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Seminário de Mecânica Estatística

Um seminário extra de Mecânica Estatística será apresentado na próxima
sexta-feira, 19/09/2014, às 10:00h, na sala 201 do Instituto de Física.

Título: Slow, bursty dynamics on complex networks

Apresentador: Géza Ódor (Hungarian Academy of Sciences)

Resumo:
Quenched disorder is known to play a relevant role in dynamical
processes and phase transitions. By studying the Contact Process (CP)
we showed that Griffiths Phases (GP) and other rare region effects,
leading rather generically to anomalously slow (algebraic,
logarithmic,...) relaxation on Erdos-Renyi networks with explicit
quenched disorder. More surprisingly, we found that GPs can also
emerge solely as the consequence of topological heterogeneity
on generalized small world networks exhibiting finite topological
dimensions [1-3]. Similar power-law dynamics can also be observed
on scale-free trees in case of disassortative weighting schemes,
in the neighborhood of smeared phase transitions [4].
Recently I have pointed out that localization, described by
quenched mean-field approximations is related to the existence of
rare region effects and GPs in case of Susceptible Infected Susceptible (SIS)
models on various complex networks [5-7], in particular on Barabasi-Albert
type of networks with aging connections.

Bursty dynamics of agents is shown to appear at criticality or in
extended GPs even in case of Poisson processes. I provide numerical
evidence for power-law type of intercommunication time distributions
by simulating the CP and SIS. This observation suggests that in
case of non-stationary bursty systems the observed non-poissonian
behavior can emerge as the consequence of an underlying hidden poissonian
network process, which is either critical or exhibits strong rare-region
effects. On contrary, in time varying networks rare-region effects do not
cause deviation from the mean-field behavior and heterogeneity induced
burstyness is absent [8].

[1] M. A. Munoz, R. Juhasz, C. Castellano, and G, Odor,
Griffiths Phases on Complex Networks,
Phys. Rev. Lett. 105, 128701 (2010)
[2] G. Odor, R. Juhasz, C. Castellano, M. A. Munoz,
Griffiths phases in the contact process on complex networks,
AIP Conf. Proc. 1332, Melville, New York (2011) p. 172-178.
Non-equilibrium Statistical Physics Today,
Proc. of the 11th Granada Seminar on Computational and Statistical
Physics, La Herradura, Spain 13-17 Sept. 2010,
Editors: P. L. Garrido, J. Marro, F. de los Santos.
[3] R. Juhasz, G. Odor, C. Castellano, M. A. Munoz
Rare region effects in the contact process on networks
Phys. Rev. E 85, 066125 (2012)
[4] G. Odor, R. Pastor-Satorras,
Slow dynamics and rare-region effects in the contact process on
weighted tree networks
Phys. Rev. E 86, 026117 (2012)
[5] Geza Odor
Rare regions of the susceptible-infected-susceptible model on Barabasi-Albert
networks, Phys. Rev. E 87, 042132 (2013)
[6] Geza Odor
Slow dynamics of the contact process on complex networks
EPJ Web of Conferences 44, 04005 (2013)
[7] Geza Odor,
Spectral analysis and slow spreading dynamics on complex networks,
Phys. Rev. E 88 032109 (2013)
[8]  G. Odor,
Slow, bursty dynamics as the consequence of quenched network topologies,
arXiv:1401.5303