2,316 research outputs found
Analogue model for anti-de Sitter as a description of point sources in fluids
We introduce an analogue model for a nonglobally hyperbolic spacetime in
terms of a two-dimensional fluid. This is done by considering the propagation
of sound waves in a radial flow with constant velocity. We show that the
equation of motion satisfied by sound waves is the wave equation on
. Since this spacetime is not globally hyperbolic, the
dynamics of the Klein-Gordon field is not well defined until boundary
conditions at the spatial boundary of are prescribed. On the analogue
model end, those extra boundary conditions provide an effective description of
the point source at . For waves with circular symmetry, we relate the
different physical evolutions to the phase difference between ingoing and
outgoing scattered waves. We also show that the fluid configuration can be
stable or unstable depending on the chosen boundary condition.Comment: 6 pages, 1 figure. To appear in Phys Rev
Comment on Market Discipline and Monetary Policy by Carl Walsh
This paper aims at correcting flaws in the way expectations are set in a paper by Walsh (2000) in order to assess with precision the impact of complex market rigidities and market expectations in the optimal choices of inflation in a monetary game between society and central bankers. After setting the expectations right, one of the results achieved indicates that the optimal inflation under any type of central banker is higher than that obtained in the original paper, suggesting that the time inconsistency phenomenon plays a more important role in explaining an inflationary bias than originally interpreted by Walsh (2000). However, if society organizes itself towards shorter tenure wage contracts, inflation will be lower. The results obtained for the output gap of the economy also differ from those achieved by Walsh in the sense that a central banker who is highly committed to previously announced inflation targets will have more opportunities to generate output growth above equilibrium rates and still commit. Finally, the stability of the premises regarding the contractual structure of the economy proposed by Walsh is tested under a game theoretic approach. The outcome of the test is that stability can be guaranteed only under strong assumptions and high symmetry in the sectoral distribution of firms. By using a social welfare function in which price surprises in any direction lead to welfare loss, the results indicate that society is better off by choosing longer tenure wage contracts, moving away from shorter tenure ones, at the cost of higher inflation.
Challenging the weak cosmic censorship conjecture with charged quantum particles
Motivated by the recent attempts to violate the weak cosmic censorship
conjecture for near-extreme black-holes, we consider the possibility of
overcharging a near-extreme Reissner-Nordstr\"om black hole by the quantum
tunneling of charged particles. We consider the scattering of spin-0 and
spin-1/2 particles by the black hole in a unified framework and obtain
analytically, for the first time, the pertinent reflection and transmission
coefficients without any small charge approximation. Based on these results, we
propose some gedanken experiments that could lead to the violation of the weak
cosmic censorship conjecture due to the (classically forbidden) absorption of
small energy charged particles by the black hole. As for the case of scattering
in Kerr spacetimes, our results demonstrate explicitly that scalar fields are
subject to (electrical) superradiance phenomenon, while spin-1/2 fields are
not. Superradiance impose some limitations on the gedanken experiments
involving spin-0 fields, favoring, in this way, the mechanisms for creation of
a naked singularity by the quantum tunneling of spin-1/2 charged fermions. We
also discuss the implications that vacuum polarization effects and quantum
statistics might have on these gedanken experiments. In particular, we show
that they are not enough to prevent the absorption of incident small energy
particles and, consequently, the formation of a naked singularity.Comment: 9 pages; Final version to appear in PR
Synchronized stationary clouds in a static fluid
The existence of stationary bound states for the hydrodynamic velocity field
between two concentric cylinders is established. We argue that rotational
motion, together with a trapping mechanism for the associated field, is
sufficient to mitigate energy dissipation between the cylinders, thus allowing
the existence of infinitely long lived modes, which we dub stationary clouds.
We demonstrate the existence of such stationary clouds for sound and surface
waves when the fluid is static and the internal cylinder rotates with constant
angular velocity . These setups provide a unique opportunity for the
first experimental observation of synchronized stationary clouds. As in the
case of bosonic fields around rotating black holes and black hole analogues,
the existence of these clouds relies on a synchronization condition between
and the angular phase velocity of the cloud.Comment: v2: 7 pages, 4 figures. Accepted for publication in Physics Letters
SIR model with vaccination: bifurcation analysis
There are few adapted SIR models in the literature that combine vaccination
and logistic growth. In this article, we study bifurcations of a SIR model
where the class of Susceptible individuals grows logistically and has been
subject to constant vaccination. We explicitly prove that the endemic
equilibrium is a codimension two singularity in the parameter space
, where is the basic reproduction number
and is the proportion of Susceptible individuals successfully vaccinated at
birth.
We exhibit explicitly the Hopf, transcritical, Belyakov, heteroclinic and
saddle-node bifurcation curves unfolding the singularity. The two parameters
are written in a useful way to evaluate the proportion of
vaccinated individuals necessary to eliminate the disease and to conclude how
the vaccination may affect the outcome of the epidemic. We also exhibit the
region in the parameter space where the disease persists and we illustrate our
main result with numerical simulations, emphasizing the role of the parameters
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