Conexão entre as redes complexas e estatística de Kaniadakis e busca eficiente das propriedades críticas do processo epidêmico difusivo 1D

• Ano de defesa: 2011
• Autor(a) principal: Macedo Filho, Antonio de
• Orientador(a): Silva, Luciano Rodrigues da
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal do Rio Grande do Norte
• Programa de Pós-Graduação: Programa de Pós-Graduação em Física
• Departamento: Física da Matéria Condensada; Astrofísica e Cosmologia; Física da Ionosfera
• País: BR
• Palavras-chave em Português: Redes complexas; Estatísticas não gaussianas; Epdemias; Difusão
• Palavras-chave em Inglês: Complex networks; not Gaussian statistics; Epdemias; Diffusion
• Área do conhecimento CNPq: CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA
• Link de acesso: https://repositorio.ufrn.br/jspui/handle/123456789/16576

In this work we study a connection between a non-Gaussian statistics, the Kaniadakis statistics, and Complex Networks. We show that the degree distribution P(k)of a scale free-network, can be calculated using a maximization of information entropy in the context of non-gaussian statistics. As an example, a numerical analysis based on the preferential attachment growth model is discussed, as well as a numerical behavior of the Kaniadakis and Tsallis degree distribution is compared. We also analyze the diffusive epidemic process (DEP) on a regular lattice one-dimensional. The model is composed of A (healthy) and B (sick) species that independently diffusive on lattice with diffusion rates DA and DB for which the probabilistic dynamical rule A + B &#8594; 2B and B &#8594; A. This model belongs to the category of non-equilibrium systems with an absorbing state and a phase transition between active an inactive states. We investigate the critical behavior of the DEP using an auto-adaptive algorithm to find critical points: the method of automatic searching for critical points (MASCP). We compare our results with the literature and we find that the MASCP successfully finds the critical exponents 1/&#1141; and 1/z&#1141; in all the cases DA =DB, DA <DB and DA >DB. The simulations show that the DEP has the same critical exponents as are expected from field-theoretical arguments. Moreover, we find that, contrary to a renormalization group prediction, the system does not show a discontinuous phase transition in the regime o DA >DB.