7,956 research outputs found
A stochastic collocation approach for parabolic PDEs with random domain deformations
This work considers the problem of numerically approximating statistical
moments of a Quantity of Interest (QoI) that depends on the solution of a
linear parabolic partial differential equation. The geometry is assumed to be
random and is parameterized by random variables. The parabolic problem is
remapped to a fixed deterministic domain with random coefficients and shown to
admit an extension on a well defined region embedded in the complex hyperplane.
A Stochastic collocation method with an isotropic Smolyak sparse grid is used
to compute the statistical moments of the QoI. In addition, convergence rates
for the stochastic moments are derived and compared to numerical experiments
Lorentz-Violating Regulator Gauge Fields as the Origin of Dynamical Flavour Oscillations
We show how a mass mixing matrix can be generated dynamically, for two
massless fermion flavours coupled to a Lorentz invariance violating (LIV) gauge
field. The LIV features play the role of a regulator for the gap equations, and
the non-analytic dependence of the dynamical masses, as functions of the gauge
coupling, allows to consider the limit where the LIV gauge field eventually
decouples from the fermions. Lorentz invariance is then recovered, to describe
the oscillation between two free fermion flavours, and we check that the finite
dynamical masses are the only effects of the original LIV theory. We also
discuss briefly a connection of our results with the case of Majorana neutrinos
in both, the standard model, where only left-handed (active) neutrinos are
considered, and extensions thereof, with sterile right-handed neutrinos.Comment: 32 page
Economic Efficiency and Growth: Evidence from Brazil, China, and India
We compare economic efficiencies in Brazil, India, and China, where economic efficiency measures the gap between potential and actual output for a given input combination and technological factor. We use stochastic production frontier models to measure the contributions of factors of production and technology to growth and estimate non-positive error terms that capture production inefficiencies in each country. The results suggest that China and India had relatively inefficient production in the early 1980s but have since improved production efficiency substantially. In the same period, production efficiency in Brazil has declined somewhat from relatively high initial levels and the gap between production efficiency between these countries has narrowed substantially, supporting more rapid growth in China and India relative to Brazil.growth, trade, production
Quasi-relativistic fermions and dynamical flavour oscillations
We introduce new Lorentz-symmetry violating kinematics for a four-fermion
interaction model, where dynamical mass generation is allowed, irrespectively
of the strength of the coupling. In addition, these kinematics lead to a
quasi-relativistic dispersion relation, in the sense that it is relativistic in
both the infrared and the ultraviolet, but not in an intermediate regime,
characterized by the mass . For two fermions, we show that a flavour-mixing
mass matrix is generated dynamically, and the Lorentz symmetric limit
leads to two free relativistic fermions, with flavour
oscillations. This model, valid for either Dirac or Majorana fermions, can
describe any set of phenomenological values for the eigen masses and the mixing
angle.Comment: 18 pages, comments adde
The Phase-Space Density Profiles of Cold Dark Matter Halos
We examine the coarse-grained phase-space density profiles of a set of
recent, high-resolution simulations of galaxy-sized Cold Dark Matter (CDM)
halos. Over two and a half decades in radius the phase-space density closely
follows a power-law, , with . This behaviour matches the self-similar solution obtained by
Bertschinger for secondary infall in a uniformly expanding universe. On the
other hand, the density profile corresponding to Bertschinger's solution (a
power-law of slope ) differs significantly from the density
profiles of CDM halos. We show that isotropic mass distributions with power-law
phase-space density profiles form a one-parameter family of structures
controlled by , the ratio of the velocity dispersion to the peak
circular velocity. For one recovers the power-law
solution . For larger than some critical
value, , solutions become non-physical, leading to negative
densities near the center. The critical solution, , has
the narrowest phase-space density distribution compatible with the power-law
phase-space density stratification constraint. Over three decades in radius the
critical solution is indistinguishable from an NFW profile. Our results thus
suggest that the NFW profile is the result of a hierarchical assembly process
that preserves the phase-space stratification of Bertschinger's infall model
but which ``mixes'' the system maximally, perhaps as a result of repeated
merging.Comment: 16 pages, 4 figures; submitted to The Astrophysical Journa
Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum
The classification of certain class of static solutions for the
Einstein-Gauss-Bonnet theory in vacuum is performed in dimensions. The
class of metrics under consideration is such that the spacelike section is a
warped product of the real line and an arbitrary base manifold. It is shown
that for a generic value of the Gauss-Bonnet coupling, the base manifold must
be necessarily Einstein, with an additional restriction on its Weyl tensor for
. The boundary admits a wider class of geometries only in the special case
when the Gauss-Bonnet coupling is such that the theory admits a unique
maximally symmetric solution. The additional freedom in the boundary metric
enlarges the class of allowed geometries in the bulk, which are classified
within three main branches, containing new black holes and wormholes in vacuum
The 1987 Mexican Disinflation Program: An Exchange-rate-based Stabilization?
We examine whether Mexicoâs disinflation experience during 1987-94 fits the widely accepted set of stylized facts of exchange-ratebased stabilization (ERBS) on inflation, the boom-recession business cycle, and the external sector. A cursory look at Mexican data shows that the experience fits quite closely the stylized facts of ERBS. However, the paper shows that there were some important differences and peculiarities of the Mexican case that deserve further study, especially regarding the role of the nominal anchor and the nature of the business cycle.stabilization, disinflation, business cycle, nominal anchor
Mass Estimates of X-Ray Clusters
We use cosmological gas dynamic simulations to investigate the accuracy of
galaxy cluster mass estimates based on X-ray observations. The experiments
follow the formation of clusters in different cosmological models and include
the effects of gravity, pressure gradients, and hydrodynamical shocks. A subset
of our ensemble also allows for feedback of mass and energy from galactic winds
into the intracluster medium. We find that mass estimates based on the
hydrostatic, isothermal beta-model are remarkably accurate when evaluated at
radii where the cluster mean density is between 500-2500 times the critical
density. Applied to 174 artificial ROSAT images constructed from the
simulations, the distribution of the estimated-to-true mass ratio is nearly
unbiased and has a standard deviation of 14-29%. The scatter can be
considerably reduced (to 8-15%) by using an alternative mass estimator that
exploits the tightness of the mass-temperature relation found in the
simulations. The improvement over beta-model estimates is due to the
elimination of the variance contributed by the gas outer slope parameter. We
discuss these findings and their implications for recent measurements of
cluster baryon fractions.Comment: TeX, 24p; 11 Postscript figs. Submitted to the Astrophysical Journa
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