Normal form for linear systems with respect to its vector relative degree

For multi-input multi-output (MIMO) linear systems with existing vector relative degree a normal form is constructed. This normal form is not only structural simple but allows to characterize the system’s zero dynamics for the design of feedback controllers. A characterization of the zero dynamics in terms of the normal form is given.     

Electromechanical modelling of skeletal muscle contractions

In the present paper, the aim was to develop a numerical method for optimisation an existing mechanical material model [1] including muscle activation concerning the excitation of skeletal muscles. The modelling idea was a weak and non-monolithic coupling of an electric current expressed by Ohm's law with a hyperelastic muscle model with transversal isotropic characteristics, see [2]. We confirmed the ability of the proposed model by applying on real reconstructed complex muscle geometry. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On Taylor-like integral representations of analytic functions

Let f be an analytic function in a complex domain D and (without loss of generality) assume 0∈D. Then the paper’s aim is to derive a Taylor-like integral expression for f, i.e. an integral representation analogous to the corresponding power series, say, ∑ _k=0^∞ a _k t ^k /k!. We start from the simplest case f(t)=e ^t , which leads to the identity

Variational formulations in continuum mechanics

Variational formulations of the governing equations are of great interest in continuum mechanics: on the one hand a deeper theoretical insight in the respective system is possible, on the other hand variational formulations give rise for the development of semi-analytical and numerical methods like Ritz' direct method, especially FEM. Despite these benefits, there are many problems in continuum mechanics for which a variational principle is not available. The reason for this is that in contrast to conservative Newtonian mechanics, where the Lagrangian is given as difference between kinetic and potential energy, no generally valid construction rule for the Lagrangian has been established in the past. In this paper a construction rule is developed, on the Galilei-invariance of the system, leading to a general scheme for Lagrangians the individual analytical form of which is determined by an inverse treatment of Noether's theorem. This procedure is demonstrated for an elastically deforming body. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel method for measuring the bending rigidity of model lipid membranes by simulating tethers

The tensile force along a cylindrical lipid bilayer tube is proportional to the membrane's bending modulus and inversely proportional to the tube radius. We show that this relation, which is experimentally exploited to measure bending rigidities, can be applied with even greater ease in computer simulations. Using a coarse-grained bilayer model we efficiently obtain bending rigidities that compare very well with complementary measurements based on an analysis of thermal undulation modes. We furthermore illustrate that no deviations from simple quadratic continuum theory occur up to a radius of curvature comparable to the bilayer thickness.     

Organic reaction pathways in the nonaqueous synthesis of metal oxide nanoparticles

Nonaqueous-solution routes to metal oxide nanoparticles are a valuable alternative to the known aqueous sol-gel processes, offering advantages such as high crystallinity at low temperatures, robust synthesis parameters and ability to control the crystal growth without the use of surfactants. In the first part of the review we give a detailed overview of the various solution routes to metal oxides in organic solvents, with a strong focus on surfactant-free processes. In most of these synthesis approaches, the organic solvent plays the role of the reactant that provides the oxygen for the metal oxide, controls the crystal growth, influences particle shape, and, in some cases, also determines the assembly behavior. We have a closer look at the following reaction systems in this order: 1) metal halides in alcohols, 2) metal alkoxides, acetates, and acetylacetonates in alcohols, 3) metal alkoxides in ketones, and 4) metal acetylacetonates in benzylamine. All these systems offer some peculiarities with respect to each other, providing many possibilities to control and tailor the particle size and shape, as well as the surface and assembly properties. In the second part we present general mechanistic principles for aqueous and nonaqueous sol-gel processes, followed by the discussion of reaction pathways relevant for nanoparticle formation in organic solvents. Depending on the system several mechanisms have been postulated: 1) alkyl halide elimination, 2) elimination of organic ethers, 3) ester elimination, 4) C--C bond formation between benzylic alcohols and alkoxides, 5) ketimine and aldol-like condensation reactions, 6) oxidation of metal nanoparticles, and 7) thermal decomposition methods.     

Twin probes as a novel tool for the detection of single-nucleotide polymorphisms

Single-nucleotide polymorphisms (SNPs) are the most common form of DNA sequence variation. There is a strong interest from both academy and industry to develop rapid, sensitive and cost effective methods for SNP detection. Here we report a novel structural concept for DNA detection based on fluorescence dequenching upon hybridization. The so-called "twin probe" consists of a central fluorene derivative as fluorophore to which two identical oligonucleotides are covalently attached. This probe architecture is applied in homogeneous hybridization assays with subsequent fluorescence spectroscopic analysis. The bioorganic hybrid structure is well suited for sequence specific DNA detection and even SNPs are identified with high efficiency. Additionally, the photophysical properties of the twin probe were investigated. The covalent attachment of two single stranded oligonucleotides leads to strong quenching of the central fluorescence dye induced by the nucleobases. The twin probe is characterized by supramolecular aggregate formation accompanied by red-shifted emission and broad fluorescence spectra.     

