On whistling of pipes with a corrugated segment: Experiment and theory

Corrugated pipes are commonly used because of their local rigidity combined with global flexibility. The flow through such a pipe can induce strong whistling tones, which is an environmental nuisance and can be a threat to the mechanical integrity of the system. This paper considers the use of a composite pipe: a shorter corrugated pipe segment embedded between smooth pipe segments. Such a pipe retains some flexibility, while the acoustical damping in the smooth pipe reduces whistling tones. Whistling is the result of coherent vortex shedding at the cavities in the wall. This vortex shedding is synchronized by longitudinal acoustic waves traveling along the pipe. The acoustic waves trigger the vortex shedding, which reinforces the acoustic field for a critical range of the Strouhal number values. A linear theory for plane wave propagation and the sound production is proposed, which allows a prediction of the Mach number at the threshold of whistling in such pipes. A semi-empirical approach is chosen to determine the sound source in this model. This source corresponds to a fluctuating force acting on the fluid as a consequence of the vortex shedding. The functional form of the Strouhal number dependency of the dimensionless sound source amplitude is based on numerical simulations. The magnitude of the source and the Strouhal number range in which it can drive whistling are determined by matching the model to results for a specific corrugated pipe segment length. This semi-empirical source model is then applied to composite pipes with different corrugated segment lengths. In addition, the effect of inlet acoustical convective losses due to flow separation is considered. The Mach number at the threshold of whistling is predicted within a factor 2.     

Hidden Uq (sl(2)) Uq (sl(2)) Quantum Group Symmetry in Two Dimensional Gravity

In a previous paper, the quantum-group-covariant chiral vertex operators in the spin 1/2 representation were shown to act, by braiding with the other covariant primaries, as generators of the well known U_q(sl(2)) quantum group symmetry (for a single screening charge). Here, this structure is transformed to the Bloch wave/Coulomb gas operator basis, thereby establishing for the first time its quantum group symmetry properties. A U_q(sl(2)) U_q(sl(2)) symmetry of a novel type emerges: The two Cartan-generator eigenvalues are specified by the choice of matrix element (Vermamodules); the two Casimir eigenvalues are equal and specified by the Virasoro weight of the vertex operator considered; the co-product is defined with a matching condition dictated by the Hilbert space structure of the operator product. This hidden symmetry possesses a novel Hopf-like structure compatible with these conditions. At roots of unity it gives the right truncation. Its (non-linear) connection with the U_q(sl(2)) previously discussed is disentangled. Received: 25 April 1996/Accepted: 20 July 1996     

Computationally simple,analytic, closed form solution of the Coulomb self-interaction problem in Kohn–Sham density functional theory

We have developed and tested in terms of atomic calculations an exact, analytic and computationally simple procedure for determining the functional derivative of the exchange energy with respect to the density in the implementation of the Kohn–Sham formulation of density functional theory (KS-DFT), providing an analytic, closed-form solution of the self-interaction problem in KS-DFT. We demonstrate the efficacy of our method through ground-state calculations of the exchange potential and energy for atomic He and Be atoms, and comparisons with experiment and the results obtained within the optimized effective potential (OEP) method.     

Conformation of N(alpha)-substituted hydrazino acetamides in CDCl3, the precious help of the analysis of Deltadelta between amidic hydrogens, and correlation to the conformation of aza-beta3-peptides

[structures: see text] We studied the conformation of a series of primary amides in a solution of chloroform. Classical NMR tools such as dilution experiments, influence of DMSO, and 2D-NOESY, together with X-ray diffraction, were combined with an analysis of the difference of the chemical shift Deltadelta between the geminal amidic protons. This study was addressed in order to understand the conformation adopted by hydrazino acetamides 1a and 1b as model compounds for aza-beta3-peptides. In this manner, it was possible to show that the amidic group of these compounds acts as a H-bond donor and interacts with two different H-bond acceptors. We concluded that the hydrazinoturn, a specific bifurcated H-bond system observed in the solid state, is also the preferred conformation of hydrazino acetamides 1a and 1b in solution. Our results show that the short-range interaction with the N(alpha)-nitrogen lone pair not only stabilizes the C8 pseudocycle but could also contribute to the folding process of aza-beta3-peptides. In light of this, it could explain why aza-beta3-peptides develop a different H-bond network in comparison to their isosteric beta3-peptides analogues. Our work is in keeping with the recent interest of hydrazino peptides as an extension of the beta-peptide concept.     

CO2 Hydroboration: Impact of the Boryl Moieties on the Reactivity of Four Bis(boryl)acetal Compounds toward 2,6-Diisopropylaniline

The hydroboration of CO₂ into bis(boryl)acetal (BBA) compounds is an important transformation, since it enabled to selectively reduce CO₂ by 4e^- and to subsequently use the BBA compounds as C₁ and C_n sources. However, the influence of the nature of the boryl moieties on the reactivity of BBA compounds has not been evaluated so far. In the present study, four BBA compounds – including two new ones – were reacted with 2,6-diisopropylaniline to afford the expected imine. Significant differences in the rate of the reaction from minutes to weeks have been observed depending on the BBA used, showing the importance of the nature of the boryl moieties. Theoretical investigations enabled to propose a mechanism involving the addition of the aniline to the BBA as the rate-determining step and to determine that the steric hindrance of the BBA compounds is the main factor driving the rate of this condensation reaction.     

