Solution of a Boundary-Value Problem associated with Diffraction of Water Waves by a Nearly Vertical Barrier

An exact solution is derived for a boundary-value problem for Laplace's equation which is a generalization of the one occurring in the course of solution of the problem of diffraction of surface water waves by a nearly vertical submerged barrier. The method of solution involves the use of complex function theory, the Schwarz reflection principle, and reduction to a system of two uncoupled Riemann-Hilbert problems. Known results, representing the reflection and transmission coefficients of the water wave problem involving a nearly vertical barrier, are derived in terms of the shape function.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

Rapid synthesis of room temperature ferromagnetic Ag-doped LaMnO3 perovskite phases by the solution combustion method

We report the rapid solution combustion synthesis and characterization of Ag-substituted LaMnO3 phases at relatively low temperature using oxalyl dihydrazide, as fuel. Structural parameters were refined by the Rietveld method using powder X-ray diffraction data. While the parent LaMnO3 crystallizes in the orthorhombic structure, the Ag-substituted compounds crystallize in the rhombohedral symmetry. On increasing Ag-content, unit cell volume and Mn-O-Mn bond angle decreases. The Fourier transform infra red spectrum shows two absorption bands corresponding to Mn-O stretching vibration (v(s) mode) and Mn-O-Mn deformation vibration (v(b) mode) around 600 cm(-1) and 400 cm(-1) for the compositions x = 0.0, 0.05 and 0.10, respectively. Electrical resistivity measurements reveal that composition-controlled metal to insulator transition, with the maximum metal to insulator being 280 K for the composition La0.75Ag0.25MnO3. Increase in magnetic moment was observed with increase in Ag-content. The maximum magnetic moment of 35 emu/g was observed for the composition La0.80Ag0.20MnO3. (C) 2010 Elsevier Ltd. All rights reserved.

Exact solution for the unsteady motion of a viscous-fluid in a porous annulus

An exact solution to the problem of time-dependent motion of a viscous fluid in an annulus with porous walls is obtained under the assumption that the rate of suction at one wall is equal to the rate of injection at the other. Finite Hankel transform is used to obtain a closed-form solution for the axial velocity. The average axial velocity profiles are depicted graphically.

Dilute solution properties of methyl methacrylate—acrylonitrile copolymer (MA2)

This article deals with studies of the dilute solution properties of methyl methacrylate-acrylonitrile (MMA-AN) copolymer of 0.415 mole fraction (mf) of acrylonitrile composition. Mark—Houwink parameters for this copolymer have been evaluated in acetonitrile (MeCN), 2-butanone (MEK), dimethyl formamide (DMF), and γ-butyrolactone (γ-BL). The Mark-Houwink exponent a in all four solvents at all temperatures is larger than the corresponding values of the parent homopolymers. The solvent power is in the order of DMF < γ–BL < MEK < MeCN; [η] decreases with an increase in temperature, which is behavior characteristic of polymers in good solvent. The unperturbed dimensions (K0) values, obtained by the Stockmayer–Fixman method, are lower than those for the parent homopolymers and depend on solvent as well as temperature. The solute—solvent interaction parameter X1 values are close to 0.5; X1 is independent of temperature. The excess interaction parameter XABvalues are negative. The results for this copolymer system in regard to low second virial coefficient A2, large X1, and high a values suggest that the large extension of these copolymer chains is due to the unusual short-range interactions.

Comparative study of different formulations and solution methods for two phase flow in saturated porous media

Six models (Simulators) are formulated and developed with all possible combinations of pressure and saturation of the phases as primary variables. A comparative study between six simulators with two numerical methods, conventional simultaneous and modified sequential methods are carried out. The results of the numerical models are compared with the laboratory experimental results to study the accuracy of the model especially in heterogeneous porous media. From the study it is observed that the simulator using pressure and saturation of the wetting fluid (PW, SW formulation) is the best among the models tested. Many simulators with nonwetting phase as one of the primary variables did not converge when used along with simultaneous method. Based on simulator 1 (PW, SW formulation), a comparison of different solution methods such as simultaneous method, modified sequential and adaptive solution modified sequential method are carried out on 4 test problems including heterogeneous and randomly heterogeneous problems. It is found that the modified sequential and adaptive solution modified sequential methods could save the memory by half and as also the CPU time required by these methods is very less when compared with that using simultaneous method. It is also found that the simulator with PNW and PW as the primary variable which had problem of convergence using the simultaneous method, converged using both the modified sequential method and also using adaptive solution modified sequential method. The present study indicates that pressure and saturation formulation along with adaptive solution modified sequential method is the best among the different simulators and methods tested.

