Continuation of travelling‐wave solutions of the Navier–Stokes equations

An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first‐order pseudospectral semi‐implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton–Raphson solver and is shown to be highly efficient in performing this task, even when high‐resolution grids are used. This method is well suited to three‐dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

Enantioselective synthesis of 1-deoxy-d-gulonojirimycin from a phenylglycinol-derived lactam

Cyclocondensation of (R)-phenylglycinol with appropriately γ-substituted δ-oxo acid derivatives provides bicyclic lactams from which the enantioselective synthesis of 1-deoxy-d-gulonojirimycin has been reported.     

Extraction-spectrophotometric determination of iron with 2-(2′-benzothiazolylazo)-4,6-dimethylphenol

An extraction-spectrophotometric method for the determination of trace amounts of iron based on its extraction into chloroform with 2-(2-benzothiazolylazo)-4,6-dimethylphenol (BTADMP) from a pH 6.5 medium has been developed. The extracted 12 FeBTADMP complex species allow the determination of 4–30gmg of iron (=3.92×10⁴1·mol^–1·cm^–1 at 790 nm). The method is highly selective and has been applied to the determination of iron in polymineral-polyvitamin pharmaceutical products.     

Biogenetically inspired enantioselective approach to Indolo[2,3-a]- and benzo[a]quinolizidine alkaloids from a synthetic equivalent of secologanin

[reaction: see text] Racemic oxodiester 1 undergoes stereoselective cyclocondensation with (S)-tryptophanol, (S)-(3,4-dimethoxyphenyl)alaninol, or the corresponding amino acids, in a process involving a tandem dynamic kinetic resolution/desymmetrization of diastereotopic groups, to give bicyclic lactams, which are cyclized to substituted indolo[2,3-a]- and benzo[a]quinolizidines.     

Extreme statistics of complex random and quantum chaotic states

Complex random states have the statistical properties of the Gaussian and circular unitary ensemble eigenstates of random matrix theory. Even though their components are correlated by the normalization constraint, it is nevertheless possible to derive compact analytic formulas for their extreme values' statistical properties for all dimensionalities. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulas.     

Cyclobutane-based peptides/terpyridine conjugates: Their use in metal catalysis and as functional organogelators

Two new conjugates, hcptpyDP and hcptpyTP, of a terpyridine derivative incorporating artificial peptide moieties, have been synthesized and their use in the preparation of metal catalysts and organogelators has been investigated. Ru(II) complexes derived from these ligands showed electrochemical behavior and activity as catalysts in the epoxidation of olefins similar to that of Beller's catalyst. As organogelators, these conjugates were able to gelate a variety of solvents, from toluene to methanol, with satisfactory mgc (minimum gelation concentration) values. The presence of 4′-(4-carboxy)phenylterpyridine (hcptpy) moiety allows tuning the gelling properties and also influences the supramolecular self-assembling mode to produce chiral aggregates with respect to parent peptides DP and TP. In the case of the conjugates, π?π interactions provided by the aromatic moieties cooperate with inter-molecular hydrogen bonding between NH and CO in the amide groups. Further properties of peptide/terpyridine conjugates are under investigation in view of future applications.     

Laboratory singing sand avalanches

Some desert sand dunes have the peculiar ability to emit a loud sound up to 110 dB, with a well-defined frequency: this phenomenon, known since early travelers (Darwin, Marco Polo, etc.), has been called the song of dunes. But only in late 19th century scientific observations were made, showing three important characteristics of singing dunes: first, not all dunes sing, but all the singing dunes are composed of dry and well-sorted sand; second, this sound occurs spontaneously during avalanches on a slip face; third this is not the only way to produce sound with this sand.More recent field observations have shown that during avalanches, the sound frequency does not depend on the dune size or shape, but on the grain diameter only, and scales as the square root of g/d - with g the gravity and d the diameter of the grains - explaining why all the singing dunes in the same vicinity sing at the same frequency.We have been able to reproduce these singing avalanches in laboratory on a hard plate, which made possible to study them more accurately than on the field. Signals of accelerometers at the flowing surface of the avalanche are compared to signals of microphones placed above, and it evidences a very strong vibration of the flowing layer at the same frequency as on the field, responsible for the emission of sound.Moreover, other characteristics of the booming dunes are reproduced and analyzed, such as a threshold under which no sound is produced, or beats in the sound that appears when the flow is too large. Finally, the size of the coherence zones emitting sound has been measured and discussed.     

A method of determining and removing sulphide to allow the determination of sulphate,phosphate, nitrite and ammonia by conventional methods in small volumes of anoxic waters

Mercury(II) chloride is used to precipitate free sulphide from <10-ml samples of anoxic water. The sulphide-free supernatant solution can be used for estimation of sulphide by measuring the concentration of unreacted mercury(II) ion and for determinations of sulphate, inorganic phosphate, ammonia and nitrite by spectrophotometric methods which normally cannot be used because of sulphide interference. Concentrations that can be determined lie within the ranges: sulphide 0.5–180 000 μg S l^?1, sulphate 0.024–2.77 g S l^?1, ammonia 1–70 000 μg N l^?1, nitrite 1–3000 μg N l^?1, inorganic phosphate 1–4000 μg P l^?1. Interstitial waters from estuarine sediments, tidal flats, mangrove swamps, and an anoxic estuarine basin were examined.