Estudo de sistemas complexos com interações de longo alcance : percolação, redes e tráfego
In this thesis we investigate physical problems which present a high degree of complexity using tools and models of Statistical Mechanics. We give a special attention to systems with long-range interactions, such as one-dimensional long-range bondpercolation, complex networks without metric and vehi...
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| Formato: | doctoralThesis |
| Idioma: | por |
| Publicado em: |
Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/16579 |
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| Resumo: | In this thesis we investigate physical problems which present a high degree of
complexity using tools and models of Statistical Mechanics. We give a special attention
to systems with long-range interactions, such as one-dimensional long-range bondpercolation,
complex networks without metric and vehicular traffic. The flux in linear
chain (percolation) with bond between first neighbor only happens if pc = 1, but when
we consider long-range interactions , the situation is completely different, i.e., the transitions
between the percolating phase and non-percolating phase happens for pc < 1. This
kind of transition happens even when the system is diluted ( dilution of sites ). Some of
these effects are investigated in this work, for example, the extensivity of the system, the
relation between critical properties and the dilution, etc. In particular we show that the
dilution does not change the universality of the system. In another work, we analyze the
implications of using a power law quality distribution for vertices in the growth dynamics
of a network studied by Bianconi and Barabási. It incorporates in the preferential attachment
the different ability (fitness) of the nodes to compete for links. Finally, we study the
vehicular traffic on road networks when it is submitted to an increasing flux of cars. In
this way, we develop two models which enable the analysis of the total flux on each road
as well as the flux leaving the system and the behavior of the total number of congested
roads |
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