A Fourier–Chebyshev spectral collocation method for simulating flow past spheres and spheroids

An accurate Fourier–Chebyshev spectral collocation method has been developed for simulating flow past prolate spheroids. The incompressible Navier–Stokes equations are transformed to the prolate spheroidal co‐ordinate system and discretized on an orthogonal body fitted mesh. The infinite flow domain is truncated to a finite extent and a Chebyshev discretization is used in the wall‐normal direction. The azimuthal direction is periodic and a conventional Fourier expansion is used in this direction. The other wall‐tangential direction requires special treatment and a restricted Fourier expansion that satisfies the parity conditions across the poles is used. Issues including spatial and temporal discretization, efficient inversion of the pressure Poisson equation, outflow boundary condition and stability restriction at the pole are discussed. The solver has been validated primarily by simulating steady and unsteady flow past a sphere at various Reynolds numbers and comparing key quantities with corresponding data from experiments and other numerical simulations. Copyright © 1999 John Wiley & Sons, Ltd.     

Improved local convergence analysis of the Landweber iteration in Banach spaces

Archiv der Mathematik - The convergence analysis of the Landweber iteration for solving inverse problems in Banach spaces via Hölder stability estimates is well studied by de Hoop et al....     

On new fractional integral inequalities using Marichev–Saigo–Maeda operator

Generalizations of fractional integral inequalities were introduced by many authors. The aim of our investigation is to establish some new fractional integral inequalities using Marichev–Saigo–Maeda (MSM) fractional integral operator for convex function. Further, we obtain some more fractional integral inequalities of Grüss type using MSM operator.     

Flux-Assisted Synthesis of Y2Ti2O5S2 for Photocatalytic Hydrogen and Oxygen Evolution Reactions

Photocatalytic water splitting is an ideal means of producing hydrogen in a sustainable manner, and developing highly efficient photocatalysts is a vital aspect of realizing this process. The photocatalyst Y₂Ti₂O₅S₂ (YTOS) is capable of absorbing at wavelengths up to 650 nm and exhibits outstanding thermal and chemical durability compared with other oxysulfides. However, the photocatalytic performance of YTOS synthesized using the conventional solid-state reaction (SSR) process is limited owing to the large particle sizes and structural defects associated with this synthetic method. Herein, we report the synthesis of YTOS particles by a flux-assisted technique. The enhanced mass transfer efficiency in the flux significantly reduced the preparation time compared with the SSR method. In addition, the resulting YTOS showed improved photocatalytic H₂ and O₂ evolution activity when loaded with Rh and Co₃O₄ co-catalysts, respectively. These improvements are attributed to the reduced particle size and enhanced crystallinity of the material as well as the slower decay of photogenerated carriers on a nanosecond to sub-microsecond time range. Further optimization of this flux-assisted method together with suitable surface modification is expected to produce high-quality YTOS crystals with superior photocatalytic activity.