ANALISE DA DINAMICA DE PARTICULAS BROWNIANAS INTERAGENTES A PARTIR DE REDES DE MAPAS ACOPLADOS

Detalhes bibliográficos
Ano de defesa: 2009
Autor(a) principal: Szmoski, Romeu Miquéias lattes
Orientador(a): Pinto, Sandro Ely de Souza lattes
Banca de defesa: Batista, Antonio Marcos lattes, Viana, Ricardo Luiz lattes, Vicentini, Eduardo lattes
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: UNIVERSIDADE ESTADUAL DE PONTA GROSSA
Programa de Pós-Graduação: Programa de Pós-Graduação em Ciências
Departamento: Fisica
País: BR
Palavras-chave em Português:
Palavras-chave em Inglês:
Área do conhecimento CNPq:
Link de acesso: http://tede2.uepg.br/jspui/handle/prefix/876
Resumo: The Brownian motion is one important topic of the non-equilibrium statistical mechanics and it is related to many natural phenomena. The first observations and theories on this motion were essential for understand the microscopic behavior of the nature and its influence on macroscopics observables. In this dissertation, we studied the dynamics of a system composed of several interacting Brownian particle from the point of view of coupled maps lattices. We use a map with a direct correlation to the abovementioned motion and we employ four different kinds of couplings in order to represent several ways of interaction among the particles. Using nonlinear dynamics tools, we observe the situations in which the particles velocities synchronize or show a tendency to the synchronized state. We also obtain algebrics expressions for the Lyapunov spectra of lattices with regular couplings whose interactions decays with distance as a power-law and we raise two hypotheses about Lyapunov exponents of a lattice with the coupling probability decreasing with the distance, as follows: the exponents of this lattice converge to the exponents of the lattice whose interactions decay with the distance in agreement to a power-law when the number of particles is very large; and the Lyapunov exponents of this lattice are given by the sum of the probabilities products of the each coupling matrix by eigenvalues of these matrixes. The values obtained for the Lyapunov exponents by means of the expressions deducted are in agreement with those obtained by numerical approximations techniques. Regarding distributions of the velocities of the particles, we observed that occur an aproximation to a Gaussian distribuition when the intensity of the coupling tends to its maximum.