Densidade Crítica no Modelo de Percolação em Rede de Bethe Não-Homogênea

Authors

  • Heliton Ribeiro Tavares Universidade Federal do Pará
  • R N C Souza Universidade Federal do Pará
  • M R Madruga Universidade Federal do Pará
  • V J C Farias Universidade Federal do Pará

DOI:

https://doi.org/10.5540/tema.2015.016.02.0173

Keywords:

Percolação não-homogênea, Rede de Bethe, Ponto Crítico

Abstract

Neste trabalho tratamos de um modelo percolaçãonão-homogênea na rede de Bethe cuja probabilidade de um elo nonível $n$ estar aberto muda de acordo com $n$. Este modelo podeser apropriado para situações onde o meio muda sua densidade deforma sistemática, tal como a proliferação de insetos que dependemda temperatura e umidade, que variam entre dia e noite.Consideramos o caso onde a probabilidade de um elo $e_n$ do nível$n$ estar aberto é dada pela função senóide $\overline{p}(e_n)=$$p \hspace{0.1cm} +(1-p)| \sen (n)|$. Para este modeloapresentarmos resultados de simulações Monte-Carlo que indicam umcomportamento da função de percolação com transição de fase desegunda ordem em $p_{c}$, mas provamos analiticamente a existênciade um ponto crítico não trivial, apresentando a expressão para aobtenção desta probabilidade crítica.

Author Biography

Heliton Ribeiro Tavares, Universidade Federal do Pará

Faculdade de Estatística

References

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Published

2015-09-07

How to Cite

Tavares, H. R., Souza, R. N. C., Madruga, M. R., & Farias, V. J. C. (2015). Densidade Crítica no Modelo de Percolação em Rede de Bethe Não-Homogênea. Trends in Computational and Applied Mathematics, 16(2), 173. https://doi.org/10.5540/tema.2015.016.02.0173

Issue

Vol. 16 No. 2 (2015)

Section

Original Article

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