Casimirs and Lax operators from the structure of Lie algebras

This paper uses the structure of the Lie algebras to identify the Casimir invariant functions and Lax operators for matrix Lie groups. A novel mapping is found from the cotangent space to the dual Lie algebra which enables Lax operators to be found. The coordinate equations of motion are given in terms of the structure constants and the Hamiltonian.

Computer-aided analysis of the structure of kinematic chains

Using the link-link incidence matrix to represent a simple-jointed kinematic chain algebraic procedures have been developed to determine its structural characteristics such as the type of freedom of the chain, the number of distinct mechanisms and driving mechanisms that can be derived from the chain. A computer program incorporating these graph theory based procedures has been applied successfully for the structural analysis of several typical chains.

Studies on crystalline complexes involving amino acids. V. The structure of L-serine-L-ascorbic acid

L-Serine-L-ascorbic acid, C3HTNOa. C6HsO6, a 1:1 complex between the amino acid serine and the vitamin ascorbic acid, crystallizes in the orthorhombic space group P2~2~2~ with four formula units in a cell of dimensions a = 5.335(3), b = 8.769(2), c = 25.782 (5) A. The structure was solved by direct methods and refined by full-matrix least squares to an R of 0.036 for 951 observed reflections. Both molecules are neutral in the structure. The conformation of the serine molecule is different from that observed in the crystal structures of L-serine, DL-serine and L-serine monohydrate. The enediol group in the ascorbic acid molecule is planar, whereas significant departures from planarity are observed in the lactone group. The conformation of this molecule is similar to that observed in arginine ascorbate. The unlike molecules aggregate into separate columns in the crystal structure. The columns are held together by hydrogen bonds. Among these, a pair of hydrogen bonds between the enediol group of ascorbic acid and the carboxylate group of serine provides a possible model for a specific interaction between ascorbic acid and a carboxylate ion.

The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows

A series of flames in a turbulent methane/air stratified swirl burner is presented. The degree of stratification and swirl are systematically varied to generate a matrix of experimental conditions, allowing their separate and combined effects to be investigated. Non-swirling flows are considered in the present paper, and the effects of swirl are considered in a companion paper (Part II). A mean equivalence ratio of φ=0.75 is used, with φ for the highest level of stratification spanning 0.375-1.125. The burner features a central bluff-body to aid flame stabilization, and the influence of the induced recirculation zone is also considered. The current work focuses on non-swirling flows where two-component particle image velocimetry (PIV) measurements are sufficient to characterize the main features of the flow field. Scalar data obtained from Rayleigh/Raman/CO laser induced fluorescence (CO-LIF) line measurements at 103μm resolution allow the behavior of key combustion species-CH 4, CO 2, CO, H 2, H 2O and O 2-to be probed within the instantaneous flame front. Simultaneous cross-planar OH-PLIF is used to determine the orientation of the instantaneous flame normal in the scalar measurement window, allowing gradients in temperature and progress variable to be angle corrected to their three dimensional values. The relationship between curvature and flame thickness is investigated using the OH-PLIF images, as well as the effect of stratification on curvature.The main findings are that the behavior of the key combustion species in temperature space is well captured on the mean by laminar flame calculations regardless of the level of stratification. H 2 and CO are significant exceptions, both appearing at elevated levels in the stratified flames. Values for surface density function and by extension thermal scalar dissipation rate are found to be substantially lower than laminar values, as the thickening of the flame due to turbulence dominates the effect of increased strain. These findings hold for both premixed and stratified flames. The current series of flames is proposed as an interesting if challenging set of test cases for existing and emerging turbulent flame models, and data are available on request. © 2012 The Combustion Institute.

A method for studying the structure of low-temperature ionic liquids by XAFS

An in situ method of studying the structure of reactive ionic materials in the solid and liquid states by XAFS is described. These salts have novel catalytic and solvent properties, and the results show that their structure may be studied using transmission XAFS by utilizing pressed disks of BN, graphite, and LiF and is not affected by the sample matrix used.

