Attractors and global averaging of non-autonomous reaction-diffusion equations in R^n

We consider a family of non-autonomous reaction-diffusion equations with almost periodic, rapidly oscillating principal part and nonlinear interactions. As the frequency of the oscillations tends to infinity, we prove that the solutions of the non-autonomous equations converge to the solutions of the autonomous averaged equation. If the nonlinearity is dissipative, we prove existence of compact attractors and their upper-semicontinuity at infinity.Comment: 31 pages; to appear on "Topological Methods in Nonlinear Analysis"; references adde

Environmental degradation and indeterminacy of equilibrium selection

This paper analyzes an intertemporal optimization problem in which agents derive utility from three goods: leisure, a public environmental good and the consumption of a produced good. The global analysis of the dynamic system generated by the optimization problem shows that global indeterminacy may arise: given the initial values of the state variables, the economy may converge to different steady states, by choosing different initial values of the control variable

The Electrostatics of Einstein's Unified Field Theory

When sources are added at their right-hand sides, and g_{(ik)} is a priori assumed to be the metric, the equations of Einstein's Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_{(ik)} in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_{(ik)}, however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by H\'ely. In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when H\'ely's physically correct metric is adopted.Comment: 15 pages. Misprints corrected. To appear in General Relativity and Gravitatio

The {\gamma} Dor stars as revealed by Kepler : A key to reveal deep-layer rotation in A and F stars

The {\gamma} Dor pulsating stars present high-order gravity modes, which make them important targets in the intermediate-and low-mass main-sequence region of the Hertzsprung-Russell diagram. Whilst we have only access to rotation in the envelope of the Sun, the g modes of {\gamma} Dor stars can in principle deliver us constraints on the inner layers. With the puzzling discovery of unexpectedly low rotation rates in the core of red giants, the {\gamma} Dor stars appear now as unique targets to explore internal angular momentum transport in the progenitors of red giants. Yet, the {\gamma} Dor pulsations remain hard to detect from the ground for their periods are close to 1 day. While the CoRoT space mission first revealed intriguing frequency spectra, the almost uninterrupted 4-year photometry from the Kepler mission eventually shed a new light on them. It revealed regularities in the spectra, expected to bear signature of physical processes, including rotation, in the shear layers close to the convective core. We present here the first results of our effort to derive exploitable seismic diagnosis for mid- to fast rotators among {\gamma} Dor stars. We confirm their potential to explore the rotation history of this early phase of stellar evolution.Comment: 4 pages, 1 figure, proceedings of the 22nd Los Alamos Stellar Pulsation Conference, "Wide-field variability surveys: a 21st-century perspective" held in San Pedro de Atacama, Chile, Nov. 28-Dec. 2, 201

TESS unveils the phase curve of WASP-33b. Characterization of the planetary atmosphere and the pulsations from the star

We present the detection and characterization of the full-orbit phase curve and secondary eclipse of the ultra-hot Jupiter WASP-33b at optical wavelengths, along with the pulsation spectrum of the host star. We analyzed data collected by the Transiting Exoplanet Survey Satellite (TESS) in sector 18. WASP-33b belongs to a very short list of highly irradiated exoplanets that were discovered from the ground and were later visited by TESS. The host star of WASP-33b is of delta Scuti-type and shows nonradial pulsations in the millimagnitude regime, with periods comparable to the period of the primary transit. These completely deform the photometric light curve, which hinders our interpretations. By carrying out a detailed determination of the pulsation spectrum of the host star, we find 29 pulsation frequencies with a signal-to-noise ratio higher than 4. After cleaning the light curve from the stellar pulsations, we confidently report a secondary eclipse depth of 305.8 +/- 35.5 parts-per-million (ppm), along with an amplitude of the phase curve of 100.4 +/- 13.1 ppm and a corresponding westward offset between the region of maximum brightness and the substellar point of 28.7 +/- 7.1 degrees, making WASP-33b one of the few planets with such an offset found so far. Our derived Bond albedo, A_B = 0.369 +/- 0.050, and heat recirculation efficiency, epsilon = 0.189 +/- 0.014, confirm again that he behavior of WASP-33b is similar to that of other hot Jupiters, despite the high irradiation received from its host star. By connecting the amplitude of the phase curve to the primary transit and depths of the secondary eclipse, we determine that the day- and nightside brightness temperatures of WASP-33b are 3014 +/- 60 K and 1605 +/- 45 K, respectively. From the detection of photometric variations due to gravitational interactions, we estimate a planet mass of M_P = 2.81 +/- 0.53 M$_J.Comment: 19 pages, 15 figure

