Processos aleatórios não-markovianos: perfis de memória
One of the mechanisms responsible for the anomalous diffusion is the existence of long-range temporal correlations, for example, Fractional Brownian Motion and walk models according to Elephant memory and Alzheimer profiles, whereas in the latter two cases the walker can always "remember&quo...
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| Formato: | doctoralThesis |
| Idioma: | por |
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Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/18624 |
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| Resumo: | One of the mechanisms responsible for the anomalous diffusion is the existence of
long-range temporal correlations, for example, Fractional Brownian Motion and walk models
according to Elephant memory and Alzheimer profiles, whereas in the latter two cases the
walker can always "remember" of his first steps. The question to be elucidated, and the
was the main motivation of our work, is if memory of the historic initial is condition for
observation anomalous diffusion (in this case, superdiffusion).
We give a conclusive answer, by studying a non-Markovian model in which the
walkers memory of the past, at time t, is given by a Gaussian centered at time t=2 and
standard deviation t which grows linearly as the walker ages. For large widths of we
find that the model behaves similarly to the Elephant model; In the opposite limit (! 0),
although the walker forget the early days, we observed similar results to the Alzheimer walk
model, in particular the presence of amnestically induced persistence, characterized by certain
log-periodic oscillations. We conclude that the memory of earlier times is not a necessary
condition for the generating of superdiffusion nor the amnestically induced persistence and
can appear even in profiles of memory that forgets the initial steps, like the Gausssian memory
profile investigated here. |
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