Increasing powers in a degenerate parabolic logistic equation

The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem $$\partial_t u-\Delta u=a u-b(x) u^p \text{in} \Omega\times \R^+, u(0)=u_0, u(t)|_{\partial \Omega}=0$$ as $p\to +\infty$, where $\Omega$ is a bounded domain and $b(x)$ is a nonnegative function. We deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards we fully describe its long time behavior.Comment: 15 page

Exchange Rates and Fiscal Adjustments: Evidence from the OECD and Implications for EMU

This paper characterizes monetary and exchange-rate policies during successful and unsuccessful fiscal adjustments by analyzing the OECD economies over the period 1970 to 1998. We find that successful adjustments are almost always preceded by large nominal and real exchange rate depreciations while unsuccessful adjustments are preceded by revaluations and followed by depreciations. The extreme adjustments of Ireland and Denmark in the 1990s fit this pattern of depreciation for success very closely. Early depreciation is a significant and quantitatively important predictor of the persistence of adjustment: each 1 percent of depreciation in the two years preceding a fiscal adjustment leads to approximately 2 percent increase in the probability of success. Since the size of the typical pre-adjustment depreciation is 5%, this is an important effect. When compared to an indicator of the composition of the fiscal adjustment, the reliance on spending cuts, the two variables have similar quantitative impacts on the likelihood of persistence. Our results are robust to alternative definitions of the depreciation period, the persistence of the adjustment, and whether we use effective, DM or US$ exchange rates. Monetary policy does not play a significant role in fiscal adjustments. Our results suggest that attaining persistent fiscal adjustment within EMU is likely to become a more costly endeavor than it was beforehand, as EMU members have adopted a single currency and therefore abandoned the use of exchange rate policies vis-`-vis each other.

Women Prefer Larger Governments: Female Labor Supply and Public Spending

The increase in income per capita is accompanied, in virtually all countries, by two changes in the structure of the economy: an increase in the share of government spending in GDP and an increase in female labor force participation. This paper suggests that the changes in female labor force participation and government size are not just coincident in time, they are causally related. We develop a growth model with endogenous fertility, labor force participation and government size to illustrate this causal link. When government consumption and/or subsidies decrease the cost of performing household chores - including, but not limited to child rearing and child care - an increase in the female market wage leads to an increase in labor force participation by women and a demand for higher government spending. As women make the decision to work outside the home, they increase their demand for services typically provided by the government, such as education and health care, which, in turn, decrease the cost of home and family activities that are overwhelmingly performed by women. We show, for a wide cross-section of developed and developing countries, that higher female participation rates in the labor market are positively associated with larger governments. We investigate the causal link by instrumenting for female labor force participation with the prevalence of contraceptive methods and the relative price of household appliances. Female labor force participation is found to cause an increase in government size, with a 10 percent rise in the former leading to a 6.5 to 9 percent rise in the latter. This e.ect is stronger for government consumption than for government subsidies and is robust to the country sample, time period, and a set of controls in the spirit of Rodrik (1998).Economic Development, Female Labor Supply, Government Size, Home Activities

Patching up dipoles: can dipolar particles be viewed as patchy colloids?

We investigate whether the liquid-vapour phase transition of strongly dipolar fluids can be understood using a model of patchy colloids. These consist of hard spherical particles with three short-ranged attractive sites (patches) on their surfaces. Two of the patches are of type A and one is of type B. Patches A on a particle may bond either to a patch A or to a patch B on another particle. Formation of an AA (AB) bond lowers the energy by epsilon AA (epsilon AB). In the limit [image omitted], this patchy model exhibits condensation driven by AB-bonds (Y-junctions). Y-junctions are also present in low-density, strongly dipolar fluids, and have been conjectured to play a key role in determining their critical behaviour. We map the dipolar Yukawa hard-sphere (DYHS) fluid onto this 2A + 1B patchy model by requiring that the latter reproduce the correct DYHS critical point as a function of the isotropic interaction strength epsilon Y. This is achieved for sensible values of epsilon AB and the bond volumes. Results for the internal energy and the particle coordination number are in qualitative agreement with simulations of DYHSs. Finally, by taking the limit [image omitted], we arrive at a new estimate for the critical point of the dipolar hard-sphere fluid, which agrees with extrapolations from simulation

Simple thermodynamics of jet engines

We use the first and second laws of thermodynamics to analyze the behavior of an ideal jet engine. Simple analytical expressions for the thermal efficiency, the overall efficiency, and the reduced thrust are derived. We show that the thermal efficiency depends only on the compression ratio r and on the velocity of the aircraft. The other two performance measures depend also on the ratio of the temperature at the turbine to the inlet temperature in the engine, T-3/T-i. An analysis of these expressions shows that it is not possible to choose an optimal set of values of r and T-3/T-i that maximize both the overall efficiency and thrust. We study how irreversibilities in the compressor and the turbine decrease the overall efficiency of jet engines and show that this effect is more pronounced for smaller T-3/T-i

Quantitative description of the self-assembly of patchy particles into chains and rings

We numerically study a simple fluid composed of particles having a hard-core repulsion complemented by two patchy attractive sites on the particle poles. An appropriate choice of the patch angular width allows for the formation of ring structures which, at low temperatures and low densities, compete with the growth of linear aggregates. The simplicity of the model makes it possible to compare simulation results and theoretical predictions based on the Wertheim perturbation theory, specialized to the case in which ring formation is allowed. Such a comparison offers a unique framework for establishing the quality of the analytic predictions. We find that the Wertheim theory describes remarkably well the simulation results

Percolation of colloids with distinct interaction sites

We generalize the Flory-Stockmayer theory of percolation to a model of associating (patchy) colloids, which consists of hard spherical particles, having on their surfaces f short-ranged-attractive sites of m different types. These sites can form bonds between particles and thus promote self-assembly. It is shown that the percolation threshold is given in terms of the eigenvalues of a m x m matrix, which describes the recursive relations for the number of bonded particles on the ith level of a cluster with no loops; percolation occurs when the largest of these eigenvalues equals unity. Expressions for the probability that a particle is not bonded to the giant cluster, for the average cluster size and the average size of a cluster to which a randomly chosen particle belongs, are also derived. Explicit results for these quantities are computed for the case f = 3 and m = 2. We show how these structural properties are related to the thermodynamics of the associating system by regarding bond formation as a (equilibrium) chemical reaction. This solution of the percolation problem, combined with Wertheim's thermodynamic first-order perturbation theory, allows the investigation of the interplay between phase behavior and cluster formation for general models of patchy colloids

The Political Economy of Fiscal Adjustments

Economic