Finite difference methods of solution of the von mises boundary layer equation with special reference to conditions near a singularity

Zusammenfassung Frühere Forscher haben die Misessche Gleichung als Mittel zur Lösung des Problems der Grenzschicht an der längsangeströmten ebenen Platte mit Druckanstieg nicht verwendet wegen ihrer unangenehmen Singularität an der Platte. In der vorliegenden Untersuchung wird eine Geschwindigkeitsverteilung berechnet, welche die Plattenbindungen berücksichtigt und folglich den Hautreibungswert durch die Geschwindigkeitswerte in der Grenzschicht berechnen lässt. Diese Werte werden ermittelt durch ein Fortsetzungsdifferenzenverfahren auf der Grundlage der Misesschen Gleichung sowie durch ein modifiziertes Differenzenverfahren in der Nähe der Platte. Dieses letzte Verfahren ist nötig wegen der Instabilität der ursprünglichen Fortsetzungsberechnung in der Nähe der Platte. Angesichts der verhältnismässig geringen Rechnungsarbeit stimmen die Ergebnisse gut überein mit den Lösungen anderer Forscher, die andere Formen der Grenzschichtgleichung benutzten. Die Genauigkeit der in dieser Untersuchung erreichten Ergebnisse lässt sich natürlich noch vermehren durch Anwendung einer kleineren Schrittweite bei der ersten Fortsetzungsberechnung.     

Purification and characterizing properties of analytical reagent quinizarin-2-sulphonic acid and its sodium salt

Quinizarin-2-sulphonic acid and its sodium salt have been purified for analytical use. The thermal analysis behaviour and the infrared and NMR spectra of the reagent have been recorded. Absorptiometry at 465 nm is recommended for the assay of solutions. Spectrophotometric measurements, corrected for fading, are treated by a PITMAP-type procedure to obtain acid dissociation constants for the reagent. Finally, some reactions with metal ions are surveyed briefly.     

SuperQuat 5,5-dimethyl-4-iso-propyloxazolidin-2-one as a mimic of Evans 4-tert-butyloxazolidin-2-one

The incorporation of a gem-dimethyl group at the 5-position of a chiral oxazolidinone biases the conformation of the adjacent C(4)-stereodirecting group such that the gem-dimethyl-4-iso-propyl combination mimics a C(4)-tert-butyl group, providing higher levels of stereocontrol than a simple 4-iso-propyloxazolidinone. The generality of this principle is demonstrated with applications in stereoselective enolate alkylations, kinetic resolutions, Diels-Alder cycloadditions and Pd-catalysed asymmetric acetalisation reactions.     

The molecular potential energy surface and vibrational energy levels of methyl fluoride. Part II

New analytical bending and stretching, ground electronic state, potential energy surfaces for CH(3)F are reported. The surfaces are expressed in bond-length, bond-angle internal coordinates. The four-dimensional stretching surface is an accurate, least squares fit to over 2000 symmetrically unique ab initio points calculated at the CCSD(T) level. Similarly, the five-dimensional bending surface is a fit to over 1200 symmetrically unique ab initio points. This is an important first stage towards a full nine-dimensional potential energy surface for the prototype CH(3)F molecule. Using these surfaces, highly excited stretching and (separately) bending vibrational energy levels of CH(3)F are calculated variationally using a finite basis representation method. The method uses the exact vibrational kinetic energy operator derived for XY(3)Z systems by Manson and Law (preceding paper, Part I, Phys. Chem. Chem. Phys., 2006, 8, DOI: 10.1039/b603106d). We use the full C(3v) symmetry and the computer codes are designed to use an arbitrary potential energy function. Ultimately, these results will be used to design a compact basis for fully coupled stretch-bend calculations of the vibrational energy levels of the CH(3)F system.     

