Taylor collocation method for the numerical solution of the nonlinear Schrödinger equation using quintic B-spline basis

In this study, we construct a Taylor collocation method for the numerical solution of the nonlinear Schrödinger (NLS) equation. We use suitable initial and boundary conditions. Taylor series expansion is used for time discretization. The cubic B-spline collocation method is applied to spatial discretization. Test problems concerning the single soliton motion, interaction of two colliding solitons, and the formation and bound states of solitons of the NLS equation are studied to evaluate the method. The L ₂ and L _∞ error norms are calculated to improve the accuracy of the numerical results.     

Symmetries of boundary layer equations of power-law fluids of second grade

A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incompressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classification with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.     

Synthesis and characterization of fully aromatic thermotropic liquid‐crystalline copolyesters containing m‐hydroxybenzoic acid units

A series of fully aromatic copolyesters based on p‐acetoxybenzoic acid (p‐ABA), hydroquinone diacetate (HQDA), terephthalic acid (TPA), and m‐acetoxybenzoic acid (m‐ABA) were prepared by a modified melt‐polycondensation reaction. The copolyesters were characterized by DSC, thermogravimetric analysis, ¹H NMR, polarized optical microscopy, X‐ray diffraction, and intrinsic viscosity measurements. The copolyesters exhibited nematic liquid‐crystalline phases in a broad temperature range of about 150 °C, when the content of linear (p‐ABA, HQDA, and TPA) units was over 67 mol %. DSC analysis of the anisotropic copolyesters revealed broad endotherms associated with the nematic phases, and the melting or flow temperatures were found to be in the processable region. The flow temperatures and crystal‐to‐nematic and nematic‐to‐isotropic transitions depend on the type of linear monomer units, and these transitions increased as the content of the p‐ABA units increased, as compared to the HQDA/TPA units. When the content of the p‐ABA units increased, as compared to other linear units (HQDA and TPA), the intrinsic viscosity and degree of crystallinity of the copolyesters also increased, implying a higher reactivity for p‐ABA in the p‐ABA/HQDA/TPA/m‐ABA polymer system. The aromatic region in the ¹H NMR spectra of the copolyesters containing equal molar compositions of p‐ABA, HQDA, and TPA units were sensitive to the sequence distribution of aromatic rings. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3263–3277, 2001     

Entropy analysis for third grade fluid flow with Vogel model viscosity in annular pipe

The steady-state flow of a third grade fluid between concentric circular cylinders is considered and entropy generation due to fluid friction and heat transfer in the annular pipe is examined. Depending upon the fluid viscosity, entropy generation in the flow system varies. The third grade fluid is employed to account for the non-Newtonian effect while Vogel model is accommodated for temperature-dependent viscosity. The analysis is based on perturbation technique. The closed form solutions for velocity, temperature and entropy fields are presented. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that entropy generation number reduces with increasing viscosity parameter A, which is more pronounced in the region close to the annular pipe inner wall and opposite is true for increasing viscosity parameter B.     

Covalent immobilization of invertase on chemically activated poly(2-hydroxyethyl methacrylate) microbeads

Properties of invertase immobilized on poly(2-hydroxyethyl methacrylate) microbeads activated by epichlorohydrin or cyanuric chloride were studied. After 20 repeated uses for 3 days, the activity of the immobilized enzyme was 92–93%. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1793–1797, October, 2006.     

Bounds on multiplicities of spherical spaces over finite fields

Let G be a reductive group scheme of type A acting on a spherical scheme X. We prove that there exists a number C such that the multiplicity $\dim \mathrm{Hom}(\rho ,\mathbb{C}[X(F)])$ is bounded by C, for any finite field F and any irreducible representation ρ of $G(F)$. We give an explicit bound for C. We conjecture that this result is true for any reductive group scheme and when F ranges (in addition) over all local fields of characteristic 0.Different aspects of this conjecture were studied in [3], [11], [6], [7].     

