The Limiting Distribution of Production in Integrated Economies: Evidence from US States and EU Countries

We show that in a fully integrated economy, in which there is free mobility of goods and factors, each member’s share of total output will equal its shares of total stocks of productive factors (i.e., physical and human capital). We label this result the equal-share relationship. This relationship also holds in the presence of technological differences or costs of factor mobility among members if outputs or inputs are properly measured to reflect such differences or costs. The equal-share relationship is the limiting distribution of output and factors among members of a fully integrated economy, and it constraints the set of policies that can affect each member’s relative growth within an integrated economy. We empirically examine for the equal-share relationship for alternative economic groups (i.e., US states, EU countries, Developing Countries and a World comprising 55 countries). Our findings indicate that the equal-share relationship holds strongly for US states, holds weakly for EU countries, but does not hold for Developing Countries or the World

On the Extent of Economic Integration: A Comparison of EU Countries and US States

European economic integration is commonly believed to be incomplete, and that further reforms are needed. In this context, the union of U.S. states is considered the benchmark of complete economic integration and is often the basis for comparison regarding the extent of E.U economic integration. Yet, with low trade barriers and with productive factors at least notionally mobile across E.U. countries, is the belief that U.S. states are more integrated than E.U. member states correct? To address this question, this paper first develops three theoretical predictions about the distribution of output and factors that would arise among members of a fully integrated economic area in which goods, capital and labor are freely mobile and policies are harmonized. These theoretical predictions are then empirically tested using data on the output and factor stocks of 14 E.U. member states and the 51 U.S. states (includes District of Columbia) for the period 1965 to 2000. The empirical results convincingly support each theoretical prediction. Hence, contrary to popular belief, the extent of E.U. economic integration is not statistically different from that among U.S. states

Zipf's Law for Integrated Economies

We first demonstrate that, within a fully integrated economy (FIE) in which there is free mobility of goods and factors, each FIE member's share of total FIE output will equal its shares of the total FIE stock of each productive factor. This equal-share property implies that, if economic policies are also largely harmonized across FIE members, the growth in any member's output and factor shares can be viewed as a random event. This then implies that the limit distribution of output and factor shares across FIE members will conform to a rank-share distribution that exhibits Zipf's law. This result means that growth models of FIE members must embody the assumption of homogeneity of random growth processes across members. Given its importance for our understanding of underlying growth mechanisms for such members, we empirically examine for evidence of Zipf's law for the distribution of output and factor shares of two (presumably) integrated economies: the 51 US states and 14 countries of the European Union (EU). Our findings support Zipf's law for US states and indicate convergence towards this law among EU countries

Impact of stirring regime on piezocatalytic dye degradation using BaTiO3 nanoparticles

There is increasing demand to use readily accessible waste energy to drive environmentally friendly processes. Piezocatalysis, the process of converting mechanical energy such as vibration into a chemical process, is a breakthrough next generation approach to meet this challenge. However, these systems currently focus on using ultrasound to drive the chemical reaction and are therefore expensive to operate. We show that by using simple mechanical stirring and BaTiO3 particles we can remove Rhodamine B dye molecules from solution. After evaluating a range of stirring parameters, we demonstrate that there is an interplay between stirring speed, volume of liquid, catalyst structure and rate of dye removal. Our maximum degradation rate was 12.05 mg. g-1 catalyst after 1 hour of mechanical stirring at favourable conditions. This development provides a new insight into a low energy physical technique that can be used in environmental remediation processes

Understanding the effect of saturated gases on catalytic performance of graphitic‐carbon nitride (g‐C₃N₄) for H₂O₂ generation and dye degradation in the presence of ultrasound

This paper examines the effect of saturated gases on H2O2 generation and dye degradation using graphitic‐carbon nitride (g‐C3N4) as a piezoelectric catalyst. A detailed catalytic evaluation was carried out using a double‐bath sono‐reactor, where the performance of g‐C3N4 for H2O2 production and degradation of rhodamine B and indigo carmine dyes was evaluated for a range of catalyst dosage levels and saturated gases. Specific gases were selected to understand their role in the sonochemical production of reactive oxygen species (ROS) and reactive nitrogen species (RNS) and to elucidate the potential catalytic mechanism. The use of an Ar‐O2 gas mixture led to the highest yield for H2O2 production and dye degradation due to the positive effect of argon and oxygen in the generation of H2O2 and reactive oxygen species, respectively. The presence of nitrogen in both air and in an Ar‐air mixture increased H2O2 generation since reactive nitrogen species improved the conversion of •OH into H2O2. In contrast, air and Ar‐air negatively influenced the generation of ROS, which resulted in a low rate of dye degradation. This work provides new insights of the mechanisms of sonochemical and piezocatalytic processes in the use of graphitic‐carbon nitride in catalytic applications.This article is protected by copyright. All rights reserved

