An operator splitting scheme for numerical simulation of spinodal decomposition and microstructure evolution of binary alloys.

This article compares the operator splitting scheme to linearly stabilized splitting and semi-implicit Euler's schemes for the numerical solution of the Cahn-Hilliard equation. For the purpose of validation, the spinodal decomposition phenomena have been simulated. The efficacy of the three schemes has been demonstrated through numerical experiments. The computed results show that the schemes are conditionally stable. It has been observed that the operator splitting scheme is computationally more efficient.

In Vitro and In Silico Protocols for the Assessment of Anti-Tick Compounds from Pinus roxburghii against Rhipicephalus (Boophilus) microplus Ticks.

Pinus roxburghii, also known by the name "Himalayan chir pine," belongs to the Pinaceae family. Rhipicephalus (Boophilus) microplus tick is one of the most significant bovine ectoparasites, making it a major vector of economically important tick-borne diseases. The researchers conducted adult immersion tests (AIT) and larval packet tests (LPT) to investigate the acaricidal effect of P. roxburghii plant extract on R. (B.) microplus and its potential modulatory function when used with cypermethrin. Eggs were also assessed for their weight, egg-laying index (IE), hatchability rate, and control rate. After exposure to essential extract concentrations ranging from 2.5 to 40 mg/mL for 48 h, adult female ticks' oviposition inhibition and unfed R. (B.) microplus larvae's mortality rates were analyzed. Engorged females exposed to P. roxburghii at 40 mg/mL had reduced biological activity (oviposition, IE) compared to positive and negative controls. A concentration of 40 mg/mL of P. roxburghii caused 90% mortality in R. (B.) microplus larvae, whereas cypermethrin (the positive control) caused 98.3% mortality in LPT. In AIT, cypermethrin inhibited 81% of oviposition, compared to the 40 mg/mL concentration of P. roxburghii, which inhibited 40% of the ticks' oviposition. Moreover, this study assessed the binding capacity of selected phytocompounds with the targeted protein. Three servers (SWISS-MODEL, RoseTTAFold, and TrRosetta) recreated the target protein RmGABACl's 3D structure. The modeled 3D structure was validated using the online servers PROCHECK, ERRAT, and Prosa. Molecular docking using Auto Dock VINA predicted the binding mechanisms of 20 drug-like compounds against the target protein. Catechin and myricetin showed significant interactions with active site residues of the target protein, with docking scores of -7.7 kcal/mol and -7.6 kcal/mol, respectively. In conclusion, this study demonstrated the acaricidal activity of P. roxburghii extract, suggesting its potential as an alternative natural acaricide for controlling R. (B.) microplus.

An approximate analytical solution of the Allen-Cahn equation using homotopy perturbation method and homotopy analysis method.

In this paper, an approximate analytical solution of the bistable Allen-Cahn equation is given. The Allen-Cahn equation is a mathematical model to study the phase separation process in binary alloys and emerged as a convection-diffusion equation in fluid dynamics or reaction-diffusion equation in material sciences. A phase transition occurs at the interface when one material changes its composition or structure. The homotopy perturbation method and homotopy analysis method are used for finding the approximate solution. These methods don't need the use of any transformation, discretization, unrealistic restriction and assumption. The error estimates are computed by comparing with a numerical method, and a good agreement is observed.