Super-Instantons, Perfect Actions, Finite-Size Scaling, and the Continuum Limit

We discuss some aspects of the continuum limit of some lattice models, in particular the 2DO(N) models. The continuum limit is taken either in an infinitevolume or in a box whose size is a fixed fraction of the infinite-volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be O(1) and thus restore the symmetry which may have been broken by the boundary conditions (b.c.). This is true in particular for the socalled super-instanton b.c. introduced earlier by us. This observation leads to a criterion to assess how close a certain lattice simulation is to the continuum limit and can be applied to uncover the true lattice artefacts, present even in the so-called “perfect actions”. It also shows that David’s recent claim that superinstanton b.c. require a different renormalization must either be incorrect or an artefact of perturbation theory.     

Experimental determination of strain-induced anisotropy during nonproportional straining of an A1/Mg alloy at room temperature

A servohydraulic, computer controlled MTSn axial-torsion testing machine with a bi-axial clip-on extensometer is used to test thin-walled tubes of an A1/Mg alloy under strain control. A plastic offset strain of 10⁻⁴ determines the yield surfaces. Straining and yield surface probing is governed by a computer program which also controls digital data acquisition. Yield surfaces in stress and in strain space as well as the axial and shear stress-strain diagrams can be reconstructed from the digitally recorded data. The specimens were subjected to a strain path in the form of a regular 16-sided polygon which was followed on some specimens by a square path. The total inelastic strain path length can exceed 15% while the equivalent strain excursion is less than 2%. It is shown that yield surfaces measured on specimens withclose initial stress-strain diagrams are very consistent and that yield surface probing has an insignificant effect on subsequent yield surfaces. Yield surfaces are shown to translate, changein shape and size and to exhibit a cross effect. A post processor which includes a least square smoothing routine calculates the area and the centroid of each yield surface. The size increase is initially rapid but the rate of increase decreases as a saturation is approached. After strining for less than 1% in a fixed direction a characteristic yield surface shape is established. Yield surfaces obtained at the same point in strain space with identical prestrain direction of at least 1% but with increased amounts of accumulated plastic strain have the same shape but show an increase in size. The yield surfaces differ in shape and size when the same strain point is reached from different directions. The centroid of the yield surface in stress space moves almost in a circular path for a polygonal strain path. All stress space yield surfaces contain the origin but this is not the case for the surfaces in strain space.     

Stepwise formation of a molecular square with bridging NH,O-substituted dicarbene building blocks

The β,β'-bis(triisopropylsiloxy)phenyl-1,4-diisocyanide 3 and [Ir(Cp*)Cl(2)](2) were used for the stepwise assembly of the [Ir(Cp*)Cl] cornered molecular square [6](Cl)(4). Synthesis of the tetrakis(diisocyanide) bridged molecular square [Ir(Cp*)Cl(3)](4)(BF(4))(4) [5](BF(4))(4) followed by cleavage of the O-Si(i-Pr)(3) bonds of the diisocyanide bridges with HCl/i-PrOH led to an intramolecular attack of the liberated hydroxyl groups at the isocyanide carbon atoms with formation of molecular square [6](Cl)(4) featuring four dicarbene linkers.     

Pressure-volume relations for Zn,Cd, Ga,In and TI at room temperature to 30 GPa and above

Abstract

The elemental metals Zn, Cd, Ga, In and TI are studied by energy dispersive X-ray diffraction under pressures up to 30 GPa and above. Room temperature equation of state (EOS) data are derived and compared with results of earlier static and dynamic measurements at lower and higher pressures, respectively.     

Über die isoperimetrische Aufgabe imn-dimensionalen Raum konstanter negativer Krümmung

Ohne ZusammenfassungHerrn Oskar Perron zum 60. Geburtstag am 7. Mai 1940 gewidmet     

Untersuchung pharmazeutischer Pr?parate

Ohne Zusammenfassung