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This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second-order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third-order accurate Adams-Moulton method and the second-order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier.     

Formulation of Cannabidiol in Colloidal Lipid Carriers

In this study, the general processability of cannabidiol (CBD) in colloidal lipid carriers was investigated. Due to its many pharmacological effects, the pharmaceutical use of this poorly water-soluble drug is currently under intensive research and colloidal lipid emulsions are a well-established formulation option for such lipophilic substances. To obtain a better understanding of the formulability of CBD in lipid emulsions, different aspects of CBD loading and its interaction with the emulsion droplets were investigated. Very high drug loads (>40% related to lipid content) could be achieved in emulsions of medium chain triglycerides, rapeseed oil, soybean oil and trimyristin. The maximum CBD load depended on the type of lipid matrix. CBD loading increased the particle size and the density of the lipid matrix. The loading capacity of a trimyristin emulsion for CBD was superior to that of a suspension of solid lipid nanoparticles based on trimyristin (69% vs. 30% related to the lipid matrix). In addition to its localization within the lipid core of the emulsion droplets, cannabidiol was associated with the droplet interface to a remarkable extent. According to a stress test, CBD destabilized the emulsions, with phospholipid-stabilized emulsions being more stable than poloxamer-stabilized ones. Furthermore, it was possible to produce emulsions with pure CBD as the dispersed phase, since CBD demonstrated such a pronounced supercooling tendency that it did not recrystallize, even if cooled to −60 °C.     

Dynamic Equilibrium of a Coupled ODE-PDE Problem for Surface Nanobubbles

We consider a mathematical model for surface nanobubbles arising from hydrogen electrolysis in polymer electrolyte membrane (PEM) electrolyzers. Experimental advances in recent years indicated longer lifetimes of surface nanobubbles than may be explained by classical theories. Contrary to [5], we state a full model of an evolving single surface nanobubble yielding a coupled system consisting of a partial differential equation (PDE) for the hydrogen concentration in water and an ordinary differential equation (ODE) for the radius evolution. In the special case of dynamic equilibrium conditions, we prove the well-posedness of this steady state problem by a fixed-point strategy, assuming an acute-angled contact angle, and that the corresponding algorithm allows for its numerical simulation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigating the Disordered and Membrane-Active Peptide A-Cage-C Using Conformational Ensembles

The driving forces and conformational pathways leading to amphitropic protein-membrane binding and in some cases also to protein misfolding and aggregation is the subject of intensive research. In this study, a chimeric polypeptide, A-Cage-C, derived from α-Lactalbumin is investigated with the aim of elucidating conformational changes promoting interaction with bilayers. From previous studies, it is known that A-Cage-C causes membrane leakages associated with the sporadic formation of amorphous aggregates on solid-supported bilayers. Here we express and purify double-labelled A-Cage-C and prepare partially deuterated bicelles as a membrane mimicking system. We investigate A-Cage-C in the presence and absence of these bicelles at non-binding (pH 7.0) and binding (pH 4.5) conditions. Using in silico analyses, NMR, conformational clustering, and Molecular Dynamics, we provide tentative insights into the conformations of bound and unbound A-Cage-C. The conformation of each state is dynamic and samples a large amount of overlapping conformational space. We identify one of the clusters as likely representing the binding conformation and conclude tentatively that the unfolding around the central W23 segment and its reorientation may be necessary for full intercalation at binding conditions (pH 4.5). We also see evidence for an overall elongation of A-Cage-C in the presence of model bilayers.     

Isomer-Specific Vibrational Spectroscopy of Microhydrated Lithium Dichloride Anions: Spectral Fingerprint of Solvent-Shared Ion Pairs

The vibrational spectroscopy of lithium dichloride anions microhydrated with one to three water molecules, [LiCl₂(H₂O)_1–3]⁻, is studied in the OH stretching region (3800–2800 cm⁻¹) using isomer-specific IR/IR double-resonance population labelling experiments. The spectroscopic fingerprints of individual isomers can only be unambiguously assigned after anharmonic effects are considered, but then yield molecular level insight into the onset of salt dissolution in these gas phase model systems. Based on the extent of the observed frequency shifts Δν^OH of the hydrogen-bonded OH stretching oscillators solvent-shared ion pair motifs (<3200 cm⁻¹) can be distinguished from intact-core structures (>3200 cm⁻¹). The characteristic fingerprint of a water molecule trapped directly in-between two ions of opposite charge provides an alternative route to evaluate the extent of ion pairing in aqueous electrolyte solutions.     

Bernstein theorems for length and area decreasing minimal maps

In this article we prove Liouville and Bernstein theorems in higher codimension for length and area decreasing maps between two Riemannian manifolds. The proofs are based on a strong elliptic maximum principle for sections in vector bundles, which we also present in this article.     

Nanoscopic optical sensors based on functional supramolecular hybrid materials

This review highlights how the combination of supramolecular principles and nanoscopic solid structures enables the design of new hybrid sensing ensembles with improved sensitivity and/or selectivity and for the targeting of analytes for which selectivity is hard to achieve by conventional methods. Such ideas are bridging the gap between molecules, materials sciences and nanotechnology. Relevant examples will be detailed, taking into account functional aspects such as (1) enhanced coordination of functionalized solids, (2) enhanced signalling through preorganization, (3) signalling by assembly–disassembly of nanoscopic objects, (4) biomimetic probes utilizing discrimination by polarity and size and (5) distinct switching and gating protocols. These strategies are opening new prospects for sensor research and signalling paradigms at the frontier between nanotechnology, smart materials and supramolecular chemistry.     

Test‐Strip‐Based Fluorometric Detection of Fluoride in Aqueous Media with a BODIPY‐Linked Hydrogen‐Bonding Receptor

The measurement of biologically relevant anions, such as fluoride, is an important task in analytical chemistry, in particular, for dental health and osteoporosis. Although a large number of fluoride probes are known, the applicability under relevant conditions is limited to a few examples. To improve this situation, BODIPY‐amidothiourea dyes with varying hydrogen‐bond donating strengths were developed, the most H‐acidic of which ( 1 c ) could detect F^? from an inorganic source (NaF) in 50 % aqueous solution (DMSO/water 1:1, v/v) with 0.01 ppm sensitivity through selective fluorescence quenching by a photoinduced electron‐transfer (PET) process. Use of the probe and a reference dye with a test‐strip assay and a portable and rapidly recording lateral‐flow fluorescence reader made determination of F^? in neat aqueous solutions, such as spiked water samples and toothpaste extracts, possible in a self‐referenced manner, achieving a detection limit of 0.2 ppm.