On the rotation of ONC stars in the Tsallis formalism context

The theoretical distribution function of the projected rotational velocity is derived in the context of the Tsallis formalism. The distribution is used to estimate the average for a stellar sample from the Orion Nebula Cloud (ONC), producing an excellent result when compared with observational data. In addition, the value of the parameter q obtained from the distribution of observed rotations reinforces the idea that there is a relation between this parameter and the age of the cluster.Comment: 6 pages, 2 figure

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

Combining exclusive semi-leptonic and hadronic B decays to measure |V_ub|

The Cabibbo-Kobayashi-Maskawa matrix element |V_ub| can be extracted from the rate for the semi-leptonic decay B -> pi + l + antineutrino_l, with little theoretical uncertainty, provided the hadronic form factor for the B -> pi transition can be measured from some other B decay. In here, we suggest using the decay B -> pi J\psi. This is a color suppressed decay, and it cannot be properly described within the usual factorization approximation; we use instead a simple and very general phenomenological model for the b d J\psi vertex. In order to relate the hadronic form factors in the B -> pi J\psi and B -> pi + l + antineutrino_l decays, we use form factor relations that hold for heavy-to-light transitions at large recoil.Comment: Latex, 7 pages, no figure

Precise calculation of the threshold of various directed percolation models on a square lattice

Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of connectivity. We conjecture that $p_{c}$ decays exactly as the inverse of the coodination number.Comment: 2 pages, 2 figures and 1 tabl

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