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Master's Dissertation
DOI
10.11606/D.54.1992.tde-05112008-123546
Document
Author
Full name
Ubiraci Pereira da Costa Neves
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1992
Supervisor
Committee
Onody, Roberto Nicolau (President)
Fontanari, Jose Fernando
Oliveira, Mario Jose de
Title in Portuguese
Percolação direcionada em redes regulares bidimensionais.
Keywords in Portuguese
Aproximantes de Padé
Matriz de transferência
Percolação
Abstract in Portuguese
Utilizando uma técnica de matriz de transferência, expandimos em série a probabilidade de percolação P(q) para o problema da percolação por sítio na rede quadrada direcionada. Nosso método revela uma inesperada conexão entre este problema e o da enumeração dos modos de se dissecar uma bola. Mostramos que o método pode também ser usado para se expandir em série o tamanho médio do cluster S (p) . Uma análise baseada nos aproximantes de Padé fornece estimativas do valor crítico pc, e também do expoente crítico β.
Title in English
Directed percolation on two-dimensional regular lattices.
Keywords in English
Padé approximants
Percolation
Transfer matrix
Abstract in English
Using a transfer matrix technique we obtain an extended series expansion of the percolation probability P(q) for the directed site percolation problem on the square lattice. Our method reveals an up to now unsuspected connection between this problem and the enumeration of the ways of dissecting a ball. We show that the method can also be used to determine a series expansion for the mean cluster size S(p). An analysis based on Padé approximants gives estimates of the critical threshold pc, and also of the critical exponent β.
 
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UbiraciNevesM.pdf (2.56 Mbytes)
Publishing Date
2008-11-06
 
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