A new network model for the integer quantum Hall effect

A Landauer–Büttiker-type formulation of backscattering between pairs of opposite directed channels is used to describe the coupling at the nodes of a network. Physically, these nodes correspond to saddle points of a slowly varying lateral potential modulation in a 2D electron system in the high magnetic field regime. We show that the network can be solved without needing a transfer matrix as used by Chalker and Coddington. We use an exponential dependence of the coupling on the filling factor of the associated Landau level. We demonstrate that our network representation allows a quantitative modeling of almost every realistic sample geometry in the quantum Hall regime, including the effect of gate electrodes across a Hall bar.     

Ring-Closing Metathesis of Functionalized Acetylene Derivatives: A New Entry into Cycloalkynes

A tungsten alkylidyne catalyst is the key to achieving ring-closing metatheses of diynes to form functionalized macrocycles [Eq. (a)]. Partial reduction of the cycloalkynes provides stereoselective Z-configured cycloalkenes, which are currently inaccessible by conventional alkene metathesis.     

New Developments in the Chemistry of Low-Valent Titanium

Among the applications of low-valent titanium in organic synthesis, the reductive coupling of carbonyl compounds to produce alkenes (the McMurry reaction) is particularly prominent. Discovered at the beginning of the 1970s, it has been developed and tested repeatedly, for example in numerous syntheses of natural products. This alkene synthesis has become a standard reaction in the repertoire of preparative chemists. However, the possibilities of low-valent titanium are by no means limited to this process: the last few years have brought some spectacular applications of the conventional McMurry reaction (for example the synthesis of taxol) along with a considerable extension of the scope of reductive carbonyl couplings. Thus, diverse heterocycles are now accessible following novel and efficient pathways based on intramolecular cross-coupling of functional groups—some of which were hitherto considered to be inert to titanium. The use of this method for the synthesis of indole and pyrrole alkaloids illustrates the new possibilities. At the same time, considerably simplified methods for conducting McMurrytype reactions have been developed. Examples include the particularly convenient “instant” method, the first ketone–amide coupling reactions requiring only catalytic amounts of titanium salts, and the first application of commercially available titanium powder as a coupling agent. Last but not least, the detailed investigation of diverse classical McMurry reagents has afforded a deeper understanding of the nature and mode of action of low-valent titanium. Revision of some of the current conceptions of the process of reductive carbonyl coupling is thus indispensable.     

Control of Electrodynamic Tether Vibrations in Space

First, we simulate the behaviour of a satellite tethered with a continuous electrodynamic cable moving on a circular orbit. Second we extinguish for a simple discrete model small angle librations by controlling the current in the tether. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Taming of Furfurylidenes by Chiral Bismuth-Rhodium Paddlewheel Catalysts. Preparation and Functionalization of Optically Active 1,1-Disubstituted (Trifluoromethyl)cyclopropanes

Although 2-furyl-carbenes (furfurylidenes) are prone to instantaneous electrocyclic ring opening, chiral [BiRh]-paddlewheel complexes empowered by London dispersion allow (trifluoromethyl)furfurylidene metal complexes to be generated from a bench-stable triftosylhydrazone precursor. These reactive intermediates engage in asymmetric [2+1] cycloadditions and hence open entry into valuable trifluoromethylated cyclopropane or -cyclopropene derivatives in optically active form, which are important building blocks for medicinal chemistry but difficult to make otherwise.