Singular solutions of the Poisson equation at edges of three‐dimensional domains and their treatment with a predictor–corrector finite element method

Solutions of boundary value problems in three‐dimensional domains with edges may exhibit singularities which are known to influence both the accuracy of the finite element solutions and the rate of convergence in the error estimates. This paper considers boundary value problems for the Poisson equation on typical domains Ω ? ?³ with edge singularities and presents, on the one hand, explicit computational formulas for the flux intensity functions. On the other hand, it proposes and analyzes a nonconforming finite element method on regular meshes for the efficient treatment of the singularities. The novelty of the present method is the use of the explicit formulas for the flux intensity functions in defining a postprocessing procedure in the finite element approximation of the solution. A priori error estimates in H¹(Ω) show that the present algorithm exhibits the same rate of convergence as it is known for problems with regular solutions.     

The crystal and molecular structure of triphenylphosphoniodithio-carboxylato-ss'-carbonylbis (trikphenylphosphine) iridium(I) tetrafluoroborate [Ir(S2CPPh3) (CO) (PPh3)2]BF4.

Crystal and molecular structures of the title compound have been determined from a three-dimensional X-ray analysis using diffractometer data. The crystals are monoclinic, space group P2₁/c, with Z = 4 in a unit cell of dimensions a = 10.5876(9), b = 31.518(10), c = 16.2164(5) Å, β = 92.521(1)°. The observed and calculated densities are 1.38 and 1.374 g cm^-1 respectively. The crystals decompose under X-rays, and three crystals were required to complete data collection. The structure was solved and refined by convetional methods to final residuals R and R_w of 0.087 and 0.107 respectively.The crystals contain monomeric cations, and BF₄ anions. The iridium atom is in a distorted trigonal bipyramidal environment consisting of the two sulphur atoms (one axial, one equatorial) of a bidentate triphenylphosphoniodi-thiocarboxylate ligand, two triphenylphosphine groups (equatorial) and the carbonyl ligand (axial). The non-equivalent Ir-s distances are 2.377 and 2.307(5) Å, the Ir-P distances are 2.334, 2.331(5) Å. Within the zwitterion, the C-S distances are 1.66 and 1.70(2) Å, while P-C is 1.78(2) Å. The condensation of PPh₃ and CS₂ to form the PH₃P⁺-CS₂ zwitterion is in contrast to that predicted previously.It is probable that the other complexes of iridium and rhodium prepared in a similar manner [2] should now be reformulated as containing Ph₃P⁺-CS₂^- ligands.     

Synthesis of a missing structural link: the first trigonal planar B4 units in the novel complex boride Ti(1+x)Os(2-x)RuB2 (x = 0.6)

The newly synthesized boride Ti(1+x)Os(2-x)RuB(2) (x = 0.6) has a novel structure featuring one-dimensional chains of titanium atoms, one-dimensional strings of face-sharing empty tetrahedral and square pyramidal clusters and, most importantly, trigonal planar and strongly bonded B4 units with a B-B distance of 1.89 A.     

Flux intensity functions for the Laplacian at axisymmetric edges

We derive explicit representation formulas for the computation of flux intensity functions for mixed boundary value problems for the Poisson equation in axisymmetric domains with edges. We rely on the decomposition of the boundary value problems in three dimensions by means of partial Fourier analysis with respect to the rotational angle into boundary value problems in the two‐dimensional meridian domain of . Utilizing smooth cutoff functions, the solutions of the reduced problems are analyzed semi‐analytically near corners of the plane meridian domain, and the edge flux intensity functions are constructed via Fourier synthesis and convergence analysis. The formulas are also applicable in the case of crack fronts. The constructive nature of the formulas provides in a straightforward way an efficient strategy for the accurate computation of edge flux intensity functions in axisymmetric domains. A demonstration example that illustrates the application of the formulas is presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparative study of the thermal behavior of Sr–Cu–O gels obtained by sol–gel and microwave-assisted sol–gel method

Journal of Thermal Analysis and Calorimetry - In the literature data, several papers reported the synthesis by various chemical or physical methods of the SrCu2O2 (SCO) having possible applications...     

Metal-Mediated Directional Capping of Rod-Packing Metal–Organic Frameworks

Two new rod-packing metal–organic frameworks (RPMOF) are constructed by regulating the in situ formation of the capping agent. In CPM-s7, carboxylate linkers extend 1D manganese-oxide chains in four additional directions, forming 3D RPMOF. The substitution of Mn²⁺ with a stronger Lewis acidic Co²⁺, leads to an acceleration of the hydrolysis-prone sulfonate linker, resulting in presence of sulfate ions to reduce two out of the four carboxylate-extending directions, and thus forming a new 2D rod-packing CPM-s8. Density functional theory calculations and magnetization measurements reveal ferrimagnetic ordering of CPM-s8, signifying the potential of exploring 2D RPMOF for effective low-dimensional magnetic materials.     

Correction to: Tuning working potential of silicon‑phosphorus anode via microstructure control for high‑energy lithium‑ion batteries

Journal of Solid State Electrochemistry -     

Capillary electrophoresis-based methods for the determination of lipids--a review

Capillary electrophoresis (CE) is a high-resolution technique for the separation of complex biological and chemical mixtures. CE continues to emerge as a powerful tool in the determination of lipids. Here we review the analytical potential of CE for the determination of a wide range of lipids. The different classes of lipids are introduced, and the different modes of CE and optimization methods for the separation of lipids are described. The advantages and disadvantages of the different modes of CE compared to traditional methods like gas chromatography (GC) and liquid chromatography (LC) in the determination of lipids are discussed. Finally, the potential of CE in the determination of lipids in the future is illustrated.     

Ladders of a magnetically active element in the structure of the novel complex boride Ti9Fe2Ru18B8: synthesis, structure, bonding, and magnetism

Polycrystalline samples and single crystals of the complex boride Ti9Fe2Ru18B8 were synthesized by arc-melting the elements and characterized by single-crystal X-ray diffraction and energy-dispersive X-ray analysis. Ti9Fe2Ru18B8 is a new substitutional variant of the Zn11Rh18B8 structure type, space group P4/mbm (No. 127), whose remarkable feature is that it contains one-dimensional chains of dumbbells of magnetically active Fe atoms, which form "ladders" along the c axis. The Fe-Fe distance within a dumbbell is 2.489(2) A, and the Fe2-Fe2 distance between two dumbbells is 2.968(1) A; in contrast, the chains are well-separated from each other by distances of at least 11.217(2) A. According to the results of tight-binding electronic structure calculations, Ru-B and Ti-Ru contacts are responsible for the structural robustness, while Fe-Fe interactions influence the magnetic behavior. According to magnetization measurements, Ti9Fe2Ru18B8 orders ferromagnetically between 10 and approximately 200 K. A model for ferromagnetism in this ladder-based structure identifies ferromagnetic coupling among neighboring spin-triplet Fe2 dimers along the c axis as the origin of the magnetic behavior.