Structures of Pd(CN)2and Pt(CN)2: intrinsically nanocrystalline materials?

Analysis and modeling of X-ray and neutron Bragg and total diffraction data show that the compounds referred to in the literature as “Pd(CN)2”and“Pt(CN)2” are nanocrystalline materials containing of small sheets of vertex-sharing square-planar M(CN)4 units, layered in a disordered manner with an intersheet separation of 3.44 A at 300 K. The small size of the crystallites means that the sheets’ edges form a significant fraction of each material. The Pd(CN)2 nanocrystallites studied using total neutron diffraction are terminated by water and the Pt(CN)2 nanocrystallites by ammonia, in place of half of the terminal cyanide groups, thus maintaining charge neutrality. The neutron samples contain sheets of approximate dimensions 30 A x 30 A. For sheets of the size we describe, our structural models predict compositions of Pd(CN)2-xH2O and Pt(CN)2-yNH3 (x = y = 0.29). These values are in good agreement with those obtained from total neutron diffraction and thermal analysis, and are also supported by infrared and Raman spectroscopy measurements. It is also possible to prepare related compounds Pd(CN)2-pNH3 and Pt(CN)2-qH2O, in which the terminating groups are exchanged. Additional samples showing sheet sizes in the range 10 A x 10 A (y = 0.67) to 80 A x 80 A (p = q = 0.12), as determined by X-ray diffraction, have been prepared. The related mixed-metal phase, Pd1/2Pt1/2(CN)2-qH2O(q = 0.50), is also nanocrystalline (sheet size 15 A x 15 A). In all cases, the interiors of the sheets are isostructural with those found in Ni(CN)2. Removal of the final traces of water or ammonia by heating results in decomposition of the compounds to Pd and Pt metal, or in the case of the mixed-metal cyanide, the alloy, Pd1/2Pt1/2, making it impossible to prepare the simple cyanides, Pd(CN)2, Pt(CN)2 or Pd1/2Pt1/2(CN)2, by this method.

Conformational analysis of oriented non-crystalline polymers using wide angle X-ray scattering

A procedure is presented for obtaining conformational parameters from oriented but non-crystalline polymers. This is achieved by comparison of the experimental wide angle X-ray scattering with that calculated from models but in such a way that foreknowledge of the orientation distribution function is not required. X-ray scattering intensity values for glassy isotactic poly(methylmethacrylate) are analysed by these techniques. The method could be usefully applied to other oriented molecular systems such as liquid crystalline materials.

Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the $p$-version

Plane wave discontinuous Galerkin (PWDG) methods are a class of Trefftz-type methods for the spatial discretization of boundary value problems for the Helmholtz operator $-\Delta-\omega^2$, $\omega>0$. They include the so-called ultra weak variational formulation from [O. Cessenat and B. Després, SIAM J. Numer. Anal., 35 (1998), pp. 255–299]. This paper is concerned with the a priori convergence analysis of PWDG in the case of $p$-refinement, that is, the study of the asymptotic behavior of relevant error norms as the number of plane wave directions in the local trial spaces is increased. For convex domains in two space dimensions, we derive convergence rates, employing mesh skeleton-based norms, duality techniques from [P. Monk and D. Wang, Comput. Methods Appl. Mech. Engrg., 175 (1999), pp. 121–136], and plane wave approximation theory.

Error analysis of Trefftz-discontinuous Galerkin methods for the time-harmonic Maxwell equations

In this paper, we extend to the time-harmonic Maxwell equations the p-version analysis technique developed in [R. Hiptmair, A. Moiola and I. Perugia, Plane wave discontinuous Galerkin methods for the 2D Helmholtz equation: analysis of the p-version, SIAM J. Numer. Anal., 49 (2011), 264-284] for Trefftz-discontinuous Galerkin approximations of the Helmholtz problem. While error estimates in a mesh-skeleton norm are derived parallel to the Helmholtz case, the derivation of estimates in a mesh-independent norm requires new twists in the duality argument. The particular case where the local Trefftz approximation spaces are built of vector-valued plane wave functions is considered, and convergence rates are derived.

