Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of “edge functions” that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1−c/a), and the notch angle is defined as (360°−α). For a very small notch angle (1° or less), the notch may be regarded as a “sharp radial crack.” Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°−α), depths (1−c/a), and thickness ratios (a/h for plates and h/a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and segmented plates and cylinders are also reported herein as interesting special cases. A generalization of the elasticity-based Ritz analysis and findings applicable here is an arbitrarily shaped V-notched cylindrical solid, being a surface traced out by a family of generatrix, which pass through the circumference of an arbitrarily shaped V-notched directrix curve, r(θ), several of which are described for future investigations and close extensions of this work.     

Cation Recombination Energy/Coulomb Repulsion Effects in ETD/ECD as Revealed by Variation of Charge per Residue at Fixed Total Charge

Electron capture dissociation (ECD) and electron transfer dissociation (ETD) experiments in electrodynamic ion traps operated in the presence of a bath gas in the 1–10 mTorr range have been conducted on a common set of doubly protonated model peptides of the form X(AG)_nX (X = lysine, arginine, or histidine, n?=?1, 2, or 4). The partitioning of reaction products was measured using thermal electrons, anions of azobenzene, and anions of 1,3-dinitrobenzene as reagents. Variation of n alters the charge per residue of the peptide cation, which affects recombination energy. The ECD experiments showed that H-atom loss is greatest for the n?=?1 peptides and decreases as n increases. Proton transfer in ETD, on the other hand, is expected to increase as charge per residue decreases (i.e., as n increases). These opposing tendencies were apparent in the data for the K(AG)_nK peptides. H-atom loss appeared to be more prevalent in ECD than in ETD and is rationalized on the basis of either internal energy differences, differences in angular momentum transfer associated with the electron capture versus electron transfer processes, or a combination of the two. The histidine peptides showed the greatest extent of charge reduction without dissociation, the arginine peptides showed the greatest extent of side-chain cleavages, and the lysine peptides generally showed the greatest extent of partitioning into the c/z?-product ion channels. The fragmentation patterns for the complementary c- and z?-ions for ETD and ECD were found to be remarkably similar, particularly for the peptides with X = lysine.

Linear and branched fluoroazo‐benzene chromophores with increased compatibility in semifluorinated polymers

A family of fluorinated azobenzene‐based push‐pull chromophores with one, two, and three trifluorovinyl ether (TFV) groups in linear and branched architecture was synthesized and utilized as active materials in the low optical loss electro‐optic (EO) composites. The fluorinated azobenzene chromophores exhibited increased solubility (30–50 wt %) in semifluorinated polymer host, such as perfluorocyclobutane (PFCB) aromatic ether resin after crosslinking, compared with the commercially available nonfluorinated azobenzene chromophore Disperse Red 1 (1–2 wt %). The impact of this approach on the optical properties on the polymer blends is assessed through optical propagation loss measurements and EO characterization. The resulting fluorinated EO composites showed excellent optical clarity, low birefringence, and low optical loss less than 0.5 dB/cm, while giving EO coefficients of about 3–7 pm/V at 1550 nm. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3166–3177, 2007     

Aurones: Small Molecule Visible Range Fluorescent Probes Suitable for Biomacromolecules

Aurones, derivatives of 2-benylidenebenzofuran-3(2H)-one, are natural products that serve as plant pigments. There have been reports that some of these substances fluoresce, but little information about their optical properties is in the literature. In this report, series of aurone derivatives were synthesized as possible fluorescent probes that can be excited by visible light. We found that an amine substituent shifted the lowest energy absorption band from the near-UV to the visible region of the electromagnetic spectrum. Four amine-substituted aurone derivatives were synthesized to explore the effect of this substituent on the absorption and emission properties of the aurone chromophore. The emission maxima and intensities of the molecules are strongly dependent on the nature of the substituent and the solvent polarity. Overall, the emission intensity increases and the maximum wavelength decreases in less polar solvents; thus, the aurones may be useful probes for hydrophobic sites on biological molecules. A limited investigation with model protein, nucleic acid and fixed cells supports this idea. It is known that the sulfur analog of aurone can undergo photo-induced E/Z isomerization. This possibility was investigated for one of the aminoaurones, which was observed to reversible photoisomerize. The two isomers have similar absorption spectra, but the emission properties are distinct. We conclude that appropriately substituted aurones are potentially useful as biological probes and photoswitches.     

