Shear stresses in elastic beams: an intrinsic approach

The theory of non-uniform flexure and torsion of Saint-Venant's beam with arbitrary multiply connected cross section is revisited in a coordinate-free form to provide a computationally convenient context. Numerical implementations, by Matlab, are performed to evaluate the maximum elastic shear stresses in beams with rectangular cross sections for different Poisson's ratios. The deviations between the maximum and mean stresses are then diagrammed to adjust the results provided by Jourawski's method.     

Singularity Curves of a Parallel Pointing System

This paper studies a parallel pointing system used in aerospace applications for orientating parabolic antennas. In the literature [6, 7], the position analysis of this device has been already solved in closed form, whereas simple and efficient tools to address singularities distribution are still lacking. In this paper, its velocity analysis is addressed, and a singularity locus analytic expression, containing the manipulator geometric parameters and the end-effector orientation parameters, is derived. Moreover, it is shown that the determined singularity locus can be represented by curves (singularity curves) on a Cartesian plane having the generalized coordinates of the mechanism on the coordinate axes. Finally, an example showing the use of the proposed relationships is given and discussed.     

Finite-Order Formulation of Vinogradov's C-Spectral Sequence

The C-spectral sequence was introduced by A. M. Vinogradov in the late Seventies as a fundamental tool for the study of the algebro-geometric properties of jet spaces and differential equations. A spectral sequence arises from the contact filtration of the modules of forms on jet spaces of a fibring (or on a differential equation). In order to avoid serious technical difficulties, the order of the jet space is not fixed, i.e., computations are performed on spaces containing forms on jet spaces of any order. In this paper we show that there exists a formulation of Vinogradov's C-spectral sequence in the case of finite-order jet spaces of a fibred manifold. We compute all cohomology groups of the finite-order C-spectral sequence. We obtain a finite-order variational sequence which is shown to be naturally isomorphic with Krupka's finite-order variational sequence.     

Shear rheology of lyotropic liquid crystals: a case study

We have investigated the rheological properties of lyotropic liquid crystals (LCs) formed by self-assembled neutral lipids and water, their relationship with the topology of the structure, and their dependence on temperature and water content. The phase diagram of a representative monoglyceride-water system, determined by combining cross-polarized optical microscopy and small-angle X-ray scattering (SAXS), included four structures: lamellar, hexagonal, gyroid bicontinuous cubic (Ia3d), and double diamond bicontinuous cubic (Pn3m), as well as several regions of two-phase coexistence of some of the above structures. Rheology in the linear viscoelastic regime revealed a specific signature that was characteristic of the topology of each structure considered. The order-order transitions lamellar-to-cubic and cubic-to-hexagonal, as well as the order-disorder transitions from each LC to an isotropic fluid, were easily identified by following the development of the storage and loss moduli, G' and G', respectively. The viscoelastic properties of both bicontinuous cubic phases were shown to be strongly frequency-dependent, following a pseudo-Maxwell behavior, with multiple relaxation times. Cubic-to-cubic transitions were nicely captured by scaling the longest relaxation time, tau, with either temperature or water volume fraction. Therefore, the set of the three main parameters used to establish the rheological behavior of the structure, that is, G', G', and relaxation time, tau, constitutes a consistent ensemble to identify the structures of the liquid crystal. Finally, relaxation spectra, extracted for all liquid crystalline phases, allowed an additional possible identification criterion of the various structures considered.     

Determination of the relative stereochemistry of flexible organic compounds by Ab initio methods: conformational analysis and Boltzmann-averaged GIAO 13C NMR chemical shifts

Ab initio calculations at the Hartree-Fock level with full-geometry optimization using the 6-31G(d) basis set, and GIAO (gauge including atomic orbitals) (13)C NMR chemical shifts, are presented here as a support in the study of the stereochemistry of low-polar organic compounds having an open-chain structure. Four linear stereoisomers, fragments of a natural product previously characterized by experimental (13)C NMR spectra, which possesses three stereogenic centers, 11 carbon atoms, and 38 atoms in total, were considered. Conformational searches, by empirical force-field molecular dynamics, pointed out the existence of 8-13 relevant conformers per stereoisomer. Thermochemical calculations at the ab initio level in the harmonic approximation of the vibrational modes, allowed the evaluation, at 298.15 K, of the standard Gibbs free energy of the conformers. The (13)C NMR chemical shift of a given carbon atom in each stereoisomer was considered as the average chemical shift value of the same atom in the different conformers. The averages were obtained by the Boltzmann distribution, using the relative standard free energies as weighting factors. Computed parameters related to linear correlation plots of experimental (13)C chemical shifts versus the corresponding computed average data allowed us to distinguish among the four stereoisomers.     

