A thermodynamic and dynamic subgrid closure model for two‐material cells

A general and robust subgrid closure model for two‐material cells is proposed. The conservative quantities of the entire cell are apportioned between two materials, and then, pressure and velocity are fully or partially equilibrated by modeling subgrid wave interactions. An unconditionally stable and entropy‐satisfying solution of the processes has been successfully found. The solution is valid for arbitrary level of relaxation. The model is numerically designed with care for general materials and is computationally efficient without recourse to subgrid iterations or subcycling in time. The model is implemented and tested in the Lagrange‐remap framework. Two interesting results are observed in 1D tests. First, on the basis of the closure model without any pressure and velocity relaxation, a material interface can be resolved without creating numerical oscillations and/or large nonphysical jumps in the problem of the modified Sod shock tube. Second, the overheating problem seen near the wall surface can be solved by the present entropy‐satisfying closure model. The generality, robustness, and efficiency of the model make it useful in principle in algorithms, such as ALE methods, volume of fluid methods, and even some mixture models, for compressible two‐phase flow computations. Copyright © 2013 John Wiley & Sons, Ltd.     

Crystal structure of the tetranickel complex with Ipropanethiolate

The title complex [Ni₄(SPrⁱ)₈] was confirmed by single crystal X-ray crystal diffraction analysis. The crystals are monoclinic, space group P2/n with a = 12.760(3), b = 10.059(2), c = 14.484(3) Å, α = 90, β = 93.70(3), γ = 90°, V = 1855.3(6) ų, Z = 4, F(000) = 880, D_c = 1.496 g/cm³, μ = 2.463 mm^?1, the final R = 0.0352 and wR = 0.0580. A total of 18,588 reflections were collected, of which 4404 were independent (R_int = 0.0631). In the crystal packing diagram, intermolecular C—H···Ni hydrogen bonds stabilize the solid state of the title complex.     

Polynomial solutions of a nonlinear difference equation

A class of nonlinear difference equations is considered. We show how their polynomial solutions can be computed in a systematic manner.     

A one‐pot method for synthesis of reduced graphene oxide‐supported Cu–Cu2O and catalytic application in tandem reaction of halides and sodium azide with terminal alkynes

Reduced graphene oxide (RGO)‐supported Cu–Cu₂O nanocomposite material (Cu‐Cu₂O@RGO) was prepared through a one‐pot reflux synthesis method. The morphology, crystal structure and composition of the prepared Cu‐Cu₂O@RGO were characterized using transmission electron microscopy, X‐ray diffraction, and X‐ray photoelectron, infrared and Raman spectroscopies. Cu‐Cu₂O@RGO as a heterogeneous catalyst was applied to tandem reactions of halides and sodium azide with terminal alkynes to synthesize effectively 1,4‐disubstituted 1,2,3‐triazoles. Moreover, the catalyst showed excellent recyclability performance with very little leaching of the metal. Compared with homogeneous catalysts, Cu‐Cu₂O@RGO as a green and efficient catalyst was recoverable, easy to separate and highly stable in the tandem method for the synthesis of 1,2,3‐triazole compounds.     

Liquid crystal mixtures for potential infrared applications

Liquid crystals (LCs) with diazo linkages have high dielectric and optical anisotropy. Two newly synthesized liquid crystalline compounds were dissolved in room temperature LC hosts, E7 and PTTP-24/36, to assess their properties. It was found that these mixtures have higher birefringence, larger dielectric anisotropy, and better elastic properties than the hosts. Satisfactory viscoelastic coefficients were also obtained for these mixtures, showing that they are promising LC materials for applications in the near IR region.