QSAR based modeling on a series of α-hydroxy amides as a novel class of bradykinin B1 selective antagonists

G-protein coupled receptors like Bradykinin (BK) B₁ represent a potential treatment route for chronic pain and inflammation. Quantitative structure activity relationship has been performed on a series of α-hydroxy amides as a novel class of bradykinin B₁ selective antagonists, using different physicochemical parameters along with appropriate indicator variables. It has been found that physicochemical parameters such as connectivity indices ³χ, ⁴χ and ⁵χ, molecular weight, molar refractivity, density along with indicator variables are significantly correlated with activity. In this paper best results were obtained by using multiple regression analysis. Different models were generated with high values of R² and low values of PRESS/SSY ratio. The significant equations were statistically tested by using leave one out (LOO) technique and cross validation methods.     

Improved diode properties in zinc telluride thin film-silicon nanowire heterojunctions

In this study, structural and optoelectronic properties and photodedection characteristics of diodes constructed from p-zinc telluride (ZnTe) thin film/n-silicon (Si) nanowire heterojunctions are reported. Dense arrays of vertically aligned Si nanowires were successfully synthesized on (1 1 0)-oriented n-type single crystalline Si wafer using simple and inexpensive metal-assisted etching (MAE) process. Following the nanowire synthesis, p-type ZnTe thin films were deposited onto vertically oriented Si nanowires via radio frequency magnetron sputtering to form three-dimensional heterojunctions. A comparative study of the structural results obtained from X-ray diffraction and Raman spectroscopy measurements showed the improved crystallinity of the ZnTe thin films deposited onto the Si nanowire arrays. The fabricated nanowire-based heterojunction devices exhibited remarkable diode characteristics and enhanced optoelectronic properties and photosensitivity in comparison to the planar reference. The electrical measurements revealed that the diodes with nanowires had a well-defined rectifying behaviour with a rectification ratio of 10⁴ at ±2 V and a relatively small ideality factor of n = 1.8 with lower reverse leakage current and series resistance at room temperature in dark condition. Moreover, an open-circuit voltage of 100 mV was also observed under illumination. Based on spectral photoresponsivity measurements, the nanowire-based device exhibited a distinct responsivity and high detectivity in visible and near-infrared (NIR) wavelength regions. The device characteristics observed here offer that the fabricated ZnTe thin film/Si nanowire-based p–n heterojunction structures will find important applications in future and will be a promising candidate for high-performance and low-cost optoelectronic device applications, NIR photodedectors in particular.     

Effect of various treatment and glazing (coating) techniques on the roughness and wettability of ceramic dental restorative surfaces

Surface treatment procedures such as grinding and polishing are needed to provide the ceramic dental restorative materials with proper fitting and occlusion. The treated surfaces are customarily glazed to improve the strength and smoothness. Though smoothness and wetting of the dental surfaces are important to minimize bacterial plaque retention, influence of the surface treatment and glazing procedures on the final surface roughness and its correlation to wettability are overlooked.

In this work, effect of various treatment (diamond fraising, stoning, sanding and aluminum oxide and rubber polishing) and glazing (auto and overglazing) techniques on the final roughness and the resulting wettability of dental ceramic surfaces were investigated using scanning electron microscopy (SEM) observations and atomic force microscopy (AFM) scans, 75 scans per sample. The surfaces were characterized and assigned an average roughness measure, R_a. The wettability of the same surfaces was evaluated using micro-contact angle measurements (25 micro-bubbles placed on a grid on each surface) to correlate the final surface roughness and wettability.

The results show that overglazing prevails over surface irregularities from different treatment procedures and provides homegeneously smooth surfaces with mean R_a < 10 nm. It also produces uniformly wetted surfaces with low contact angles around 20°. The autoglazed surfaces are less smooth (mean R_a around 50 nm) and displays sporadic topographic irregularities. They display larger and less uniform contact angles ranging between 35° and 50°. The results suggest that overglazing should be preferred after surface treatment to obtain a smooth and well-wetted dental ceramic surface.