First principles calculations of optical and magnetic properties of SrFe2O4 compound under pressure

In this research, the magnetic and optical properties of SrFe₂O₄ ceramic were studied. The calculations were performed by Full Potential Linearized Augmented Plane Wave method in Density Functional Theory framework with generalized gradient (GGA), GGA+U and modified Becke–Johnson approximations for the exchange and correlation functionals. The results show that SrFe₂O₄ is a ferrimagnetic ceramics with six different spin configurations. The Hubbard parameter was calculated (_Ueff=4.5 eV$U_{\mathit{eff}}=4.5\text{eV}$) by an ab initio method. The optical properties such as dielectric function, refraction index, electron energy-loss function, reflectivity, absorption coefficient and optical conductivity were investigated at zero up to 20 GPa pressure in x, y and z directions. The pressure coefficients of optical band, static dielectric constant, plasmon peak, static refraction index and the maximum of absorption were determined. Moreover, the pressure dependence of the static dielectric constant, plasmon peak, static refraction index, the maximum of absorption and the optical gap were investigated.     

Solving heat conduction problems by the Direct Meshless Local Petrov-Galerkin (DMLPG) method

As an improvement of the Meshless Local Petrov–Galerkin (MLPG), the Direct Meshless Local Petrov–Galerkin (DMLPG) method is applied here to the numerical solution of transient heat conduction problem. The new technique is based on direct recoveries of test functionals (local weak forms) from values at nodes without any detour via classical moving least squares (MLS) shape functions. This leads to an absolutely cheaper scheme where the numerical integrations will be done over low–degree polynomials rather than complicated MLS shape functions. This eliminates the main disadvantage of MLS based methods in comparison with finite element methods (FEM), namely the costs of numerical integration.     

Exact 3D elasticity solution for free vibrations of an eccentric hollow sphere

An exact three-dimensional elastodynamic analysis for describing the natural oscillations of a freely suspended, isotropic, and homogeneous elastic sphere with an eccentrically located inner spherical cavity is developed. The translational addition theorem for spherical vector wave functions is employed to impose the zero traction boundary conditions, leading to frequency equations in the form of exact determinantal equations involving spherical Bessel functions and Wigner 3j symbols. Extensive numerical calculations have been carried out for the first five clusters of eigenfrequencies associated with both the axisymmetric and non-axisymmetric spheroidal as well as toroidal oscillation modes for selected inner-outer radii ratios in a wide range of cavity eccentricities. Also, the corresponding three-dimensional deformed mode shapes are illustrated in vivid graphical forms for selected eccentricities. The numerical results describe the imperative influence of cavity eccentricity, mode type, and radii ratio on the vibrational characteristics of the hollow sphere. The existence of “multiple degeneracies” and the trigger of “frequency splitting” are demonstrated and discussed. The accuracy of solution is checked through appropriate convergence studies, and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature.     

H5BW12O40 as a green and efficient homogeneous but recyclable catalyst in the synthesis of 4H‐Pyrans via multicomponent reaction

Keggin‐type heteropolyacid, H₅BW₁₂O₄₀ (BWA) with a higher negative charge and stronger Brønsted acidity comparing to Si and P derivatives was used as an efficient, green, and reusable catalyst in a three‐component reaction involving the cyclocondensation of various β‐dicarbonyl compounds, differently substituted aromatic aldehydes and malononitrile in EtOH/H₂O for the facile, clean, and high yielding synthesis of 4H‐pyrans. All reactions were completed in short times and the products were obtained in good to excellent yields. The reaction medium could be recycled and reused several times without any loss of efficiency.     

Investigation of flow and heat transfer of nanofluid in microchannel with variable property approach

Laminar flow and heat transfer of water-Al₂O₃ nanofluid under constant heat flux have been investigated numerically. Single-phase with temperature dependant effective properties has been assumed for fluid. Enhancement in heat transfer and increase in friction factor have been obtained by the use of nanofluid. Heat transfer enhancement is more obvious by the use of variable properties. Also, effects of temperature variation on nanofluid heat transfer are greater than the pure water.     

Syntheses of thiopyrylium-tungsten complexes

Hexacarbonyltungsten reacts with 2,4,6-triphenylthiopyrylium perchlorate and 2,6-dianisyl-4-phenylthiopyrylium perchlorate in diglyme to afford cationic thiopyrylium salts, 2,4,6-[H₂(C₆H₅)₃C₅SW(CO)₃]⁺ClO₄ ⁻ and 2,6,4-[H₂(C₆H₅)(C₆H₄OCH₃)₂C₅SW(CO)₃]⁺ClO₄ ⁻. Both compounds were characterized by physico-chemical and spectroscopic methods. The HMQC, DEPT-45, and COSY experiments were used to assign carbon and proton signals in the ¹H and ¹³C NMR spectra.     

Continuous and Discrete Adjoint Approach Based on Lattice Boltzmann Method in Aerodynamic Optimization Part I: Mathematical Derivation of Adjoint Lattice Boltzmann Equations

The significance of flow optimization utilizing the lattice Boltzmann (LB) method becomes obvious regarding its advantages as a novel flow field solution method compared to the other conventional computational fluid dynamics techniques. These unique characteristics of the LB method form the main idea of its application to optimization problems. In this research, for the first time, both continuous and discrete adjoint equations were extracted based on the LB method using a general procedure with low implementation cost. The proposed approach could be performed similarly for any optimization problem with the corresponding cost function and design variables vector. Moreover, this approach was not limited to flow fields and could be employed for steady as well as unsteady flows. Initially, the continuous and discrete adjoint LB equations and the cost function gradient vector were derived mathematically in detail using the continuous and discrete LB equations in space and time, respectively. Meanwhile, new adjoint concepts in lattice space were introduced. Finally, the analytical evaluation of the adjoint distribution functions and the cost function gradients was carried out.     

A Petrov–Galerkin RBF method for diffusion equation on the unit sphere

This paper concerns a numerical solution for the diffusion equation on the unit sphere. The given method is based on the spherical basis function approximation and the Petrov–Galerkin test discretization. The method is meshless because spherical triangulation is not required neither for approximation nor for numerical integration. This feature is achieved through the spherical basis function approximation and the use of local weak forms instead of a global variational formulation. The local Petrov–Galerkin formulation allows to compute the integrals on small independent spherical caps without any dependence on a connected background mesh. Experimental results show the accuracy and the efficiency of the new method.