An intrinsic Proper Generalized Decomposition for parametric symmetric elliptic problems

We introduce in this paper a technique for the reduced order approximation of parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension which realizes the best approximation in mean of the error with respect to the parameter in the quadratic norm associated to the elliptic operator, between the exact solution and the Galerkin solution calculated on the subspace. This is analogous to the best approximation property of the Proper Orthogonal Decomposition (POD) subspaces, excepting that in our case the norm is parameter-depending, and then the POD optimal sub-spaces cannot be characterized by means of a spectral problem. We apply a deflation technique to build a series of approximating solutions on finite-dimensional optimal subspaces, directly in the on-line step. We prove that the partial sums converge to the continuous solutions, in mean quadratic elliptic norm.Comment: 18 page

Understanding chemical evolution in resolved galaxies -- I The local star fraction-metallicity relation

This work studies the relation between gas-phase oxygen abundance and stellar-to-gas fraction in nearby galaxies. We first derive the theoretical prediction, and argue that this relation is fundamental, in the sense that it must be verified regardless of the details of the gas accretion and star formation histories. Moreover, it should hold on "local" scales, i.e. in regions of the order of 1 kpc. These predictions are then compared with a set of spectroscopic observations, including both integrated and resolved data. Although the results depend somewhat on the adopted metallicity calibration, observed galaxies are consistent with the predicted relation, imposing tight constraints on the mass-loading factor of (enriched) galactic winds. The proposed parametrization of the star fraction-metallicity relation is able to describe the observed dependence of the oxygen abundance on gas mass at fixed stellar mass. However, the "local" mass-metallicity relation also depends on the relation between stellar and gas surface densities.Comment: 10 pages, 4 figures. Matches accepted version (significant typo corrected

Imposición y bienestar social bajo discriminación espacial de precios

Este trabajo analiza los efectos de la imposición directa e indirecta sobre el bienestar social, en un modelo de entrada en el que las empresas practican discriminación espacial de precios. Se muestra que en un oligopolio la imposición directa puede afectar positiva o negativamente al bienestar social, mientras la imposición indirecta es neutral. Cuando el mercado está monopolizado en ausencia de impuestos, los efectos de los impuestos nunca pueden ser beneficiosos desde la perspectiva del bienestar social.Discriminación espacial de precios, impuestos directos, impuestos indirectos.

Phase-dependent exciton transport and energy harvesting from thermal environments

Non-Markovian effects in the evolution of open quantum systems have recently attracted widespread interest, particularly in the context of assessing the efficiency of energy and charge transfer in nanoscale biomolecular networks and quantum technologies. With the aid of many-body simulation methods, we uncover and analyse an ultrafast environmental process that causes energy relaxation in the reduced system to depend explicitly on the phase relation of the initial state preparation. Remarkably, for particular phases and system parameters, the net energy flow is uphill, transiently violating the principle of detailed balance, and implying that energy is spontaneously taken up from the environment. A theoretical analysis reveals that non-secular contributions, significant only within the environmental correlation time, underlie this effect. This suggests that environmental energy harvesting will be observable across a wide range of coupled quantum systems.Comment: 5 + 4 pages, 3 + 2 figures. Comments welcom

Vacuum fluctuations and the conditional homodyne detection of squeezed light

Conditional homodyne detection of quadrature squeezing is compared with standard nonconditional detection. Whereas the latter identifies nonclassicality in a quantitative way, as a reduction of the noise power below the shot noise level, conditional detection makes a qualitative distinction between vacuum state squeezing and squeezed classical noise. Implications of this comparison for the realistic interpretation of vacuum fluctuations (stochastic electrodynamics) are discussed.Comment: 14 pages, 7 figures, to appear in J. Opt. B: Quantum Semiclass. Op