Should I stay or should I go? Carbon leakage and ETS in an evolutionary model

Emissions trading is gaining increasing importance around the world as a suitable instrument to address climate change. In the absence of a global carbon market, however, unilateral carbon policies may end up causing carbon leakage effects, the more so if carbon prices are to increase in the future to achieve more ambitious emissions abatement targets. This paper intends to explore the possible delocalization effects of an Emissions Trading System (ETS) by proposing an evolutionary theoretical model in which regulated firms decide whether to stay (keep their production activities in the domestic country) or leave (move production abroad where no ETS is in place) imitating what other firms do. We investigate how this decision is affected by some key ETS design features, such as the emissions cap, the number of allowances granted for free to ETS firms, the level of a floor price for allowances. Numerical simulations show that the firms' decision on whether to abate emissions or relocate abroad are more sensitive to policies that reduce the cost of green technologies than to changes in specific features of the ETS design such as the emissions cap, the floor price and the number of permits granted for free.Web of Science103art. no. 10556

The role of turbulent pressure as a coherent pulsational driving mechanism: the case of the delta Scuti star HD 187547

HD 187547 was the first candidate that led to the suggestion that solar-like oscillations are present in delta Scuti stars. Longer observations, however, show that the modes interpreted as solar-like oscillations have either very long mode lifetimes, longer than 960 days, or are coherent. These results are incompatible with the nature of `pure' stochastic excitation as observed in solar-like stars. Nonetheless, one point is certain: the opacity mechanism alone cannot explain the oscillation spectrum of HD 187547. Here we present new theoretical investigations showing that convection dynamics can intrinsically excite coherent pulsations in the chemically peculiar delta Scuti star HD 187547. More precisely, it is the perturbations of the mean Reynold stresses (turbulent pressure) that drives the pulsations and the excitation takes place predominantly in the hydrogen ionization zone.Comment: 8 pages, 4 figures, accepted to Ap

Theology, Metaphysics, and Science: Twenty-First Century Hermeneutical Allies, Strangers, or Enemies?

This article answers the question of whether the study of theology and metaphysics can be classified currently, or ever qualify in the future, as a scientific endeavor. Rather than choose a particular theology or metaphysics as the subject of inquiry, this essay argues that it is not only necessary to recognize the role of hermeneutics within different fields of study, but that it is also necessary to begin a human hermeneutic with human experience. Changes in our global context, whether social, economic, political, or environmental, are important drivers of hermeneutical evolution. We should expect no less change in the areas of theology, metaphysics, and science. The question of truth, whether subjective or objective, is a hermeneutical one

Searching for solar-like oscillations in the delta Scuti star rho Puppis

Despite the shallow convective envelopes of delta Scuti pulsators, solar-like oscillations are theoretically predicted to be excited in those stars as well. To search for such stochastic oscillations we organised a spectroscopic multi-site campaign for the bright, metal-rich delta Sct star rho Puppis. We obtained a total of 2763 high-resolution spectra using four telescopes. We discuss the reduction and analysis with the iodine cell technique, developed for searching for low-amplitude radial velocity variations, in the presence of high-amplitude variability. Furthermore, we have determined the angular diameter of rho Puppis to be 1.68 \pm 0.03 mas, translating into a radius of 3.52 \pm 0.07Rsun. Using this value, the frequency of maximum power of possible solar-like oscillations, is expected at ~43 \pm 2 c/d (498 \pm 23 muHz). The dominant delta Scuti-type pulsation mode of rho Puppis is known to be the radial fundamental mode which allows us to determine the mean density of the star, and therefore an expected large frequency separation of 2.73 c/d (31.6 muHz). We conclude that 1) the radial velocity amplitudes of the delta Scuti pulsations are different for different spectral lines; 2) we can exclude solar-like oscillations to be present in rho Puppis with an amplitude per radial mode larger than 0.5 m/s.Comment: 14 pages, 12 figure, accepted for MNRA