New Imperfect Conjugate Gradient Algorithm

We present a method which generates conjugate search directions and maintains the quadratic convergence property, when applied to a quadratic function, even when the line searches are not exact. The method is similar to that given by Dixon, but needs one less vector store. When the method is applied to a number of general functions of different dimensionality, results show the efficiency of the method.     

Toughening of epoxies via craze-like damage

The fracture behavior of a core-shell rubber (CSR) modified epoxy is investigated using both fracture mechanics and microscopy tools. The CSR-modified epoxy is found to be toughened via numerous line-array cavitations of the CSR particles, followed by plastic flow of the epoxy matrix. The toughening effect via the above craze-like damage process is found to be as effective as that of the well-known widespread rubber cavitation/matrix shear yielding mechanisms. The conditions for triggering the craze-like damage appear to be both stress state and rubber concentration dependent. The type of rubber tougheners utilized also plays a critical role in triggering this rather unusual craze-like damage in epoxy systems. © 1993 John Wiley & Sons, Inc.     

Current correlators to all orders in the quark masses

The contributions to the coefficient functions of the quark and the mixed quark-gluon condensate to mesonic correlators are calculated for the first time to all orders in the quark masses, and to lowest order in the strong coupling constant. Existing results on the coefficient functions of the unit operator and the gluon condensate are reviewed. The proper factorization of short- and long-distance contributions in the operator product expansion is discussed in detail. It is found that to accomplish this task rigorously the operator product expansion has to be performed in terms ofnon-normal-ordered condensates. The resulting coefficient functions are improved with the help of the renormalization group. The scale invariant combination of dimension 5 operators, including mixing with the mass operator, which is needed for the renormalization group improvement, is calculated in the leading order.Supported by the German Bundesministerium für Forschung und Technologie, under the contract 06 TM 761     

Preparation and Eh--pH diagrams of Fe(II)--Fe(III) green rust compounds; hyperfine interaction characteristics and stoichiometry of hydroxy-chloride, -sulphate and -carbonate

Fe(II)--Fe(III) hydroxy-chloride, -sulphate and -carbonate were prepared by oxidation of a ferrous hydroxide precipitate in anion-containing aqueous solutions. The compounds are characterized by monitoring the redox potential E_h and the pH of stochiometric suspension vs time with the appropriate concentration ratios. X-ray diffraction allows us to characterize the crystal structure by distinguishing “green rust one” (GR1) from “green rust two” (GR2). Since green rusts (GRs) are of a pyroaurite-sjögrenite-like structure, i.e., consisting of intercalated foreign anions and water molecules in the interlayers between the brucite-like layers of Fe(OH)₂, their chemical formulae can be determined from the Mössbauer spectra. Three quadrupole doublets are observed: D₁ and D₂ correspond to a ferrous state with isomershift IS of about 1.27 mm s^-1 and quadrupole splittings QS of about 2.85 and 2.60 mm s^-1, respectively, whereas D₃ corresponds to a ferric state with IS and QS of about 0.4 mm s^-1. The hyperfine parameters of these doublets are similar from one green rust to another but their intensity ratios vary considerably. Finally, E_h and pH equilibrium diagrams of the Fe species in the presence of chloride, sulphate and carbonate anions contained within the water solution are drawn and the thermodynamic conditions of existence and degrees of oxidation of green rusts are discussed.     

Small angle neutron scattering from oxygen precipitates in silicon

The formation of silicon oxide precipitates from Czochralski grown silicon depends on the time and temperature of the heat treatment as well as on the initial content of interstitially dissolved oxygen. Samples containing between 5×10¹⁷ O_i/cm³ and 13×10¹⁷ O_i/cm³ have been heated at 750° C for 96 h. SiO₂ precipitates of various shape and size have been obtained and investigated by means of small angle neutron scattering (SANS) in the Q-range 0.05 Å^–1<Q<0.2 Å^–1. The obtained SANS patterns reveal a typical anisotropy of their intensity distribution, which splits into a central peak at Q<0.1 Å^–1 due to the shape of the individual particles and a number of weak intensities for large Q-values, originating from a correlation between defects, possibly between the precipitates. While these correlation peaks in the SANS patterns are seen best for rather low values of about (5–7)×10¹⁷ O_i/cm³ oxygen content, the central peak anisotropy is most pronounced for higher values of ca 10×10¹⁷ O_i/cm³. The integrated intensity of the central peak increases with increasing initial oxygen content. For comparison, untreated samples of the same initial oxygen content do not reveal any anisotropic SAN scattering or a broadened central peak beam.     

Projective-type axioms for the hyperbolic plane

It is shown that the Laws of Pappus and Desargues may replace the Axiom of Projectivities in Menger's development of hyperbolic geometry from axioms of alignment.