Long-time tails of translational and rotational Brownian motion in a suspension of hard spheres

The long-time translational and rotational Brownian motion of a sphere in a suspension of hard spheres is studied on the basis of the linearized Navier-Stokes equations and the fluctuation-dissipation theorem. It is shown that for the rotational long-time coefficient an effective medium conjecture is incorrect. There are short-range velocity correlations that decay at the same rate as the macroscopic flow pattern used in the effective medium conjecture. An estimate of the short-range correction is made on the basis of the pair term in the cluster expansion of the rotational admittance.     

New mechanistic aspects and structure activity relationships in the allyl nickel complex catalysed butadiene polymerization

The present state of knowledge of the mechanism of the allyl nickel complex catalysed stereoselective butadiene polymerization is outlined. On the basis of the reaction model, which has been worked out more thoroughly and comprehensively by our systematic experimental investigations during the last years, the thermodynamic and kinetic control of the catalytic activity and selectivity in dependence on the structure of the allylnickel complexes will be discussed. Finally, it will be shown how the structure of the technical nickel catalyst could be elucidated for the first time and how its catalytic properties can be explained in the framework of the derived structure-activity relationships.     

N-Heterocyclic Carbene Organocatalysis: With or Without Carbenes?

In this work the mechanism of the aldehyde umpolung reactions, catalyzed by azolium cations in the presence of bases, was studied through computational methods. Next to the mechanism established by Breslow in the 1950s that takes effect through the formation of a free carbene, we have suggested that these processes can follow a concerted asynchronous path, in which the azolium cation directly reacts with the substrate, avoiding the formation of the carbene intermediate. We hereby show that substituting the azolium cation, and varying the base or the substrate do not affect the preference for the concerted reaction mechanism. The concerted path was found to exhibit low barriers also for the reactions of thiamine with model substrates, showing that this path might have biological relevance. The dominance of the concerted mechanism can be explained through the specific structure of the key transition state, avoiding the liberation of the highly reactive, and thus unstable carbene lone pair, whereas activating the substrate through hydrogen-bonding interactions. Polar and hydrogen-bonding solvents, as well as the presence of the counterions of the azolium salts facilitate the reaction through carbenes, bringing the barriers of the two reaction mechanisms closer, in many cases making the concerted path less favorable. Thus, our data show that by choosing the exact components in a reaction, the mechanism can be switched to occur with or without carbenes.     

Canonical extensions: an algebraic approach to Stone duality

This note aims to highlight some of the conceptual contributions to duality theory made by Bjarni Jónsson through the theory of canonical extensions.     

Combining imaging ellipsometry and grazing incidence small angle X-ray scattering for in situ characterization of polymer nanostructures

A combination of microbeam grazing incidence small angle X-ray scattering (μGISAXS) and imaging ellipsometry is introduced as a new versatile tool for the characterization of nanostructures. μGISAXS provides a local lateral and depth-sensitive structural characterization, and imaging ellipsometry adds the position-sensitive determination of the three-dimensional morphology in terms of thickness, roughness, refractive index, and extinction coefficient. Together μGISAXS and imaging ellipsometry enable a complete characterization of structure and morphology. On the basis of an example of buildup of nanostructures from monodisperse colloidal polystyrene nanospheres on a rough solid support, the scope of this new combination is demonstrated. Roughness is introduced by a dewetting structure of a diblock copolymer film with one block being compatible with the colloidal nanoparticles and one block being incompatible. To demonstrate the potential for kinetic investigations, μGISAXS and imaging ellipsometry are applied to probe the drying process of an aqueous dispersion of nanospheres on such a type of rough substrate.     

Prescribed nondegenerate high-order modes in an axial-asymmetric high-finesse Fabry-Perot microcavity

We report an axial-asymmetric high-Q Fabry-Perot cavity supporting nondegenerate Hermite-Gaussian modes of the same mode order. Axial asymmetry of mirror surface was introduced by mechanically grinding off one side of a cylindrical mirror substrate without degrading the original mirror quality. The bases of the resulting Hermite-Gaussian modes were aligned with respect to the direction of grinding, making it possible to prescribe the mirror principal axes.     

Canonical extensions for congruential logics with the deduction theorem

We introduce a new and general notion of canonical extension for algebras in the algebraic counterpart of any finitary and congruential logic S. This definition is logic-based rather than purely order-theoretic and is in general different from the definition of canonical extensions for monotone poset expansions, but the two definitions agree whenever the algebras in are based on lattices. As a case study on logics purely based on implication, we prove that the varieties of Hilbert and Tarski algebras are canonical in this new sense.     

Four-qubit device with mixed couplings

We present the first experimental results on a device with more than two superconducting qubits. The circuit consists of four three-junction flux qubits, with simultaneous ferro- and antiferromagnetic coupling implemented using shared Josephson junctions. Its response, which is dominated by the ground state, is characterized using low-frequency impedance measurement with a superconducting tank circuit coupled to the qubits. The results are found to be in excellent agreement with the quantum-mechanical predictions.