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.     

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     

Untersuchungen über sprengstoffbetriebene MHD-Generatoren

Three types of explosive-driven MHD-generators have been studied. The explosives were seeded as to give high magnetic Reynolds numbers via high electric conductivity and/or magnetic permeability. The highest power peaks were attained with a rectangular-channel-type generator fed from a hollow-cylinder shaped charge. Tests with magnetically loaded explosives seem to indicate that these might prove useful (e.g. in space engineering), in particular when used in a cylindrical induction-type MHD-generator designed by the authors. This type also, though run with smaller charges only, seems to be the most efficient one.     

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     

Upper and Lower Hausdorff Dimension Estimates for Invariant Sets of k — 1 — Endomorphisms

For a special class of non–injective maps on Riemannian manifolds upper and lower bounds for the Hausdorff dimension of invariant sets are given in terms of the singular values of the tangent map. The upper estimation is based on a theorem by Douady and Oesterlé and its generalization to Riemannian manifolds by Noack and Reitmann , but additionally information about the noninjectivity is used. The lower estimation can be reached by modifying a method, derived by Shereshevskij for geometric constructions on the real line (also described by Barreira , for similar constructions in general metric spaces. The upper and lower dimension estimates for k — 1 — endomorphisms can for instance be applied to Julia sets of quadratic maps on the complex plane.     

The optimisation of ultrasonic cleaning procedures for dairy fouled ultrafiltration membranes

Ultrafiltration (UF) of whey is a major membrane based process in the dairy industry. However, commercialization of this application has been limited by membrane fouling, which has a detrimental influence on the permeation rate. There are a number of different chemical and physical cleaning methods currently used for cleaning a fouled membrane. It has been suggested that the cleaning frequency and the severity of such cleaning procedures control the membrane lifetime. The development of an optimal cleaning strategy should therefore have a direct implication on the process economics. Recently, the use of ultrasound has attracted considerable interest as an alternative approach to the conventional methods. In the present study, we have studied the ultrasonic cleaning of polysulfone ultrafiltration membranes fouled with dairy whey solutions. The effects of a number of cleaning process parameters have been examined in the presence of ultrasound and results compared with the conventional operation. Experiments were conducted using a small single sheet membrane unit that was immersed totally within an ultrasonic bath. Results show that ultrasonic cleaning improves the cleaning efficiency under all experimental conditions. The ultrasonic effect is more significant in the absence of surfactant, but is less influenced by temperature and transmembrane pressure. Our results suggest that the ultrasonic energy acts primarily by increasing the turbulence within the cleaning solution.