Vibrational force constant and electron relaxation in H2 and Li2

The force constants of H2 and Li2 are evaluated employing their extended Hartree-Fock wavefunctions by a polynomial fit of their force curves. It is suggested that, based on incomplete multiconfiguration Hartree-Fock wavefunctions, force constants calculated from the energy derivatives are numerically more accurate than those obtained from the derivatives of the Hellmann-Feynman forces. It is observed that electrons relax during the nuclear vibrations in such a fashion as to facilitate the nuclear motions.

Active vibration suppression of beams with discrete actuators using optimal dynamic inversion

Most of the structural elements like beams, cables etc. are flexible and should be modeled as distributed parameter systems (DPS) to represent the reality better. For large structures, the usual approach of 'modal representation' is not an accurate representation. Moreover, for excessive vibrations (possibly due to strong wind, earthquake etc.), external power source (controller) is needed to suppress it, as the natural damping of these structures is usually small. In this paper, we propose to use a recently developed optinial dynamic inversion technique to design a set of discrete controllers for this purpose. We assume that the control force to the structure is applied through finite number of actuators, which are located at predefined locations in the spatial domain. The method used in this paper determines control forces directly from the partial differential equation (PDE) model of the system. The formulation has better practical significance, both because it leads to a closed form solution of the controller (hence avoids computational issues) as well as because a set of discrete actuators along the spatial domain can be implemented with relative ease (as compared to a continuous actuator).

A singularity-free cosmological model in ECSK theory

In the framework of the ECSK [Einstein-Cartan-Sciama-Kibble] theory of cosmology, a scalar field nonminimally coupled to the gravitational field is considered. For a Robertson-Walker open universe (k=0) in the radiation era, the field equations admit a singularity-free solution for the scale factor. In theory, the torsion is generated through nonminimal coupling of a scalar field to the gravitation field. The nonsingular nature of the cosmological model automatically solves the flatness problem. Further absence of event horizon and particle horizon explains the high degree of isotropy, especially of 2.7-K background radiation.

Gauge theory of a group of diffeomorphisms. III. The fiber bundle description

A new fiber bundle approach to the gauge theory of a group G that involves space‐time symmetries as well as internal symmetries is presented. The ungauged group G is regarded as the group of left translations on a fiber bundle G(G/H,H), where H is a closed subgroup and G/H is space‐time. The Yang–Mills potential is the pullback of the Maurer–Cartan form and the Yang–Mills fields are zero. More general diffeomorphisms on the bundle space are then identified as the appropriate gauged generalizations of the left translations, and the Yang–Mills potential is identified as the pullback of the dual of a certain kind of vielbein on the group manifold. The Yang–Mills fields include a torsion on space‐time.

Stability Analysis of Composite Skew Plates Using a Dynamic Method

Stability analysis is carried out considering free lateral vibrations of simply supported composite skew plates that are subjected to both direct and shear in-plane forces. An oblique stress component representation is used, consistent with the skew-geometry of the plate. A double series, expressed in Chebyshev polynomials, is used here as the assumed deflection surface and Ritz method of solution is employed. Numerical results for different combinations of side ratios, skew angle, and in-plane loadings that act individually or in combination are obtained. In this method, the in-plane load parameter is varied until the fundamental frequency goes to zero. The value of the in-plane load then corresponds to a critical buckling load. Plots of frequency parameter versus in-plane loading are given for a few typical cases. Details of crossings and quasi degeneracies of these curves are presented.

Conformation of a 16-residue zervamicin IIA analog peptide containing three different structural features: 310-helix, alpha helix and ß-bend ribbon

