* Data: 14/11
Neste seminário discutiremos um modelo para redes complexas fora do equilíbrio onde levamos em conta a idade dos sítios desde o seu “nascimento”, ou seja, a medida que a rede cresce os sítios envelhecem, e consideramos este envelhecimento exponencial. A cada passo de tempo, um novo sítio é acrescentado à rede; simultaneamente, uma ligação não-direcionada conecta 2 sítios aleatoriamente escolhidos com uma probabilidade proporcional à conectividade e a exponencial da idade dos sítios. O parâmetro que controla o envelhecimento leva a uma transição de fase dinâmica, de uma fase onde a rede apresenta um numero muito grande de aglomerados a uma fase com um único aglomerado que ocupa toda a rede. Este aglomerado gigante emerge em uma transição de fase de primeira ordem, e a localização do ponto crítico da transição e os expoentes críticos são determinados via finite-size scaling. Mostramos que a distribuição de tamanhos de aglomerados tem uma cauda exponencial abaixo do ponto critico. Medimos também o menor caminho médio entre dois sítios, e esta quantidade nos mostrou que esta transição pode ser vista como uma transição de mundo pequeno para mundo grande (“small to large world”), ou seja, o menor caminho médio escala com log N abaixo do ponto critico e escala com N acima do ponto critico, onde N é o número total de sítios da rede.
Discussão
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