walk model and walk model with
a gaussian memory with profile. It is noticed that these models shows superdiffusion with
a Hurst exponent H > 1/2. We study in this work a superdiffusive random walk model
with exponentially decaying memory. This seems to be a self-contradictory statement,
since it is well known that random walks with exponentially decaying temporal correlations
can be approximated arbitrarily well by Markov processes and that central limit
theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes.
The solution to the apparent paradox is that the model is genuinely non-Markovian, due
to a time-dependent decay constant associated with the exponential behavior. In the end,
we discuss ideas for future investigations.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/19905 |
| Date | 12 September 2014 |
| Creators | Alves, Gladstone de Alencar |
| Contributors | 04295882755, http://lattes.cnpq.br/1995273890709490, Moreira, Francisco George Brady, 51165104849, http://lattes.cnpq.br/7639883073103206, Cressoni, Jos? Carlos, 51203197853, http://lattes.cnpq.br/5225216368135366, Silva, Marco Antonio Alves da, 70791872815, http://lattes.cnpq.br/1188741573332436, Silva, Luciano Rodrigues da, Mohan, Madras Viswanathan Gandhi |
| Publisher | Universidade Federal do Rio Grande do Norte, PROGRAMA DE P?S-GRADUA??O EM F?SICA, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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