Dual solutions in mixed convection boundary layer flow of micropolar fluids

The steady mixed convection boundary layer flow over a vertical surface immersed in an incompressible micropolar fluid is considered in this paper. Employing suitable similarity transformations, the governing partial differential equations are transformed into ordinary differential equations, and the transformed equations are solved numerically by the Keller-box method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity, angular velocity and temperature profiles. Both cases of assisting and opposing buoyant flows are considered. It is found that dual solutions exist for the assisting flow, besides that usually reported in the literature for the opposing flow. Moreover, in contrast to the classical boundary layer theory, the separation point of the boundary layer is found to be distinct from the point of vanishing skin friction.     

Comparison between the homotopy analysis method and homotopy perturbation method to solve coupled Schrodinger-KdV equation

In this paper, we apply the homotopy analysis method (HAM) and the homotopy perturbation method (HPM) to obtain approximate analytical solutions of the coupled Schrodinger-KdV equation. The results show that HAM is a very efficient method and that HPM is a special case of HAM.     

Solution of Delay Differential Equation by Means of Homotopy Analysis Method

The algorithm of approximate analytical solution for delay differential equations (DDE) is obtained via homotopy analysis method (HAM) and modified homotopy analysis method (MHAM). Various examples of linear, nonlinear and system of initial value problems of DDE are solved and the results obtained show that these algorithms are accurate and efficient for the DDE. The convergence of this algorithm is also proved.     

Regioselective and Scalable Total Synthesis of Licochalcone C and Related Licoagrochalcones

A novel efficient method for the synthesis of licochalcone C in good yield on up to 30 g scale was developed. The reaction sequence included relied on the directed ortho-metalation (DOM) of bis-O-MOM-protected resorcinol for the regioselective C-prenylation, followed by metalation-formylation, selective O-deprotection of a hydroxyl group located between the formyl and prenyl groups, its methylation, and aldol reaction with p-hydroxyacetophenone. Synthesis of structurally related retrochalcones, i.e., licoagrochalcones B, C, and D, was also proposed.     

A New Sodium Thioborate Fast Ion Conductor: Na3B5S9

We report a new sodium fast-ion conductor, Na₃B₅S₉, that exhibits a high Na ion total conductivity of 0.80 mS cm⁻¹ (sintered pellet; cold-pressed pellet=0.21 mS cm⁻¹). The structure consists of corner-sharing B₁₀S₂₀ supertetrahedral clusters, which create a framework that supports 3D Na ion diffusion channels. The Na ions are well-distributed in the channels and form a disordered sublattice spanning five Na crystallographic sites. The combination of structural elucidation via single crystal X-ray diffraction and powder synchrotron X-ray diffraction at variable temperatures, solid-state nuclear magnetic resonance spectra and ab initio molecular dynamics simulations reveal high Na-ion mobility (predicted conductivity: 0.96 mS cm⁻¹) and the nature of the 3D diffusion pathways. Notably, the Na ion sublattice orders at low temperatures, resulting in isolated Na polyhedra and thus much lower ionic conductivity. This highlights the importance of a disordered Na ion sublattice—and existence of well-connected Na ion migration pathways formed via face-sharing polyhedra—in dictating Na ion diffusion.