Second-harmonic resonance with Faraday excitation

Capillary-gravity waves in an inviscid liquid exhibit second- or sub-harmonic resonance at precise frequencies. When the container performs small periodic vertical vibrations, either wave may also experience Faraday (‘parametric’) excitation. Equations describing this situation are derived, incorporating slight detuning from two-wave and Faraday resonances. Similar equations arise in other physical contexts.With Faraday forcing of the wave with lower frequency, the evolution equations (without detuning) are transformable to the corresponding unforced equations, the general solution of which is known. With Faraday forcing of the wave with higher frequency no such simplification is possible. Here, various transformed equations are considered and numerical results elucidate their solutions. For some initial data, solutions remain bounded; but other initial values give unbounded solutions. We establish the form of the boundaries that separate these two classes.     

Improving on Nature: Making a Cyclic Heptapeptide Orally Bioavailable

The use of peptides in medicine is limited by low membrane permeability, metabolic instability, high clearance, and negligible oral bioavailability. The prediction of oral bioavailability of drugs relies on physicochemical properties that favor passive permeability and oxidative metabolic stability, but these may not be useful for peptides. Here we investigate effects of heterocyclic constraints, intramolecular hydrogen bonds, and side chains on the oral bioavailability of cyclic heptapeptides. NMR‐derived structures, amide H–D exchange rates, and temperature‐dependent chemical shifts showed that the combination of rigidification, stronger hydrogen bonds, and solvent shielding by branched side chains enhances the oral bioavailability of cyclic heptapeptides in rats without the need for N‐methylation.     

Isolation and Characterization of Bioactive Cyclotides from Viola labridorica

Many Violaceae plants contain cyclotides, which are plant cyclopeptides distinguished by a cyclic cystine knot motif with 28–37 amino acid residues. In the current study, four new cyclotides, vila A–D ( 1 – 4 , resp.), together with a known cyclotide, varv D ( 5 ), were isolated from Viola labridorica (Violaceae). A chromatography‐based method was used to isolate the cyclotides, which were characterized using tandem mass spectrometry and 2D‐NMR spectroscopy. Several of the cyclotides showed cytotoxic activities against five cancer cell lines, i.e., U251, MDA‐MB‐231, A549, DU145, and BEL‐7402, with vila A and B ( 1 and 2 , resp.) being the most cytotoxic. The isolated cyclotides showed no antibacterial activity against Staphyloccocus aureus and Candida albicans. Homology modeling of the cyclotide structures was used to analyze structure–activity relationships.     

The relationship between 19F and 13C substituent chemical shifts and electron densities. 2—p-phenylacetyl fluorides

The ¹⁹F substituent chemical shifts (SCS) of a series of para-phenylacetyl fluorides (X? Ph? CH₂? COF) are reported and compared with the related benzoyl fluoride series (X? Ph? COF). A dual substituent parameter analysis of the results for the new series shows that both inductive and resonance effects are reduced by one third when compared with the benzoyl fluorides. ¹³C shifts for the side chain carbonyl were also measured and found to follow a reversed trend in substituent effects, consistent with a pi polarization mechanism. SCS values for the fluorine and its adjacent carbon are not directly related. Ab initio (STO-3G) calculations of the carbon and fluorine electron density for this series have been compared with the appropriate SCS values. From the electron densities and the observation that the fluorine SCS values follow a normal direction, whilst those for electron densities and the observation that the fluorine SCS values follow a normal direction, whilst those for the adjacent carbon are reversed, it is concluded that fluorine SCS values (and Δqπ values) result from polarization of the C? F pi bond and do not merely monitor changes in electron density of the adjacent carbon.     

The effect of random errors on a large statistical energy analysis model

The framework of analysis known as Statistical Energy Analysis has many important applications particularly in systems where detailed information is not available. As a result of the approximations made, to simplify the calculations, random error can be introduced into the SEA model. For large systems this gives rise to uncertainty in the energy levels. It is shown that the effect of these errors on the model depends on the “shape” of the model. A compact model dominated by short paths is less affected than a model controlled by long paths. In either case the ratio of the average error in the resultant energy level to the average error in the coupling loss factor decreases as the errors increase. This means that large models may be used with confidence even when based on data that is known to be approximate.     

The prediction of sound transmission through buildings using statistical energy analysis

Measurements were carried out on a building to evaluate the uses of statistical energy analysis for determining sound transmission performance. Coupling loss factors were measured and compared with predicted values. It was found that, in general, good agreement was obtained. The coupling loss factors were also used to calculate the sound pressure level, or surface velocity, of each subsystem in the building for a number of different sources. Comparison with the measured results gave an average error of 4 dB. Some large errors were obtained but these were due mainly to the omission of airborne flanking paths from the SEA model or due to the breakdown of the theory for specific coupling loss factors.