We consider the numerical solutions of the MagnetoHydroDynamic (MHD) equations both in 2D and 3D domains using Fundamental Solution Method (FSM) also known as meshless method and Boundary Element Method (BEM) where both of them uses the fundamental solution of the differential operator. The considered MHD equations are transformed to the convection-diffusion type and modified Helmholtz type forms in order to apply the considered numerical methods. Formulized four different types of numerical schemes are compared with the either the exact solution if possible or with the Finite Element Method (FEM) results for the different Hartmann number values. Obtained solutions are displayed in terms of tables and visualized with figures of the contour plots.
Quantum behavior of protons in their transport through narrow, single-file water channels is an increasingly hot topic of discussion due to its possible far-reaching effects on fundamental biological and bioenergetic activities. It is well understood that ions move in an environment where there is electro-diffusion due to the electric field and concentration gradients which classical electro-diffusion models can explain. However, such models fall short of a full explanation of proton transport especially when quantum tunneling plays a role. This paper presents a semi-analytical approach based on combining Fick's law, the Poisson-Nernst-Planck equation, and the Wentzel-Kramers-Brillouin approximation to study through which pathways proton transfer in single and multiple proton regimes can be modulated by channel length and energy barriers. A proton tunnelling example revealed that tunneling really allows for the alternative crossing of the barrier besides just the extra parallel path. Yet, in cooperation, multi-proton systems may produce an even stronger flux. The computational work results suggested that tunneling probability is dependent on (bio)structural changes and thus proton flow may be regulated in vivo. Moreover, a transition state theory derived correction to a Gibbs barrier height demonstrates the quantum tunneling influence on the proton transfer energy surface. In conclusion, these findings highlight the importance of path-dependent quantum effects in the comprehension of proton transport in a restricting environment and thus, they set the stage for the future experimental and computational research work aiming to help biomimetic membranes and synthetic nanochannels for efficient proton transport.
The Zn–5.0Al–0.5Cu (wt.%) eutectic alloy was produced using melting and casting furnaces operating under vacuum during the production stage. The prepared alloy was subjected to unidirectional solidification in a Bridgman-type directional solidification apparatus under a constant temperature gradient (G = 3.67 K/mm) and a wide range of growth rates (V = 8.45–2087.15 μm/s). The resulting microstructures were examined using a field emission scanning electron microscope (FESEM). Experimental results indicate that the acceleration in solidification kinetics directly modifies the microstructure, leading to a superior mechanical combination of mechanical properties in terms of both microhardness and tensile strength. This correlation provides a new perspective for optimizing Zn–Al–Cu alloy systems for high-performance engineering applications. The obtained data were comprehensively evaluated by comparing them with Zn-Al based alloys in the literature.
In the present paper, we are investigated an elliptic problem concerning (p(x),q(x))-Laplacian and (p(x),q(x))-biharmonic operator under Navier boundary conditions. Under some appropriate conditions, we prove the existence of at least one nontrivial weak solution using the Mountain Pass theorem together with Ambrosetti-Rabinowitz’s Condition
Combining retinol and vitamin C (Vit C) in one topical formulation is challenging: retinol is lipophilic and easily oxidised, whereas Vit C is hydrophilic, and both are chemically unstable. This study aimed to co-encapsulate retinol and a stable Vit C derivative, 3-O-ethyl ascorbic acid, in ethosomes produced by high-pressure microfluidization. The ethosomes were characterised by particle size, polydispersity index, zeta potential, pH and transmission electron microscopy, and their physical stability was followed for 60 days at 2–8 °C, 25 °C, 30 °C and 40 °C. In vitro release through a cellulose acetate membrane and permeation across the synthetic skin-mimetic Strat-M® membrane were studied in Franz diffusion cells and compared with a solution and a conventional gel. The loaded ethosomes were spherical, with sizes of approximately 140–160 nm that remained essentially unchanged for 60 days at 2–8 °C, whereas samples stored at 30 °C and 40 °C had markedly larger vesicles; refrigerated storage is required. Encapsulation efficiency was 98.9% for retinol and 33.1% for Vit C. Expressed as a percentage of the applied dose, the cumulative amounts of both actives released or permeated from the ethosomal product over 2 h were significantly lower than those from the solution and the gel (28–50% of the solution values at 120 min; p < 0.001). Microfluidization is a simple and suitable method for producing ethosomes that co-encapsulate hydrophilic and lipophilic anti-ageing actives with a release-retarding effect. Because synthetic membranes were used, ex vivo and in vivo studies are needed to confirm skin delivery.
