Crystal and molecular structure of 2.2′-dihydroxyazobenzene

C₁₂H₁₀N₂O₂; monoclinic, space group P1 2₁/c 1 (Z = 2), 826 observed independent reflexions, R = 0.043; lattice dimensions at 25 °C, a = 975.8(3) pm, b = 466.8(1) pm, c = 1186.8(2) pm, β = 108.51(1)°.     

Über den Satz von Poincaré in der Störungstheorie Briot-Bouquetscher Differentialgleichungen

The well known theorem of H. Poincaré concerning the analytic continuation and representation along a curve of solutions of differential equations depending on a parameter is generalized to solutions of Differential Equations of Briot-Bouquet type depending on a parameter.

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Herrn Professor Dr. N. Hofreiter zum 70. Geburtstag     

Four-wave mixing in semiconductor laser amplifiers: Applications for optical communication systems

Four-wave mixing in semiconductor laser amplifiers enables various applications in photonic switching including wavelength conversion, space and time switching, optical phase conjugation, and demultiplexing. Switching times faster than 1 ps are possible.     

Non-projectability of polytope skeleta

We investigate necessary conditions for the existence of projections of polytopes that preserve full k-skeleta. More precisely, given the combinatorics of a polytope and the dimension e of the target space, what are obstructions to the existence of a geometric realization of a polytope with the given combinatorial type such that a linear projection to e-space strictly preserves the k-skeleton. Building on the work of Sanyal (2009), we develop a general framework to calculate obstructions to the existence of such realizations using topological combinatorics. Our obstructions take the form of graph colorings and linear integer programs. We focus on polytopes of product type and calculate the obstructions for products of polygons, products of simplices, and wedge products of polytopes. Our results show the limitations of constructions for the deformed products of polygons of Sanyal and Ziegler (2010) and the wedge product surfaces of Rörig and Ziegler (2011) and complement their results.     

A framework for the automated real-time detection of short tonal sounds from ocean observatories

Acquisition of acoustic data from ocean observatories is expected to play a key role for the long-term monitoring of marine mammals and anthropogenic noise. It typically requires processing of a large volume of acoustic data and it must rely on automated identification of signals. We present an algorithmic framework for the detection of short tonal sounds (e.g. cetacean calls, anthropogenic pings) intended to act as a first stage in a system for the automated real-time detection, classification, and localisation of acoustic sources. The algorithm was validated under a diversity of scenarios expected at ocean observatories. Using simulated signals that emulate a variety of cetacean call-types, perfect identification of signal position was obtained for signal to noise ratios of ?15 to ?5 dB, depending on the signal-type. Separation of real-world data segments with short tonal sounds (mainly cetacean calls) from segments with other sounds or noise resulted in Area Under the ROC Curve values between 0.96 and 0.98. The algorithm can be used to automatically identify cetacean calls and anthropogenic short tonal sounds much faster than in real-time, thereby reducing the burden put on data transmission, storage, or processing by classification and localisation algorithms.     

A variational approach to the construction and Malliavin differentiability of strong solutions of SDE’s

In this article we develop a new approach to construct solutions of stochastic equations with merely measurable drift coefficients. We aim at demonstrating the principles of our technique by analyzing strong solutions of stochastic differential equations driven by Brownian motion. An important and rather surprising consequence of our method which is based on Malliavin calculus is that the solutions derived by Veretennikov (Theory Probab Appl 24:354–366, 1979) for Brownian motion with bounded and measurable drift in $\mathbb{R }^{d}$ are Malliavin differentiable. Further, a strength of our approach, which does not rely on a pathwise uniqueness argument, is that it can be transferred and applied to the analysis of various other types of (stochastic) equations: We obtain a Bismut–Elworthy–Li formula (Elworthy and Li, J Funct Anal 125:252–286, 1994) for spatial derivatives of solutions to the Kolmogorov equation with bounded and measurable drift coefficients. To derive the formula, we use that our approach can be applied to obtain Sobolev differentiability in the initial condition in addition to Malliavin differentiability of the associated stochastic differential equations. Another application of our technique is the construction of unique solutions of the stochastic transport equation with irregular vector fields. Moreover, our approach is also applicable to the construction of solutions of stochastic evolution equations on Hilbert spaces.     

On the Validity of Stokes–Einstein and Stokes–Einstein–Debye Relations in Ionic Liquids and Ionic‐Liquid Mixtures

Stokes–Einstein (SE) and Stokes–Einstein–Debye (SED) relations in the neat ionic liquid (IL) [C₂mim][NTf₂] and IL/chloroform mixtures are studied by means of molecular dynamics (MD) simulations. For this purpose, we simulate the translational diffusion coefficients of the cations and anions, the rotational correlation times of the C(2)? H bond in the cation C₂mim⁺, and the viscosities of the whole system. We find that the SE and SED relations are not valid for the pure ionic liquid, nor for IL/chloroform mixtures down to the miscibility gap (at 50 wt % IL). The deviations from both relations could be related to dynamical heterogeneities described by the non‐Gaussian parameter α(t). If α(t) is close to zero, at a concentration of 1 wt % IL in chloroform, both relations become valid. Then, the effective radii and volumes calculated from the SE and SED equations can be related to the structures found in the MD simulations, such as aggregates of ion pairs. Overall, similarities are observed between the dynamical properties of supercooled water and those of ionic liquids.     

Stabilization of foams with inorganic colloidal particles

Wet foams are used in many important technologies either as end or intermediate products. However, the thermodynamic instability of wet foams leads to undesired bubble coarsening over time. Foam stability can be drastically improved by using particles instead of surfactants as foam stabilizers, since particles tend to adsorb irreversibly at the air-water interface. Recently, we presented a novel method for the preparation of high-volume particle-stabilized foams which show neither bubble growth nor drainage over more than 4 days. The method is based on the in-situ hydrophobization of initially hydrophilic particles to enable their adsorption on the surface of air bubbles. In-situ hydrophobization is accomplished through the adsorption of short-chain amphiphiles on the particle surface. In this work, we illustrate how this novel method can be applied to particles with various surface chemistries. For that purpose, the functional group of the amphiphilic molecule was tailored according to the surface chemistry of the particles to be used as foam stabilizers. Short-chain carboxylic acids, alkyl gallates, and alkylamines were shown to be appropriate amphiphiles to in-situ hydrophobize the surface of different inorganic particles. Ultrastable wet foams of various chemical compositions were prepared using these amphiphiles. The simplicity and versatility of this approach is expected to aid the formulation of stable wet foams for a variety of applications in materials manufacturing, food, cosmetics, and oil recovery, among others.