On the use of two QMR algorithms for solving singular systems and applications in Markov chain modeling

Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix—vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov-subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported.     

Energy flux into the tip of an extending crack in an elastic solid

Summary An expression for the energy flux into the tip of an extending crack in terms of the dynamic elastic field of the crack is derived on the basis of an overall energy rate balance. It is shown that the energy flux depends only on the near-tip elastic field. The expression is compared to other expressions for this dependence which have been proposed by Atkinson and Eshelby, by Achenbach and by Erdogan. The energy flux is calculated in terms of the stress intensity factor for a particular plane strain problem and an antiplane strain problem.

---

Résumé Sur la base d'un équilibre énergétique dynamique global, le flux d'énergie convergeant vers l'extrémité d'une tissure en propagation est exprimé en fonction du champ élastique dynamique de la fissure. II est démontré que ce flux d'énergie ne dépend que du champ élastique au voisinage immédiat de l'extremité de la fissure, L'expression obtenue est comparée aux expressions précédemment proposées par MM. Atkinson et Eshelby, Mr. Achenbach, et Mr. Erdogan. Le flux d'énergie est évalué en fonction du facteur d'intensité des contraintes dans les cas particuliers d'un problème de déformation plane et d'un problème dans lequel la direction du cisaillement est horizontale.

---

---

Supported by the United States Atomic Energy Commission through Contract AT (11-1)-3084 with Brown University.     

Oxidation of Au by surface OH: nucleation and electronic structure of gold on hydroxylated MgO(001)

The nucleation and electronic structure of vapor-deposited Au on hydroxylated MgO(001) surfaces has been investigated under ultrahigh vacuum conditions. Hydroxylated MgO(001) surfaces with two different hydroxyl coverages, 0.4 and 1 monolayer, respectively, were prepared by exposure to water (D(2)O) at room temperature. Scanning tunneling microscopy experiments show significantly higher gold particle densities and smaller particle sizes on the hydroxylated MgO surface as compared to gold deposited on clean MgO(001). Infrared spectroscopy and X-ray photoelectron spectroscopy experiments were performed to reveal details about the initial nucleation of gold. Gold atoms are found to chemically interact with a specific type of hydroxyl groups on the MgO surface, leading to the formation of oxidized gold particles. The enhanced adhesion of Au particles, which is due to the formation of strong Au-O interfacial bonds, is responsible for the observed higher stability of small Au clusters toward thermal sintering on hydroxylated MgO surfaces. The results are compared to similar studies on Au/TiO(2)(110) model systems and powder samples prepared by the deposition-precipitation route.     

Adsorption energetics of CO on supported Pd nanoparticles as a function of particle size by single crystal microcalorimetry

The heat of adsorption and sticking probability of CO on well-defined Pd nanoparticles were measured as a function of particle size using single crystal adsorption microcalorimetry. Pd particles of different average sizes ranging from 120 to 4900 atoms per particle (or from 1.8 to 8 nm) and Pd(111) were used that were supported on a model in situ grown Fe(3)O(4)/Pt(111) oxide film. To precisely quantify the adsorption energies, the reflectivities of the investigated model surfaces were measured as a function of the thickness of the Fe(3)O(4) oxide layer and the amount of deposited Pd. A substantial decrease of the binding energy of CO was found with decreasing particle size. Initial heat of adsorption obtained on the virtually adsorbate-free surface was observed to be reduced by about 20-40 kJ mol(-1) on the smallest 1.8 nm sized Pd particles as compared to the larger Pd clusters and the extended Pd(111) single crystal surface. This effect is discussed in terms of the size-dependent properties of the Pd nanoparticles. The CO adsorption kinetics indicates a strong enhancement of the adsorbate flux onto the metal particles due to a capture zone effect, which involves trapping of adsorbates on the support and diffusion to metal clusters. The CO adsorption rate was found to be enhanced by a factor of ～8 for the smallest 1.8 nm sized particles and by ～1.4 for the particles of 7-8 nm size.     

Pressure calibration in high pressure EXAFS experiments

Abstract

To avoid glitches due to Bragg reflection we use boron carbide anvils for our high pressure EXAFS experiments. Since boron carbide precludes the ruby fluorescence pressure calibration we use the EXAFS of selected materials to measure the reduction with pressure of the nearest neighbor distance and infer the pressure from an isothermal equation of state. The requirements for a good pressure calibrant and the difficulties in EXAFS data analysis are discussed. Cu, NaBr and RbCl have successfully been tested as pressure calibrants.     

Mehrstufige Redoxsysteme. XLIX. Mitteilung. Mit π-Systemen substituierte 1,3-Dimethylidencyclobutane: Synthese und Eigenschaften

Multistep Redox Systems. 1,3-Dimethylidenecyclobutanes Substituted by π-Syntheses and Properties As potential redox systems 1,3-dimethylidenecyclobutanes are synthesized in which the ‘exo’-methylidene group participates in a cyclopentadienyl (type C4 )or cycloheptatrienyl (type A5 ) system. Benzo-annellated systems are also described. The formation of the C?C bond by the reaction of thioketones ( 3 and 31 ) with diazo compounds is extended to extended to 1,6,7,21 , and 24 , which so far had not been employed. In some cases, intermediate thiiranes can be isolated (e.g. 4 ) which are smoothly transformed into the target compounds of types C4 and A5 by extrusion of sulfur. The new C?C bonds may be introduced stepwise, thereby allowing the synthesis of unsymmetrically substituted 1,3-dimethylidenecyclobutanes (e.g. 20 and 35 ). Reduction of by Na does not produce bicyclobutanes but compounds 43 and 44 with one dihydrofulvene unit.     

A QMR-based interior-point algorithm for solving linear programs

A new approach for the implementation of interior-point methods for solving linear programs is proposed. Its main feature is the iterative solution of the symmetric, but highly indefinite 2×2-block systems of linear equations that arise within the interior-point algorithm. These linear systems are solved by a symmetric variant of the quasi-minimal residual (QMR) algorithm, which is an iterative solver for general linear systems. The symmetric QMR algorithm can be combined with indefinite preconditioners, which is crucial for the efficient solution of highly indefinite linear systems, yet it still fully exploits the symmetry of the linear systems to be solved. To support the use of the symmetric QMR iteration, a novel stable reduction of the original unsymmetric 3×3-block systems to symmetric 2×2-block systems is introduced, and a measure for a low relative accuracy for the solution of these linear systems within the interior-point algorithm is proposed. Some indefinite preconditioners are discussed. Finally, we report results of a few preliminary numerical experiments to illustrate the features of the new approach.     

Über die Aggregation von Aerosolen mittels Schallwellen

Zeitschrift für Physik A Hadrons and nuclei - Es wird an Hand von mikrokinematographischen Aufnahmen das Verhalten eines Aerosols während der Einwirkung intensiver kurzer Schallwellen...