Vibrational properties of vacancy in bcc transition metals using embedded atom method potentials

The embedded atom method (EAM) potentials, with the universal form of the embedding function along with the Morse form of pair potential, have been employed to determine the potential parameters for three bcc transition metals: Fe, Mo, and W, by fitting to Cauchy pressure (C ₁₂???C ₄₄)/2, shear constants $G_\textrm{v} =({C_{11} -C_{12} +3C_{44}})/5$ and C ₄₄, cohesive energy and the vacancy formation energy. The obtained potential parameters are used to calculate the phonon dispersion spectra of these metals. Large discrepancies are found between the calculated results of phonon dispersion using the EAM and the experimental phonon dispersion results. Therefore, to overcome this inadequacy of the EAM model, we employ the modified embedded atom method (MEAM) in which a modified term along with the pair potential and embedding function is added in the total energy. The phonon dispersions calculated using potential parameters obtained from the MEAM show good agreement with experimental results compared to those obtained from the EAM. Using the calculated phonons, we evaluate the local density of states of the neighbours of vacancy using the Green’s function method. The local frequency spectrum of first neighbours of vacancy in Mo shows an increase at higher frequencies and a shift towards the lower frequencies whereas in Fe and W, the frequency spectrum shows a small decrease towards higher frequency and small shift towards lower frequency. For the second neighbours of vacancy in all the three metals, the local frequency spectrum is not much different from that of the host atom. The local density of states of the neighbours of the vacancy has been used to calculate the mean square displacements and the formation entropy of vacancy. The calculated mean square displacements of the first neighbours of vacancy are found to be higher than that of the host atom, whereas it is lower for the second neighbours. The calculated results of the formation entropy of the vacancy compared well with other available results.     

Numerical Algorithm Based on Quintic Nonpolynomial Spline for Solving Third-Order Boundary Value Problems Associated with Draining and Coating Flows

A numerical algorithm is developed for the approximation of the solution to certain boundary value problems involving the third-order ordinary differential equation associated with draining and coating flows. The authors show that the approximate solutions obtained by the numerical algorithm developed by using nonpolynomial quintic spline functions are better than those produced by other spline and domain decomposition methods. The algorithm is tested on two problems associated with draining and coating flows to demonstrate the practical usefulness of the approach.     

Applications of hypergeometric summation theorems of kummer and dixon involving double series

Using series iteration techniques, we derive a number of general double series identities and apply each of these identities in order to deduce several hypergeometric reduction formulas involving the Srivastava-Daoust double hypergeometric function. The results presented in this article are based essentially upon the hypergeometric summation theorems of Kummer and Dixon.     

Some Polynomial Expansions for Functions of Several Variables

In the present paper three new expansion formulae are givenfor a function of several variables, which is defined by a multiplepower series with arbitrary terms. It is also indicated howthese general results can be applied to derive various knownor new multiplication theorems for certain hypergeometric functionsof one and more variables.     

Spherical means in annular regions in the <Emphasis Type="Italic">n</Emphasis>-dimensional real hyperbolic spaces

Let Z _r,R be the class of all continuous functions f on the annulus Ann(r, R) in the real hyperbolic space \(\mathbb B^n\) with spherical means M _s f(x)?=?0, whenever s?>?0 and \(x\in\mathbb B^n\) are such that the sphere S _s (x)???Ann(r, R) and \(B_r(o)\subseteq B_s(x).\) In this article, we give a characterization for functions in Z _r,R . In the case R?=?∞, this result gives a new proof of Helgason’s support theorem for spherical means in the real hyperbolic spaces.     

An Elementary Proof of Bailey's Bilinear Generating Function for Jacobi Polynomials and of Its q-Analogue

Some simple ideas are used to give an elementary proof of Bailey'sbilinear generating functionof Jacobi polynomials. The proofpresented here depends only upon certain hypergeometric seriesrepresentations of Jacobi polynomials and the familiar Vandermondesummation theorem; indeed, it can be applied mutatis mutandisto derive analogous bilinear generating functions for the littleq-Jacobi polynomials. This paper concludes by outlining an alternativeproof of one such bilinear q-generating function.     

Kinetics of the Oxidation of D‐Glucose and Cellobiose by Acidic Solution of N‐Bromoacetamide Using Transition Metal Complex Species, [RuCl3(H2O)2OH] −, as Catalyst

The kinetics of Ru(III)‐catalyzed and Hg(II)‐co‐catalyzed oxidation of D‐glucose (Glc) and cellobiose (Cel) by N‐bromoacetamide (NBA) in the presence of perchloric acid at 40 °C have been investigated. The reactions exhibit the first order kinetics with respect to NBA, but tend towards the zeroth order to higher NBA. The reactions are the first order with respect to Ru(III) and are fractional positive order with respect to [reducing sugar]. Positive effect of Cl^? and Hg(OAc)₂ on the rate of reaction is also evident in the oxidation of both reducing sugars. A negative effect of variation of H⁺ and acetamide was observed whereas the ionic strength (µ) of the medium had no influence on the oxidation rate. The rate of reaction decreased with the increase in dielectric constant and this enabled the computation of d_AB, the size of the activated complex. Various activation parameters have been evaluated and suitable explanation for the formation of the most reactive activated complex has been given. The main products of the oxidation are the corresponding arabinonic acid and formic acid. HOBr and [RuCl₃(H₂O)₂OH]^? were postulated as the reactive species of oxidant and catalyst respectively. A common mechanism, consistent with the kinetic data and supported by the observed effect of ionic strength, dielectric constant and multiple regression analysis, has been proposed. Formation of complex species such as [RuCl₃·S·(H₂O)OH]^? and RuCl₃·S·OHgBr·OH during the course of reaction was fully supported by kinetic and spectral evidences.     

双金属氰化物在多组分偶联反应中的催化活性(英文)

Several dual metal cyanide catalysts were prepared from potassium ferrocyanide,metal chloride(where metal = Zn2+,Mn2+,Ni2+,Co2+ and Fe2+),t-butanol(complexing agent) and PEG-4000(co-complexing agent).The catalysts were characterized by elemental analysis(CHN and X-ray fluorescence),X-ray diffraction,N2 adsorption-desorption,scanning electron microscopy,Fourier-transform infrared spectroscopy,and UV-Visible spectroscopy.The dual metal cyanide catalysts were used in several acid catalyzed multi-component coup...     

Equation of state of long chain molecules and rings

An equation of state for long chain molecules has been proposed using statistical associating fluid theory (SAFT). The formalism derived here is based on the assumption that the chain is formed by the pairs of trimers. The equations of state for 48-mers and 192-mers are formulated and compared with Monte Carlo results. The theory has been developed to treat hard sphere molecules with two attraction sites to form a ring molecule. The equations of state for trimer, hexamer and 12-mer ring molecules have been formulated. There is excellent agreement with available Monte Carlo results. Second virial coefficients of tangent chain molecules and ring molecules have been determined numerically and compared with simulation results.