Montmorillonite (MMT) effect on the structure of poly(oxyethylene) (PEO)-MMT nanocomposites and silica-PEO-MMT hybrid materials

In this work we report the effects of incorporation of variable amounts (0.5-25%w/w) of montmorillonite in poly(oxyethylene) based materials in order to decrease the polymer crystallinity. Two different classes of materials were studied: silica-poly(oxyethylene)-montmorillonite hybrids prepared by the sol-gel route and poly(oxyethylene)-montmorillonite nanocomposites prepared by mixing the dry clay or the clay aqueous suspension into the melt poly(oxyethylene). The effects of monternorillonite loading on the poly(oxyethylene) crystallization control and on the nanostructural features were investigated by X-ray powder diffraction, small-angle X-ray scattering and differential scanning calorimetry. Experimental results show that free montmorillonite layers coexist with open aggregates and tactoids in the poly(oxyethylene)-montmorillonite nanocomposites, with different features depending on the filler proportion and preparation route. The intercalation of polymer chains in montmorillonite galleries markedly hinders the crystallization of the poly(oxyethylene) matrix. For hybrids materials the silica phase favors the exfoliation of montmorillonite tactoids, so that samples are predominantly constituted by dispersed platelets. (c) 2006 Elsevier B.V. All rights reserved.

Specimen specific parameter identification of ovine lumbar intervertebral discs: On the influence of fibre-matrix and fibre-fibre shear interactions.

Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.

Comparison of the capacity of enamel matrix derivative gel and enamel matrix derivative in liquid formulation to adsorb to bone grafting materials.

BACKGROUND The use of an enamel matrix derivative (EMD) has been shown to enhance periodontal regeneration (e.g., formation of root cementum, periodontal ligament, and alveolar bone). However, in certain clinical situations, the use of EMD alone may not be sufficient to prevent flap collapse or provide sufficient stability of the blood clot. Data from clinical and preclinical studies have demonstrated controversial results after application of EMD combined with different types of bone grafting materials in periodontal regenerative procedures. The aim of the present study is to investigate the adsorption properties of enamel matrix proteins to bone grafts after surface coating with either EMD (as a liquid formulation) or EMD (as a gel formulation). METHODS Three different types of grafting materials, including a natural bone mineral (NBM), demineralized freeze-dried bone allograft (DFDBA), or a calcium phosphate (CaP), were coated with either EMD liquid or EMD gel. Samples were analyzed by scanning electron microscopy or transmission electron microscopy (TEM) using an immunostaining assay with gold-conjugated anti-EMD antibody. Total protein adsorption to bone grafting material was quantified using an enzyme-linked immunosorbent assay (ELISA) kit for amelogenin. RESULTS The adsorption of amelogenin to the surface of grafting material varied substantially based on the carrier system used. EMD gel adsorbed less protein to the surface of grafting particles, which easily dissociated from the graft surface after phosphate-buffered saline rinsing. Analyses by TEM revealed that adsorption of amelogenin proteins were significantly farther from the grafting material surface, likely a result of the thick polyglycolic acid gel carrier. ELISA protein quantification assay demonstrated that the combination of EMD liquid + NBM and EMD liquid + DFDBA adsorbed higher amounts of amelogenin than all other treatment modalities. Furthermore, amelogenin proteins delivered by EMD liquid were able to penetrate the porous surface structure of NBM and DFDBA and adsorb to the interior of bone grafting particles. Grafting materials coated with EMD gel adsorbed more frequently to the exterior of grafting particles with little interior penetration. CONCLUSIONS The present study demonstrates a large variability of adsorbed amelogenin to the surface of bone grafting materials when enamel matrix proteins were delivered in either a liquid formulation or gel carrier. Furthermore, differences in amelogenin adsorption were observed among NBM, DFDBA, and biphasic CaP particles. Thus, the potential for a liquid carrier system for EMD, used to coat EMD, may be advantageous for better surface coating.

The effect of zinc and titanium on the structure of calcium-sodium phosphate based glass

An array of different structural probes has been used to define the effect of adding Zn and Ti to a sodium-calcium phosphate glass. X-ray absorption spectroscopy at the Zn K-edge suggests that the Zn atoms occupy mixed (4- and 6-fold) sites within the glass matrix. X-ray diffraction reveals a feature at 2.03 angstrom that develops with the addition of Zn and Ti and is consistent with Zn-O and Ti-O near-neighbour distances. Neutron diffraction is used to resolve two distinct P-O distances and highlights the decrease in P center dot center dot center dot P coordination number from 2.0 to 1.7 as the Ti metal concentration rises, which is attributed to the O/P fraction moving away from the metaphosphate value of 3.0 to 3.1 with the addition of Ti. Other correlations, such as those associated with CaO(x) and NaO(x) polyhedra, remain largely unaffected. These results suggest that the network forming P center dot center dot center dot P correlation is most disrupted, with the disorder parameter rising from 0.07 to 0.10 angstrom with the additional modifiers. Zn appears to be introduced into the network as a direct replacement for Ca and causes no structural variation over the composition range studied.