Direct probing of sorbent-solvent interactions for amylose tris(3,5-dimethylphenylcarbamate) using infrared spectroscopy, X-ray diffraction, solid-state NMR, and DFT modeling

The sorbent-solvent interactions for amylose tris(3, 5-dimethylphenylcarbamate) (ADMPC) with five commonly used solvents, hexane, methanol, ethanol, 2-propanol (IPA), and acetonitrile (ACN), are studied using attenuated total reflection infrared spectroscopy (ATR-IR) of thin sorbent films, X-ray diffraction (XRD) of thin films, (13)C cross polarization/magic angle spinning (CP/MAS) and MAS solid state NMR of polymer-coated silica beads (commercially termed "Chiralpak AD"), and DFT modeling. The ADMPC-polymer-coated silica beads are used commercially for analytical and preparative scale separations of chiral enantiomers. The polymer forms helical rods with intra- and inter-rod hydrogen bonds (H-bonds). There are various nm-sized cavities formed between the polymer side-chains and rods. The changes in the H-bonding states of the C=O and NH groups of the polymer upon absorption of each of the five solvents at 25 degrees C are determined with ATR-IR. The IR wavenumbers, the H-bonding interaction energies, and the H-bonding distances of the polymer side-chains with each of the solvent molecules are predicted using the DFT/B3LYP/6-311+g(d,p) level of theory. The changes in the polymer crystallinity upon absorption of each solvent are characterized with XRD. The changes in the polymer crystallinity and the H-bonding states of C=O groups are also probed with (13)C CP/MAS solid-state NMR. The changes in the polymer side-chain mobility are detected using (13)C MAS solid-state NMR. The H-bonding states of the polymer change upon absorption of each polar solvent and usually result in an increase in the polymer crystallinity and the side-chain mobility. The polymer rods are reorganized upon solvent absorption, and the distance between the rods increases with the increase in the solvent molecular size. These results have implications for understanding the role of the solvent in modifying the structure and behavior of the polymer sorbents.     

Smoothness properties of Newtonian potentials in the study of elastic plates

The Hölder continuity and differentiability are investigated of Newtonian potentials arising in the theory of bending of elastic plates with transverse shear deformation. These properties play an essential role in the study by means of boundary integral equation techniques of boundary value problems for the equilibrium and harmonic oscillation states, and in the construction of associated boundary element methods.     

A Lagrangian stochastic model for tetrad dispersion

We present results for tetrad (four-particle) dispersion in homogeneous isotropic turbulence by means of a simple Lagrangian stochastic model with a focus on the inertial subrange. We show that for appropriate values of C ₀, the constant of proportionality in the second-order Lagrangian velocity structure function, the shape statistics agree well with equivalent results from a direct numerical simulation (DNS) of turbulence. Moreover, we show that the shape statistics are independent of C ₀ for a wide range of C ₀-values. We also show that the parameters which characterise the shape of the tetrads can be approximately related to appropriate ratios of the growth rates of the mean square separation, the mean square area and the mean square volume of the tetrads. By means of exit times, we are able to estimate the equivalent values for the DNS data. We also consider the statistics of four-point velocity differences (via a diffusion tensor) which agree well with the DNS. We show that the nature of the velocity field experienced by the tetrad varies significantly with C ₀.     

Ultrashort laser ablation of PMMA and intraocular lenses

The use of intraocular lenses (IOLs) is the most promising method to restore vision after cataract surgery. Several new materials, techniques, and patterns have been studied for forming and etching IOLs to improve their optical properties and reduce diffractive aberrations. This study is aimed at investigating the use of ultrashort laser pulses to ablate the surface of PMMA and intraocular lenses, and thus provide an alternative to conventional techniques. Ablation experiments were conducted using various polymer substrates (PMMA samples, hydrophobic acrylic IOL, yellow azo dye doped IOL, and hydrophilic acrylic IOL consist of 25% H₂O). The irradiation was performed using 100 fs pulses of 800 nm radiation from a regeneratively amplified Ti:sapphire laser system. We investigated the ablation efficiency and the phenomenology of the ablated patterns by probing the ablation depth using a profilometer. The surface modification was examined using a high resolution optical microscope (IOLs) or atomic force microscope—AFM (PMMA samples). It was found that different polymers exhibited different ablation characteristics, a result that we attribute to the differing optical properties of the materials. In particular, it was observed that the topography of the ablation tracks created on the hydrophilic intraocular lenses was smoother in comparison to those created on the PMMA and hydrophobic lens. The yellow doped hydrophobic intraocular lenses show higher ablation efficiency than undoped hydrophobic acrylic lenses.