Boc-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib- Pro-Ala-Aib-Pro-Aib-Pro-Phe-OM(we here Boc is t-butoxycarbonyla nd Aib is a-aminoisobutyriac cid), a synthetica polar analog of the membrane-activefu ngal peptide antibioticz ervamtycinII A, crystallizesi n spaceg roupP 1 withZ =1 and cell parameters a = 9.086 ?0.002 A, b = 10.410 ?+ 0.002 A, c = 28.188 ? 0.004 A, a = 86.13 ? 0.01?, 13 = 87.90 ? 0.01?, and y = 89.27 ? 0.01?;o veralla greementf actorR = 7.3% for 7180 data (Fo > 3cr) and 0.91-A resolution. The peptide backbone makes a continuous spiral that begins as a 310-helix at the N-terminus, changes to an a-helix for two turns, and ends in a spiral of three fl-bends in a ribbon. Each of the fl-bends contains a proline residue at one of the corners. The torsion angles 4i range from -51? to -91? (average value -64o), and the torsion angles ai range from -1? to -46? (average value -31?). There are 10 intramolecularN H...OCh ydrogenb onds in the helix and two directh ead-to-taihl ydrogenb ondsb etween successive molecules. Two H20 and two CH30H solvent molecules fill additional space with appropriate hydrogen bonding in the head-to-tail region, and two additional H20 molecules form hydrogen bonds with carbonyl oxygens near the curve in the helix at Pro-10. Since there is only one peptide molecule per cell in space group P1, the molecules repeat only by translation, and consequently the helices pack parallel to each other.

Aqueous channels within apolar peptide aggregates. Solvated helix of Boc-Aib-Ala-Leu-Aib-Ala-Leu-Aib- -Ala-Leu-Aib-OMe. H2O.CH3OH

Although the peptide Boc-Aibl-Ala2-Leu3- Aib4-Alas Leu'-Aib7-Ala8-Leu9-Aib'0-OMe [with a t-butoxycarbonyl(Boc) blocking group at the amino terminus, a methyl ester (OMe) at the carboxyl terminus, and four a-aminoisobutyric (Aib) residues] has a 3-fold repeat of residues, the helix formed by the peptide backbone is irregular. The carboxyl-terminal half assumes an at-helical form with torsion angles ) and r of approximately -60° and -45°, respectively, whereas the amino-terminal half is distorted by an insertion of a water molecule between the amide nitrogen of Ala5 [N(5)] and the carbonyl oxygen of Ala2 [0(2)]. The water molecule W(1) acts as a bridge by forming hydrogen bonds N(5).W(1) (2.93 A) and W(1)---0(2) (2.86 A). The distortion of the helix exposes the carbonyl oxygens of Aib' and Aib4 to the outside environment, with the consequence that the helix assumes an amphiphilic character despite having all apolar residues. Neighboring helices in the crystal run in antiparallel directions. On one side of a helix there are only hydrophobic contacts with efficient interdigitation of leucine side chains with those from the neighboring helix. On the other side of the helix there are hydrogen bonds between protruding carbonyl oxygens and four water molecules that separate two neighboring helices. Along the helix axis the helices bind head-to-tail with a direct hydrogen bond N(2)-0(9) (3.00 A). Crystals grown from methanol/water solution are in space group P2, with a = 15.778 ± 0.004 A, b = 11.228 ± 0.002 A, c = 18.415 ± 0.003 A, = 102.10 ± 0.02ur and two formula units per cell for C49HON1003 2H2OCH3OH. The overall agreement factorR is 7.5% for 3394 reflections observed with intensities >3a(F), and the resolution is 0.90 A.

Crystallographic characterization of the conformation of the 1-aminocyclohexane-1-carboxylic acid residue in simple derivatives and peptides

The crystal structures of 1-aminocyclohexane-1-carboxylic acid (H-Acc6-OH) and six derivatives (including dipeptides) have been determined. The derivatives are Boc-Acc6-OH, Boc-(Acc6)2-OH, Boc-L-Met-Acc6-OMe, ClCH2CO-Acc6-OH, p-BrC6H4CO-Acc6-OH oxazolone, and the symmetrical anhydride from Z-Acc6-OH, [(Z-Acc6)2O]. The cyclohexane rings in all the structures adopt an almost perfect chair conformation. The amino group occupies the axial position in six structures; the free amino acid is the only example where the carbonyl group occupies an axial position. The values determined for the torsion angles about the N–Cα(φ) and Cα–CO (ψ) bonds correspond to folded, potentially helical conformations for the Acc6 residue.

