Generalization of tangential trace spaces of H(curl,Ω) for curvilinear Lipschitz polyhedral domains Ω

For curvilinear Lipschitz polyhedral domains Ω, explicit characterizations of the tangential trace spaces of H ¹(Ω) are presented. These extend the original characterizations given by Buffa and Ciarlet that hold on Lipschitz polyhedral domains with plane faces. The tangential trace spaces of H ¹(Ω) are fundamental for the definition, analysis and intuitive understanding of the trace spaces of H ( curl ,Ω) and therefore, more general characterizations of the latter are obtained at the same time. Copyright © 2013 John Wiley & Sons, Ltd.     

A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in

The aim of this paper is to establish a well‐posedness result for a boundary value problem of transmission‐type for the standard and generalized Brinkman systems in two Lipschitz domains in , the former being bounded, and the latter, its complement in . As a first step, we establish a well‐posedness result for a transmission problem for the standard Brinkman systems on complementary Lipschitz domains in by making use of the Potential theory developed for such a system. As a second step, we prove our desired result (in L²‐based Sobolev spaces) by using a method based on Fredholm operator theory and the well‐posedness result from the previous step.     

3D Organic–Inorganic Perovskite Ferroelastic Materials with Two Ferroelastic Phases: [Et3P(CH2)2F][Mn(dca)3] and [Et3P(CH2)2Cl][Mn(dca)3]

Organic–inorganic hybrid perovskite-type multiferroics have attracted considerable research interest owing to their fundamental scientific significance and promising technological applications in sensors and multiple-state memories. The recent achievements with divalent metal dicyanamide compounds revealed such malleable frameworks as a unique platform for developing novel functional materials. Herein, two 3D organic–inorganic hybrid perovskites [Et₃P(CH₂)₂F][Mn(dca)₃] ( 1 ) and [Et₃P(CH₂)₂Cl][Mn(dca)₃] ( 2 ) (dca=dicyanamide, N(CN)₂⁻) are presented. Accompanying the sequential phase transitions, they display a broad range of intriguing physical properties, including above room temperature ferroelastic behavior, switchable dielectricity, and low-temperature antiferromagnetic ordering (T_c=2.4 K for both 1 and 2 ). It is also worth noting that the spontaneous strain value of 1 is far beyond that of 2 in the first ferroelastic phase, as a result of the precise halogen substitution. From the point view of molecular design, this work should inspire further exploration of multifunctional molecular materials with desirable properties.     

Was Pauling Mistaken about Metals?

Pauling described metallic bonds using resonance. The maximum probability domains in the Kronig–Penney model can show a picture of it. When the walls are opaque (and the band gap is large) the maximum probability domain for an electron pair essentially corresponds to the region between the walls: the electron pairs are localized within two consecutive walls. However, when the walls become transparent (and the band gaps closes), the maximum probability domain can be moved through the system without a significant loss in probability.     

Evolution and properties of antiphase boundaries in silicate minerals

Experimental and observational evidence is reviewed for the mechanisms and kinetics of antiphase domain coarsening in silicate minerals. The expected rate law has the form (domain size)ⁿ ≈ annealing time, but the ideal value of n=2 has been observed in only one of three cases. Values of n≈8 or 10 are interpreted as implying adsorption of impurity atoms onto the antiphase boundaries. Diffusion of these impurities can then provide the rate determining step for boundary migration. Local ordering at the boundaries can also provide some stabilising influence, though this does not appear to affect the coarsening rate law. If the stabilisation is sufficient it might result in the development of an incommensurate superstructure, either as a stable phase or as a metastable phase under non-equilibrium conditions. The effective width of these boundaries appears to be ～ 25°, or approximately two unit cells, and their maximum effective interaction length appears to be ～ 4 times this width.     

Multidimensional space groups: Tables and standards

The previous speakers have dealt with tangible physical objects; I am to deal with organizational and symbolic problems. The symbolic problems are of greater scientific importance, but I must begin with those of human organization and in particular with the structure of the International Union of Crystallography (acronym IUCr).