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 $N$ 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 $M$. For two fermions, we show that a flavour-mixing mass matrix is generated dynamically, and the Lorentz symmetric limit $M\to\infty$ 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, $\rho/\sigma^3 \propto r^{-\alpha}$, with $\alpha = 1.875$. 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 $r^{2\alpha-6}$) 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 $\kappa$, the ratio of the velocity dispersion to the peak circular velocity. For $\kappa=\alpha=1.875$ one recovers the power-law solution $\rho \propto r^{2\alpha-6}$. For $\kappa$ larger than some critical value, $\kappa_{cr}$, solutions become non-physical, leading to negative densities near the center. The critical solution, $\kappa =\kappa_{cr}$, 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 $d\geq5$ 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 $d>5$. 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 Mexico’s 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