Radial terrace solutions and propagation profile of multistable reaction-diffusion equations over RN\mathbb R^N

We study the propagation profile of the solution $u(x,t)$ to the nonlinear diffusion problem $u_t-\Delta u=f(u)\; (x\in \mathbb R^N,\;t>0)$, $u(x,0)=u_0(x) \; (x\in\mathbb R^N)$, where $f(u)$ is of multistable type: $f(0)=f(p)=0$, $f'(0)<0$, $f'(p)<0$, where $p$ is a positive constant, and $f$ may have finitely many nondegenerate zeros in the interval $(0, p)$. The class of initial functions $u_0$ includes in particular those which are nonnegative and decay to 0 at infinity. We show that, if $u(\cdot, t)$ converges to $p$ as $t\to\infty$ in $L^\infty_{loc}(\mathbb R^N)$, then the long-time dynamical behavior of $u$ is determined by the one dimensional propagating terraces introduced by Ducrot, Giletti and Matano [DGM]. For example, we will show that in such a case, in any given direction $\nu\in\mathbb{S}^{N-1}$, $u(x\cdot \nu, t)$ converges to a pair of one dimensional propagating terraces, one moving in the direction of $x\cdot \nu>0$, and the other is its reflection moving in the opposite direction $x\cdot\nu<0$. Our approach relies on the introduction of the notion "radial terrace solution", by which we mean a special solution $V(|x|, t)$ of $V_t-\Delta V=f(V)$ such that, as $t\to\infty$, $V(r,t)$ converges to the corresponding one dimensional propagating terrace of [DGM]. We show that such radial terrace solutions exist in our setting, and the general solution $u(x,t)$ can be well approximated by a suitablly shifted radial terrace solution $V(|x|, t)$. These will enable us to obtain better convergence result for $u(x,t)$. We stress that $u(x,t)$ is a high dimensional solution without any symmetry. Our results indicate that the one dimensional propagating terrace is a rather fundamental concept; it provides the basic structure and ingredients for the long-time profile of solutions in all space dimensions

Wage distribution and the spatial sorting of workers and firms

Spatial sorting plays an important role in accounting for disparities in average wages among locations. This paper shows that sorting also matters when addressing the relation between spatial externalities and wage distribution, i.e. across workers located at dierent percentiles of the wage distribution. Using Italian employer-employee panel data we can control for individual and firm heterogeneity as well as for unobserved individual heterogeneity by means of quantile fixed eects estimates. After controlling for the sorting of workers the spatial externality impacts dampen along the whole wage distribution and generally remain positive only in the upper tail. As for firm sorting, it becomes uniform along the wage distribution once individual fixed effects are considered. We also point out that the impact of worker sorting is not homogeneous across sectors: along the density dimension it occurs mainly in skill-intensive sectors, while along the specialization dimension it is concentrated in the unskill-intensive sectors.Spatial Externalities, Spatial Sorting, Wage Distribution, Quantile Fixed Effects

The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system

We consider an Allen-Cahn type equation with a bistable nonlinearity associated to a double-well potential whose well-depths can be slightly unbalanced, and where the coefficient of the nonlinear reaction term is very small. Given rather general initial data, we perform a rigorous analysis of both the generation and the motion of interface. More precisely we show that the solution develops a steep transition layer within a small time, and we present an optimal estimate for its width. We then consider a class of reaction-diffusion systems which includes the FitzHugh-Nagumo system as a special case. Given rather general initial data, we show that the first component of the solution vector develops a steep transition layer and that all the results mentioned above remain true for this component

Is There Rent Sharing in Italy? Evidence from Employer-Employee Data

Using a unique employer-employee panel database, we investigate the extent of rent sharing in Italy from 1996 to 2003. We derive the following findings. First, after controlling for the national bargaining level, there is robust evidence of rent sharing at firm level. Second, by means of fixed effects estimates we show that the sorting of high-ability workers into high-profit firms appears to play a substantial role, since it captures a significant amount of cross sectional estimates of rent sharing. Third, in accordance to the related literature the endogeneity of profits causes a severe underestimation of rent sharing. Our final IV estimate of the elasticity of wages with respect to profits per employee amounts to 6%, with a "Lester" range of 24%. Moreover, we point out that the impact of rent sharing is not homogeneous across several dimensions (gender, occupation, sector and macroarea).Rent Sharing, Sorting, Wage, Italy