Predicting the Timing of Spikes Evoked by Tactile Stimulation of the Hand

Kim SS, Sripati AP, Bensmaia SJ. Predicting the timing of spikes evoked by tactile stimulation of the hand. J Neurophysiol 104: 1484-1496, 2010. First published July 7, 2010; doi: 10.1152/jn.00187.2010. What does the hand tell the brain? Tactile stimulation of the hand evokes remarkably precise patterns of neural activity, suggesting that the timing of individual spikes may convey information. However, many aspects of the transformation of mechanical deformations of the skin into spike trains remain unknown. Here we describe an integrate-and-fire model that accurately predicts the timing of individual spikes evoked by arbitrary mechanical vibrations in three types of mechanoreceptive afferent fibers that innervate the hand. The model accounts for most known properties of the three fiber types, including rectification, frequency-sensitivity, and patterns of spike entrainment as a function of stimulus frequency. These results not only shed light on the mechanisms of mechanotransduction but can be used to provide realistic tactile feedback in upper-limb neuroprostheses.

An Experimental and Numerical Study of Calliphora Wing Structure

Experiments are performed to determine the mass and stiffness variations along the wing of the blowfly Calliphora. The results are obtained for a pairs of wings of 10 male flies and fresh wings are used. The wing is divided into nine locations along the span and seven locations along the chord based on venation patterns. The length and mass of the sections is measured and the mass per unit length is calculated. The bending stiffness measurements are taken at three locations, basal (near root), medial and distal (near tip) of the fly wing. Torsional stiffness measurements are also made and the elastic axis of the wing is approximately located. The experimental data is then used for structural modeling of the wing as a stepped cantilever beam with nine spanwise sections of varying mass per unit lengths, flexural rigidity (EI) and torsional rigidity (GJ) values. Inertial values of nine sections are found to approximately vary according to an exponentially decreasing law over the nine sections from root to tip and it is used to calculate an approximate value of Young's modulus of the wing biomaterial. Shear modulus is obtained assuming the wing biomaterial to be isotropic. Natural frequencies, both in bending and torsion, are obtained by solving the homogeneous part of the respective governing differential equations using the finite element method. The results provide a complete analysis of Calliphora wing structure and also provide guidelines for the biomimetic structural design of insect-scale flapping wings.

Correlation of helicopter rotor aeroelastic response with HART-II wind tunnel test data

Purpose - This paper aims to validate a comprehensive aeroelastic analysis for a helicopter rotor with the higher harmonic control aeroacoustic rotor test (HART-II) wind tunnel test data. Design/methodology/approach - Aeroelastic analysis of helicopter rotor with elastic blades based on finite element method in space and time and capable of considering higher harmonic control inputs is carried out. Moderate deflection and coriolis nonlinearities are included in the analysis. The rotor aerodynamics are represented using free wake and unsteady aerodynamic models. Findings - Good correlation between analysis and HART-II wind tunnel test data is obtained for blade natural frequencies across a range of rotating speeds. The basic physics of the blade mode shapes are also well captured. In particular, the fundamental flap, lag and torsion modes compare very well. The blade response compares well with HART-II result and other high-fidelity aeroelastic code predictions for flap and torsion mode. For the lead-lag response, the present analysis prediction is somewhat better than other aeroelastic analyses. Research limitations/implications - Predicted blade response trend with higher harmonic pitch control agreed well with the wind tunnel test data, but usually contained a constant offset in the mean values of lead-lag and elastic torsion response. Improvements in the modeling of the aerodynamic environment around the rotor can help reduce this gap between the experimental and numerical results. Practical implications - Correlation of predicted aeroelastic response with wind tunnel test data is a vital step towards validating any helicopter aeroelastic analysis. Such efforts lend confidence in using the numerical analysis to understand the actual physical behavior of the helicopter system. Also, validated numerical analyses can take the place of time-consuming and expensive wind tunnel tests during the initial stage of the design process. Originality/value - While the basic physics appears to be well captured by the aeroelastic analysis, there is need for improvement in the aerodynamic modeling which appears to be the source of the gap between numerical predictions and HART-II wind tunnel experiments.

