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Sepulveda, N., Josserand, C., & Rica, S. (2010). Superfluid density in a two-dimensional model of supersolid. Eur. Phys. J. B, 78(4), 439–447.
Abstract: We study in 2-dimensions the superfluid density of periodically modulated states in the framework of the mean-field Gross-Pitaevskii model of a quantum solid. We obtain a full agreement for the superfluid fraction between a semi-theoretical approach and direct numerical simulations. As in 1-dimension, the superfluid density decreases exponentially with the amplitude of the particle interaction. We discuss the case when defects are present in this modulated structure. In the case of isolated defects (e.g. dislocations) the superfluid density only shows small changes. Finally, we report an increase of the superfluid fraction up to 50% in the case of extended macroscopical defects. We show also that this excess of superfluid fraction depends on the length of the complex network of grain boundaries in the system.
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Cortez, V., Medina, P., Goles, E., Zarama, R., & Rica, S. (2015). Attractors, statistics and fluctuations of the dynamics of the Schelling's model for social segregation. Eur. Phys. J. B, 88(1), 12 pp.
Abstract: Statistical properties, fluctuations and probabilistic arguments are shown to explain the robust dynamics of the Schelling's social segregation model. With the aid of probability density functions we characterize the attractors for multiple external parameters and conditions. We discuss the role of the initial states and we show that, indeed, the system evolves towards well defined attractors. Finally, we provide probabilistic arguments to explain quantitatively the observed behavior.
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