Comparison of Thiophene–Pyrrole Oligomers with Oligothiophenes: A Joint Experimental and Theoretical Investigation of Their Structural and Spectroscopic Properties

We have prepared a new series of mixed thiophene–pyrrole oligomers to investigate the electronic benefits arising from the combination of these two heterocycles. The oligomers are functionalized with several hexyl and aryl groups to improve both processability and chemical robustness. An analysis of their spectroscopic (absorption and emission), photophysical, electrochemical, solid state, and vibrational properties is performed in combination with quantum‐chemical calculations. This analysis provides relevant information regarding the use of these materials as organic semiconductors. The balance between the high aromatic character of pyrrole and the moderate aromaticity of thiophene allows us to address the impact of the coupling of these heterocycles in conjugated systems. The data are interpreted on the basis of the aromaticity, molecular conformations, ground and excited electronic state structures, frontier orbital topologies and energies, oxidative states, and quinoidal versus aromatic competition.     

Frequency- and level-dependent changes in auditory brainstem responses (ABRS) in developing mice

The development of the auditory brainstem response was studied to quantitatively assess its dependence on stimulus frequency and level. Responses were not observed to stimuli > or =16 kHz on P12, however, the full range of responsive frequencies included in the study was observed by P14. Response thresholds were high on P12, exceeding 100 dB SPL for all stimuli tested. The rate of threshold development increased progressively for stimulus frequencies between -2 and 10 kHz, with the most rapid changes occurring at frequencies >10 kHz. Adultlike thresholds were observed by P18. Response latencies and interpeak intervals matured rapidly over the course of the second and third postnatal weeks and did not achieve adultlike characteristics until after P18. Latencies of higher-order peaks were progressively and sequentially delayed relative to wave I. Wave I amplitudes developed nonmonotonically, growing during the first 24 days and stabilizing at adult values by approximately P36. Slopes of wave I amplitude-and latency-level curves were significantly steeper than those of adults during the neonatal period and the outcome of input-output analyses, as well as frequency-specific maturational profiles, support developmental models in which function initially matures in the mid-frequency range and proceeds, simultaneously, in both apical and basal directions.     

Development of auditory-evoked potentials in the cat. II. Wave latencies

Brain stem and forebrain auditory-evoked potentials were studied parametrically during the first 90 postnatal days in unanesthetized kittens using tonal and click stimuli. This paper describes changes that occur in transmission time through the auditory pathway during development by analyses of the maturational time courses of latencies associated with waves of both auditory brain stem responses (ABR's) and late-occurring auditory-evoked potentials (AER's), recorded subdermally from the vertex. In response to click stimuli, ABR latencies were found to decay rapidly early in postnatal life and more slowly after the third postnatal week. Those trends were modeled as a two-stage sequential process, with a linear stage occurring between 7 and 18 postnatal days followed by an exponential stage during which adult latencies were achieved. AER latencies changes during development were less complicated, and followed a single-stage exponential time course. When threshold influences were taken into account--that is, when data were adjusted so that sensation level (SL) was constant across age--the latency-maturation curves associated with all ABR waves were adequately described by a single exponential, and latencies recorded from young animals were substantially shorter than latencies associated with the same aged animals when analyses were carried out with constant sound-pressure level (SPL) stimuli across age. In addition, the difference function, generated when isoasymptotic SPL and SL latency versus age functions were subtracted from one another, was also represented by an exponential curve, suggesting that at least two processes underlie the latency decay that occurs during postnatal development. Evoked responses to tonal stimuli throughout development were consistent with the basoapical developmental gradient that is observed anatomically.     

Metal cluster catalysis: III. Selective homogeneous hydrogenations catalyzed by [n5-C5H5)Fe(u3-CO)l4

The iron cluster, [(n⁵-C₅H₅)Fe(μ₃-CO)]₄, 1, catalyzes the selective hydrogenation of alkynes to alkenes at 100–130° and 100–1000 psig and the selective reduction of terminal alkynes to olefins in the presence of alkenes or internal alkynes. Internal alkynes are slowly reduced to $\text{cis}$ olefins, aryl nitro groups to aniline derivatives, and terminal activated carbon-carbon double bonds (methyl acrylate, acrylonitrile) are hydrogenated. The cluster concentration, monitored by high pressure liquid chromatography, was unchanged after 1148 and 1410 turnovers. Cluster 1 was isolated in 95–97% yields after catalytic reduction (1000 turnovers) and no other iron-containing species were detected. After 280 turnovers, the catalyst solution was filtered through an ultrafiltration membrane into a second vessel where hydrogenation of 1-pentyne continued. Fragmentation of 1 tc