116 resultados para Geometry of numbers
Resumo:
Cobalt (11) phthalocyanine (CoPc) molecules have been encapsulated within the supercage of zeolite-Y. The square-planar complex, being larger than the almost spherical cage, is forced to adopt a distorted geometry on encapsulation. A comparative spectroscopic and magnetic investigation of CoPc encapsulated in zeolite-Y and in the unencapsulated state is reported. These results supported by molecular modeling have been used to understand the nature and extent of the loss of planarity of CoPc on encapsulation. The encapsulated molecule is shown to be the trans-diprotonated species in which the center of inversion is lost due to distortions required to accommodate the square complex within the zeolite. Encapsulation also leads to an enhancement of the magnetic moment of the CoPc. This is shown to be a consequence of the nonplanar geometry of the encapsulated molecule resulting in an excited high-spin state being thermally accessible.
Resumo:
Stochastic modelling is a useful way of simulating complex hard-rock aquifers as hydrological properties (permeability, porosity etc.) can be described using random variables with known statistics. However, very few studies have assessed the influence of topological uncertainty (i.e. the variability of thickness of conductive zones in the aquifer), probably because it is not easy to retrieve accurate statistics of the aquifer geometry, especially in hard rock context. In this paper, we assessed the potential of using geophysical surveys to describe the geometry of a hard rock-aquifer in a stochastic modelling framework. The study site was a small experimental watershed in South India, where the aquifer consisted of a clayey to loamy-sandy zone (regolith) underlain by a conductive fissured rock layer (protolith) and the unweathered gneiss (bedrock) at the bottom. The spatial variability of the thickness of the regolith and fissured layers was estimated by electrical resistivity tomography (ERT) profiles, which were performed along a few cross sections in the watershed. For stochastic analysis using Monte Carlo simulation, the generated random layer thickness was made conditional to the available data from the geophysics. In order to simulate steady state flow in the irregular domain with variable geometry, we used an isoparametric finite element method to discretize the flow equation over an unstructured grid with irregular hexahedral elements. The results indicated that the spatial variability of the layer thickness had a significant effect on reducing the simulated effective steady seepage flux and that using the conditional simulations reduced the uncertainty of the simulated seepage flux. As a conclusion, combining information on the aquifer geometry obtained from geophysical surveys with stochastic modelling is a promising methodology to improve the simulation of groundwater flow in complex hard-rock aquifers. (C) 2013 Elsevier B.V. All rights reserved.
Resumo:
Fracture toughness measurements at the small scale have gained prominence over the years due to the continuing miniaturization of structural systems. Measurements carried out on bulk materials cannot be extrapolated to smaller length scales either due to the complexity of the microstructure or due to the size and geometric effect. Many new geometries have been proposed for fracture property measurements at small-length scales depending on the material behaviour and the type of device used in service. In situ testing provides the necessary environment to observe fracture at these length scales so as to determine the actual failure mechanism in these systems. In this paper, several improvements are incorporated to a previously proposed geometry of bending a doubly clamped beam for fracture toughness measurements. Both monotonic and cyclic loading conditions have been imposed on the beam to study R-curve and fatigue effects. In addition to the advantages that in situ SEM-based testing offers in such tests, FEM has been used as a simulation tool to replace cumbersome and expensive experiments to optimize the geometry. A description of all the improvements made to this specific geometry of clamped beam bending to make a variety of fracture property measurements is given in this paper.
Resumo:
Elucidation of the detailed structural features and sequence requirements for iv helices of various lengths could be very important in understanding secondary structure formation in proteins and, hence. in the protein folding mechanism. An algorithm to characterize the geometry of an alpha helix from its C-alpha coordinates has been developed and used to analyze the structures of long cu helices (number of residues greater than or equal to 25) found in globular proteins, the crystal structure coordinates of which are available from the Brookhaven Protein Data Bank, Ail long a helices can be unambiguously characterized as belonging to one of three classes: linear, curved, or kinked, with a majority being curved. Analysis of the sequences of these helices reveals that the long alpha helices have unique sequence characteristics that distinguish them from the short alpha helices in globular proteins, The distribution and statistical propensities of individual amino acids to occur in long alpha heices are different from those found in short alpha helices, with amino acids having longer side chains and/or having a greater number of functional groups occurring more frequently in these helices, The sequences of the long alpha helices can be correlated with their gross structural features, i.e., whether they are curved, linear, or kinked, and in case of the curved helices, with their curvature.
