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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.     

Zur analytischen Beschreibung des Füllstoffeinflusses auf das Fließverhalten von Kunststoff-Schmelzen

From literature some representative equations have been compiled describing the influence of filler on the viscosity of polymer melts. By application of these on the experimental results obtained from GF-SAN it was found that the relative viscosity _R , i.e. the ratio of the viscosities of the filled and unfilled melt, shows a pronounced dependence on the shear rate but not on the shear stress. Defining _R with constant and not with constant (as it is usually done), an analytical approach is possible independent of Further the influence of pressure, temperature and filler content on the zero-shear viscosity of filled polymer melts may be expressed by a modified Arrhenius equation.

     

A mass conservative well‐balanced reconstruction at wet/dry interfaces for the Godunov‐type shallow water model

This paper presents a novel mass conservative, positivity preserving wetting and drying treatment for Godunov‐type shallow water models with second‐order bed elevation discretization. The novel method allows to compute water depths equal to machine accuracy without any restrictions on the time step or any threshold that defines whether the finite volume cell is considered to be wet or dry. The resulting scheme is second‐order accurate in space and keeps the C‐property condition at fully flooded area and also at the wet/dry interface. For the time integration, a second‐order accurate Runge–Kutta method is used. The method is tested in two well‐known computational benchmarks for which an analytical solution can be derived, a C‐property benchmark and in an additional example where the experimental results are reproduced. Overall, the presented scheme shows very good agreement with the reference solutions. The method can also be used in the discontinuous Galerkin method. Copyright © 2016 John Wiley & Sons, Ltd.     

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.