On an integral method for backward boundary layers

Zusammenfassung Eine Integralmethode für die Lösung von zweidimensionalen Grenzschichtgleichungen wird entwickelt für Fälle, in denen die Lösungen sich anfänglich wie diejenigen von End-Grenzschichten benehmen. Diese Lösungen sind von Goldstein behandelt worden. Die bedeutendste Anwendung betrifft den Fall, wo ein zweidimensionaler Strom gegen eine Öffnung fliesst, durch welche die Flüssigkeit entleert wird. In erster Annäherung wird die Grenzschichtströmung für grosse Entfernungen von der Öffnung durch die Ähnlichkeitsgesetze der konvergenten Strömung in einem keilförmigen Kanal beschrieben. Um Strömungen dieser Art zu studieren, die über lange Entfernungen laufen, wird die Geschwindigkeit am Rande der Grenzschicht an Stelle der Entfernung längs der Grenzschicht als unabhängige Veränderliche eingeführt. Die beschriebene Methode wird auf den Fall der Strömung in Richtung eines Schlitzes angewendet, ausgehend von einem unendlichen Halbraum, ferner auf den Fall einer Strömung um eine endliche Platte, die senkrecht zur Strömungsrichtung steht. In beiden Beispielen ist die Potentialströmung in der Form des Kirchhoff-Rayleighschen Gesetzes angenommen, wobei die freien Stromlinien an die scharfen Kanten gebunden sind. Die Methode wird verallgemeinert, so dass sie für allgemeinere End-Grenzschichten benutzt werden kann. Die Resultate stimmen ausgezeichnet mit denen der Methode von Thwaites sowie mit den Ähnlichkeitslösungen von Falkner-Skan überein.     

Finite time blowup of the <Emphasis Type="Italic">n</Emphasis>-harmonic flow on <Emphasis Type="Italic">n</Emphasis>-manifolds

In this paper, we generalize the no-neck result of Qing and Tian (in Commun Pure Appl Math 50:295–310, 1997) to show that there is no neck during blowing up for the n-harmonic flow as \(t\rightarrow \infty \). As an application of the no-neck result, we settle a conjecture of Hungerbühler (in Ann Scuola Norm Sup Pisa Cl Sci 4:593–631, 1997) by constructing an example to show that the n-harmonic map flow on an n-dimensional Riemannian manifold blows up in finite time for \(n\ge 3\).     

Electrochemical and Spectroscopic Properties of Fly Ash–Polyaniline Matrix Nanorod Composites

Polyaniline (PANI) nanocomposites were prepared with fly ash (FA) either by aging the starting materials (aniline and FA) before oxidative polymerisation or by including poly(styrene sulphonic acid) (PSSA) eliminating the aging step. The aging procedure formed polymer nanotubes that have cross-sectional diameters of 50–110 nm. The procedure involving PSSA produced nanorods and nanofibres composites that have diameters of 100–500 nm and length of up to 10 μm attributed to the presence of metal oxides and silica in FA. The electrochemical analysis of the PANI–PSSA–FA nanorod composites shows three redox couples with formal potentials, , values of 105 mV, 455 mV and 670 mV, and conductance, C, value of 1.21 × 10⁻² S. The UV-Vis spectroscopy of the polymeric nanorod shows absorption maxima at 340 and 370 nm (due to π–π^* transition of the benzoid rings), and 600–650 nm (due to charge transfer excitons of the quinoid structure), which are characteristic of emeraldine base.     

Single-ion heat capacities, C(p)(298)ion, of solids: with a novel route to heat-capacity estimation of complex anions

Single-ion heat capacities, C(p)(298)(ion), are additive values for the estimation of room-temperature (298 K) heat capacities of ionic solids. They may be used for inferring the heat capacities of ionic solids for which values are unavailable and for checking reported values, thus complementing our independent method of estimation from formula unit volumes (termed volume-based thermodynamics, VBT). Analysis of the reported heat-capacity data presented here provides a new self-consistent set of heat capacities for both cations and anions that is compatible (and thus may be combined) with an extensive set developed by Spencer. The addition of a large range of silicate species permits the estimation of the heat capacities of many silicate minerals. The single-ion heat capacities of individual silicate anions are observed to be strictly proportional to the total number of atoms (Si plus O), n, contained within the silicate anion complex itself (e.g., for the anion Si(2)O(7)(2-), n = 9, for SiO(4)(2-), n = 5), C(p)(silicate anion)/J K(-1) mol(-1) = 13.8n, in a new rule that is an extension of the Neumann-Kopp relationship. The same linear relationship applies to other homologous anion series (for example, oxygenated heavy-metal anion complexes such as niobates, bismuthates, and tantalates), although with a different proportionality constant. A similar proportionality, C(p)(complex anion)/J K(-1) mol(-1) ≈ 17.5n, which may be regarded as a convenient "rule of thumb", also applies, although less strictly, to complex anions in general. The proportionality constants reflect the rigidity of the complex anion, being always less than the Dulong-Petit value of 25 J K(-1) mol(-1). An emergent feature of our VBT and single-ion approaches to an estimation of the thermodynamic properties is the identification of anomalies in measured values, as is illustrated in this paper.     

Hydrogen-bonding contributions to the lattice energy of salts for second harmonic generation

The lattice energies of a series of organic dihydrogenphosphate salts capable of second harmonic generation (SHG) have been calculated. These calculations, coupled with empirical data, indicate that a minimum of 20–25% of the lattice energy arises from hydrogen-bond interactions. Hydrogen bonding is shown to be a strong enough force to have a profound effect on the overall packing and crystal geometry of such ionic materials, and is thus an important factor to consider for crystal engineering.     

Synthesis of the insecticidal 1′-acetoxy-mammeins and surangin b

Methods are examined for the synthesis of 4-(1′-acetoxy) alkylcoumarins having hexasubstituted aromatic rings. This has led to synthesis of the three insecticidal coumarins mammea E/BB, mammea E/BA and surangin B.     

A facile synthesis and structure determination from 13c-nmr spectroscopy of a novel heterocycle 1,1′-ethylenebis[2,3,8,8a-tetrahydro-5,8a-dimethyl-1H-imidazo[2,1-c][1,4]thiazine], a case of transannular stabilization

The condensation of 4-thiaheptane-2,6-dione with triethylenetetramine does not produce the macrocycle 1-thia-3,14-dimethyl-4,7,10-13-tetrazacyclopentadeca-3,13-diene; instead two molecules of the dione condense with one of the amine to give the title compound.