Healable supramolecular polymeric materials

This chapter details the design, synthesis and evaluation techniques required to produce healable supramolecular materials. Key developments in supramolecular polymer chemistry that laid down the design concepts necessary to produce responsive materials are summarized. Subsequently, select examples from the literature concerning the synthesis and analysis of healable materials containing hydrogen bonding, π−π stacking and metal–ligand interactions are evaluated. The last section describes the most recent efforts to produce healable gels for niche applications, including electrolytes and tissue engineering scaffolds. The chapter also describes the design criteria and production of nano-composite materials that exhibit dramatically increased strength compared to previous generations of supramolecular materials, whilst still retaining the key healing characteristics.

Developing construction professional services in the international market: SWOT analysis of China

Construction professional services (CPSs), such as architecture, engineering, and consultancy, are not only high value-added profit centers in their own right but also have a knock-on effect on other businesses, such as construction and the export of materials and machinery. Arguably, competition in the international construction market has shifted to these knowledge-intensive CPS areas. Yet CPSs represent a research frontier that has received scant attention. This research aims to enrich the body of knowledge on CPSs by examining strengths, weaknesses, opportunities, and threats (SWOT) of Chinese CPSs (CCPSs) in the international context. It does so by triangulating theories with quantitative and qualitative data gleaned from yearbooks, annual reports, interviews, seminars, and interactions with managers in major CCPS companies. It is found that CCPSs present both strengths and weaknesses in talents, administration systems, and development strategies in dealing with the external opportunities and threats brought about by globalization and market evolution. Low price, which has helped the Chinese construction business to succeed in the international market, is also a major CCPS strength. An opportunity for CCPSs is the relatively strong delivery capability possessed by Chinese contractors; by partnering with them CCPSs can better establish themselves in the international arena. This is probably the first ever comprehensive study on the performance of CCPSs in the international marketplace. The research is conducted at an opportune time, particularly when the world is witnessing the burgeoning force of Chinese businesses in many areas including manufacturing, construction, and, potentially, professional services. It adds new insights to the knowledge body of CPSs and provides valuable references to other countries faced with the challenge of developing CPS business efficiently in the international market.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Developing construction professional services in the international market: a SWOT analysis of China

In contrast to their bustling construction counterparts, Chinese construction professional services (CPS) such as architecture, engineering, and consultancy, seem still to be stagnant in the international market. CPS are not only high value-added profit centers in their own right, but also have a knock-on effect on subsequent businesses such as construction, and the export of materials and machinery. Arguably, competition in the international construction market has shifted to knowledge-intensive CPS. Yet,CPS represent a research area that has been paid scant attention. This research aims to add to the body of knowledge of CPS by examining strengths, weaknesses, opportunities, and threats (SWOT) of Chinese CPS (CCPS) in the international context. It does so by triangulating theories with quantitative and qualitative data gleaned from yearbooks, annual reports, interviews, seminars, and interactions with managers in major CCPS companies. It is found that CCPS present both strengths and weaknesses in talents, administration systems, and development strategies in dealing with the external opportunities and threats brought about by globalization and market evolvement. Low price, which has helped the Chinese construction business to succeed in the international market, is also a CCPS major strength. An opportunity for CCPS is the relatively strong delivery capability possessed by Chinese contractors. By partnering with them CCPS can better edge into the international arena. This is probably the first ever comprehensive study in investigating the performance of CCPS in the international market. The research is also timely, particularly when the world is witnessing the burgeoning force of Chinese businesses in many areas including manufacturing, construction, and potentially, professional services.