Educational mismatches in the EU: immigrants vs native

The purpose of this paper is to analyse and explain the factors contributing to the observed differences in skill mismatches (vertical and horizontal) between natives and immigrants in EU countries. Using microdata from the 2007 wave of the Adult Education Survey (AES), different probit models are specified and estimated to analyse differences in the probability of each type of skill mismatch between natives and immigrants. Yun's decomposition method is used to identify the relative contribution of characteristics and returns to explain the differences between the two groups. Findings: Immigrants are more likely to be skill mismatched than natives. The difference is much larger for vertical mismatch, wherein the difference is higher for immigrants coming from non-EU countries than for those coming from other EU countries. We find that immigrants from non-EU countries are less valued in EU labour markets than natives with similar characteristics -a result that is not observed for immigrants from EU countries. These results could be related to the limited transferability of human capital acquired in non-EU countries. Social implications: The findings suggest that specific programs to adapt immigrants' human capital acquired in the home country are required to reduce differences in the incidence of skill mismatch and better integration into EU labour markets. Originality: This research is original, because it distinguishes between horizontal and vertical mismatch -an issue that has not been considered in the literature on differences between native and immigrant workers- and due to the wide geographical scope of our analysis, which considers EU and non EU-countries

Comparison of big event with calculations of the air shower development

The incidence of high energy hadrons and electron-photons in air showers at various stages of development is calculated. Numerical calculation is used to solve the diffusion equation for a nuclear cascade and analytical calculation for cascade shower induced gamma rays. From these calculations, one can get the longitudinal development of the high energy hadron and electron-photon components, and the energy spectra of these components at various depths of air shower development. The total number of hadrons (N sub H) and electron-photon components (N sub gamma) are related according to stages of the air shower development and primary energy. The relation of the total energy of hadron and electron-photon component above the threshold energy is given. The energy balance between both components is also a useful parameter to study high energy events accompanying air showers. The relation of N sub H and fractional hadronic energy E (sum E sub H sup gamma/sum E sub H sup gamma + Sum E sub gamma) is calculated. This relation is helpful to understand the stage of air shower development(t) and primary energy (E sub p)

The Burdwood Bank Circulation

A suite of high-resolution numerical simulations characterizes the oceanic circulation in the Burdwood Bank, a shallow seamount located in the northeastern end of the Drake Passage. Model analysis shows energetic upwelling and mixing uplifting deep and benthic waters into the photic layer. Tides and the Antarctic Circumpolar Current are the primary drivers of the bank's circulation. Tidal forcing is the main driver for the entrainment of deep waters into the upper layers of the bank and local wind forcing for the detrainment of these waters into the deep ocean. Passive tracer diagnostics suggest that the dynamical processes triggered by the Burdwood Bank could have a significant impact on local ecosystems and the biogeochemical balance of the southwestern Atlantic region, which is one of the most fertile portions of the Southern Ocean. Model results are robust—they are reproduced in a wide array of model configurations—but there is insufficient observational evidence to corroborate them. Satellite color imagery does not show substantial chlorophyll blooms in this region but it shows strong phytoplankton plumes emanating from the bank. There are several potential explanations for the chlorophyll deficit, including lack of light due to persistent cloud cover, deep mixing layers, fast ocean currents, and the likelihood that blooms, while extant, might not develop on the surface. None of these possibilities can be confirmed at this stage.Fil: Matano, Ricardo P.. State University of Oregon; Estados UnidosFil: Palma, Elbio Daniel. Universidad Nacional del Sur. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto Argentino de Oceanografía. Universidad Nacional del Sur. Instituto Argentino de Oceanografía; ArgentinaFil: Combes, Vincent. State University of Oregon; Estados Unido