Stabilization of the radial equilibrium of a tethered satellite with respect to out-of-plane initial perturbations

We investigate the stabilization of the radial equilibrium of a tethered satellite by tension control, if both in-plane and out-of-plane deviations from the vertical position are taken into account. While in-plane perturbations can be eliminated in finite time, the length rate change of the tether acts as parametric control on the out-of-plane deviations. Therefore the control becomes less effective, if the perturbation decreases. In order to improve the convergence we investigate the optimal control problem assuming no costs for the applied tension force but restricting the control force to a finite interval. For tether cconfigurations close to the vertical target position this approach yields a solution with singular control, which leads to a faster decay of the deviations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mode-coupling theory for the dynamics of tunnelling systems in dielectrics

A mode-coupling theory (MCT) is presented for the spin-boson model with a spectral density which accounts for a heat bath made up of lattice vibrations of a dielectric solid (superohmic dissipation). A usual decoupling approximation provides a set of non-linear integral equations which are solved both numerically by iteration on a computer and analytically by means of a frequency dependent ansatz for the memory functions. There is a transition to incoherent motion at a temperatureT ^* where the bare two-level energy is equal to the damping rate, in contradiction to results obtained previously from a path integral formulation. The discrepancy arises since in the MCT the relevant self-energy function does not exhibit a 1/z-pole atz=0. For tunnelling systems in dielectrics this yields a new relaxation mechanism due to incoherent tunnelling: the present results might require to modify some of the basic assumptions of the standard tunnelling model for dielectric glasses.     

The First Crystal Structure of a Reactive Dirhodium Carbene Complex and a Versatile Method for the Preparation of Gold Carbenes by Rhodium‐to‐Gold Transmetalation

The dirhodium carbene derived from bis(4‐methoxyphenyl)diazomethane and [Rh(tpa)₄]?CH₂Cl₂ (tpa=triphenylacetate) was characterized by UV, IR, and NMR spectroscopy, HRMS, as well as by X‐ray diffraction. The isolated complex exhibits prototypical rhodium carbene reactivity in that it cyclopropanates 4‐methoxystyrene at low temperature. Experimental structural information on this important type of reactive intermediate is extremely scarce and thus serves as a reference point for mechanistic discussions of rhodium catalysis in general. Moreover, dirhodium carbenes are shown to undergo remarkably facile carbene transfer on treatment with [LAuNTf₂] (L=phosphine). This formal transmetalation opens a valuable new entry into gold carbene complexes that cannot easily be made otherwise; three fully characterized representatives illustrate this aspect.     

trans‐Hydrogenation: Application to a Concise and Scalable Synthesis of Brefeldin A

The important biochemical probe molecule brefeldin A ( 1 ) has served as an inspirational target in the past, but none of the many routes has actually delivered more than just a few milligrams of product, where documented. The approach described herein is clearly more efficient; it hinges upon the first implementation of ruthenium‐catalyzed trans‐hydrogenation in natural products total synthesis. Because this unorthodox reaction is selective for the triple bond and does not touch the transannular alkene or the lactone site of the cycloalkyne, it outperforms the classical Birch‐type reduction that could not be applied at such a late stage. Other key steps en route to 1 comprise an iron‐catalyzed reductive formation of a non‐terminal alkyne, an asymmetric propiolate carbonyl addition mediated by a bulky amino alcohol, and a macrocyclization by ring‐closing alkyne metathesis catalyzed by a molybdenum alkylidyne.