A fully-discrete Semi-Lagrangian scheme for a first order mean field game problem

In this work we propose a fully-discrete Semi-Lagrangian scheme for a {\it first order mean field game system}. We prove that the resulting discretization admits at least one solution and, in the scalar case, we prove a convergence result for the scheme. Numerical simulations and examples are also discussed.Comment: 28 pages,16 figure

Non-Gaussian statistics, maxwellian derivation and stellar polytropes

In this letter we discuss the Non-gaussian statistics considering two aspects. In the first, we show that the Maxwell's first derivation of the stationary distribution function for a dilute gas can be extended in the context of Kaniadakis statistics. The second one, by investigating the stellar system, we study the Kaniadakis analytical relation between the entropic parameter $\kappa$ and stellar polytrope index $n$. We compare also the Kaniadakis relation $n=n(\kappa)$ with $n=n(q)$ proposed in the Tsallis framework.Comment: 10 pages, 1 figur

Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics

We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.Comment: 12 pages, 7 figure

Physical constraints on interacting dark energy models

Physical limits on the equation-of-state (EoS) parameter of a dark energy component non-minimally coupled with the dark matter field are examined in light of the second law of thermodynamics and the positiveness of entropy. Such constraints are combined with observational data sets of type Ia supernovae, baryon acoustic oscillations and the angular acoustic scale of the cosmic microwave background to impose restrictions on the behaviour of the dark matter/dark energy interaction. Considering two EoS parameterisations of the type $w = w_0 + w_a\zeta(z)$, we derive a general expression for the evolution of the dark energy density and show that the combination of thermodynamic limits and observational data provide tight bounds on the $w_0 - w_a$ parameter space.Comment: 7 pages, 4 figures. Accepted for publication in European Physical Journal

Phase transitions and statistical mechanics for BPS Black Holes in AdS/CFT

Using the general framework developed in hep-th/0607056, we study in detail the phase space of BPS Black Holes in AdS, for the case where all three electric charges are equal. Although these solitons are supersymmetric with zero Hawking temperature, it turns out that these Black Holes have rich phase structure with sharp phase transitions associated to a corresponding critical generalized temperature. We are able to rewrite the gravity variables in terms of dual CFT variables and compare the gravity phase diagram with the free dual CFT phase diagram. In particular, the elusive supergravity constraint characteristic of these Black Holes is particulary simple and in fact appears naturally in the dual CFT in the definition of the BPS Index. Armed with this constraint, we find perfect match between BH and free CFT charges up to expected constant factors.Comment: 14 pages, 5 figures, corrected typos and references adde