Analysis of DNA polymorphism in ancient barley herbarium material: validation of the KASP SNP genotyping platform

The availability of crop specimens archived in herbaria and old seed collections represent valuable resources for the analysis of plant genetic diversity and crop domestication. The ability to extract ancient DNA (aDNA) from such samples has recently allowed molecular genetic investigations to be undertaken in ancient materials. While analyses of aDNA initially focused on the use of markers which occur in multiple copies such as the internal transcribed spacer region (ITS) within ribosomal DNA and those requiring amplification of short DNA regions of variable length such as simple sequence repeats (SSRs), emphasis is now moving towards the genotyping of single nucleotide polymorphisms (SNPs), traditionally undertaken in aDNA by Sanger sequencing. Here, using a panel of barley aDNA samples previously surveyed by Sanger sequencing for putative causative SNPs within the flowering-time gene PPD-H1, we assess the utility of the Kompetitive Allele Specific PCR (KASP) genotyping platform for aDNA analysis. We find KASP to out-perform Sanger sequencing in the genotyping of aDNA samples (78% versus 61% success, respectively), as well as being robust to contamination. The small template size (≥46 bp) and one-step, closed-tube amplification/genotyping process make this platform ideally suited to the genotypic analysis of aDNA, a process which is often hampered by template DNA degradation and sample cross-contamination. Such attributes, as well as its flexibility of use and relatively low cost, make KASP particularly relevant to the genetic analysis of aDNA samples. Furthermore, KASP provides a common platform for the genotyping and analysis of corresponding SNPs in ancient, landrace and modern plant materials. The extended haplotype analysis of PPD-H1 undertaken here (allelic variation at which is thought to be important for the spread of domestication and local adaptation) provides further resolution to the previously identified geographic cline of flowering-time allele distribution, illustrating how KASP can be used to aid genetic analyses of aDNA from plant species. We further demonstrate the utility of KASP by genotyping ten additional genetic markers diagnostic for morphological traits in barley, shedding light on the phenotypic traits, alleles and allele combinations present in these unviable ancient specimens, as well as their geographic distributions.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilization waves on eggs

Wave solutions to a mechanochemical model for cytoskeletal activity are studied and the results applied to the waves of chemical and mechanical activity that sweep over an egg shortly after fertilization. The model takes into account the calcium-controlled presence of actively contractile units in the cytoplasm, and consists of a viscoelastic force equilibrium equation and a conservation equation for calcium. Using piecewise linear caricatures, we obtain analytic solutions for travelling waves on a strip and demonstrate uiat the full nonlinear system behaves as predicted by the analytic solutions. The equations are solved on a sphere and the numerical results are similar to the analytic solutions. We indicate how the speed of the waves can be used as a diagnostic tool with which the chemical reactivity of the egg surface can be measured.

Supramolecular materials for inkjet printing: self-assembling polymer networks

Electronically complementary, low molecular weight polymers that self-assemble through tuneable π-π stacking interactions to form extended supramolecular polymer networks have been developed for inkjet printing applications and successfully deposited using three different printing techniques. Sequential overprinting of the complementary components results in supramolecular network formation through complexation of π-electron rich pyrenyl or perylenyl chain-ends in one component with π-electron deficient naphthalene diimide residues in a chain-folding polyimide. The complementary π-π stacked polymer blends generate strongly coloured materials as a result of charge-transfer absorptions in the visible spectrum, potentially negating the need for pigments or dyes in the ink formulation. Indeed, the final colour of the deposited material can be tailored by changing varying the end-groups of the π electron rich polymer component. Piezoelectric printing techniques were employed in a proof of concept study to allow characterisation of the materials deposited, and a thermal inkjet printer adapted with imaging software enabled a detailed analysis of the ink-drops as they formed, and of their physical properties. Finally, continuous inkjet printing allowed greater volumes of material to be deposited, on a variety of different substrate surfaces, and demonstrated the utility and versatility of this novel type of ink for industrial applications.

A Posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator.

On aposteriori error analysis of dG schemes approximating hyperbolic conservation laws

This contribution is concerned with aposteriori error analysis of discontinuous Galerkin (dG) schemes approximating hyperbolic conservation laws. In the scalar case the aposteriori analysis is based on the L1 contraction property and the doubling of variables technique. In the system case the appropriate stability framework is in L2, based on relative entropies. It is only applicable if one of the solutions, which are compared to each other, is Lipschitz. For dG schemes approximating hyperbolic conservation laws neither the entropy solution nor the numerical solution need to be Lipschitz. We explain how this obstacle can be overcome using a reconstruction approach which leads to an aposteriori error estimate.