Stability and slightly supercritical oscillatory regimes of natural convection in a 8:1 cavity: solution of the benchmark problem by a global Galerkin method

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two‐dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each mode. The oscillatory flow regimes corresponding to each of the three modes are approximated asymptotically. No direct time integration is applied. Good agreement with the previously published results obtained by solution of the time‐dependent Boussinesq equations is reported. Copyright © 2004 John Wiley & Sons, Ltd.     

Studies on calcium‐containing poly(urethane ether)s

The calcium salt of mono(hydroxyethoxyethyl)phthalate [Ca(HEEP)₂] was synthesized by the reaction of diethylene glycol, phthalic anhydride, and calcium acetate. Calcium‐containing poly(urethane ether)s (PUEs) were synthesized by the reaction of hexamethylene diisocyanate (HMDI) or tolylene 2,4‐diisocyanate (TDI) with a mixture of Ca(HEEP)₂ and poly(ethylene glycol) (PEG₃₀₀ or PEG₄₀₀) with di‐n‐butyltin dilaurate as a catalyst. A series of calcium‐containing PUEs of different compositions were synthesized with Ca(HEEP)₂/PEG₃₀₀ (or PEG₄₀₀)/diisocyanate (HMDI or TDI) molar ratios of 2:2:4, 3:1:4, and 1:3:4 so that the coating properties of the PUEs could be studied. Blank PUEs without calcium‐containing ionic diols were also prepared by the reaction of PEG₃₀₀ or PEG₄₀₀ with HMDI or TDI. The PUEs were well characterized by Fourier transform infrared, ¹H and ¹³C NMR, solid‐state cross‐polarity/magic‐angle‐spinning ¹³C NMR, viscosity, solubility, and X‐ray diffraction studies. The thermal properties of the polymers were also studied with thermogravimetric analysis and differential scanning calorimetry. The PUEs were applied as top coats on acrylic‐coated leather, and their physicomechanical properties were also studied. The coating properties of PUEs, such as the tensile strength, elongation at break, tear strength, water vapor permeability, flexing endurance, cold crack resistance, abrasion resistance, color fastness, and adhesive strength, were better than the standard values. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2865–2878, 2003     

TERNARY OPERATIONS AS PRIMITIVE NOTIONS FOR PLANE GEOMETRY II

We proved in the first part [1] that plane geometry over Pythagorean fields is axiomatizable by quantifier-free axioms in a language with three individual constants, one binary and three ternary operation symbols. In this paper we prove that two of these operation symbols are superfluous.     

Gradient‐enhanced one‐dimensional pulse schemes for quaternary and methylene carbon detection

Gradient‐enhanced pulse schemes are presented for the detection of quaternary and methylene carbons. The new pulse schemes permit the detection of quaternary and methylene (—CH₂) carbons or CH₂ carbons alone from a single experiment. Efficient suppression of CH and CH₃ carbons in all the pulse schemes is achieved by creating their antiphase magnetization and then dephasing using gradients. In the pulse schemes for detection of only CH₂ carbons, the quaternary carbons are also suppressed either by dephasing using gradients or by rendering them unobservable by retaining in longitudinal order. The experimental results of the gradient pulse schemes are demonstrated on cholesteryl acetate and cyclosporin A. These one‐dimensional techniques, because of their simplicity and the ease of performing the experiments, can be important for routine chemical applications. Copyright © 2003 John Wiley & Sons, Ltd.     

The solution of the neutron transport equation in a slab with anisotropic scattering

The neutron transport equation for a slab geometry with the extremely anisotropic scattering kernel is considered. The albedo and transmission factors are calculated using the variation method. The effect of the extremely anisotropic parameter on the variation of the slab albedo and transmission factor is calculated. The obtained results are compared with the published data.     