Low-pressure pyrolysis of tBu2SO: synthesis and IR spectroscopic detection of HSOH

Sulfenic acid (HSOH, 1 ) has been synthesized in the gas‐phase by low‐pressure high‐temperature (1150 °C) pyrolysis of di‐tert‐butyl sulfoxide (tBu₂SO, 2 ) and characterized by means of matrix isolation and gas‐phase IR spectroscopy. High‐level coupled‐cluster (CC) calculations (CCSD(T)/cc‐pVTZ and CCSD(T)/cc‐pVQZ) support the first identification of the gas‐phase IR spectrum of 1 and enable its spectral characterization. Five of the six vibrational fundamentals of matrix‐isolated 1 have been assigned, and its rotational‐resolved gas‐phase IR spectrum provides additional information on the O–H and S–H stretching fundamentals. Investigations of the pyrolysis reaction by mass spectrometry, matrix isolation, and gas‐phase FT‐IR spectroscopy reveal that, up to 500 °C, 2 decomposes selectively into tert‐butylsulfenic acid, (tBuSOH, 3 ), and 2‐methylpropene. The formation of the isomeric sulfoxide (tBu(H)SO, 3 a ) has been excluded. Transient 3 has been characterized by a comprehensive matrix and gas‐phase vibrational IR study guided by the predicted vibrational spectrum calculated at the density functional theory (DFT) level (B3LYP/6‐311+G(2d,p)). At higher temperatures, the intramolecular decomposition of 3 , monitored by matrix IR spectroscopy, yields short‐lived 1 along with 2‐methylpropene, but also H₂O, and most probably sulfur atoms. In addition, HSSOH ( 6 ), H₂, and S₂O are found among the final pyrolysis products observed at 1150 °C in the gas phase owing to competing intra‐ and intermolecular decomposition routes of 3 . The decomposition routes of the starting compound 2 and of the primary intermediate 3 are discussed on the basis of experimental results and a computational study performed at the B3LYP/6‐311G* and second‐order Møller–Plesset (MP2/6‐311G* and RI‐MP2/QZVPP) levels of theory.     

A photocontrolled beta-hairpin peptide

Beta-hairpins constitute the smallest beta-type structures in peptides and proteins. The development of highly stable, yet monomeric beta-hairpins based on the tryptophan zipper motif was therefore a remarkable success [A. G. Cochran, N. J. Skelton, M. A. Starovasnik, Proc. Natl. Acad. Sci USA 2001, 98, 5578-5583]. We have been able to design, synthesize and characterize a hairpin based on this motif which incorporates an azobenzene-based photoswitch, that allows for time-resolved folding studies of beta-structures with unprecedented time resolution. At room temperature the trans-azo isomer exhibits a mostly disordered structure; however, light-induced isomerization to the cis-azo form leads to a predominantly extended and parallel conformation of the two peptide parts, which are linked by the novel photoswitch, [3-(3-aminomethyl)phenylazo]phenylacetic acid (AMPP). While in the original sequence the dipeptide Asn-Gly forms a type I' beta-turn which connects the two strands of the hairpin, this role is adopted by the AMPP chromophore in our photoresponsive beta-hairpin that can apparently act as a beta I'-turn mimetic. The beta-hairpin structure was determined and confirmed by NMR spectroscopy, but the folding process can be monitored by pronounced changes in the CD, IR and fluorescence spectra. Finally, incorporation of the structurally and functionally important beta-hairpin motif into proteins by chemical ligation might allow for the photocontrol of protein structures and/or functions.     

Rapid online equilibration method to determine the D/H ratios of non-exchangeable hydrogen in cellulose

An improved method for the determination of deuterium-to-hydrogen (D/H) ratios of non-exchangeable hydrogen in cellulose is presented. The method is based on the equilibration reaction of the hydroxyl hydrogen of cellulose and water vapour of known isotopic composition. The equilibrated cellulose is pyrolysed and the total D/H ratio determined by subsequent online isotope ratio mass spectrometry (IRMS). With a mass balance system the D/H ratio of non-exchangeable hydrogen is recalculated after an empirical calibration has been performed, yielding a mean exchangeability of 0.239 and an equilibrium fractionation factor of 1.082 between the hydroxyl hydrogen of cellulose and water hydrogen at 110 degrees C. Equilibration takes 10 min per sample. Results obtained by this online equilibration method agree very well with values obtained by the nitration technique (R2 = 0.941). The uncertainty of the equilibration method is +/-4 per thousand resulting from a single standard deviation of +/-2.8 per thousand for the equilibration determined by standard cellulose and 2.8 per thousand from the variable exchangeability of the hydroxyl hydrogen in cellulose due to crystalline areas. The latter uncertainty may be lowered by minimising the crystallinity of the cellulose. Advantages of this new technique are (i) the considerably reduced sample amount required (as low as 0.2 mg, ideally 0.5 mg compared with 20 mg for the conventional nitration technique); (ii) an approximately 100-fold reduced process time; and (iii) no need for the hazardous chemicals used in the nitration technique.