Disordered system withn orbitals per site: 1/n expansion

Averaged Green's functions for a disordered electronic system withn orbitals per site are expanded in powers of 1/n. These expansions should be valid in the region of extended states. The expansion coefficients for the d.c. conductivity are finite for dimensionalityd>2 and diverge asd approaches 2. Similarities of two types of two-particle Green's functions with the transverse and longitudinal susceptibilities of a ferromagnet with broken continuous symmetry are pointed out. Arguments for two being the lower critical dimensionality for the hydrodynamics and the mobility edge are given. Provided our series can be exponentiated we find that no metallic conductivity exists for finiten andd=2 in one of our models. Critical exponents ford infinitesimal above two are given. In this limitv diverges like 1/(d–2) and the conductivity vanishes linearly at the mobility edge.The diagrams of the Green's functions are given in terms of vertices of short-range order and of the two-particle propagators of then= limit. Diagrams withs loops contribute in ordern ^–s . The diagrams can be rearranged so that a number of vertices vanishes like the square of the wavevector. This feature prevents infrared divergencies for the d.c. conductivity ford>2.Work supported in part by a DFG fellowship (R.O.), by the Material Research Laboratory of the National Science Foundation at the University of Chicago (F.W.), and by the Deutsche Forschungsgemeinschaft through the Sonderforschungsbereich 123 (Stochastic Mathematical Models) at the Universität Heidelberg     

Weak distributive laws and their role in free lattices

In this note we use concepts from Marcel Erné's work on weak distributive laws to show that free lattices have a property called *-distributivity. While this property, which is preserved by bounded epimorphisms, is equivalent to a -semidistributivity for finite lattices, it is much stronger in the infinity case, entailing not only -continuity but staircase distributivity, a property that is inherited by sublattices.Presented by R. Freese.     

A Test Concept for Lifetime Prediction of Polyethylene Pressure Pipes

The present paper describes the main elements of a novel concept for lifetime and safety assessment of polyethylene pressure pipes for arbitrary installation conditions based on modern methods of fracture mechanics. At the core of the proposed concept is the accelerated generation of so-called synthetic crack growth curves and corresponding material laws for crack growth initiation and slow crack growth for service-near temperature conditions without the use of stress cracking liquids.     

Experimental investigation into three-dimensional wavy liquid films under the influence of electrostatic forces

Three-dimensional interfacial waves that develop on the free surface of falling liquid films are known to intensify heat and mass transfer. In this context, the present paper studies the effect of electrostatic forces applied to a falling film of dielectric liquid on its three-dimensional nonlinear wave dynamics. Therefore, measurements of the local film thickness using a confocal chromatic imaging method were taken, and the complex wave topology was characterized through photography. The experiments show a complex interaction between the electric field and the hydrodynamics of the falling film, whereby electrostatic forces were found to both increase and decrease wave peak height in different regions of the wave. Additionally, an electrically induced breakup of the three-dimensional wave fronts, which leads to a locally doubled frequency in streamwise direction, is found. The ability to influence the wave topology demonstrated here opens the possibility to optimize heat transfer processes in falling liquid films.     

Reciprocity Relations in Newtonian and Eshelbian Mechanics

By considering a stressed body subjected sequentially to a material displacement of a defect and the application of a physical force, a reciprocity theorem analogous to that of Betti/Maxwell has been established which couples Newtonian and Eshelbian mechanics. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient Syntheses of New Super Lewis Basic Tris(dialkylamino)-Substituted Terpyridines and Comparison of Their Methyl Cation Affinities

Syntheses of very electron-rich dialkylamino-substituted 2,2':6',2''-terpyridines (TPYs) were adapted to moderate scale preparation without tedious purification of intermediates. The key 4'-bromo-6,6''-dimethyl-2,2':6',2''-terpyridine-4,4''-diyl bisnonaflate is now available in gram quantities. Its nucleophilic aromatic substitution with dimethylamine provided mixtures of 4'-bromo-substituted 4,4''-bis(dimethylamino)-TPY and the tris(dimethylamino)-TPY. The bromo compound was used in a Buchwald–Hartwig amination to provide the tris(dimethylamino)-TPY in excellent yield. The 4'-bromo substituent was reductively removed to furnish the bis(dimethylamino)-TPY. The same sequence of reactions with pyrrolidine as nucleophile leads to the hitherto unknown pyrrolidino-TPYs. Calculations at the MP2(FC)/6–31+G(2d,p)//B98/6-31G(d) level predict very high methyl cation affinities for compounds of this type, with the 4,4',4''-tri(pyrrolidin-1-yl)-TPY being the most Lewis basic TPY synthesized to date. The efficiently prepared electron-rich TPYs should be excellent ligands for many applications.     

Real or not real that is the question...

The European Physical Journal H - My discussions with John Bell about reality in quantum mechanics are recollected. I would like to introduce the reader to Bell’s vision of reality which was...     

Noethersche Gruppen

Ohne Zusammenfassung