Comparing initial-data sets for binary black holes

We compare the results of constructing binary black hole initial data with three different decompositions of the constraint equations of general relativity. For each decomposition we compute the initial data using a superposition of two Kerr-Schild black holes to fix the freely specifiable data. We find that these initial-data sets differ significantly, with the ADM energy varying by as much as 5% of the total mass. We find that all initial-data sets currently used for evolutions might contain unphysical gravitational radiation of the order of several percent of the total mass. This is comparable to the amount of gravitational-wave energy observed during the evolved collision. More astrophysically realistic initial data will require more careful choices of the freely specifiable data and boundary conditions for both the metric and extrinsic curvature. However, we find that the choice of extrinsic curvature affects the resulting data sets more strongly than the choice of conformal metric.Comment: 18 pages, 12 figures, accepted for publication in Phys. Rev.

A skeleton approximate solution of the Einstein field equations for multiple black-hole systems

An approximate analytical and non-linear solution of the Einstein field equations is derived for a system of multiple non-rotating black holes. The associated space-time has the same asymptotic structure as the Brill-Lindquist initial data solution for multiple black holes. The system admits an Arnowitt-Deser-Misner (ADM) Hamiltonian that can particularly evolve the Brill-Lindquist solution over finite time intervals. The gravitational field of this model may properly be referred to as a skeleton approximate solution of the Einstein field equations. The approximation is based on a conformally flat truncation, which excludes gravitational radiation, as well as a removal of some additional gravitational field energy. After these two simplifications, only source terms proportional to Dirac delta distributions remain in the constraint equations. The skeleton Hamiltonian is exact in the test-body limit, it leads to the Einsteinian dynamics up to the first post-Newtonian approximation, and in the time-symmetric limit it gives the energy of the Brill-Lindquist solution exactly. The skeleton model for binary systems may be regarded as a kind of analytical counterpart to the numerical treatment of orbiting Misner-Lindquist binary black holes proposed by Gourgoulhon, Grandclement, and Bonazzola, even if they actually treat the corotating case. Along circular orbits, the two-black-hole skeleton solution is quasi-stationary and it fulfills the important property of equality of Komar and ADM masses. Explicit calculations for the determination of the last stable circular orbit of the binary system are performed up to the tenth post-Newtonian order within the skeleton model.Comment: 15 pages, 1 figure, submitted to Phys. Rev. D, 3 references added, minor correction

Radiation content of Conformally flat initial data

We study the radiation of energy and linear momentum emitted to infinity by the headon collision of binary black holes, starting from rest at a finite initial separation, in the extreme mass ratio limit. For these configurations we identify the radiation produced by the initially conformally flat choice of the three geometry. This identification suggests that the radiated energy and momentum of headon collisions will not be dominated by the details of the initial data for evolution of holes from initial proper separations $L_0\geq7M$. For non-headon orbits, where the amount of radiation is orders of magnitude larger, the conformally flat initial data may provide a relative even better approximation.Comment: 4 pages, 4 figure

Corotating and irrotational binary black holes in quasi-circular orbits

A complete formalism for constructing initial data representing black-hole binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in general, true equilibrium binary configurations. However, when the timescale for orbital decay is much longer than the orbital period, a binary can be considered to be in quasi-equilibrium. If each black hole is assumed to be in quasi-equilibrium, then a complete set of boundary conditions for all initial data variables can be developed. These boundary conditions are applied on the apparent horizon of each black hole, and in fact force a specified surface to be an apparent horizon. A global assumption of quasi-equilibrium is also used to fix some of the freely specifiable pieces of the initial data and to uniquely fix the asymptotic boundary conditions. This formalism should allow for the construction of completely general quasi-equilibrium black hole binary initial data.Comment: 13 pages, no figures, revtex4; Content changed slightly to reflect fact that regularized shift solutions do satisfy the isometry boundary condition

Conformal-thin-sandwich initial data for a single boosted or spinning black hole puncture

Sequences of initial-data sets representing binary black holes in quasi-circular orbits have been used to calculate what may be interpreted as the innermost stable circular orbit. These sequences have been computed with two approaches. One method is based on the traditional conformal-transverse-traceless decomposition and locates quasi-circular orbits from the turning points in an effective potential. The second method uses a conformal-thin-sandwich decomposition and determines quasi-circular orbits by requiring the existence of an approximate helical Killing vector. Although the parameters defining the innermost stable circular orbit obtained from these two methods differ significantly, both approaches yield approximately the same initial data, as the separation of the binary system increases. To help understanding this agreement between data sets, we consider the case of initial data representing a single boosted or spinning black hole puncture of the Bowen-York type and show that the conformal-transverse-traceless and conformal-thin-sandwich methods yield identical data, both satisfying the conditions for the existence of an approximate Killing vector.Comment: 13 pages, 2 figure