Vibration of strings with nonlinear supports

The dynamic string motion, which displacement is unilaterally constrained by the rigid termination condition of an arbitrary geometry has been simulated and analyzed. The treble strings of a grand piano usually terminate at a capo bar, which is situated above the strings. The apex of a V-shaped section of the capo bar defines the end of the speaking length of the strings. A numerical calculation based on the traveling wave solution is proposed for modeling the nonlinearity inducing interactions between the vibrating string and the contact condition at the point of string termination. It was shown that the lossless string vibrates in two distinct vibration regimes. In the beginning the string starts to interact in a nonlinear fashion with the rigid terminator, and the resulting string motion is aperiodic. Consequently, the spectrum of the string motion depends on the amplitude of string vibrations, and its spectral structure changes continuously with the passage of time. The duration of that vibration regime depends on the geometry of the terminator. After some time of aperiodic vibration, the string vibrations settle in a periodic regime where the resulting spectrum remains constant.     

Towards predicting the solubility of CO2 and N2 in different polymers using a quasi-SMILES based QSPR approach

The solubility of gases in various polymers plays an important role for the design of new polymeric materials. Quantitative structure–property relationship (QSPR) models were designed to predict the solubility of gases such as CO₂ and N₂ in polyethylene (PE), polypropylene (PP), polystyrene (PS), polyvinyl acetate (PVA) and poly (butylene succinate) (PBS) at different temperatures and pressures by using quasi-SMILES codes. The dataset of 315 systems was split randomly into training, calibration and validation sets; random split 1 led to 214 training (r² = 0.870 and RMSE = 0.019), 51 calibration (r² = 0.858 and RMSE = 0.020) and 50 validation (r² = 0.869 and RMSE = 0.017) sets. The suggested approach based on the quasi-SMILES, which are analogues of the traditional SMILES gives reasonable good predictions for solubility of CO₂ and N₂ in different polymers. The described methodology is universal for situations where the aim is to predict the response of an eclectic system upon a variety of physicochemical and/or biochemical conditions.     

Conference summary on the first international workshop on advanced superhard materials

Composite diamond anvils have been developed for high-pressure/high-temperature measurements of diamond anvil cells. The anvils are fabricated using single-crystal chemical vapor deposition (CVD) from previously used and/or slightly damaged anvils made of natural or synthetic diamond. These composite anvils can be fabricated to possess optical characteristics at least comparable to conventional diamond anvils, whereas the single-crystal CVD portion is more durable because of its enhanced toughness relative to natural diamond. The viability of such anvils is demonstrated in measurements on hydrogen at megabar pressures and high temperature.     

Facile synthesis of 4″-O-alkyl-(–)-EGCG derivatives through regioselective deacetylative alkylation

Therapeutic potential of the D-ring methyl ethers of (–)-epigallocatechin-3-gallate [(–)-EGCG] warrants extensive structure–activity relationship study of various D-ring ethers of (–)-EGCG but, for this purpose, efficient synthetic strategy needs to be developed. In this study, efficient preparation of the 4″-O-alkyl-(–)-EGCGs (4a–e) was demonstrated using KI/K₂CO₃-promoted deacetylative alkylation of peracetyl (–)-EGCG, which could be broadly utilized for the preparation of various D-ring alkyl ethers of (–)-EGCG and thereby extensive structure–activity relationship study.     

Synthesis of New Ferrocenyl‐Substituted Aziridines via the Gabriel–Cromwell Reaction

Abstract

The Gabriel–Cromwell method is applied successfully in the synthesis of ferrocenyl‐substituted aziridines. Acryloyl‐ and crotonoylferrocenes are brominated first and then reacted with benzylamine, diisopropylamine, and furfurylamine in the presence of triethylamine. The aziridines are obtained in more than 90% isolated yields.     

Induced twisted-grain-boundary phases in the binary mixtures of a cholesteric and a nematic compound

Thermodynamical, optical-texture and dielectric studies have been performed to study the phase diagram of the binary system of 5-cholesten-3β-ol-octanoate and 4-n-nonyloxybenzoic acid. It is observed that low concentrations of 5-cholesten-3β-ol-octanoate (2–30?mol?%) in 4-n-nonyloxybenzoic acid induce a mean-field phase diagram derived by Renn within the framework of the chiral Chen–Lubenski model. Various optical textures of the twisted-grain-boundary (TGB) phases under different conditions of molecular anchoring have been observed. Weak transitions related to the TGB phases have been detected by temperature dependent dielectric spectroscopy.     

Poisson–Boltzmann for oppositely charged bodies: an explicit derivation

The interaction between two parallel charged plates in ionic solution is a general starting point for studying colloidal complexes. An intuitive expression of the pressure exerted on the plates is usually proposed, which includes an electrostatic plus an osmotic contribution. We present here an explicit and self-consistent derivation of this formula in the only framework of the Poisson–Boltzmann (PB) theory. We also show that, depending on external constraints, the correct thermodynamic potential can differ from the usual PB free energy. For asymmetric, oppositely charged plates, the resulting expression predicts a non-trivial equilibrium position with the plates separated by a finite distance. The depth of this energy minimum is decisive for the stability of the complex. It is therefore crucial to obtain its explicit dependence on the charge densities of the plates and on the ion concentration. Analytic expressions for the position and depth of the energy minimum were derived in 1975 by Ohshima [Colloid Polym. Sci. 253, 150 (1975)] but, surprisingly, these important results seem to have been overlooked. We retrieve these expressions in a simpler formalism, more familiar to the physics community, and give a physical interpretation of the observed behavior.     

Far-Red Dibenzo[a,j]Perylene-8,16-Dione Dyes as Fluorescent Enzyme Substrates and Tags for Biomolecules

The synthesis of fluorescent 2,10-derivatives of the title chromophore are described. The substituents contain amino-reactive N-hydroxysuccinimde ester and thiol-reactive iodoacetamide groups for attachment to biomolecules. A phosphate derivative was also prepared as an enzyme substrate.