Improving the convergence rate of the inverse iteration method

Solution of generalized eigenproblem, K phi = lambda M phi, by the classical inverse iteration method exhibits slow convergence for some eigenproblems. In this paper, a modified inverse iteration algorithm is presented for improving the convergence rate. At every iteration, an optimal linear combination of the latest and the preceding iteration vectors is used as the input vector for the next iteration. The effectiveness of the proposed algorithm is demonstrated for three typical eigenproblems, i.e. eigenproblems with distinct, close and repeated eigenvalues. The algorithm yields 29, 96 and 23% savings in computational time, respectively, for these problems. The algorithm is simple and easy to implement, and this renders the algorithm even more attractive.

Homogenization of periodic structures via Bloch decomposition

In this paper, the classical problem of homogenization of elliptic operators in arbitrary domains with periodically oscillating coefficients is considered. Using Bloch wave decomposition, a new proof of convergence is furnished. It sheds new light and offers an alternate way to view the classical results. In a natural way, this method leads us to work in the Fourier space and thus in a framework dual to the one used by L. Tartar [Problemes d'Homogeneisation dans les Equations aux: Derivees Partielles, Cours Peccot au College de Prance, 1977] in his method of homogenization. Further, this technique offers a nontraditional way of calculating the homogenized coefficients which is easy to implement in the computer.

X-ray photoelectron spectroscopic investigations of Cu-Ni, Au-Ag, Ni-Pd, and Cu-Pd bimetallic clusters

Core-level binding energies of the component metals in bimetallic clusters of various compositions in the Ni-Cu, Au-Ag, Ni-Pd, and Cu-Pd systems have been measured as functions of coverage or cluster size, after having characterized the clusters with respect to sizes and compositions. The core-level binding energy shifts, relative to the bulk metals, at large coverages or cluster size, Delta E(a), are found to be identical to those of bulk alloys. By substracting the Delta E(a) values from the observed binding energy shifts, Delta E, we obtain the shifts, Delta E(c), due to cluster size. The Delta E(c) values in all the alloy systems increase with the decrease in cluster size. These results establish the additivity of the binding energy shifts due to alloying and cluster size effects in bimetallic clusters.

Characterization and catalytic properties of combustion synthesized Au/CeO2 catalyst

Ceria-supported Au catalyst has been synthesized by the solution combustion method for the first time and characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM) and X-ray photoelectron spectroscopy (XPS). Au is dispersed as Au as well as Au3+ states on CeO2 surface of 20-30 nm crystallites. On heating the as-prepared 1% Au/CeO2 in air, the concentration of Au3- ions on CeO2 increases at the expense of Au. Catalytic activities for CO and hydrocarbon oxidation and NO reduction over the as-prepared and the heat-treated 1% Au/CeO2 have been carried out using a temperature-programmed reaction technique in a packed bed tubular reactor. The results are compared with nano-sized Au metal particles dispersed on alpha-Al2O3 substrate prepared by the same method. All the reactions over heat-treated Au/CeO2 occur at lower temperature in comparison with the as-prepared Au/CeO2 and Au/Al2O3. The rate of NO + CO reaction over as-prepared and heat-treated 1% Au/CeO2 are 28.3 and 54.0 mumol g(-1) s(-1) at 250 and 300 degreesC respeceively. Activation energy (E,) values are 106 and 90 kJ mol(-1) for CO + O-2 reaction respectively over as-prepared and heat-treated 1% Au/CeO2 respectively.

