Calculation of sequence‐dependent free energies of hydration of dipeptides formed by alanine and glycine

The relative free energies of hydration of the dipeptides glycylalanine and alanyl‐glycine in their naturally occurring form have been calculated both for the zwitterionic and protonated species. Emphasis was laid on comparisons between the conventional cutoff method and the Particle Mesh Ewald method to account for possible differences in electrostatic contributions to the free energy. Furthermore, the convergence behavior of the total free energy and its individual contributions were examined. The results, obtained by means of the thermodynamic integration technique as implemented in the free energy module of the AMBER program suite, suggest that in aqueous solution glycylalanine is more stable than alanylglycine by 2.7 kcal/mol in the zwitterionic form and by 3.5 kcal/mol in the protonated form. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 846–860, 2001     

Resonance in viscous film flow over topography

We study viscous gravity-driven films flowing over periodically undulated substrates. Linear analysis describes resonance in steady flow along small bottom corrugations for films of arbitrary thickness. Depending on the dimensionless film thickness we find different regimes for the resonance, which is associated with the interaction of the undulated film with capillarygravity waves traveling against the flow. Nonlinear resonance produces higher harmonics and bistable resonance. The higher harmonics are due to higher harmonics resonance and due to the nonlinear coupling to lower harmonics. For the bistable resonance we derive a minimum model showing that the bistability corresponds essentially to that of the driven Duffing oscillator. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Control and stability analysis of a turbocharged Diesel engine using singular perturbation methods

The control of the air path of a diesel engine with a variable geometry turbocharger and exhaust gas recirculation can be improved significantly by nonlinear methods. The control objective is to supply an amount of fresh air by the compressor and to achieve a desired pressure in the intake manifold in the neighborhood of an operating point of the engine. The mathematical model of the air path is split into a slow and a fast part. For the proposed controller, asymptotic stability of the closed loop system in the sense of Lyapunov is guaranteed by the use of singular perturbation methods. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Justification of the nonlinear Schr?dinger equation in spatially periodic media

The dynamics of the envelopes of spatially and temporarily oscillating wave packets advancing in spatially periodic media can approximately be described by solutions of a Nonlinear Schr?dinger equation. Here we prove estimates for the error made by this formal approximation using Bloch wave analysis, normal form transformations, and Gronwall’s inequality.     

Tutorial on off-axis electron holography.

Through recent years, off-axis electron holography has helped us to understand and to overcome some experimental restrictions in transmission electron microscopy. With development of powerful electron microscopes, slow-scan CCD cameras, and computers, holography is not an academic technique anymore used by specialized laboratories. Holography has proven its wide range of applications in solving real-world problems in materials science and biology. At medium resolution, that is, on nanometer scale, holography allows access to large area phase contrast produced by magnetic fields and electric potentials. In the high-resolution domain, holography unveils its power by unscrambling amplitude and phase of the electron wave, resulting in an improved lateral resolution up to the information limit. Holography is a thoroughly quantitative method, and, in combination with the perfect zero-loss filtering inherent to this method, the interpretation of the reconstructed data is strongly simplified. After outlining the basics of holography, in this tutorial we focus on development of a step-by-step procedure for recording and reconstruction of holograms. At the end, some recent applications are discussed.     

Microwave-mediated intramolecular Diels-Alder cyclization of biodihydroxylated benzoic acid derivatives

The synthetic utility of biodihydroxylated benzoic acid derivatives for the construction of bridge bicyclo scaffolds was investigated. Biodihydroxylation of benzoic acid using Ralstonia eutropha B9 gave (1S,2R)-1,2-dihydroxycyclohexa-3,5-diene-1-carboxylic acid (DCD) in high optical purity (>95% ee). Protection of the intermediate and subsequent functional group transformation gave the required cyclization precursors in moderate to excellent overall yields. Subsequent intramolecular Diels-Alder cyclization of biodihydroxylated benzoic acid derivatives was carried out using either thermal or microwave conditions. Enantiomerically pure products with five chiral centers were obtained in 4-6 steps from achiral starting material.