Sulfur derivatives of 3-methyl-5-phenyl-1,2,4,3-triazaphosphole

The triazaphosphole 1 adds sulfur along with HCl or H₂S to yield, respectively, the dihydrotriazaphosphole thiochloride 4 and sesquisulfide 5 (two diastereomers). In pyridine solution, 1 adds sulfur alone to yield the trimer of a triazaphosphole monosulfide 7 . Its central cyclotriphosphazane trisulfide ring has a trans structure and a boat conformation.     

New fluorine derivatives of methylcyclohexasilane

1,1-Difluorodecamethyl- and 1,1,4,4-tetrafluorooctamethylcyclohexasilane were synthesized by the reaction of LiF with the corresponding trifluoromethanesulfonic derivatives and were characterized by spectroscopic methods, mainly by modern NMR techniques. The stability of the fluorinated cyclosilanes decreases with an increase of fluorine substituents. This seems to be the reason for the instability of perfluorinated cyclosilanes.     

The crystal structure of zinc azide · 2-methylpyridine at 98 K

The crystal structure of the title compound has been determined by single crystal X-ray diffraction methods at 98 K. Zinc azide · 2-methyl pyridine crystallizes in the space group P1 with a = 6.028(2) Å, b = 7.610(3) Å, c = 10.052(4) Å, α = 92.81(3)°, β = 101.08(2)·, γ = 94.64(3)° and Z = 2. Least-squares refinement gave an R value of R_w = 0.039 for 2096 observed reflections. Each zinc atom is surrounded by four nitrogen atoms of different azide groups and one nitrogen atom of the pyridine adduct in a distorted trigonal bipyramidal fashion. The ZnN₅-polyhedra share common edges to form chains along the crystallographic a-axis.     

Crystal plasticity study on stress and strain partitioning in a measured 3D dual phase steel microstructure

Dual phase steels are advanced high strength alloys typically used for structural parts and reinforcements in car bodies. Their good combination of strength and ductility and their lean composition render them an economically competitive option for realizing multiple lightweight design options in automotive engineering. The mechanical response of dual phase steels is the result of the strain and stress partitioning among the ferritic and martensitic phases and the individual crystallographic grains and subgrains of these phases. Therefore, understanding how these microstructural features influence the global and local mechanical properties is of utmost importance for the design of improved dual phase steel grades. While multiple corresponding simulation studies have been dedicated to the investigation of dual phase steel micromechanics, numerical tools and experiment techniques for characterizing and simulating real 3D microstructures of such complex materials have been emerged only recently. Here we present a crystal plasticity simulation study based on a 3D dual phase microstructure which is obtained by EBSD tomography, also referred to as 3D EBSD (EBSD—electron backscatter diffraction). In the present case we utilized a 3D EBSD serial sectioning approach based on mechanical polishing. Moreover, sections of the 3D microstructure are used as 2D models to study the effect of this simplification on the stress and strain distribution. The simulations are conducted using a phenomenological crystal plasticity model and a spectral method approach implemented in the Düsseldorf Advanced Material Simulation Kit (DAMASK).     

Covariant Spectator Theory: Foundations and Applications

We provide a short overview of the covariant spectator theory and its applications. The basic ideas are introduced through the example of a ${\phi^4}$ -type theory. High-precision models of the two-nucleon interaction are presented and the results of their use in calculations of properties of the two- and three-nucleon systems are discussed. A short summary of applications of this framework to other few-body systems is also presented.     

Target fragmentation in proton-nucleus and16O-nucleus reactions at 60 and 200 GeV/nucleon

Target remnants withZ<3 from proton-nucleus and¹⁶O-nucleus reactions at 60 and 200 GeV/nucleon were measured in the angular range from 30° to 160° (?1.7<η<1.3) employing the Plastic Ball detector. The excitation energy of the target spectator matter in central oxygen-induced collisions is found to be high enough to allow for complete disintegration of the target nucleus into fragments withZ<3. The average longitudinal momentum transfer per proton to the target in central collisions is considerably higher in the case of¹⁶O-induced reactions (≈300 MeV/c) than in proton-induced reactions (≈130 MeV/c). The baryon rapidity distributions are roughly in agreement with one-fluid hydrodynamical calculations at 60 GeV/nucleon¹⁶O+Au but are in disagreement at 200 GeV/nucleon, indicating the higher degree of transparency at the higher bombarding energy. Both, the transverse momenta of target spectators and the entropy produced in the target fragmentation region are compared to those attained in head-on collisions of two heavy nuclei at Bevalac energies. They are found to be comparable or do even exceed the values for the participant matter at beam energies of about 1–2 GeV/nucleon.     

Charge-Conjugation Invariance of the Spectator Equations

 In response to recent criticism, we show how to define the spectator equations for negative energies so that charge-conjugation invariance is preserved. The result, which emerges naturally from the application of spectator principles to systems of particles with negative energies, is to replace all factors of the external energies W _i by W _i ², insuring that the amplitudes are independent of the sign of the energies W _i . Received August 30, 1999; accepted for publication February 24, 2000     

Computational experience with a bundle approach for semidefinite cutting plane relaxations of Max-Cut and Equipartition

We propose a dynamic version of the bundle method to get approximate solutions to semidefinite programs with a nearly arbitrary number of linear inequalities. Our approach is based on Lagrangian duality, where the inequalities are dualized, and only a basic set of constraints is maintained explicitly. This leads to function evaluations requiring to solve a relatively simple semidefinite program. Our approach provides accurate solutions to semidefinite relaxations of the Max-Cut and the Equipartition problem, which are not achievable by direct approaches based only on interior-point methods. Received: April, 2004 The last author gratefully acknowledges the support from the Austrian Science Foundation FWF Project P12660-MAT.     

Phase transition of the principal Dirichlet eigenvalue in a scaled Poissonian potential

We consider d-dimensional Brownian motion in a scaled Poissonian potential and the principal Dirichlet eigenvalue (ground state energy) of the corresponding Schr?dinger operator. The scaling is chosen to be of critical order, i.e. it is determined by the typical size of large holes in the Poissonian cloud. We prove existence of a phase transition in dimensions d≥ 4: There exists a critical scaling constant for the potential. Below this constant the scaled infinite volume limit of the corresponding principal Dirichlet eigenvalue is linear in the scale. On the other hand, for large values of the scaling constant this limit is strictly smaller than the linear bound. For d > 4 we prove that this phase transition does not take place on that scale. Further we show that the analogous picture holds true for the partition sum of the underlying motion process. Received: 10 December 1999 / Revised version: 14 July 2000/?Published online: 15 February 2001