Vibrational analysis of amino acids and short peptides in hydrated media. 3. Successive KL repeats induce highly stable beta-strands capable of forming non-H-bonded aggregates

Circular dichroism (CD) and Raman scattering were applied to the aqueous solution of minimalist LK peptides constructed with successive KL repeats leading to the following generic primary sequence: (KL)nK. Three peptides of this family, a 3-mer (n=1), a 9-mer (n=4), and a 15-mer (n=7), are analyzed in this report. Raman spectra of the 3-mer (KLK, a random chain) and its labile-hydrogen deuterated species yield a set of interesting information for analyzing longer peptides of this series. Although the CD spectrum of the 9-mer (KLKLKLKLK) reveals a signal traditionally assigned to a random structure, the corresponding Raman spectrum allows finding a mixture of conformations in solution, adopting predominantly beta-type structures. This fact proves the utility of Raman spectroscopy to eliminate eventual ambiguity concerning conformational assignments in peptides based only on the use of CD technique. Finally, the 15-mer (KLKLKLKLKLKLKLK) gives rise to CD and Raman spectra clearly assignable to a beta-type structure. On the basis of all the observed results on the 15-mer, we can confirm that this peptide may exist as isolated beta-strands at low concentration (sub-micromolar), flat-oriented at the air/water interface, whereas at high concentrations (millimolar), non-H-bonded immersible aggregates might be formed. A hypothetical model for these beta-strand aggregates could be proposed as stabilized by an interior hydrophobic core and a hydrophilic external face, formed by leucine and lysine side chains, respectively.     

A selective synthesis of hydroxyborate anions as novel anchors for zirconocene catalysts

A new family of hydroxytris(pentafluorophenyl)borate anions [B(C6F5)3OH](-) associated with organic and aprotic cations c+ (imidazolium, pyrrolidinium and phosphonium) has been prepared by a general one-pot synthesis that implies the chloride borate analogues [B(C6F5)3Cl](-)[c]+. The [c]+[B(C6F5)3OH](-) salts have been isolated and fully characterized. The borate anion [B(C6F5)3OH](-) has been shown to protonate the Zr-Me bond in the Cp2ZrMe2 complex forming CH4 and the first published example of anionic [Cp2Zr(Me)OB(C6F5)3](-) species. Standard spectroscopic methods demonstrate the covalent character of the Zr metal center and the anionic character of the boron atom. This protonolysis methodology using [B(C6F5)3OH](-) anion affords a new route for the incorporation of a covalently bonded anionic functionality on organometallic complexes. This provides a new way to immobilize transition metal complexes in ionic liquids.     

Young's moduli of surface-bound liposomes by atomic force microscopy force measurements

Mechanical properties of layers of intact liposomes attached by specific interactions on solid surfaces were studied by atomic force microscopy (AFM) force measurements. Force-distance measurements using colloidal probe tips were obtained over liposome layers and used to calculate Young's moduli by using the Hertz contact theory. A classical Hertz model and a modified Hertz one have been used to extract Young's moduli from AFM force curves. The modified model, proposed by Dimitriadis, is correcting for the finite sample thickness since Hertz's classical model is assuming that the sample is infinitely thick. Values for Young's moduli of 40 and 8 kPa have been obtained using the Hertz model for one and three layers of intact liposomes, respectively. Young's moduli of approximately 3 kPa have been obtained using the corrected Hertz model for both one and three layers of surface-bound liposomes. Compression work performed by the colloidal probe to compress these liposome layers has also been calculated.     

Infrared characterization of hydroxyl groups on MgO: a periodic and cluster density functional theory study

The infrared OH stretching frequencies of the various types of hydroxyl groups on MgO surfaces have been calculated by periodic (VASP) and cluster (Gaussian) DFT simulations. Surface irregularities (mono and diatomic steps, corners, step divacancies, and kinks) have been considered to model the IR spectra of hydroxylated MgO powders. A good correspondence between calculated and experimental frequencies is obtained with the B3LYP functional. Hydrogen-bonding is the parameter which influences most the IR frequency of OH groups, followed by location of OH groups in concave or convex areas of the surface and then oxygen coordination. The evolution of experimental IR spectra upon evacuation at increasing temperature can be rationalized on the basis of calculated thermal stabilities of each kind of OH groups. A new model is finally proposed to help assign the experimental bands, in terms of hydrogen-bonding, local topology of the hydroxylated sites, and coordination of oxygen.     

A heteronuclear bidentate Lewis acid as a phosphorescent fluoride sensor

Reaction of dimesityl-1,8-naphthalenediylborate (1) with C6F5HgCl results in the formation of a B/Hg heteronuclear bidentate Lewis acid (2), which complexes fluoride to afford [2-mu2-F]-. Structural and photophysical studies carried out in solution and in the solid state indicate that 2 is a highly selective and sensitive phosphorescent fluoride sensor. The proximity of the two Lewis acidic sites enforced by the 1,8-naphthalenediyl backbone promotes fluoride anion chelation and is, therefore, responsible for the high binding constant. The interplay of conjugative and spin-orbit coupling effects mediated by the boron and mercury atoms, respectively, results in the phosphorescent signaling of fluoride binding. Remarkably, fluoride binding occurs in partially aqueous solutions and results in a drastic change of the phosphorescence observed when the solutions are frozen.