A three‐dimensional Cartesian cut cell method for incompressible viscous flow with irregular domains

A three‐dimensional Cartesion cut cell method is presented for the simulations of incompressible viscous flows with irregular domains. A new model (referred to as ‘6+N’ model) is proposed to describe arbitrarily shaped cut cells and treat all the cells as polyhedrons with 6+N faces. The finite volume discretization of the Navier–Stokes equation is then implemented by using the ‘6+N’ model to separate the surface flux integrals into two parts, that is, the fluxes through the basic face of the hexahedron and those through the cutting surfaces. The previously proposed Kitta Cube algorithm and volume computer‐aided design platform (J. Comput. Aided. Des. 2005; 37(4): 1509–1520. Doi:10.1016/j.cad.2005.03.006) are adopted to generate cut cells and provide shape data and physical attributes for the numerical analysis. A modified SIMPLE‐based smoothing pressure correction scheme is applied to suppress checkerboard pressure oscillations caused by the collocated arrangement of velocities and pressure. The calculation accuracy of the numerical method expressed by L₁ and L _∞ norm errors is first demonstrated by the simulation of a pipe flow. Then its feasibility, efficiency, and potential in engineering applications are verified by applying it to solve natural convections between concentric spheres and between eccentric spheres. The heat transfer patterns in eccentric spheres are also obtained by using the numerical method. Copyright © 2011 John Wiley & Sons, Ltd.     

Meromorphic functions on compact Riemann surfaces and value sharing

Let X be a smooth and connected Riemann surface of genus g 0 and f: X P1, h: X P1 non-constant meromorphic functions on X. Fix an integer n 4 and assume the existence of n distinct points a1, , an P1 such that [image omitted] (set-theoretically) for every i. Here we prove that either f = h or [image omitted].     

Correction to the Paper - Determination of a Domain in Complex Space by its Automorphism Group

The author offers some corrections to his article which appeared in Vol. 47, No. 3 of this journal.     

Enveloping algebras that are principal ideal rings

Let L be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of L is a principal ideal ring if and only if L is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.     

Studies of phase transitions and ferroelastic domain walls in Pb5Al3F19 crystals by optical measurements

Three phase transitions between 100 and 400 K were previously shown by X-ray diffraction measurements. Such results have been confirmed by optical measurements on crystals. The thermal dependence of the birefringence has been determined. A new phase transformation has been shown at around 590 K not only by optical study but also by dielectric measurements. Ferroelastic domain-walls have been visualized. The sequence transition has been discussed taking into account the various space groups.     

Synthesis of S-monofluoromethyl phosphorothioates from PⅤ-H compounds and PhSO2SCH2F

S-Monofluoromethyl phosphorothioates represent an important class of organofluorine compounds and are re ported here for the first time.A series of S-monofluoromethyl phosphorothioates are conveniently synthesized from different P^Ⅴ-H compounds and PhSO₂SCH₂F under mild conditions.The method is compatible with common functional groups and provides potential opportunities to synthesize new bioactive molecules for medicinal chemistry.     

Separation of Xylene Isomers in the Anion-Pillared Square Grid Material SIFSIX-1-Cu

Xylene isomer separation is considered one of the seven separation challenges that changed the world. In addition, the high-energy demand of xylene separation highlights the need for efficient novel adsorbents. Herein, the liquid-phase separation potential of the anion-pillared hybrid material SIFSIX-1-Cu was studied for preferential adsorption of o-xylene and m-xylene over p-xylene, which was inspired by a previous complexation crystallization method for separating m-xylene. We report detailed experimental liquid-phase adsorption experiments, yielding selectivities of 3.0 for o-xylene versus p-xylene and 2.6 for m-xylene versus p-xylene. Our theoretical calculations thus provide a reasonable explanation that the xylene adsorption selectivity is attributed to the C−H⋅⋅⋅F interaction, and the host–guest interaction order agrees with the adsorption priority: o-xylene > m-xylene > p-xylene.     

Chemical aspects of the radiation stability of macrocyclic extractants designed for 90Sr separation

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