A comparison of the Discontinuous-Galerkin- and Spectral-Difference-Method on triangulations using PKD polynomials

This paper gives a first numerical comparison of the Discontinuous-Galerkin-(DG) and Spectral-Difference-Method (SD) under almost equivalent conditions for smooth test cases.     

Modeling the propagation of ultrasonic waves in the interface region between two bonded elements

An important task in nondestructive materials evaluation is the development of techniques to characterize the bond quality of adherent joints. Binding forces are nonlinear and cause a nonlinear modulation of transmitted and reflected ultrasonic waves. As a consequence, the higher harmonics generated by an insonified monochromatic wave give information about the adhesive bonds. The local binding forces in thin bonded interfaces can be obtained by the amplitudes of the ultrasonic waves of the insonified frequency and its higher harmonics as transmitted through the interface. Additional phase measurements may enable one to obtain the evaluation of the full hysteretic cycle of the interaction force. In order to gain a deeper understanding of the interface region and to improve the technique, numerical simulations of the ultrasonic wave propagation through specimens of two bonded elements can be used. A simple model based on the local interaction simulation approach (LISA) is described in this contribution, and a comparison between the results of the simulations and the experimental data is presented. Besides its intrinsic relevance for NDE, the problem considered in this paper may be very useful to analyze and test models for the simulation of ultrasonic wave propagation in nonclassical nonlinear mesoscopic elastic materials.     

A unified treatment of nonclassical nonlinear effects in the propagation of ultrasound in heterogeneous media

Recent experiments on rocks and other materials, such as soil, cement, concrete and damaged elastic materials, have led to the discovery of nonlinear (NL) hysteretic effects in their elastic behaviour. These observations suggest the existence of a NL mesoscopic elasticity universality class, to which all the aforementioned materials belong. The purpose of the present contribution is to search for the basic mathematical roots for nonclassical nonlinearity, in order to explain its universality, classify it and correlate it with the underlying meso- or microscopic interaction mechanisms. In our discussions we explicitly consider two quite different kinds of specimens: a two-bonded-elements structure and a thin multigrained bar. It is remarkable that, although the former includes only one interface and the latter very many interstices, the same "interaction box" formalism can be applied to both. Another important result of the proposed formalism is that the spectral contents of an arbitrary system for any input amplitude may be predicted, under certain assumptions, from the result of a single experiment at a higher amplitude.     

Conception of a new technique in cell cultivation using a lab-on-chip aided miniaturised device with calibratable electrochemical sensors

Continuous electrochemical sensing is often carried out in order to track the growth of cells as an alternative to optical monitoring. Planar sensors and multi-sensor chips are applied in case of adhered growing cells, and usually introduced into lab-on-chip systems. Repeated recalibration is necessary with most chemosensors so far and this limits the operational lifetime of such lab-on-chip systems to a few days. An assembly is presented here that eliminates this disadvantage and enables the monitoring of a long-term cultivation of tissue. Cell cultures and sensor are arranged such that they can be separated or contacted at variable times without having an impact on the growth of the cells. The use of a biocompatible nano-porous membrane is especially important. A multi-well system is described where each well is supplied with a planar multi-sensor chip below the adhered cells to determine (a) pH, (b) glucose, (c) oxygen, and—optionally—impedance, for example during the cultivation of cartilage tissue.     

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)     

Fast and comprehensive analysis of secondary metabolites in cocoa products using ultra high‐performance liquid chromatography directly after pressurized liquid extraction

Fast methods for the extraction and analysis of various secondary metabolites from cocoa products were developed and optimized regarding speed and separation efficiency. Extraction by pressurized liquid extraction is automated and the extracts are analyzed by rapid reversed‐phase ultra high‐performance liquid chromatography and normal‐phase high‐performance liquid chromatography methods. After extraction, no further sample treatment is required before chromatographic analysis. The analytes comprise monomeric and oligomeric flavanols, flavonols, methylxanthins, N‐phenylpropenoyl amino acids, and phenolic acids. Polyphenols and N‐phenylpropenoyl amino acids are separated in a single run of 33 min, procyanidins are analyzed by normal‐phase high‐performance liquid chromatography within 16 min, and methylxanthins require only 6 min total run time. A fourth method is suitable for phenolic acids, but only protocatechuic acid was found in relevant quantities. The optimized methods were validated and applied to 27 dark chocolates, one milk chocolate, two cocoa powders and two food supplements based on cocoa extract.     

A dynamical systems result on asymptotic integration of linear differential systems

We are interested in the asymptotic integration of linear differential systems of the form x′=[Λ(t)+R(t)]x, where Λ is diagonal and R∈L^p[t₀,∞) for p∈[1,2]. Our dichotomy condition is in terms of the spectrum of the omega-limit set ω_Λ. Our results include examples that are not covered by the Hartman-Wintner theorem.     

[3+2] Cycloaddition nach addition von allylalkohol und allylaminen an 5-diazourazile

The non-isolable allylalcohol adduct 2c of 5-diazouracil 1 undergoes intramolecular [3+2] cycloaddition to afford the tricyclic pyrazolofuropyrimidine 3 . In a similar way the reaction of the 5-diazouracils 2 , 2a and 2d with allylamine and diallylamine proceeds via the 6-amino-adducts to provide the tricyclic pyrazolopyrrolopyrimidines 5 , 5a , 7 and 7a . With allylamine and 2a , the 1,2,3-triazolederivative 6 is obtained as a byproduct.     

Reaktionen von 5-diazourazilen mit primären aminen zu 1,2,3-triazolcarbonsäurederivaten

The reaction of 5-diazouracils with saturated primary amines affords [(1-alkyl-1,2,3-triazol-4-yl) carbonyl]ureas. The primary formation of a non-isolable 6-amine-adduct 2 is followed by 1,6-ring opening of the pyrimidone and ring closure to the triazole derivative.