Equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model

This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov-Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov-Poisson model to the astrophysical systems like globular clusters or galaxies. In a second part we will recall some recent numerical results which may give us some some quantitative hints about the equilibrium state associated to those systems.Comment: 8 pages, no figures, accepted in Communications in Nonlinear Science and Numerical Simulatio

Lepton Masses and Mixing Angles with Spontaneously Broken O(3) Flavor Symmetry

We present a model based on an O(3) flavor symmetry and a minimal extension of the scalar sector to induce hierarchical breaking, O(3) -> O(2) -> SO(2) -> nothing. The model naturally accounts for all the known lepton parameters and yields various interesting predictions for others: (i) Neutrinos are nearly degenerate, m_\nu \sim 0.1 eV; (ii) The solar neutrino problem is solved by the MSW small mixing angle solution; (iii) The MNS mixing angle theta_{13} is unobservably small, theta_{13} = O(10^{-5}).Comment: 8 pages, LaTeX2e, published version, typos corrected and some of the notations were improve

Statistical and entanglement entropy for black holes in quantum geometry

We analyze the relationship between entanglement (or geometric) entropy with statistical mechanical entropy of horizon degrees of freedom when described in the framework of isolated horizons in loop quantum gravity. We show that, once the relevant degrees of freedom are identified, the two notions coincide. The key ingredient linking the two notions is the structure of quantum geometry at Planck scale implied by loop quantum gravity, where correlations between the inside and outside of the black hole are mediated by eigenstates of the horizon area operator.Comment: References adde

ON SOME SMARANDACHE PROBLEMS

Solving some problems proposed by F. Smarandache

Single Inclusive Distribution and Two-Particle Correlations Inside One Jet at "Modified Leading Logarithmic Approximation" of Quantum Chromodynamics II : Steepest Descent Evaluation at Small X

The MLLA single inclusive distribution inside one high energy (gluon) jet at small x is estimated by the steepest descent method. Its analytical expression is obtained outside the "limiting spectrum". It is then used to evaluate 2-particle correlations at the same level of generality. The dependence of both observables on the ratio between the infrared cutoff Q\_0 and Lambda\_QCD is studied. Fong & Webber's results for correlations are recovered at the limits when this ratio goes to 1 and when one stays close to the peak of the single inclusive distribution.Comment: LaTeX, 22 pages, 18 .eps figure