Processos estocásticos não-markovianos em difusão anômala

• Ano de defesa: 2010
• Autor(a) principal: Lima, Marcelo Felisberto de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Alagoas; BR; Física geral; Física teórica e computacional; Mecânica estatística; Ótica; Ótica não linear; Proprie; Programa de Pós-Graduação em Física da Matéria Condensada; UFAL
• Palavras-chave em Português: Caminhadas aleatórias de Alzheimer; Caminhadas aleatórias markovianas e não-markovianas; Expoentes críticos; Alzheimer random walk; Markovian and non-markovian random walk; Critical exponents; CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::FISICA DA MATERIA CONDENSADA
• Link de acesso: http://repositorio.ufal.br/handle/riufal/1017

A classic problem in physics concerns normal versus anomalous diffusion. Fractal analysis of random walks with memory aims at quantitatively describing the complex phenomenology observed in economic, ecological, biological and physical systems. Markov processes exhaustively account for random walks with short-range memory. In contrast, long-range memory typically gives rise to non-Markovian walks. The most extreme case of a non-Markovian random walk corresponds to a stochastic process with dependence on the entire history of the system. We study a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of 4 phases, for this system: (i) classical nonpersistence, (ii) classical persistence (iii) log-periodic nonpersistence and (iv) log-periodic persistence driven by negative feedback. The first two phases possess continuous scale invariance symmetry, however log-periodicity breaks this symmetry. Instead, log-periodic motion satisfies discrete scale invariance symmetry, with complex rather than real fractal dimensions. We find for log-periodic persistence evidence not only of statistical but also of geometric self-similarity.