Stability of spatially developing boundary layers in pressure gradients

A new formulation of the stability of boundary-layer flows in pressure gradients is presented, taking into account the spatial development of the flow and utilizing a special coordinate transformation. The formulation assumes that disturbance wavelength and eigenfunction vary downstream no more rapidly than the boundary-layer thickness, and includes all terms nominally of order R(-1) in the boundary-layer Reynolds number R. In Blasius flow, the present approach is consistent with that of Bertolotti et al. (1992) to O(R(-1)) but simpler (i.e. has fewer terms), and may best be seen as providing a parametric differential equation which can be solved without having to march in space. The computed neutral boundaries depend strongly on distance from the surface, but the one corresponding to the inner maximum of the streamwise velocity perturbation happens to be close to the parallel flow (Orr-Sommerfeld) boundary. For this quantity, solutions for the Falkner-Skan flows show the effects of spatial growth to be striking only in the presence of strong adverse pressure gradients. As a rational analysis to O(R(-1)) demands inclusion of higher-order corrections on the mean flow, an illustrative calculation of one such correction, due to the displacement effect of the boundary layer, is made, and shown to have a significant destabilizing influence on the stability boundary in strong adverse pressure gradients. The effect of non-parallelism on the growth of relatively high frequencies can be significant at low Reynolds numbers, but is marginal in other cases. As an extension of the present approach, a method of dealing with non-similar flows is also presented and illustrated. However, inherent in the transformation underlying the present approach is a lower-order non-parallel theory, which is obtained by dropping all terms of nominal order R(-1) except those required for obtaining the lowest-order solution in the critical and wall layers. It is shown that a reduced Orr-Sommerfeld equation (in transformed coordinates) already contains the major effects of non-parallelism.

Structural evolution and electronic properties of La1+xSr2-xMn2O7

A detailed study of the layered manganite La1+xSr2-xMn2O7 has been performed, establishing that within the composition range 0.1 less than or equal to x less than or equal to 0.45 the phases crystallize in the I4/mmm space group. The evolution of structural parameters with x: in this composition range has been followed using a novel application of an existing program for the Rietveld analysis of powder diffraction data. The structure, a familiar intergrowth of rock-salt (La,Sr)O slabs and double perovskite (La,Sr)(2)Mn2O6 units, is characterized by a reluctance to deform the latter. This manifests as a ''pumping'' of the larger Sr-II ion into the 12-coordinate site of the structure as x is increased. We report these features of the structure as well as electrical transport and magnetic properties, in light of recent observations of giant, negative magnetoresistance in these systems.

Crystal structure of nonadentate tricompartmental ligand derived from pyridine-2,6-dicarboxylic acid: Spectroscopic, electrochemical and thermal investigations of its transition metal(II) complexes

The coordinating behavior of a new dihydrazone ligand, 2,6-bis(3-methoxysalicylidene) hydrazinocarbonyl]pyridine towards manganese(II), cobalt(II), nickel(II), copper(II), zinc(II) and cadmium(II) has been described. The metal complexes were characterized by magnetic moments, conductivity measurements, spectral (IR, NMR, UV-Vis, FAB-Mass and EPR) and thermal studies. The ligand crystallizes in triclinic system, space group P-1, with alpha=98.491(10)degrees, beta=110.820(10)degrees and gamma=92.228(10)degrees. The cell dimensions are a=10.196(7)angstrom, b=10.814(7)angstrom, c=10.017(7)angstrom, Z=2 and V=1117.4(12). IR spectral studies reveal the nonadentate behavior of the ligand. All the complexes are neutral in nature and possess six-coordinate geometry around each metal center. The X-band EPR spectra of copper(II) complex at both room temperature and liquid nitrogen temperature showed unresolved broad signals with g(iso) = 2.106. Cyclic voltametric studies of copper(II) complex at different scan rates reveal that all the reaction occurring are irreversible. (C) 2011 Elsevier B.V. All rights reserved.

The Equations of Equilibrium in Orthogonal Curvilinear Reference Coordinates

Analytical solutions to problems in finite elasticity are most often derived using the semi-inverse approach along with the spatial form of the equations of motion involving the Cauchy stress tensor. This procedure is somewhat indirect since the spatial equations involve derivatives with respect to spatial coordinates while the unknown functions are in terms of material coordinates, thus necessitating the use of the chain rule. In this classroom note, we derive compact expressions for the components of the divergence, with respect to orthogonal material coordinates, of the first Piola-Kirchhoff stress tensor. The spatial coordinate system is also assumed to be an orthogonal curvilinear one, although, not necessarily of the same type as the material coordinate system. We show by means of some example applications how analytical solutions can be derived more directly using the derived results.