Vibrational analysis of 1,3-thiazolidine-2-thione and its selenium analogue

The i.r. spectra of 1,3-thiazolidine-2-thione, ?2-selone and their N-deuteriated derivatives have been investigated in the region between 4000 and 20 cm?1. A complete assignment of the fundamental vibrational frequencies has been made based upon the normal coordinate analysis carried out using a simple Urey�Bradley force field supplemented by the valence force constants for the out-of-plane vibrations of the planar molecular skeleton. The proposed assignments are discussed in relation to the group frequencies in structurally related molecules and in terms of the computed potential energy distributions among the symmetry coordinates.

Conformational properties of hybrid peptides containing alpha and omega-amino acids

This review briefly surveys the conformational properties of guest omega-amino acid residues when incorporated into host alpha-peptide sequences. The results presented focus primarily on the use of beta- and gamma-residues in alphaomega sequences. The insertion of additional methylene groups into peptide backbones enhances the range of accessible conformations, introducing additional torsional variables. A nomenclature system, which permits ready comparisons between alpha-peptides and hybrid sequences, is defined. Crystal structure determination of hybrid peptides, which adopt helical and beta-hairpin conformations permits the characterization of backbone conformational parameters for beta- and gamma-residues inserted into regular alpha-polypeptide structures. Substituted beta- and gamma-residues are more limited in the range of accessible conformation than their unsubstituted counterparts. The achiral beta,beta-disubstituted gamma-amino acid, gabapentin, is an example of a stereochemically constrained residue in which the torsion angles about the C-beta-C-gamma (theta(1)) and C-alpha-C-beta (theta(2)) bonds are restricted to the gauche conformation. Hybrid sequences permit the design of novel hydrogen bonded rings in peptide structures.

Solution structure of Am2766: A highly hydrophobic d-conotoxin from Conus amadis that inhibits inactivation of brain voltage gated sodium channels

The three-dimensional (3D) NMR solution structure (MeOH) of the highly hydrophobic δ-conotoxin δ-Am2766 from the molluscivorous snail Conus amadis has been determined. Fifteen converged structures were obtained on the basis of 262 distance constraints, 25 torsion-angle constraints, and ten constraints based on disulfide linkages and H-bonds. The root-mean-square deviations (rmsd) about the averaged coordinates of the backbone (N, Cα, C) and (all) heavy atoms were 0.62±0.20 and 1.12±0.23 Å, respectively. The structures determined are of good stereochemical quality, as evidenced by the high percentage (100%) of backbone dihedral angles that occupy favorable and additionally allowed regions of the Ramachandran map. The structure of δ-Am2766 consists of a triple-stranded antiparallel β-sheet, and of four turns. The three disulfides form the classical ‘inhibitory cysteine knot’ motif. So far, only one tertiary structure of a δ-conotoxin has been reported; thus, the tertiary structure of δ-Am2766 is the second such example.Another Conus peptide, Am2735 from C. amadis, has also been purified and sequenced. Am2735 shares 96% sequence identity with δ-Am2766. Unlike δ-Am2766, Am2735 does not inhibit the fast inactivation of Na+ currents in rat brain Nav1.2 Na+ channels at concentrations up to 200 nM.

Modelling, Design and Analysis of Low Frequency Platform for Attenuating Micro-Vibration in Spacecraft

One of the most important factors that affect the pointing of precision payloads and devices in space platforms is the vibration generated due to static and dynamic unbalanced forces of rotary equipments placed in the neighborhood of payload. Generally, such disturbances are of low amplitude, less than 1 kHz, and are termed as ‘micro-vibrations’. Due to low damping in the space structure, these vibrations have long decay time and they degrade the performance of payload. This paper addresses the design, modeling and analysis of a low frequency space frame platform for passive and active attenuation of micro-vibrations. This flexible platform has been designed to act as a mount for devices like reaction wheels, and consists of four folded continuous beams arranged in three dimensions. Frequency and response analysis have been carried out by varying the number of folds, and thickness of vertical beam. Results show that lower frequencies can be achieved by increasing the number of folds and by decreasing the thickness of the blade. In addition, active vibration control is studied by incorporating piezoelectric actuators and sensors in the dynamic model. It is shown using simulation that a control strategy using optimal control is effective for vibration suppression under a wide variety of loading conditions.