A model of the spatial and temporal variation of the Uranus thermal structure

Seasonal variability of the temperature structure of Uranus is modeled for all latitudes in the .0004 to 2 bar pressure range in anticipation of the Voyager encounter in January 1986. Atmospheric heating in the model results on the one hand from an internal heat source and, on the other hand, from absorption of solar energy by methane and by non-conservative aerosols located between the 0.5 and 2 bar levels. Various cases for the behavior of the internal heat flux are investigated, such as constant with latitude or constrained to yield a time-averaged thermal emission independent of latitude. Meridional transport of heat in the stably stratified atmosphere is not taken into account. The results indicate that the Voyager encounter time, very small north-south temperature asymmetry should be expected. Moreover, the northern hemisphere, although not illuminated, should emit as much energy (within one percent) as the southern hemisphere at this date. At a given latitude, extreme temperatures are reached at the equinoxes. At the poles, seasonal amplitudes of about 10 K in the upper stratosphere and 6 K at the 0.6 bar level are predicted, and the variation with time of the emission to space is found to be at most 20 percent. The atmosphere of Uranus appears to be characterized by very long radiative response times (mainly due to its cold temperature) which inhibit the large seasonal variations that one could otherwise expect in view of the high obliquity of the planet and its long orbital period

Wage rigidity, collective bargaining and the minimum wage: evidence from French agreement data.

We highlight different stylized facts concerning wage stickiness. First, in France, the typical duration of a wage agreement is one year. Consequently, a Taylor (1980) -type model appears to reproduce appropriately the distribution of agreement durations. Some 30 percent of settlements stipulate several predetermined wage changes during the year following the date of signature of the agreement. The frequency of wage agreements is highly seasonal, but the dates at which agreements take effect are more staggered. The date at which the national minimum wage level is revised each year has a significant impact on the timetable of wage agreements, both at the firm- and at the industry-levels. Wage increases negotiated at these two levels mainly depend on the inflation regime, the firm profitability and the proportion of minimum-wage workers in the same industry.Wage Stickiness, Wage Bargaining, Minimum Wage, Downward nominal Wage Rigidity.

Sensitivity analysis of a branching process evolving on a network with application in epidemiology

We perform an analytical sensitivity analysis for a model of a continuous-time branching process evolving on a fixed network. This allows us to determine the relative importance of the model parameters to the growth of the population on the network. We then apply our results to the early stages of an influenza-like epidemic spreading among a set of cities connected by air routes in the United States. We also consider vaccination and analyze the sensitivity of the total size of the epidemic with respect to the fraction of vaccinated people. Our analysis shows that the epidemic growth is more sensitive with respect to transmission rates within cities than travel rates between cities. More generally, we highlight the fact that branching processes offer a powerful stochastic modeling tool with analytical formulas for sensitivity which are easy to use in practice.Comment: 17 pages (30 with SI), Journal of Complex Networks, Feb 201

Coefficients and terms of the liquid drop model and mass formula

The coefficients of different combinations of terms of the liquid drop model have been determined by a least square fitting procedure to the experimental atomic masses. The nuclear masses can also be reproduced using a Coulomb radius taking into account the increase of the ratio $R\_0/A^{1/3}$ with increasing mass, the fitted surface energy coefficient remaining around 18 MeV

Institutional features of wage bargaining in 23 European countries, the US and Japan.

This paper presents information on wage bargaining institutions, collected using a standardised questionnaire. Our data provide information from 1995 and 2006, for four sectors of activity and the aggregate economy, considering 23 European countries, plus the US and Japan. Main findings include a high degree of regulation in wage setting in most countries. Although union membership is low in many countries, union coverage is high and almost all countries also have some form of national minimum wage. Most countries negotiate wages on several levels, the sectoral level still being the most dominant, with an increasingly important role for bargaining at the firm level. The average length of collective bargaining agreements is found to lie between one and three years. Most agreements are strongly driven by developments in prices and eleven countries have some form of indexation mechanism which affects wages. Cluster analysis identifies three country groupings of wage-setting institutions.Wage Bargaining ; Institutions ; Indexation ; Trade Union Membership, Cluster Analysis

Effects of Helium Phase Separation on the Evolution of Extrasolar Giant Planets

We build on recent new evolutionary models of Jupiter and Saturn and here extend our calculations to investigate the evolution of extrasolar giant planets of mass 0.15 to 3.0 M_J. Our inhomogeneous thermal history models show that the possible phase separation of helium from liquid metallic hydrogen in the deep interiors of these planets can lead to luminosities ~2 times greater than have been predicted by homogeneous models. For our chosen phase diagram this phase separation will begin to affect the planets' evolution at ~700 Myr for a 0.15 M_J object and ~10 Gyr for a 3.0 M_J object. We show how phase separation affects the luminosity, effective temperature, radii, and atmospheric helium mass fraction as a function of age for planets of various masses, with and without heavy element cores, and with and without the effect of modest stellar irradiation. This phase separation process will likely not affect giant planets within a few AU of their parent star, as these planets will cool to their equilibrium temperatures, determined by stellar heating, before the onset of phase separation. We discuss the detectability of these objects and the likelihood that the energy provided by helium phase separation can change the timescales for formation and settling of ammonia clouds by several Gyr. We discuss how correctly incorporating stellar irradiation into giant planet atmosphere and albedo modeling may lead to a consistent evolutionary history for Jupiter and Saturn.Comment: 22 pages, including 14 figures. Accepted to the Astrophysical Journa

Spatial variation of the thermal structure of Jupiter's atmosphere

The radiative seasonal model described by Bezard and Gautier for the case of Saturn was adapted to Jupiter. That the atmosphere is radiatively controlled above the 500 mb pressure level and that the temperature at the radiative-convective boundary level is constant for all latitudes is assumed. An internal heat source and absorption by methane and aerosols contribute to atmospheric heating. Absorption by aerosols was adjusted to give a planetary Bond albedo equal to 0.343. Despite Jupiter's low obliquity, the model predicts seasonal variations of temperature of several degrees for the 1 mb pressure level at mid-latitude regions