Mean first passage time approach to the problem of optimal barrier subdivision for Kramer's escape rate

We consider the effect of subdividing the potential barrier along the reaction coordinate on Kramer's escape rate for a model potential, Using the known supersymmetric potential approach, we show the existence of an optimal number of subdivisions that maximizes the rate, We cast the problem as a mean first passage time problem of a biased random walker and obtain equivalent results, We briefly summarize the results of our investigation on the increase in the escape rate by placing a blow-torch in the unstable part of one of the potential wells. (C) 1999 Elsevier Science B.V. All rights reserved.

Minimal set of generators for the derivation module of certain monomial curves

Let K be a field of characteristic zero and let m(0),..., m(e-1) be a sequence of positive integers. Let C be an algebroid monomial curve in the affine e-space A(K)(e) defined parametrically by X-0 = T-m0,..., Xe-1 = Tme-1 and let A be the coordinate ring of C. In this paper, we assume that some e - 1 terms of m(0),..., m(e-1) form an arithmetic sequence and construct a minimal set of generators for the derivation module Der(K)(A) of A and write an explicit formula for mu (Der(K)(A)).

Studies on the Effect of Li2SO4 on the Structure of Lithium Borate Glasses

Thermal and spectroscopic investigations have been carried out on a number of glasses with a wide range of compositions in the pseudoternary glass system, Li2SO4-Li2O-B2O3, to understand the role of sulfate ions in modifying the borate glass structure. Both nuclear magnetic resonance (NMR) and infrared (IR) spectroscopic results indicate that four-coordinate boron atoms are retained in the glass structure to a greater extent in sulfate-containing glasses than in pure lithium borate glasses. There seems to be some evidence for the existence of sulfoborate-type units in Raman spectra in the region of 800-960 cm(-1). These conclusions are supported by the observed behavior of glass transition temperatures and molar volumes. The possibility of formation of sulfoborate-type units is discussed from bonding and thermodynamic points of view.

Molecular self-assembly of cadmium-triazolate complexes via hydrogen bonding: Synthesis, structures and photoluminescent properties

Two new cadmium coordination polymers namely Cd(HAmTrz-COO)(4)(NH4+)(2)] 1; and Cd(HAmTrz)(2)I-2](n) 2; (HAmTrz-COOH = 3-amino-1,2,4-triazole-5-carboxylic acid), have been prepared based on HAmTrz-COOH as ligand. The crystal structures of 1 and 2 have been determined by single-crystal X-ray diffraction technique. In coordination-complex 1 four triazole ligands coordinate via N1 nitrogen leading to a tetrahedral geometry around cadmium ion, while in 2 the ligand prefers to coordinate to the metal in a bidentate bridging mode. The structures of both the coordination polymers can be envisaged as 3D hydrogen bonded networks. Thermogravimetric analysis shows that 2 is more stable than 1 owing to different coordination numbers of cadmium atoms. Photoluminescence properties of both the compounds have been investigated in the solid state. (C) 2011 Elsevier B.V. All rights reserved.

An interesting feature of the vapour pressure curve

There exists a maximum in the products of the saturation properties such as T(p(c) - p) and p(T-c - T) in the vapour-liquid coexistence region for all liquids. The magnitudes of those maxima on the reduced coordinate system provide an insight to the molecular complexity of the liquid. It is shown that the gradients of the vapour pressure curve at temperatures where those maxima occur are directly given by simple relations involving the reduced pressures and temperatures at that point. A linear relation between the maximum values of those products of the form [p(r)(1 - T-r)](max) = 0.2095 - 0.2415 [T-r(1 - p(r))](max) has been found based on a study of 55 liquids ranging from non-polar monatomic cryogenic liquids to polar high boiling point liquids.