Resumo:
[NiL2(NCS)2] (1) [L = 2-(aminomethyl)pyridine], [NiL02(NCS)2] (2) [(L0) = 2-(2-aminoethyl)pyridine and [NiL00 2(NCS)2] (3) [L00 = 2-(2-methylaminoethyl)pyridine] have been synthesized from solution. All the complexes possess trans geometry as is evident from solid state UV–Vis spectral study and X-ray single crystal structure analysis of complex 2 unambiguously proves trans geometry of the species.
Resumo:
The wedge shape is a fairly common cross-section found in many non-axisymmetric components used in machines, aircraft, ships and automobiles. If such components are forged between two mutually inclined dies the metal displaced by the dies flows into the converging as well as into the diverging channels created by the inclined dies. The extent of each type of flow (convergent/divergent) depends on the die—material interface friction and the included die angle. Given the initial cross-section, the length as well as the exact geometry of the forged cross-section are therefore uniquely determined by these parameters. In this paper a simple stress analysis is used to predict changes in the geometry of a wedge undergoing compression between inclined platens. The flow in directions normal to the cross-section is assumed to be negligible. Experiments carried out using wedge-shaped lead billets show that, knowing the interface friction and as long as the deformation is not too large, the dimensional changes in the wedge can be predicted with reasonable accuracy. The predicted flow behaviour of metal for a wide range of die angles and interface friction is presented: these characteristics can be used by the die designer to choose the die lubricant (only) if the die angle is specified and to choose both of these parameters if there is no restriction on the exact die angle. The present work shows that the length of a wedge undergoing compression is highly sensitive to die—material interface friction. Thus in a situation where the top and bottom dies are inclined to each other, a wedge made of the material to be forged could be put between the dies and then compressed, whereupon the length of the compressed wedge — given the degree of compression — affords an estimate of the die—material interface friction.
Resumo:
Using computer modeling of three-dimensional structures and structural information available on the crystal structures of HIV-1 protease, we investigated the structural effects of mutations, in treatment-naive and treatment-exposed individuals from India and postulated mechanisms of resistance in clade C variants. A large number of models (14) have been generated by computational mutation of the available crystal structures of drug bound proteases. Localized energy minimization was carried out in and around the sites of mutation in order to optimize the geometry of interactions present. Most of the mutations result in structural differences at the flap that favors the semiopen state of the enzyme. Some of the mutations were also found to confer resistance by affecting the geometry of the active site. The E35D mutation affects the flap structure in clade B strains and E35N and E35K mutation, seen in our modeled strains, have a more profound effect. Common polymorphisms at positions 36 and 63 in clade C also affected flap structure. Apart from a few other residues Gln-58, Asn-83, Asn-88, and Gln-92 and their interactions are important for the transition from the closed to the open state. Development of protease inhibitors by structure-based design requires investigation of mechanisms operative for clade C to improve the efficacy of therapy.
Resumo:
The unsteady pseudo plane motions have been investigated in which each point of the parallel planes is subjected to non-torsional oscillations in their own plane and at any given instant the streamlines are concentric circles. Exact solutions are obtained and the form of the curve , the locus of the centers of these concentric circles, is discussed. The existence of three infinite sets of exact solutions, for the flow in the geometry of an orthogonal rheometer in which the above non-torsional oscillations are superposed on the disks, is established. Three cases arise according to whether is greater than, equal to or less than , where is angular velocity of the basic rotation and is the frequency of the superposed oscillations. For a symmetric solution of the flow these solutions reduce to a single unique solution. The nature of the curve is illustrated graphically by considering an example of the flow between coaxial rotating disks.
Resumo:
Crystals of C I4HsN40 are monoclinic, space group P21, Unit-cell constants are a = 13.241(4), b = 7.446 (2), c = 6.436 (2)/A, B= 93.23 (2) °. V= 633.5 /A3, Z = 2, Dob s = 1.30 (flotation), Dealt = 1.300 Mg m -3 and #(Cu Ka) = 0.72 mm -1. The structure, solved by direct methods, has been refined to an R value of 3.5% using 1245 intensity measurements. The combined effect of electron-withdrawing and –donating substituents on the geometry of the cyclopropane ring is discussed.
Resumo:
The complexing ability of a new series of ligands, β-N-arylimine hydrazones, toward Ni (II) and Cu (II) ions has been studied. The isolated complexes are characterised on the basis of elemental analysis, spectroscopic methods and magnetic susceptibility measurements. The ligands are notentially bidentate in character coordinating to divalent metal ions through the N1 and N5 nitrogens. Square planar geometry of the metal ions is suggested on the basis of experimental evidence.