Durable electrocatalytic-activity of Pt-Au/C cathode in PEMFCs

Longevity remains as one of the central issues in the successful commercialization of polymer electrolyte membrane fuel cells (PEMFCs) and primarily hinges on the durability of the cathode. Incorporation of gold (Au) to platinum (Pt) is known to ameliorate both the electrocatalytic activity and stability of cathode in relation to pristine Pt-cathodes that are currently being used in PEMFCs. In this study, an accelerated stress test (AST) is conducted to simulate prolonged fuel-cell operating conditions by potential cycling the carbon-supported Pt-Au (Pt-Au/C) cathode. The loss in performance of PEMFC with Pt-Au/C cathode is found to be similar to 10% after 7000 accelerated potential-cycles as against similar to 60% for Pt/C cathode under similar conditions. These data are in conformity with the electrochemical surface-area values. PEMFC with Pt-Au/C cathode can withstand > 10 000 potential cycles with very little effect on its performance. X-ray diffraction and transmission electron microscopy studies on the catalyst before and after AST suggest that incorporating Au with Pt helps mitigate aggregation of Pt particles during prolonged fuel-cell operations while X-ray photoelectron spectroscopy reflects that the metallic nature of Pt is retained in the Pt-Au catalyst during AST in comparison to Pt/C that shows a major portion of Pt to be present as oxidic platinum. Field-emission scanning electron microscopy conducted on the membrane electrode assembly before and after AST suggests that incorporating Au with Pt helps mitigating deformations in the catalyst layer.

First-principles electronic structure of the delafossites ABO(2) (A=Cu, Ag, Au; B=Al, Ga, Sc, In, Y): evolution of d(10)-d(10) interactions

While bonding between d(10) atoms and ions in molecular systems has been well studied, less attention has been paid to interactions between such seemingly closed shell species in extended inorganic solids. In this contribution, we present visualizations of the electronic structures of the delafossites ABO(2) (A = Cu, Ag, Au) with particular emphasis on the nature of d(10)-d(10) interactions in the close packed plane of the coinage metal ion. We find that on going from Cu to Ag to Au, the extent of bonding between A and A increases. However, the structures (in terms of distances) of these compounds are largely determined by the strongly ionic 13,11 0 interaction and for the larger B ions Sc, In and Y, the A atoms are sufficiently well-separated that A-A bonding is almost negligible. We also analyze some interesting differences between Ag and Au, including the larger A-O covalency of the Au. The trends in electronic structure suggest that the Ag and Au compounds are not good candidate transparent conducting oxides. (C) 2002 Editions scientifiques et medicales Elsevier SAS. All rights reserved.

Electrical transport characteristics of Au/n-GaAs Schottky diodes on n-Ge at low temperatures

The current�voltage characteristics of Au/n-GaAs Schottky diodes grown by metal-organic vapor-phase epitaxy on Ge substrates were determined in the temperature range 80�300 K. The zero-bias barrier height for current transport decreases and the ideality factor increases at low temperatures. The ideality factor was found to show the T0 effect and a higher characteristic energy. The excellent matching between the homogeneous barrier height and the effective barrier height was observed and infer good quality of the GaAs film. No generation�recombination current due to deep levels arising during the GaAs/Ge heteroepitaxy was observed in this study. The value of the Richardson constant was found to be 7.04 A K?2 cm?2, which is close to the value used for the determination of the zero-bias barrier height.

Synthesis and metallic probe induced conductance of Au tipped ultranarrow PbS rods

Au tipped ultranarrow PbS nanorods are synthesized. DFT electronic structure calculations and transport studies show that Au probes modify the nature and energies of PbS nanorod orbitals creating efficient electron conduction channels for enhanced conductance even at low applied bias.

From polarization to convergence: need to mend the broken patent system

For more than two hundred years, the world has discussed the issue of whether to continue the process of patenting or whether to do away with it. Developed countries remain polarized for various reasons but nevertheless the pro patent regime continued. The result was a huge volume of patents. The present article explains the implications of excessive volume of patents and conditions under which prior art search fails. This article highlights the importance and necessity of standardization efforts so as to bring about convergence of views on patenting.