Training-Embedded, Single-Symbol ML-Decodable, Distributed STBCs for Relay Networks

Recently, a special class of complex designs called Training-Embedded Complex Orthogonal Designs (TE-CODs) has been introduced to construct single-symbol Maximum Likelihood decodable (SSD) distributed space-time block codes (DSTBCs) for two-hop wireless relay networks using the amplify and forward protocol. However, to implement DSTBCs from square TE-CODs, the overhead due to the transmission of training symbols becomes prohibitively large as the number of relays increase. In this paper, we propose TE-Coordinate Interleaved Orthogonal Designs (TE-CIODs) to construct SSD DSTBCs. Exploiting the block diagonal structure of TE-CIODs, we show that the overhead due to the transmission of training symbols to implement DSTBCs from TE-CIODs is smaller than that for TE-CODs. We also show that DSTBCs from TE-CIODs offer higher rate than those from TE-CODs for identical number of relays while maintaining the SSD and full-diversity properties.

Performance analysis of single-symbol maximum likelihood decodable linear STBCs

Performance of space-time block codes can be improved using the coordinate interleaving of the input symbols from rotated M-ary phase shift keying (MPSK) and M-ary quadrature amplitude modulation (MQAM) constellations. This paper is on the performance analysis of coordinate-interleaved space-time codes, which are a subset of single-symbol maximum likelihood decodable linear space-time block codes, for wireless multiple antenna terminals. The analytical and simulation results show that full diversity is achievable. Using the equivalent single-input single-output model, simple expressions for the average bit error rates are derived over flat uncorrelated Rayleigh fading channels. Optimum rotation angles are found by finding the minimum of the average bit error rate curves.

Chemistry of dihydrogen complexes containing only phosphorus co-ligands

A series of new dicationic dihydrogen complexes of ruthenium of the type cis-[(dppm)(2)Ru(eta(2)-H-2)(L)][BF4](2) (dppm = Ph2PCH2PPh2; L = phosphite) have been prepared by protonating the precursor hydride complexes cis-[(dPPM)(2)Ru(H)(L)][BF4] using HBF4.Et2O. The precursor hydride complexes have been obtained from trans-[(dppm)(2)Ru(H)(L)][BF4][(L = phospfiite) via a rare acid-catalysed isomerization reaction in six coordinate species. The trans-[(dppm)(2)Ru(H)(L)][BF4] complexes (L = phosphine) upon protonation gave the isomerized derivatives, however, further addition of acid resulted in a five-coordinate species, [(dppm)(2)RuCl](+) presumably via an intermediate phosphine dihydrogen complex. The electronic as well as the steric properties of the co-ligands seem to strongly influence the structure-reactivity behaviour of this series of complexes.

PDB Goodies - a web-based GUI to manipulate the Protein Data Bank file

PDB Goodies is a web-based graphical user interface (GUI) to manipulate the Protein Data Bank file containing the three-dimensional atomic coordinates of protein structures. The program also allows users to save the manipulated three-dimensional atomic coordinate file on their local client system. These fragments are used in various stages of structure elucidation and analysis. This software is incorporated with all the three-dimensional protein structures available in the Protein Data Bank, which presently holds approximately 18 000 structures. In addition, this program works on a three-dimensional atomic coordinate file (Protein Data Bank format) uploaded from the client machine. The program is written using CGI/PERL scripts and is platform independent. The program PDB Goodies can be accessed over the World Wide Web at http:// 144.16.71.11/pdbgoodies/.

Structural model for the Cu-B site of dopamine beta-hydroxylase: Crystal structure of a copper(II) complex showing N3OS coordination with an axial sulfur ligation

A copper(II) complex containing a NSO-donor Schiff base and NN-donor 2,2'-bipyridine has been prepared and structurally characterized. The square pyramidal complex with an axial sulfur ligation is a structural model for the CUB site of dopamine-hydroxylase in its oxidized form. The copper(II) complex is catalytically active in the oxidation of ascorbic acid by dioxygen mediated by a copper(I) species which is proposed to have a four-coordinate structure with a N3S coordination geometry.

An economical method for direct numerical simulation studies of transitional round jets

A pseudo-spectral method based on Fourier expansions in a Cartesian coordinate system is shown to be an economical method for direct numerical simulation studies of transitional round jets, Several characteristics of the solutions are presented to establish the validity of the solutions in spite of the unnatural choices. We show that neither periodicity, nor the use of a Cartesian system have adversely affected the simulations, Instead, there are benefits in terms of ease of computing and lack of the usual restrictions due to grid structure near the jet axis. By computing the simultaneous evolution of passive scalers, the process of reaction in round jet burners, between a fuel-laden jet and an ambient oxidizer, was also simulated. Some typical solutions are shown and then the results of analysis of these data are summarized. (C) 2001 Elsevier Science Ltd, All rights reserved.