Bem vindo ao site do Grupo de Sistemas Complexos do Instituto de Física da Universidade Federal Fluminense. O grupo de Sistemas Complexos do Instituto de Física da UFF já tem tradição como um dos mais importantes em simulações de sistemas estatísticos, no Brasil e no exterior, tendo já formado vários pesquisadores que ocupam posições em várias instituições de pesquisa no país. O caráter interdisciplinar do grupo é um fator de atração de estudantes, tanto do Brasil quanto do exterior, em especial da América do Sul. Já há vários anos que o grupo se reúne semanalmente para apresentação e discussão do andamento de seus vários projetos de pesquisa.

**Novidades**

O estudante de doutorado Angelo Mondaini Calvão defendeu sua tese intitulada “Estudos de Sistemas Dinâmicos não lineares: Pêndulo Duplo, Batimentos Cardíacos e Coletivos de Animais”. A defesa ocorreu no prédio do Instituto de Física, Campus da Praia Vermelha, no último dia 19/02/2014. O orientador foi o Professor Thadeu Penna. Parabéns Angelo!

**Seminários**

- Data: 22/09/14 às 16:00
- Local: Sl A5-01
- Apresentador: Ana Carolina Ribeiro Teixeira - UFRGS

Resumo: Long-range interacting (LRI) systems are ubiquitous in nature. They range from the astronomical scale (e.g. self-gravitating systems), to the macroscopic (e.g. non-neutral plasmas, wave-plasma interacting systems, two-dimensional geophysical vortex systems), down to the atomic scale (e.g. classical and quantum cold atoms interacting via quasi-resonant lasers). Despite their importance, much of the behaviour of these systems still remains poorly understood. It is known that LRI systems can exhibit ergodicity-breaking, anomalous relaxation and diffusion, quasi-stationary states (qSS), vanishing Lyapunov exponents, ensemble inequivalence, negative specific heat, temperature discontinuities. Thermodynamic anomalies result from the non-additivity of energy, while dynamical ones arise from the complexity of collisionless relaxation driven by the wave-particle interactions.

In the thermodynamic limit, dynamics is governed by the Vlasov equation, which has an infinity of stationary solutions. Approaching the thermodynamic limit, LRI systems do not relax to equilibrium, but become trapped in qSS, whose life-time diverges with the particle number, whence the importance of studying Vlasov stationary states.

In this talk we will explore the relaxation to qSS of two long-range potential models, namely, the Hamiltonian Mean-Field (HMF) model and gravitation in three dimensions, for some classes of initial conditions (ICs) of interest. In the case of the HMF we show that if the initial distribution satisfies the virial condition, thereby reducing mean-field changes, the final distribution in the qSS can be predicted very accurately using a reduced exactly integrable model. For gravitation in 3d, we have tested spherically symmetric initial conditions satisfying the virial condition and isotropy in velocity. Again, the integrable approximation fits well qSS radial and velocity marginal distributions obtained through molecular dynamics. The distribution functions obtained using this approach are found to be more accurate than the ones predicted by the ergodic Lynden-Bell theory.

For ICs not obeying the virial condition, ergodicity-breaking has been shown to happen through parametric resonances between certain particles and the strong mean-field oscillations felt by particles. This mechanism is analogous to the nonlinear Landau damping seen in particle-wave interactions in plasmas. For these ICs Lynden-Bell distributions do not coincide with qSS distributions obtained through molecular dynamics. The present work goes a step beyond, showing that the ergodicity hypothesis is neither applicable to ICs obeying the virial condition, since an exactly integrable model provides a better approximation to the aforementioned distributions.

* Ana C. Ribeiro-Teixeira, Fernanda P. C. Benetti, Renato Pakter, Yan Levin, Phys. Rev. E 89 (2014) 022130

* Fernanda P. C. Benetti, Ana C. Ribeiro-Teixeira, Renato Pakter, Yan Levin, Phys. Rev. Lett. 113 (2014) 100602.

- Data: 19/09/14 às 10:00 h
- Local: Sl A5-01
- 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

**Parcerias**

**Apoio**

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