Resumo:
The crystal and molecular structures of C ,,H,IN302 (I) and C14HIsN302 (II) have been determined by direct methods using three-dimensional X-ray diffractometer data. Crystals of (I) are orthorhombic, space group Pna21, with a = 14.662(6), b = 10.492(5), c = 7.375 (3)A, Z = 4, V = 1134.5 A 3, D O = 1.25 (by flotation), D e = 1.269 Mgm -a, g(MoKa) = 0.085 mm -1. Crystals of (II) are monoclinic, space group P21/a, with a = 7.886 (5), b = 22.011 (8), c = 8.100 (3) A, fl = 103.12 (5) °, Z = 4, V = 1369.2 A 3, D O = 1.23 (by flotation), D e = 1.255 Mg m -3, g(Mo Kct) = 0.080 mm -1. Least-squares full-matrix refinement based on 782 (I) and 1400 independent reflections (II) converged at R = 0.040 (I) and 0.042 (II). The effect of electron-withdrawing substituents on the geometry of the cyclopropane ring is discussed.
Resumo:
CI1H19N4OIIP2.Na+.TH2 O, Mr = 594.08, is orthorhombic, space group P21212 l, with a = 6.946 (2), b = 12.503 (4), c = 28.264 (8)/k, U = 2454.6 A, a, D x = 1.61 Mg m -a, Z = 4, ~t(CuKa) = 2.612 mm -1, F(000) = 1244. Final R = 0.101 for 1454 observed reflections. The cytosine base is in the anti conformation with respect to the sugar (ZCN = 62"60) . The ribose exhibits an uncommon C(l')exo-C(2')endo puckering. The pyrophosphate has a characteristic staggered geometry. The conformation about P(2)-O(7') is trans (-103.4°). This makes CDPethanolamine more extended compared to the folded geometry of CDP-choline, which has a gauche conformation (71.3 o). The molecular interactions in the extended crystal structure, however, are similar to those found in CDP-choline, with the CMP-5' portions tightly bound by metal ligation and the phosphorylethanolamine parts only loosely held by water molecules.
Resumo:
L-Lysine d-pantothenate, a 1:1 amino acid-vitamin complex, crystallizes in the monoclinic space group P21 with Image Full-size image (1K) .The structure has been solved by direct methods and refined to an R value of 0.053 for 1868 observed reflections. The zwitterionic positively charged lysine molecules in the structure assume the sterically most favourable conformation with an all-trans side chain trans to the α-carboxylate group. The pantothenate anion has a somewhat folded conformation stabilised by an intramolecular bifurcated hydrogen bond. The unlike molecules aggregate into separate alternating layers. The molecules in the lysine layers form a head-to-tail sequence parallel to the a-axis. The interactions which hold the adjacent layers together include those between the side chain amino group of lysine and the carboxylate group in the pantothenate anion. The geometry of these interactions is such that each carboxylate group is sandwiched between two amino groups in a periodic arrangement of alternating carboxylate and amino groups.
Resumo:
NICOTINAMIDE adenine dinucleotide (NAD) has a fundamental role in metabolic processes as an electron transport molecule. Although its chemical structure was elucidated1 in 1934, its detailed conformation remains still to be established in spite of numerous physicochemical applications2. NAD analogues with a variety of substitutions on the bases are known to retain considerable activity of the natural coenzyme as long as the pyrophosphate diester group has been retained3,4. The geometry of this backbone moiety is therefore indispensable to our understanding of the conformation and function of the coenzyme. We have so far no experimental evidence on this in NAD or any other nucleotide coenzyme molecule. X-ray studies have been possible only on those analogues5,6 where the nicotinamide and adenine rings are linked by a trimethylene bridge. The results are conflicting and it is difficult to use them to provide a structural basis for the NAD molecule itself, particularly as the phosphate backbone is absent from these analogues.
Resumo:
Vibration problem of generally orthotropic plates with particular attention to plates of skew geometry is studied. The formulation is based on orthotropic plate theory with arbitrary orientation of the principal axes of orthotropy. The boundary conditions considered are combinations of simply supported, clamped, and free-edge conditions. Approximate solution for frequencies and modes is obtained by the Ritz method using products of appropriate beam characteristic functions as admissible functions. The variation of frequencies and modes with orientation of the axes of orthotropy is examined for different skew angles and boundary conditions. Features such as "crossings" and "quasi-degeneracies" of the frequency curves are found to occur with variation of the orientation of the axes of orthotropy for a given geometry of the skew plate. It is also found that for each combination of skew angle and side ratio, a particular orientation of the axes gives the highest value for the fundamental frequency of the plate.