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

A nonextensive insight to the stellar initial mass function

the present paper, we propose that the stellar initial mass distributions as known as IMF are best fitted by $q$-Weibulls that emerge within nonextensive statistical mechanics. As a result, we show that the Salpeter's slope of $\sim$2.35 is replaced when a $q$-Weibull distribution is used. Our results point out that the nonextensive entropic index $q$ represents a new approach for understanding the process of the star-forming and evolution of massive stars.Comment: 5 pages, 2 figures, Accepted to EP

Notes on the Two-brane Model with Variable Tension

Motivated by possible extensions of the braneworld models with two branes, we investigate some consequences of a variable brane tension using the well established results on consistency conditions. By a slight modification of the usual stress-tensor used in order to derive the braneworld sum rules, we find out some important constraints obeyed by time dependent brane tensions. In particular it is shown that the tensions of two Randall-Sundrum like branes obeying, at the same time, an Eotvos law, aggravate the fine tuning problem. Also, it is shown that if the hidden brane tension obeys an Eotvos law, then the visible brane has a mixed behavior allowing a bouncing-like period at early times while it is dominated by an Eotvos law nowadays. To finalize, we discuss some qualitative characteristics which may arise in the scope of dynamical brane tensions, as anisotropic background and branons production.Comment: 7 pages, 1 figure, accepted for publication in Physical Review

Electric properties of granitic rocks

The objective of this work is to clarify the role of water content on the charge trans- port mechanisms of different granitic rocks. The mineralogical content of the rocks will also be taken into account. From the electrical point of view these materials are rather insulating porous media where charge injection creates different phenomena like build-up charges, space charge limited currents, surface effects and other behav- iors that resemble much a variety of oxides, like AlO

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