Precursor Dependent Microstructure Evolution and Nonstoichiometry in Nanostructured Cerium Oxide Coatings Using the Solution Precursor Plasma Spray Technique

A solution precursor plasma spray (SPPS) technique has been used for direct deposition of cerium oxide nanoparticles (CNPs) from various cerium salt solutions as precursors. Solution precursors were injected into the hot zone of a plasma plume to deposit CNP coatings. A numerical study of the droplet injection model has been employed for microstructure development during SPPS. The decomposition of each precursor to cerium oxide was analyzed by thermogravimetric-differential thermal analysis and validated by thermodynamic calculations. The presence of the cerium oxide phase in the coatings was confirmed by X-ray diffraction studies. Transmission electron microscopy studies confirmed nanocrystalline (grain size <14 nm) characteristic of the coatings. X-ray photoelectron spectroscopy studies indicated the presence of a high concentration of Ce3+ (up to 0.32) in the coating prepared by SPPS. The processing and microstructure evolution of cerium oxide coatings with high nonstoichiometry are reported.

Nonnegative integral solution of linear equations

A method to obtain a nonnegative integral solution of a system of linear equations, if such a solution exists is given. The method writes linear equations as an integer programming problem and then solves the problem using a combination of artificial basis technique and a method of integer forms.

A divisive scheme for constructing minimal spanning trees in coordinate space

An algorithm to generate a minimal spanning tree is presented when the nodes with their coordinates in some m-dimensional Euclidean space and the corresponding metric are given. This algorithm is tested on manually generated data sets. The worst case time complexity of this algorithm is O(n log2n) for a collection of n data samples.

An improved iterative finite element solution for pin joints

Accurate, reliable and economical methods of determining stress distributions are important for fastener joints. In the past the contact stress problems in these mechanically fastened joints using interference or push or clearance fit pins were solved using both inverse and iterative techniques. Inverse techniques were found to be most efficient, but at times inadequate in the presence of asymmetries. Iterative techniques based on the finite element method of analysis have wider applications, but they have the major drawbacks of being expensive and time-consuming. In this paper an improved finite element technique for iteration is presented to overcome these drawbacks. The improved iterative technique employs a frontal solver for elimination of variables not requiring iteration, by creation of a dummy element. This automatically results in a large reduction in computer time and in the size of the problem to be handled during iteration. Numerical results are compared with those available in the literature. The method is used to study an eccentrically located pin in a quasi-isotropic laminated plate under uniform tension.

Analytical solution of the laminar mean flow wave equation in a lined or unlined two-dimensional rectangular duct

The prediction of the sound attenuation in lined ducts with sheared mean flow has been a topic of research for many years. This involves solving the sheared mean flow wave equation, satisfying the relevant boundary condition. As far as the authors' knowledge goes, this has always been done using numerical techniques. Here, an analytical solution is presented for the wave propagation in two-dimensional rectangular lined ducts with laminar mean flow. The effect of laminar mean flow is studied for both the downstream and the upstream wave propagation. The attenuation values predicted for the laminar mean flow case are compared with those for the case of uniform mean flow. Analytical expressions are derived for the transfer matrices.

A photoelastic approach to framed structure-foundation beam-soil interaction

The interaction of a framed structure with a foundation beam resting on an elastic medium, representing the soil, has been studied using the photoelastic method. The contact pressure distribution, the fibre stress in the foundation beam and frame structure, as well as the stresses in the elastic medium, have been obtained. These have been compared with theoretical results obtained by idealizing the soil as (a) elastic half plane, and (b) elastic half space. It is shown that the photoelastic method can provide an easy solution to this type of problem if the soil can be idealized as an elastic continuum.

Exact traveling- wave solution for model geophysical systems

Exact traveling-wave solutions of time-dependent nonlinear inhomogeneous PDEs, describing several model systems in geophysical fluid dynamics, are found. The reduced nonlinear ODEs are treated as systems of linear algebraic equations in the derivatives. A variety of solutions are found, depending on the rank of the algebraic systems. The geophysical systems include acoustic gravity waves, inertial waves, and Rossby waves. The solutions describe waves which are, in general, either periodic or monoclinic. The present approach is compared with the earlier one due to Grundland (1974) for finding exact solutions of inhomogeneous systems of nonlinear PDEs.

Conformation of substituted polyacetylenes in solution : relationship between electronic properties and local order

A study of the chain conformation in solutions of polyphenylacetylene and poly(2-octyne) has been performed. The two polymers differ in many ways : polyphenylacetylene gives a red solution while poly(2-octyne) is transparent and, a marked difference on the chain rigidity is observed : the statistical length are 45 Å and 135 Å respectively. From the study of these two systems, one deduces that curvature fluctuations play a minor role on the π electrons localization, and that the torsion between monomer units is the pertinent parameter to understand the chain conformation and the π electrons localization.