95,543 research outputs found
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 and stellar polytrope index . We compare also the
Kaniadakis relation with 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 and , 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
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 , 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 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
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