Symmetry Properties of the Elastic Energy of a Woven Fabric with Bending and Twisting Resistance

A woven fabric can be described as a surface made of two families of fibers: in this work we study how the geometry of the weave pattern affects the symmetry properties of the elastic energy of the surface. Four basic symmetry classes of weave patterns are possible, depending on the angle between the fibers and their material properties. The properties of the pattern determine the material symmetry group of the network, under which the elastic energy is invariant. We derive representations for the energy of a woven fabric that are invariant under the symmetry group of the network, and discuss the relation of these invariants with the curvature and twist of the fibers.      

Systematic remarks on objectivity and frame-indifference,liquid crystal theory as an example

In this paper objectivity and material frame-indifference are systematically discussed, because changing the observer and changing the motion of a material with respect to an observer independent standard frame of reference have to be distinguished carefully. Objectivity and observer invariance of the physical laws and of the constitutive mappings are introduced. Semi-objectivity and objectivity of different time derivative operators are investigated. As examples, changing the observer in liquid crystal theory and changing the motion in linear heat conducting materials is considered.     

Grab vs. composite sampling of particulate materials with significant spatial heterogeneity—A simulation study of “correct sampling errors”

Sampling errors can be divided into two classes, incorrect sampling and correct sampling errors. Incorrect sampling errors arise from incorrectly designed sampling equipment or procedures. Correct sampling errors are due to the heterogeneity of the material in sampling targets. Excluding the incorrect sampling errors, which can all be eliminated in practice although informed and diligent work is often needed, five factors dominate sampling variance: two factors related to material heterogeneity (analyte concentration; distributional heterogeneity) and three factors related to the sampling process itself (sample type, sample size, sampling modus). Due to highly significant interactions, a comprehensive appreciation of their combined effects is far from trivial and has in fact never been illustrated in detail. Heterogeneous materials can be well characterized by the two first factors, while all essential sampling process characteristics can be summarized by combinations of the latter three. We here present simulations based on an experimental design that varies all five factors. Within the framework of the Theory of Sampling, the empirical Total Sampling Error is a function of the fundamental sampling error and the grouping and segregation error interacting with a specific sampling process. We here illustrate absolute and relative sampling variance levels resulting from a wide array of simulated repeated samplings and express the effects by pertinent lot mean estimates and associated Root Mean Squared Errors/sampling variances, covering specific combinations of materials’ heterogeneity and typical sampling procedures as used in current science, technology and industry. Factors, levels and interactions are varied within limits selected to match realistic materials and sampling situations that mimic, e.g., sampling for genetically modified organisms; sampling of geological drill cores; sampling during off-loading 3-dimensional lots (shiploads, railroad cars, truckloads etc.) and scenarios representing a range of industrial manufacturing and production processes. A new simulation facility “SIMSAMP” is presented with selected results designed to show also the wider applicability potential. This contribution furthers a general exposé of all essential effects in the regimen covered by “correct sampling errors”, valid for all types of materials in which non-bias sampling can be achieved.     

On the independence complex of square grids

The enumeration of independent sets of regular graphs is of interest in statistical mechanics, as it corresponds to the solution of hard-particle models. In 2004, it was conjectured by Fendley et al., that for some rectangular grids, with toric boundary conditions, the alternating number of independent sets is extremely simple. More precisely, under a coprimality condition on the sides of the rectangle, the number of independent sets of even and odd cardinality always differ by 1. In physics terms, this means looking at the hard-particle model on these grids at activity −1. This conjecture was recently proved by Jonsson. Here we produce other families of grid graphs, with open or cylindric boundary conditions, for which similar properties hold without any size restriction: the number of independent sets of even and odd cardinality always differ by 0, ±1, or, in the cylindric case, by some power of 2. We show that these results reflect a stronger property of the independence complexes of our graphs. We determine the homotopy type of these complexes using Forman’s discrete Morse theory. We find that these complexes are either contractible, or homotopic to a sphere, or, in the cylindric case, to a wedge of spheres. Finally, we use our enumerative results to determine the spectra of certain transfer matrices describing the hard-particle model on our graphs at activity −1. These results parallel certain conjectures of Fendley et al., proved by Jonsson in the toric case.     

Characterization of bilayer coatings of TiN/ZrN grown using pulsed arc PAPVD

Nitride coatings have been used to increase hardness and to improve the wear and corrosion resistance of structural materials. Coatings of TiN/ZrN were grown on stainless steel substrates using a physical vapour deposition system assisted by pulsed arc plasma (PAPVD). The coatings have been characterized by X-ray diffraction (XRD) in order to identify the present phases of the films, microstrain level generated, crystallite size and the variation of the lattice parameter. The results showed plane orientations (1 1 1) and (2 0 0) in both TiN and ZrN films. Morphology surface analysis of the samples were performed using a scanning probe microscope to characterize the grain size and roughness in the mode of the atomic force microscopy (AFM) hence it was observed that the root-mean-squared (rms) roughness for ZrN is smaller than for TiN. Besides elastic and friction properties of the films were characterized qualitatively, and then, they were compared with those of the substrates by using force modulation microscopy (FMM) and lateral force microscopy (LFM) modes. In addition, an elemental analysis of the samples was realized by means of energy dispersive spectroscopy (EDS). Both, XRD and AFM results are given as a function of the number of shots. Chemical states of the TiN and ZrN films were determined by X-ray photoelectron spectroscopy (XPS).     

