Quantitative stability analysis of optimal solutions in PDE-constrained optimization

PDE-constrained optimization problems under the influence of perturbation parameters are considered. A quantitative stability analysis for local optimal solutions is performed. The perturbation directions of greatest impact on an observed quantity are characterized using the singular value decomposition of a certain linear operator. An efficient numerical method is proposed to compute a partial singular value decomposition for discretized problems, with an emphasis on infinite-dimensional parameter and observation spaces. Numerical examples are provided.     

Dispersion effects in unreplicated factorial designs

Methods for estimation of dispersion effects in two‐level unreplicated factorial designs are studied. The consequences of non‐constant variance are discussed. A natural assumption concerning the form of the covariance of location effects leads to a particular normal model. Some linear combinations of the response variables are constructed in order to make a simple structure for inference. The precision of point estimators of dispersion effects, where one is based on experiments with replicates, are compared. A numerical example is given as an illustration of a test. Finally, estimations in fractional designs are described and discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Structural Revision and Elucidation of the Biosynthesis of Hypodoratoxide by 13C,13C COSY NMR Spectroscopy

Feeding of (2,3,4,5,6‐¹³C₅)mevalonolactone to the fungus Hypomyces odoratus resulted in a completely labeled sesquiterpene ether. The connectivity of the carbon atoms was easily deduced from a ¹³C,¹³C COSY spectrum, revealing a structure that was different from the previously reported structure of hypodoratoxide, even though the reported ¹³C NMR data matched. A structural revision of hypodoratoxide is thus presented. Its absolute configuration was tentatively assigned from its co‐metabolite cis‐dihydroagarofuran. Its biosynthesis was investigated by feeding of (3‐¹³C)‐ and (4,6‐¹³C₂)mevalonolactone, which gave insights into the complex rearrangement of the carbon skeleton during terpene cyclization by analysis of the ¹³C,¹³C couplings.     

Characterization of different substrates for Raman spectroscopic imaging of eukaryotic cells

For Raman spectroscopic analyses of the cells and other biological samples, the choice of the right substrate material is very important to avoid loss of information in characteristic spectral features because of competing background signals. In the current study, Raman spectroscopy is used to characterize several potential Raman substrates. Raman vibrational bands of the substrate material are discussed. The surface topography is analyzed by atomic force microscopy, and the root mean square surface roughness values are reported. Biocompatibility of the substrates is tested with Hep G2 cells evaluating cellular morphology as well as live/dead staining. Calcium fluoride, silicon, fused silica, borofloat glass, and silicon nitride membranes support cell growth and adherence. Silicon, borofloat glass, and fused silica give rise to Raman signals in the region of interest. Calcium fluoride substrate (UV grade) is suitable for Raman spectroscopic investigation of living cells. Nickel foil is suitable substrate for Raman spectroscopic investigation but cellular adherence and viability depend on the quality of the foil. Silicon nitride membranes coated with nickel chrome is a suitable Raman substrate in closed microfluidic systems. Copyright © 2016 John Wiley & Sons, Ltd.     

A Combined Experimental and Theoretical Study on the Stereodynamics of Monoaza[5]helicenes: Solvent‐Induced Increase of the Enantiomerization Barrier in 1‐Aza‐[5]helicene

Helicenes and heterohelicenes are attractive compounds with great potential in materials sciences to be used in optoelectronics as ligand backbones in enantioselective catalysis and as chiral sensors. The properties of these materials are related to the stereodynamics of these helical chiral compounds. However, little is known about features controlling stereodynamics in helicenes; in particular, for heterohelicenes the position of the heteroatom could be relevant in this respect. Herein the complete stereodynamic characterization of monoaza[5]helicenes is shown by enantioselective dynamic HPLC and DFT calculations. At variance with previous theoretical calculations, 1‐aza[5]helicene shows a surprisingly high enantiomerization barrier, which is triggered by specific solvent interactions.     

Diffusion induced void nucleation in SnPb solder joints

Towards a simple and robust model for void-based fatigue prediction, we investigate the interaction of voids with its surrounding by using a multi-field method. We couple the concentration fields of tin c₁ and lead c₂ with an additional field c₃, where the latter is assigned with a void field. The interaction potential manifests three stable states. Two are obtained by experimental results of tin-lead (SnPb) and the void stable state is postulated by construction. The logarithmic form of the thermodynamically consistent configurational entropy is approximated within this study by a fourth order polynom. It has been shown that the interfacial energy coefficient is independent of void's size, but rather depends numerically on the mesh size, which is used in the model presented here. Both governing equations follows a Cahn-Hilliard-type equation to mimic the microstructural changes. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)