Pt-Au/C cathode with enhanced oxygen-reduction activity in PEFCs

Carbon-supported Pt-Au (Pt-Au/C) catalyst is prepared separately by impregnation, colloidal and micro-emulsion methods, and characterized by physical and electrochemical methods. Highest catalytic activity towards oxygen-reduction reaction (ORR) is exhibited by Pt-Au/C catalyst prepared by colloidal method. The optimum atomic ratio of Pt to Au in Pt-Au/C catalyst prepared by colloidal method is determined using linear-sweep and cyclic voltammetry in conjunction with cell-polarization studies. Among 3:1, 2:1 and 1:1 Pt-Au/C catalysts, (3:1) Pt-Au/C exhibits maximum electrochemical activity towards ORR. Powder X-ray diffraction pattern and transmission electron micrograph suggest Pt-Au alloy nanoparticles to be well dispersed onto the carbon-support. Energy dispersive X-ray analysis and inductively coupled plasma-optical emission spectroscopy data suggest that the atomic ratios of the alloying elements match well with the expected values. A polymer electrolyte fuel cell (PEFC) operating at 0 center dot 6 V with (3:1) Pt-Au/C cathode delivers a maximum power-density of 0 center dot 65 W/cm (2) in relation to 0 center dot 53 W/cm (2) delivered by the PEFC with pristine carbon-supported Pt cathode.

Activities of indium in solid solutions of Cu+In, Au+In and Cu+Au+In alloys

Thin foils of Cu, Au and Cu + Au alloys embedded in indium sesquioxide were equilibrated with controlled streams of CO-CO2 mixtures. The equilibrium concentrations of indium in the foils were determined by neutron activation analysis. The corresponding chemical potentials of indium were calculated from the standard free energies of formation of carbon monoxide, carbon dioxide, and indium oxide. It was found that the size difference between the solute and the solvent does not make significant contributions to the solute—solute interaction energy in the α-phase. The chemical potential of indium at one at.% concentration is 8.6 Kcals more negative in gold than in copper at 900°K. The variation of this chemical potential with alloy composition in Cu + Au system was in good agreement with Alcock and Richardson's quasichemical equation. The agreement is strengthened by the accurate knowledge of the co-ordination number in these substitutional solid solutions from X-ray diffraction studies.

Chemical potential of germanium in its solid solutions with Cu, Ag and Au

Thin foils of copper, silver and gold were equilibrated with tetragonal GeO2 under controlled View the MathML source gas streams at 1000 K. The equilibrium concentration of germanium in the foils was determined by the X-ray fluorescence technique. The standard free energy of formation of tetragonal GeO2 was measured by a solid oxide galvanic cell. The chemical potential of germanium calculated from the experimental data and the free energies of formation of carbon monoxide and carbon dioxide was found to decrease in the sequence Ag + Ge > Au + Ge > Cu + Ge. The more negative value for the chemical potential of germanium in solid copper, compared to that in solid gold, cannot be explained in terms of the strain energy factor, electro-negativity differences or the vaporization energies of the solvent, and suggests that the d band and its hybridization with s electrons are an important factor in determining the absolute values for the chemical potential in dilute solutions. However, the variation of the chemical potential with solute concentration can be correlated to the concentration of s and p electrons in the outer shell.

Solute solute and solvent solute interactions in solid solutions of Cu+Sn, Au+Sn and Cu+Au+Sn alloys

The chemical potentials of tin in its α-solid solutions with Cu, Au and Cu + Au alloys have been measured using a gas-solid equilibration technique. The variation of the excess chemical potential of tin with its composition in the alloy is related to the solute-solute repulsive interaction, while the excess chemical potential at infinite dilution of the solute is a measure of solvent-solute interaction energies. It is shown that solute-solute interaction is primarily determined by the concentration of (s + p) electrons in the conduction band, although the interaction energies are smaller than those predicted by either the rigid band model or calculation based on Friedel oscillations in the potential function. Finally, the variation of the solvent-solute interaction with solvent composition in the ternary system can be accounted for in terms of a quasi-chemical treatment which takes into account the clustering of the solvent atoms around the solute.

On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

Convergence problems in a class of model reference adaptive control systems

A class of model reference adaptive control system which make use of an augmented error signal has been introduced by Monopoli. Convergence problems in this attractive class of systems have been investigated in this paper using concepts from hyperstability theory. It is shown that the condition on the linear part of the system has to be stronger than the one given earlier. A boundedness condition on the input to the linear part of the system has been taken into account in the analysis - this condition appears to have been missed in the previous applications of hyperstability theory. Sufficient conditions for the convergence of the adaptive gain to the desired value are also given.