Time-adaptive multirate generalized-structure additively partitioned Runge-Kutta schemes for mechanical fluid-structure interaction

We extend the multirate GARK approach by Günther and Sandu [1, 2] to the case of non-constant micro steps per macro step to be able to cover time adaptivity, arriving at our so-called TAMGARK scheme and derive order conditions for arbitrary non-constant micro step sizes. The TAMGARK scheme is applied to the classical piston problem [3] to study the interaction between the piston and inviscid fluid flow in one spatial dimension. We demonstrate the functionality of the chosen time-adaptation strategy and the ability of the overall scheme to preserve the order of the basic schemes. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structural dynamics of surfaces by ultrafast electron crystallography: experimental and multiple scattering theory

Recent studies in ultrafast electron crystallography (UEC) using a reflection diffraction geometry have enabled the investigation of a wide range of phenomena on the femtosecond and picosecond time scales. In all these studies, the analysis of the diffraction patterns and their temporal change after excitation was performed within the kinematical scattering theory. In this contribution, we address the question, to what extent dynamical scattering effects have to be included in order to obtain quantitative information about structural dynamics. We discuss different scattering regimes and provide diffraction maps that describe all essential features of scatterings and observables. The effects are quantified by dynamical scattering simulations and examined by direct comparison to the results of ultrafast electron diffraction experiments on an in situ prepared Ni(100) surface, for which structural dynamics can be well described by a two-temperature model. We also report calculations for graphite surfaces. The theoretical framework provided here allows for further UEC studies of surfaces especially at larger penetration depths and for those of heavy-atom materials.     

Cu(I) catalysed cyclopropanation with enantiopure scorpionate type ligands derived from (+)-camphor or (-)-menthone

One-pot syntheses of three new enantiopure heteroscorpionate ligands derived from (+)-camphor or (-)-menthone are described. The ligands are obtained by reacting pyrazoles derived from (+)-camphor or (-)-menthone with sodium hydride and thionyl chloride. Subsequent reactions with pyridine and various aldehydes afford the tripod ligands in multi-gram amounts. Especially the menthopyrazole based ligand 6 showed encouraging ee values up to 69% in the Cu(I) catalysed enantioselective cyclopropanation of styrene with ethyl diazoacetate.     

Neurotoxin II bound to acetylcholine receptors in native membranes studied by dynamic nuclear polarization NMR

Methods enabling structural studies of membrane-integrated receptor systems without the necessity of purification provide an attractive perspective in membrane protein structural and molecular biology. This has become feasible in principle since the advent of dynamic nuclear polarization (DNP) magic-angle-spinning NMR spectroscopy, which delivers the required sensitivity. In this pilot study, we observed well-resolved solid-state NMR spectra of extensively (13)C-labeled neurotoxin II bound to the nicotinic acetylcholine receptor (nAChR) in native membranes. We show that TOTAPOL, a biradical required for DNP, is localized at membrane and protein surfaces. The concentration of active, membrane-attached biradical decreases with time, probably because of reactive components of the membrane preparation. An optimal distribution of active biradical has strong effects on the NMR data. The presence of inactive TOTAPOL in membrane-proximal situations but active biradical in the surrounding water/glycerol "glass" leads to well-resolved spectra, yet a considerable enhancement (ε = 12) is observed. The resulting spectra of a protein ligand bound to its receptor are paving the way for further DNP investigations of proteins embedded in native membrane patches.     

Alkynyl Ti-M complexes with M = Cd and Hg: Synthesis, characterization, and reaction chemistry

The synthesis and properties of heterobimetallic Ti-Cd complexes of type {[Ti](μ-η¹:η²-CCR)₂}CdX₂ ([Ti] = Ti(η⁵-C₅H₄SiMe₃)₂; R = SiMe₃: 3a, X = Cl; 3b, X = Br; 3c, X = I; R = Fc: 3d, X = Br; Fc = Fe(η⁵-C₅H₄)(η⁵-C₅H₅) is reported. These compounds were accessible by treatment of [Ti](CCR)₂ (1a, R = SiMe₃; 1b, R = Fc) with the cadmium salts CdX₂ (2a, X = Cl; 2b, X = Br; 2c, X = I) in a 1:1 M ratio in diethyl ether. Dissolving, for example, 3b in tetrahydrofuran afforded coordination polymer [Cd(μ-Br)₂(thf)₂]_n (4) along with the tweezer molecule 1a. Treatment of 3b with two equiv of LiCCFc (5) gave {[Ti](μ-η¹:η²-CCSiMe₃)₂}Cd(CCFc)₂ (6) which eliminated at ambient temperature the all-carbon buta-1,3-diyne FcCC-CCFc (7) producing 1a and elemental Cd. The same reaction behavior was observed, when 2b was reacted with 5. The thus obtained bis(alkynyl) cadmium complex Cd(CCFc)₂ (8) is redox-active at low temperature producing 7 and Cd(0). When mercury halides HgX₂ (9a, X = Cl; 9b, X = Br) are used, then the titanocene dihalides [Ti]X₂ (10a, X = Cl; 10b, X = Br) together with Me₃SiCC-CCSiMe₃ (11) and Hg(0) were formed. Nevertheless, mercury acetylides were available by treatment of Hg(OAc)₂ (12) with HCCFc (13) in a 1:2 M ratio. Thus obtained Hg(CCFc)₂ (14) gave with [CuBr] (15) coordination polymer [{Hg(η²-CCFc)₂}(Cu₂(μ-Br)₂]_n (16), while with [AgPF₆] oxidation of the ferrocenyl moieties took place affording dicationic [Hg(CCFc)₂]²⁺ (18).The structures of 3b and 4 in the solid state are reported. Compound 3b shows the typical characteristics for heterobimetallic organometallic π-tweezer complexes with cadmium in a tetrahedral environment, while 4 corresponds to a one-dimensional coordination polymer in which the Cd(II) ions are linked in a edge-sharing fashion by bromide bridges in the pseudo-equatorial plane. The appropriate tetrahydrofuran molecules are completing the pseudo-octahedral coordination sphere at cadmium.The cyclic voltammogram of 14 is reported showing a single reversible redox event at E⁰ = 0.108 V with ΔE_p = 76 mV indicating that there is no communication between the Fc termini along the mercury acetylide unit.     

On differential–algebraic equations in infinite dimensions

We consider a class of differential–algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the associated DAE. Moreover, we show that for arbitrary initial values we obtain mild solutions for the associated problem. We discuss the asymptotic behaviour of solutions for both problems. In particular, we provide a characterisation for exponential stability and exponential dichotomies in terms of the spectrum of the associated operator pencil.     

Exploring inequality violations by classical hidden variables numerically

There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser–Horne–Shimony–Holt (CHSH) inequality is very robust. However, we argue that with the Einstein–Podolsky–Rosen setup, the CHSH is inferior to the Bell inequality, although and because the latter must assume anti-correlation of entangled photon singlet states. We simulate how often quantum behavior violates both inequalities, depending on the number of photons. Violating Bell 99% of the time is argued to be an ideal benchmark. We present hidden variables that violate the Bell and CHSH inequalities with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. We discuss how to present the quantum correlations to a wide audience and conclude that, when defending against claims of hidden classicality, one should demand numerical simulations and insist on anti-correlation and the full amount of Bell violation.