Strong evidences for a nonextensive behavior of the rotation period in Open Clusters

Time-dependent nonextensivity in a stellar astrophysical scenario combines nonextensive entropic indices $q_{K}$ derived from the modified Kawaler's parametrization, and $q$, obtained from rotational velocity distribution. These $q$'s are related through a heuristic single relation given by $q\approx q_{0}(1-\Delta t/q_{K})$, where $t$ is the cluster age. In a nonextensive scenario, these indices are quantities that measure the degree of nonextensivity present in the system. Recent studies reveal that the index $q$ is correlated to the formation rate of high-energy tails present in the distribution of rotation velocity. On the other hand, the index $q_{K}$ is determined by the stellar rotation-age relationship. This depends on the magnetic field configuration through the expression $q_{K}=1+4aN/3$, where $a$ and $N$ denote the saturation level of the star magnetic field and its topology, respectively. In the present study, we show that the connection $q-q_{K}$ is also consistent with 548 rotation period data for single main-sequence stars in 11 Open Clusters aged less than 1 Gyr. The value of $q_{K}\sim$ 2.5 from our unsaturated model shows that the mean magnetic field topology of these stars is slightly more complex than a purely radial field. Our results also suggest that stellar rotational braking behavior affects the degree of anti-correlation between $q$ and cluster age $t$. Finally, we suggest that stellar magnetic braking can be scaled by the entropic index $q$.Comment: 6 pages and 2 figures, accepted to EPL on October 17, 201

An extended formalism for preferential attachment in heterogeneous complex networks

In this paper we present a framework for the extension of the preferential attachment (PA) model to heterogeneous complex networks. We define a class of heterogeneous PA models, where node properties are described by fixed states in an arbitrary metric space, and introduce an affinity function that biases the attachment probabilities of links. We perform an analytical study of the stationary degree distributions in heterogeneous PA networks. We show that their degree densities exhibit a richer scaling behavior than their homogeneous counterparts, and that the power law scaling in the degree distribution is robust in presence of heterogeneity

Preferential attachment growth model and nonextensive statistical mechanics

We introduce a two-dimensional growth model where every new site is located, at a distance $r$ from the barycenter of the pre-existing graph, according to the probability law $1/r^{2+\alpha_G} (\alpha_G \ge 0)$, and is attached to (only) one pre-existing site with a probability $\propto k_i/r^{\alpha_A}_i (\alpha_A \ge 0$; $k_i$ is the number of links of the $i^{th}$ site of the pre-existing graph, and $r_i$ its distance to the new site). Then we numerically determine that the probability distribution for a site to have $k$ links is asymptotically given, for all values of $\alpha_G$, by $P(k) \propto e_q^{-k/\kappa}$, where $e_q^x \equiv [1+(1-q)x]^{1/(1-q)}$ is the function naturally emerging within nonextensive statistical mechanics. The entropic index is numerically given (at least for $\alpha_A$ not too large) by $q = 1+(1/3) e^{-0.526 \alpha_A}$, and the characteristic number of links by $\kappa \simeq 0.1+0.08 \alpha_A$. The $\alpha_A=0$ particular case belongs to the same universality class to which the Barabasi-Albert model belongs. In addition to this, we have numerically studied the rate at which the average number of links $$ increases with the scaled time $t/i$; asymptotically, $\propto (t/i)^\beta$, the exponent being close to $\beta={1/2}(1-\alpha_A)$ for $0 \le \alpha_A \le 1$, and zero otherwise. The present results reinforce the conjecture that the microscopic dynamics of nonextensive systems typically build (for instance, in Gibbs $\Gamma$-space for Hamiltonian systems) a scale-free network.Comment: 5 pages including 5 figures (the original colored figures 1 and 5a can be asked directly to the authors

New species and new record of anthomedusae from southern Brazil

A new species of Hydromedusa belonging to the genus Octocanna Haeckel 1879, here revived, is described from the coastal waters off Santos. The new species belongs to the family Phialuciidae, it is named Octocanna haeckeli sp. n. and differs from the other two species of the genus in being smaller, in having a high dome shaped umbrella, four tentacles, eight bulbs and eight marginal vesicles at sexual maturity. The genus Octocanna is here revived for Phialuciidae with eight radial canals, eight gonads, four or more tentacles and never more than four lips. The genus Octophialucium Kramp 1955 is considered valid for Phialuciidae with eight radial canals, eight gonads and eight lips. In the same series of samples, some specimens of Octophialucium bigelowi Kramp 1955 were taken which are very similar to Octocanna haeckeli but have eight lips, eight tentacles, rudimentary bulbs and a larger number of marginal vesicles at sexual maturity, which is reached at approximately the same umbrella size. The two similar species were taken in the same water mass at approximately the same time of the same year.Descreve-se uma nova espécie de hidromedusa, coletada em águas costeiras próximas a Santos, pertencente ao gênero Octocanna Haeckel 1879. Este gênero foi considerado obsoleto por KRAMP, mas o achado presente mostra que deve ser reestabelecido. A nova espécie chamada Otocanna haeckeli pertence à família Phialuciidae. Difere das outras duas espécies do mesmo gênero por ser menor, ter umbrela alta em forma de domo, 4 tentáculos, 8 bulbos e 8 vesículas marginais quando atinge a maturidade sexual. A validade do gênero Octocanna fica restabelecida para as Phialuciidae com 8 canais radiais, 8 gônadas, 4 ou mais tentáculos e nunca mais do que 4 lábios. O gênero Octophialucium Kramp 1955 é mantido como válido para Phialuciidae com 8 canais radiais, 8 gônadas e 8 lábios. Na mesma série de amostras foram coletados alguns espécimes de Octophialucium bigelowi Kramp 1955 que se assemelham à primeira vista a Octocanna haeckeli, mas têm 8 lábios, 8 tentáculos, bulbos rudimentares e um número maior de vesículas marginais quando sexualmente maduros. Ambas as espécies atingem a maturidade com aproximadamente o mesmo tamanho e foram coletadas na mesma massa d'água, em datas próximas do mesmo ano