Insertion Reactions of 1,2‐Disubstituted Olefins with an α‐Diimine Palladium(II) Complex

The migratory insertions of cis or trans olefins CH(X)?CH(Me) (X = Ph, Br, or Et) into the metal–acyl bond of the complex [Pd(Me)(CO)(ⁱPr₂dab)]⁺ [B{3,5‐(CF₃)₂C₆H₃}₄]^? ( 1 ) (ⁱPr₂dab = 1,4‐diisopropyl‐1,4‐diazabuta‐1,3‐diene = N,N′‐(ethane‐1,2‐diylidene)bis[1‐methylethanamine]) are described (Scheme 1). The resulting five‐membered palladacycles were characterized by NMR spectroscopy and X‐ray analysis. Experimental data reveal some important aspects concerning the regio‐ and stereochemistry of the insertion process. In particular, the presence of a Ph or Br substituent at the alkene leads to the formation of highly regiospecific products. Moreover, in all cases, the geometry of the substituents in the formed palladacycle was the same as in the starting olefin, as a consequence of a cis addition of the Pd–acyl fragment to the C?C bond. Reaction with CO and MeOH of the five‐membered complex derived from trans‐β‐methylstyrene (= [(1E)‐prop‐1‐enyl]benzene) insertion, yielded the 2,3‐substituted γ‐keto ester 9 with an (2RS,3SR)‐configuration (Scheme 3).     

Effect of copper salts on peptide bond formation using peptide thioesters

[reaction: see text] In the present paper, systematic studies revealed that Cu(I) salts in general and Cu(II) salts under certain circumstances promote effective reaction between peptide thiol esters and the N-terminal amino function of a second peptide segment to give the native amide bond for both solution- and solid-phase syntheses. Chiral integrity was retained. Reaction conditions were optimized and applied to the synthesis of a small protein, the identity of which was confirmed by NMR analysis.     

Cross linking and rheological characterization of adsorbed protein layers at the oil-water interface

The dilatational rheological properties of cross-linked protein layers adsorbed at the oil-water interface were investigated with help of a modified drop tensiometer allowing successive replacements of the external phase. This setup enables one to perform cross-linking reactions at the interface only, that is, without any contact between the cross-linking agent and protein molecules in solution, under continuous monitoring of the interfacial tension. The mechanical properties of the resulting interface were investigated with dilatational large strain experiments. Measured rheological properties were related to the expected stability of an emulsion against disproportionation by considering the ratio of the interfacial elasticity to the interfacial tension. In an attempt to increase this ratio to improve the resistance against disproportionation, experiments were performed with densified protein layers obtained via reduction of the droplet area prior to cross linking. To highlight the influence of the protein morphology on the dilatational rheological properties of the cross-linked adsorbed layers, experiments were performed with random coil (beta-casein) as well as globular (beta-lactoglobulin) proteins. Glutaraldehyde was used as a cross-linking agent. Experiments were performed at 55 degrees C and pH 7.0 in 20 mM imidazole buffer for later comparison with enzymatically cross-linked adsorbed protein layers. The present work demonstrated substantial qualitative and quantitative differences in the interfacial rheological properties of cross-linked random coil and globular proteins.     

Stereocontrol in alkyne cyclocarbonylation reactions promoted by a bioxazoline palladium(II) complex

Insertion of 1,2-disubstituted alkynes into [Pd(CH3)(CO)(BIOX)]+[B{3,5-(CF3)2C6H3}4]- (1), where BIOX=(4S,4'S)-(-)-4,4',5,5'-tetrahydro-4,4'-bis(1-methylethyl)-2,2'-bioxazole, leads to the formation of five-membered palladacycles, which, by reaction with carbon monoxide, produce a mixture of two diastereomeric forms of a palladium complex containing an eta3-allylic gamma-lactone ligand. On leaving the mixture in solution, one isomer was converted into the other, reaching a diastereomeric excess of up to 94 %. The steric and electronic factors responsible for the epimerization process were investigated by theoretical methods. Cleavage of the eta3-allyl--palladium bond by nucleophiles allowed highly substituted chiral butenolides to be synthesized in good enantiomeric excess.