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.     

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.     

Exploitation of the coil-globule plasmid DNA transition induced by small changes in temperature, pH salt, and poly(ethylene glycol) compositions for directed partitioning in aqueous two-phase systems

In this study, the interplay of two linked equilibria is examined, one concerning an aqueous two-phase system (ATPS) composed of poly(ethylene glycol) (PEG) and salt employed to partition plasmid DNA (pDNA), and the other a potential structural transition of pDNA depending on PEG and salt concentration and other system parameters. The boundary conditions for pDNA partitioning are set by PEG and salt concentrations, PEG molecular weight, pH, and temperature. While investigating these parameters, it was found that a small increase/decrease of the respective values led to a drastic and significant change in pDNA behavior. This behavior could be attributed to a coil-globule transition of the pDNA triggered by the respective phase conditions. The combination of this structural change, aggregation effects linked to the transition process, and the electrostatic potential difference found in PEG-salt systems thus offers a sensitive way to separate nucleic acid forms on the basis of their unique property to undergo coil-globule transitions under distinct system properties.     

Coupling artificial actin cortices to biofunctionalized lipid monolayers

We report the assembly of protein supramolecular structures at an air-water interface and coupling of artificial actin cortices to such structures. The coupling strategies adopted include electrostatic binding of actin to monolayers doped with lipids, exposing positively charged poly(ethylene glycol) headgroups; binding of biotinylated actin to lipids carrying biotin headgroups through avidin; binding of actin to membranes through biotinylated hisactophilin (a cellular actin-membrane coupler) using an avidin-biotin linkage; and coupling of actin to membranes carrying chelating lipids through a 15-nm-diameter protein capsid (bacterial lumazine synthase or LuSy) exhibiting histidine tags (which bind both to actin and to the chelating lipid). The distribution of the proteins in a direction normal to the interface was measured by neutron reflectivity under different conditions of pH and ionic strength. In the case of the first three binding methods, the thickness of the actin film was found to correspond to a single actin filament. Multilayers of actin could be formed only by using the multifunctional LuSy couplers that exhibit 60 hexahistidine tags and can thus act as actin cross-linkers. The LuSy-mediated binding can be reversibly switched by pH variations.     

Calculation of absorption spectra for light-harvesting systems using non-Markovian approaches as well as modified Redfield theory

For an ensemble of B850 rings of the light-harvesting system LH2 of purple bacteria the linear absorption spectrum is calculated. Using different Markovian and non-Markovian, time-dependent and time-independent methods based on second-order perturbation theory in the coupling between the excitonic system and its surrounding environment as well as the modified Redfield theory, the influence of the shape of the spectral density on the linear absorption spectrum is demonstrated for single samples and in the ensemble average. For long bath correlation times non-Markovian effects clearly show up in the static absorption line shapes. Among the different spectral densities studied is one of the purple bacterium Rhodospirillum molischianum obtained by a molecular-dynamics simulation earlier. The effect of static disorder on its line shapes in the ensemble average is analyzed and the results of the present calculations are compared to experimental data.     

Brewster-angled chirped mirrors for broadband pulse compression without dispersion oscillations

We use Brewster-angled chirped mirrors for dispersion compensation of a noncollinear optical parametric amplifier. This novel mirror design virtually eliminates spurious surface reflections and resultant dispersion ripple. The absence of compression artifacts is demonstrated by the generation of clean 5.6 fs pulses, with what is believed to be an unprecedented low ripple-induced satellite content for a nonadaptive scheme. In addition, the 270 THz spectral coverage allows generation of widely tunable visible pulses of 8 to 15 fs duration.     

Combined coherent anti-Stokes Raman spectroscopy and linear Raman spectroscopy for simultaneous temperature and multiple species measurements

The simultaneous application of pure rotational coherent anti-Stokes Raman spectroscopy (CARS) and vibrational linear Raman spectroscopy (LRS) for the measurement of temperature and species concentrations in combustion systems is demonstrated. In addition to the standard rotational CARS experimental setup, only one detection system (spectrometer and intensified CCD camera) for the collection of the LRS signals was applied. The emission of the broadband dye laser used for CARS was shifted to the deep red to avoid interferences with the LRS signals located in the visible region. First experimental results from a vaporizing propane spray using an engine injection system are shown.     

The 15N chemical shifts in mixed NB2Si and NBSi2 environments of Si3B3N7--a theoretical investigation

Nuclear magnetic resonance (NMR) chemical shifts in solids may be calculated by ab initio methods approximating the solid state by molecular clusters. We employed this technique to obtain estimates of (15)N chemical shifts in NB(2)Si and NBSi(2) environments in the solid state. Such nitrogen environments are found in amorphous (Si/B/N-)ceramics which exhibit very interesting features such as high thermal and mechanical stability. We based our calculations on cutouts of hypothetical Si(3)B(3)N(7) crystals suggested by Kroll and Hoffmann [Silicon boron nitrides: hypothetical polymorphs of Si(3)B(3)N(7), Angew. Chem. Int. Ed. 37 (1998) 2527]. Taking the systematic errors of our calculations into account we expect the chemical shifts in NBSi(2) environments around -293+/-5ppm. Chemical shifts in NB(2)Si environments are expected at -272+/-6ppm. The range of the calculated chemical shifts in NBSi(2) environments coincides with experimental chemical shifts in molecular compounds. Experimental chemical shifts of NB(2)Si nitrogen in molecules appear at lower field than our calculated chemical shifts in the solid state.