On the use of the Galerkin method for 3D numerical modelling of the general circulation: the South Atlantic eperiment

A linear three‐dimensional hydrodynamical numerical model, with the application of the Galerkin Method for the vertical dependence, is here presented. The spherical coordinate system is used, in order to allow large‐scale simulations. The equations and mathematical development of the model are shown in detail, together with the boundary and initial conditions, and the sequence of equations' solution. The model is applied to the South Atlantic Ocean, for estimating typical seasonal circulations, and the results are summarized in maps of currents at surface and 1000 m depth, and in transport values of the Brazil Current between 30°S and 40°S. Copyright © 2002 John Wiley & Sons, Ltd.     

Essential spectrum and -solutions of one-dimensional Schrödinger operators

In 1949, Hartman and Wintner showed that if the eigenvalue equations of a one-dimensional Schrödinger operator possess square integrable solutions, then the essential spectrum is nowhere dense. Furthermore, they conjectured that this statement could be improved and that under this condition the essential spectrum might always be void. This is shown to be false. It is proved that, on the contrary, every closed, nowhere dense set does occur as the essential spectrum of Schrödinger operators which satisfy the condition of existence of -solutions. The proof of this theorem is based on inverse spectral theory.

     

柱几何Rayleigh-Taylor不稳定性的数值模拟

给出了柱几何中流体力学方程组及其在数值模拟中采用的计算方法。对二维柱几何Rayleigh-Taylor不稳定性进行数值模拟,在线性阶段与线性理论符合得很好;不稳定性增长进入非线性区域的阈值依赖于界面的位置,并且明显不同于平面情况。     

Hydrophobic effect for anionic dye - cationic surfactant interaction in aqueous and mixed solvent

Abstract

The interaction between anionic dyes [Reactive Orange 122 (R.O 122), Reactive Blue 19 (R.B 19), Reactive Violet 5 (R.V 5) and Acid Green 20 (A.G 20)] with cationic surfactant cetyltrimethylammoniun bromide (CTAB) has been investigated by spectrophotometry and conductance technique. The used dyes are characterized by tautomeric behavior which affects the mechanism of the interaction. Various parameters such as dye structure, surfactant composition, solvent composition, temperature and pH of the medium were studied. The spectral data were applied for calculating the binding constant between dye and surfactant (K_b), fraction of micellization (?_mic), and standard free energy change of binding (ΔG°_b) in 0,10,20 and 30 v/v % acetonitile (AN). Conductance technique was constructed to estimate the ion pairing constant (K_a) at different temperatures and v/v % AN. Thermodynamic parameters (ΔG°, ΔH° and ΔS°) for ion pair formation were evaluated. The role of hydrophobic and electrostatic effect on dye-surfactant interaction was discussed.     

Synthesis,thermal, and photocrosslinking studies of thermotropic liquid crystalline poly(benzylidene‐ether)esters containing α,β‐unsaturated ketone moiety in the main chain

A series of poly(benzylidene‐ether)esters containing a photoreactive benzylidene chromophore in the main chain were synthesized from 2,6‐bis(4‐hydroxy‐3‐methoxybenzylidene)cyclohexanone (BHMBCH) with various aliphatic and aromatic diacid chlorides by an interfacial polycondensation technique. The intrinsic viscosity of the synthesized homo and copolymers determined by Ubbelohde viscometer was found to be 0.12 to 0.17 dL/g. The molecular structure of the monomer and polymers was confirmed by FT‐IR, ¹H NMR, and ¹³C NMR spectral analyses. These polymers were studied for their thermal stability and photochemical properties. Thermal properties were evaluated by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). It was found that the polymers were stable up to 280 °C and start degrading thereafter. Increase in acid methylene spacer length decreased the thermal stability. The self‐extinguishing property of the synthesized polymers was studied by calculating the limiting oxygen index (LOI) value using a Van Krevelen's equation. The influence of the length of methylene spacer on phase transition was investigated using DSC and odd‐even effect has been observed. Hot‐stage optical polarizing microscopic (HOPM) study showed that most of the polymers exhibited birefringence and opalescence properties. The photolysis of liquid crystalline poly(benzylidene‐ether)esters revealed that α,β‐unsaturated ketone moiety in the main chain dimerises through 2π + 2π cycloaddition reaction to form a cyclobutane derivative and leads to crosslinking. © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013