Dynamic fuzzy reliability models of degraded hold-down structures for folded solar array

The hold-down structures are of considerable importance to the launch of solar array. Due to the difficulties in obtaining sufficient load specimen, it is imprecise to construct the stress as random variables. Therefore, dynamic fuzzy reliability models are developed in this paper, which resolve the problems in dealing with the interaction between the fuzzy stress process and the stochastic strength process. Even for a deterministic fuzzy stress process, the influences of material statistical properties on reliability can be affected by the level α of fuzzy stress. Meanwhile, the level α relates to investment in the collection of information about the fuzzy stress on hold-down bar. Hence, the models can be used for the economic analysis and optimal design of hold-down bar. Finally, key fuzzy parameters of stress, which have significant influences on both the reliability behavior and the effects of material statistical properties on reliability, are identified and some suggestions for the reliability enhancement of hold-down bar are provided in this paper.     

Mechanochemical Synthesis of Aryl Fluorides by Using Ball Milling and a Piezoelectric Material as the Redox Catalyst

Aryl fluorides are important structural motifs in many pharmaceuticals. Although the Balz–Schiemann reaction provides an entry to aryl fluorides from aryldiazonium tetrafluoroborates, it suffers from drawbacks such as long reaction time, high temperature, toxic solvent, toxic gas release, and low functional group tolerance. Here, we describe a general method for the synthesis of aryl fluorides from aryldiazonium tetrafluoroborates using a piezoelectric material as redox catalyst under ball milling conditions in the presence of Selectfluor. This approach effectively addresses the aforementioned limitations. Furthermore, the piezoelectric material can be recycled multiple times. Mechanistic investigations indicate that this fluorination reaction may proceed via a radical pathway, and Selectfluor plays a dual role as both a source of fluorine and a terminal reductant.     

Direct correlation function of the hard-sphere fluid

Two analytic approximations for the direct correlation function of a hard-sphere fluid are considered. The first follows from a generalization of the Percus–Yevick result in d dimensions, whereas the second arises in the Rational Function Approximation (RFA) method. Both approximations require the equation of state of the hard-sphere fluid as input. The results, derived after use of the Carnahan–Starling and the Padé 4 Ripoll, MS and Tejero, CF. 1995. Molec. Phys., 85: 423[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar],3 Wertheim, MS. 1963. Phys. Rev. Lett., 10: 321 J. Math. Phys. 5, 643 (1964); E. Thiele, J. Chem. Phys. 39, 474 (1963).[Crossref], [Web of Science ®] , [Google Scholar] equations of state in both approaches, are compared with simulation data. The comparison shows that the first approximation is rather accurate in the region inside the core, but inherits the limitation of the Percus–Yevick theory for distances beyond the hard-sphere diameter. On the other hand, the results of the RFA method are also accurate inside the core and capture well the initial part of the tail beyond the hard-sphere diameter, but fail to account for the subsequent oscillations observed in the simulations. Other merits and limitations of the two approaches are reported.     

Pt(II) Complexes with Azolate‐containing Bidentate Chelate: Design,Photophysics, and Application

This review is aimed at the current research progression of a unique class of Pt(II ) metal complexes bearing at least one azolate‐containing bidentate chelate. The azole fragment can link to a neutral heteroaromatic entity or another azole and form bidentate chelates, such as monoanionic 3‐pyridyl‐1H ‐pyrazole and derivatives, dianionic 3,3′‐bi‐1H ‐pyrazole, 3,3′‐(1‐methylethylidene)‐bis‐1H ‐pyrazole, and their analogs. These azole‐containing chelates readily react with a variety of Pt(II) reagents to afford the corresponding bis‐bidentate Pt(II) complexes. Most of them were highly emissive in solution, doped polymer matrix, thin film, and even as crystal or powder, due to the high ligand field strength exerted by these chelates and their high propensity in forming the singular square‐planar architecture and intermolecular aggregates with substantially strengthened Pt⋯Pt interaction, according to their structural design. Therefore, they hold bright prospects in academic research and future optoelectronic applications such as organic light‐emitting diodes.     

基于宏观三角形分区平板壳单元的非线性有限元分析

针对剪切闭锁效应,本文研究了一种基于假设自然应变方法的宏观三角形分区平板壳单元。利用通用有限元软件ABAQUS所提供的用户自定义单元(UEL)和用户自定义材料(UMAT)子程序,本文将宏观三角形分区平板壳单元和基于损伤能释放率的混凝土弹塑性损伤本构模型成功嵌入了ABAQUS的主分析模块。经典试验McNeice双向混凝土板的数值模拟结果表明:宏观三角形分区平板壳单元对于描述板壳结构的非线性损伤行为是行之有效的。