Application of the z-transform to composite materials

Applications of the z-transform were made earlier to interfacial electron transfer involving semi-infinite solids, e.g., semiconductor/liquid and metal/liquid interfaces and scanning tunneling microscopy. It is shown how the method is readily adapted to treat composite materials, such as solid/solid interfaces or "molecular wire"/solid interfaces

Pressure effects on bimolecular recombination and unimolecular dissociation reactions

The treatment of pressure effects on bimolecular recombinations and unimolecular dissociations is discussed. The analysis of recombination and dissociation reactions is made by showing how the nonequilibrium energy (E) and angular momentum (J)-dependent steady-state population distribution functions for the two reactions are related to each other and to the equilibrium population distribution function at the given E and J. As a special case a strong collision model is then used for the collisional rotational angular momentum transfer, and a ladder model for the collisional energy transfer. An analytical result is obtained for states below the dissociation threshold. The extension to recombinations with two exit channels is described, for application to ozone formation and isotopic effects

The dynamic effects of currency union on trade

A currency union’s ability to increase international trade is one of the most debated questions in international macroeconomics. This paper studies the dynamics of these trade effects over time. First, empirical work with data from the European Monetary Union finds that the extensive margin of trade (entry of new firms or goods) responds several years ahead of overall trade volume and actual implementation of the monetary union. This implies a fall at the intensive margin (previously traded goods) in the run-up to EMU. A dynamic stochastic general equilibrium model of trade studies the announcement of a future monetary union as a news shock lowering future trade costs, and finds that the early entry of new firms in anticipation is explainable as a rational forward-looking response under certain conditions. Required elements are sunk costs of exporting and ex-ante heterogeneity among firms. The findings help identify which types of trading frictions are reduced by adopting a currency union. Findings also indicate that a significant fraction of the welfare gains from a monetary union are based upon expectations for the future, so that continued gains depend upon long-term credibility of the union

On the theory of electron transfer reactions at semiconductor/liquid interfaces. II. A free electron model

Electron transfer reactions at semiconductor/liquid interfaces are studied using the Fermi Golden rule and a free electron model for the semiconductor and the redox molecule. Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states where the effective electron mass in the semiconductor need not equal the actual electron mass. The calculated maximum electron transfer rate constants are compared with the experimental results as well as with the theoretical results obtained in Part I using tight-binding calculations. The results, which are analytic for an s-electron in the redox agent and reduced to a quadrature for pz- and dz2-electrons, add to the insight of the earlier calculations

An approximate theory of the ozone isotopic effects: Rate constant ratios and pressure dependence

The isotopic effects in ozone recombination reactions at low pressures are studied using an approximate theory which yields simple analytic expressions for the individual rate constant ratios, observed under “unscrambled” conditions. It is shown that the rate constant ratio between the two competing channels XYZ-->X+YZ and XYZ-->XY+Z is mainly determined by the difference of the zero-point energies of diatomic molecules YZ and XY and by the efficiency of the deactivation of the newly formed excited ozone molecules, whereas the mass-independent fractionation depends on a “nonstatistical” symmetry factor eta and the collisional deactivation efficiency. Formulas for the pressure effects on the enrichment and on the rate constant ratios are obtained, and the calculated results are compared with experiments and more exact calculations. In all cases, ratios of isotope rates and the pressure dependence of enrichments, the agreement is good. While the initial focus was on isotope effects in the formation of O3, predictions are made for isotope effects on ratios of rate constants in other reactions such as O+CO-->CO2, O+NO-->NO2, and O+SO-->SO2