Productivity growth and the structure of production

In this study, interactions between potential hierarchical value chains existing in the production structure and industry-wise productivity growths are sought. We applied generalized Chenery-Watanabe heuristics for matrix linearity maximization to triangulate the input-output incidence matrix for both Japan and the Republic of Korea, finding the potential directed flow of values spanning the industrial sectors of the basic (disaggregated) industry classifications for both countries. Sector specific productivity growths were measured by way of the Trönquvist index, using the 2000-2005 linked input-output tables for both Japan and Korea.

Assessing the structure of learning outcomes from counselling using the SOLO taxonomy: an exploratory study

Thirty-five clients who had received counselling completed a letter to a friend describing in as much detail as possible what they had learned from counselling. The participants' written responses were analysed and classified using the Structure of Learning Outcomes (SOLO) taxonomy. The results suggested that an expanded SOLO offers a promising and exciting way to view the outcomes of counselling within a learning framework. If the SOLO taxonomy is found to be stable in subsequent research, and clients are easily able to be classified using the taxonomy, then this approach may have implications for the process of counselling. To maximise the learning outcomes, counsellors could use strategies and techniques to enhance their clients' learning.

The structure of selected magnesium carbonate minerals : a near infrared and mid-infrared spectroscopic study

The approach to remove green house gases by pumping liquid CO2 several kilometres below the ground implies that many carbonate containing minerals will be formed. Among these minerals the formation of dypingite and artinite are possible; thus necessitating a study of such minerals. Two carbonate bearing minerals dypingite and artinite with a hydrotalcite related formulae have been characterised by a combination of infrared and near-infrared spectroscopy. The infrared spectra of both minerals are characterised by OH and water stretching vibrations. Both the first and second fundamental overtones of these bands are observed in the NIR spectra in the 7030 to 7235 cm-1 and 10490 to 10570 cm-1. Intense (CO3)2- symmetric and antisymmetric stretching vibrations confirm the distortion of the carbonate anion. The position of the water bending vibration indicates water is strongly hydrogen bonded to the carbonate anion in the mineral structure. Split NIR bands at around 8675 and 11100 cm-1 indicates that some replacement of magnesium ions by ferrous ions in the mineral structure has occurred.

The structure of the copper(II) complex with 4,5-dichlorophthalic acid: The 1:1 complex 'adduct' salt trans-tetraaqua(2-carboxy-4,5-dichlorobenzoato)(4,5-dichlorobenzene-1,2-dicarboxylic acid)copper(II) 2-carboxy-4,5-dichlorobenzoate

The unusual (1:1) complex ‘adduct’ salt of copper(II) with 4,5-dichlorophthalic acid (H2DCPA), having formula [Cu(H2O)4(C8H3Cl2O4) (C8H4Cl2O4)] . (C8H3Cl2O4) has been synthesized and characterized using single-crystal X-ray diffraction. Crystals are monoclinic, space group P21/c, with Z = 4 in a cell with dimensions a = 20.1376(7), b =12.8408(4) c = 12.1910(4) Å, β = 105.509(4)o. The complex is based on discrete tetragonally distorted octahedral [CuO6] coordination centres with the four water ligands occupying the square planar sites [Cu-O, 1.962(4)-1.987(4) Å] and the monodentate carboxyl-O donors of two DCPA ligand species in the axial sites. The first of these bonds [Cu-O, 2.341(4) Å] is with an oxygen of a HDCPA monoanion, the second with an oxygen of a H2DCPA acid species [Cu-O, 2.418(4) Å]. The un-coordinated ‘adduct’ molecule is a HDCPA counter anion which is strongly hydrogen-bonded to the coordinated H2DCPA ligand [O… O, 2.503(6) Å] while a number of peripheral intra- and intermolecular hydrogen-bonding interactions give a two-dimensional network structure.