A new numerical approach for solving a class of singular two-point boundary value problems

In this paper, we consider the following class of singular two-point boundary value problem posed on the interval x ?? (0, 1]

$$\begin{array}{@{}rcl@{}} (g(x)y^{\prime})^{\prime}=g(x)f(x,y),\\ y^{\prime}(0)=0,\mu y(1)+\sigma y^{\prime}(1)=B. \end{array} $$

A recursive scheme is developed, and its convergence properties are studied. Further, the error estimation of the method is discussed. The proposed scheme is based on the integral equation formalism and optimal homotopy analysis method in which a recursive scheme is established without any undetermined coefficients. The original differential equation is transformed into an equivalent integral equation to remove the singularity. The integral equation is then made free of undetermined coefficients by imposing the boundary conditions on it. Finally, the integral equation without any undetermined coefficients is efficiently treated by using optimal homotopy analysis method for finding the numerical solution. The optimal control-convergence parameter involved in the components of the series solution is obtained by minimizing the squared residual error equation. The present method is applied to obtain numerical solution of singular boundary value problems arising in various physical models, and numerical results show the advantages of our method over the existing methods.     

Fully sp2-Carbon-Linked Crystalline Two-Dimensional Conjugated Polymers: Insight into 2D Poly(phenylenecyanovinylene) Formation and its Optoelectronic Properties

Cyano-substituted polyphenylene vinylenes (PPVs) have been the focus of research for several decades owing to their interesting optoelectronic properties and potential applications in organic electronics. With the advent of organic two-dimensional (2D) crystals, the question arose as to how the chemical and optoelectronic advantages of PPVs evolve in 2D compared with their linear counterparts. In this work, we present the efficient synthesis of two novel 2D fully sp²-carbon-linked crystalline PPVs and investigate the essentiality of inorganic bases for their catalytic formation. Notably, among all bases screened, cesium carbonate (Cs₂CO₃) plays a crucial role and enables reversibility in the first step with subsequent structure locking by formation of a C=C double bond to maintain crystallinity, which is supported by density functional theory (DFT) calculations. A quantifiable energy diagram of a “quasi-reversible reaction” is proposed, which allows the identification of further suitable C−C bond formation reactions for 2D polymerizations. Moreover, the narrowing of the HOMO–LUMO gap is delineated by expanding the conjugation into two dimensions. To enable environmentally benign processing, the post-modification of 2D PPVs is further performed, which renders stable dispersions in the aqueous phase.     

Determination of aluminium contents in selected food samples by instrumental neutron activation analysis

Food and food products are the main sources of Aluminium entering the human body. In order to know aluminium contents in food and food products, selected 26 samples from local market were analyzed by instrumental neutron activation analysis (INAA) using reactor neutrons and high resolution gamma-ray spectrometry. INAA using 1,779 keV γ-ray of ²⁸Al (2.24 min) was used for aluminium concentrations in the range of 33–529 mg kg^?1. Two NIST standard reference materials (SRMs) and two IAEA reference materials (RMs) were analyzed by INAA for quantification of aluminium as a part of method validation.     

Preparation, characterization, and photocatalytic activity of sulfate-modified titania for degradation of methyl orange under visible light

Hydrated titania was prepared by a sol-gel method, taking tetraisopropyl orthotitanate as starting material, and then promoted with different weight percentages of sulfate by an incipient wetness impregnation method. The materials were characterized by various advanced techniques such as PXRD, BET surface area, N(2) adsorption-desorption measurements, FTIR, and SEM. Analytical results demonstrated that TiO(2) is mesoporous in nature, and sulfate modification could inhibit the phase transformation and enhance the thermal stability of TiO(2). It was also found that sulfate modification could reduce the crystallite size and increase the specific surface area of the catalysts. The degradation of methyl orange under solar radiation was investigated to evaluate the photocatalytic activity of these materials. Effects of different parameters such as pH of the solution, amount of catalyst, additives, and kinetics were investigated. At 2.5 wt% sulfate loading, the average percentage of degradation of methyl orange was nearly two times than that of neat TiO(2). The photocatalytic degradation followed first-order kinetics.     

Continuum reconstruction of the pore scale microstructure for Fontainebleau sandstone

A stochastic geometrical modeling technique is used to reconstruct a laboratory scale Fontainebleau sandstone with a sidelength of 1.5 cm. The model reconstruction is based on crystallite properties and diagenetic parameters determined from two-dimensional images. The three-dimensional pore scale microstructure of the sandstone is represented by a list of quartz crystallites defined geometrically and placed in the continuum. This allows generation of synthetic μ-CT images of the rock model at arbitrary resolutions. Quantitative microstructure comparison based on Minkowski functionals, two-point correlation function and local porosity theory indicates that this modeling technique can provide more realistic and accurate models of sandstones than many existing techniques used currently. Synthetic μ-CT images at different resolutions from a laboratory scale model of Fontainebleau sandstone are made available to the scientific community for resolution dependent petrophysical analysis.     

Five Dimensional Bulk Viscous String Cosmological Models in Saez and Ballester Theory of Gravitation

LRS Bianchi type-I bulk viscous string cosmological models are obtained in scalar tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986). It is shown that cosmic string does not survive for ρ+λ=0 whereas it survives for the equations of state ρ=(1+ω)λ (Takabayasi string) and ρ=λ (Geometric string). Some physical and geometrical properties of the exhibited model are discussed.