Inclusion agglomeration in electrified molten metal: thermodynamic consideration

The effect of electric current on inclusion agglomeration in molten metal has been investigated. It is found that the agglomeration is dependent on the electric current density, distance between inclusions and orientation of electric field. Electric current retards the agglomeration unless two inclusions are aligned along or closely to the current flow streamlines and the distance between inclusions is less than a critical value. The mechanism is also validated in the computation of cluster agglomeration. The numerical results provide a comprehensive indication for the current-induced inclusion removal and current-induced inclusion elongation. When the inclusions are in long-thin shape, the calculation predicts the current-induced microstructure alignment and current-induced microstructure refinement phenomena

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

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

An Inequality Approach to Approximate Solutions of Set Optimization Problems in Real Linear Spaces

This paper explores new notions of approximate minimality in set optimization using a set approach. We propose characterizations of several approximate minimal elements of families of sets in real linear spaces by means of general functionals, which can be unified in an inequality approach. As particular cases, we investigate the use of the prominent Tammer–Weidner nonlinear scalarizing functionals, without assuming any topology, in our context. We also derive numerical methods to obtain approximate minimal elements of families of finitely many sets by means of our obtained results

Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations

Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$. The wave structure which contains four waves: the transonic(or degenerate) boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and 3-rarefaction wave to the inflow problem is described and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible Navier-Stokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the degeneracies of the transonic boundary layer solution and the wave interactions in the superposition wave.Comment: 27 page