A new algebraic approach to the eigenvalue problems of linear differential operators without integrations

In this work, a new approximation scheme based on the evaluation of the pointwise expectation of the Hamiltonian (H) via a conveniently chosen basis set is proposed. This scheme does not necessitate integration; however, physical and mathematical considerations in choosing the basis set are considerably important when very precise and rapidly convergent results are desired. In this method, the best linear combination of “well-selected” basis functions are sought in a way such that H ψ / ψ is flat in the neighborhood of a conveniently chosen point in the domain of H. This yields an algebraic eigenvalue problem. Some concrete applications that have already been realized confirm the efficiency of this approach.     

Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow

This experimental investigation deals with transition phenomena of a separated boundary layer under unsteady inlet flow conditions. The main purpose of this investigation is to understand the influence of the rotor-stator interaction in turbomachinery on the subsequent, highly loaded boundary layer. The research project is divided into two phases. In the first phase, which has been completed recently, only the variation of mean velocity caused by upstream blades was simulated in the experiments while the free-stream turbulence intensity was retained at a constant low level. The experiments are carried out in an Eifel-type wind tunnel to investigate the laminar separated boundary layer of a flat plate under oscillating inlet conditions. The adverse pressure gradient, similar to that of turbomachines, is generated by the contoured upper wall. The unsteadiness is produced by a rotating flap located downstream of the test section. The reduced frequency, the amplitude and the mean Reynolds number are varied to simulate the conditions prevailing in turbomachines. In addition to the Kelvin–Helmholtz instability of the separated shear layer, a lower frequency instability was observed. This is frequently referred to as `free shear layer flapping' and results in two distinctly different ways of re-attachment, depending primarily on the Reynolds number. For low momentum thickness Reynolds numbers at the separation point, large-scale vortices locked to the frequency of the unsteady main flow are identified. They originate nearly at the top of the separation bubble and are ejected downstream. A fully turbulent boundary layer develops after these vortices mix out. For higher Reynolds numbers, transition is completed within a short length of the free shear layer and there-attachment region. The characteristic momentum thickness Reynolds number separating these two regimes in unsteady flow is about 125. The Strouhal number (reduced frequency) does not appear to have any significant effect. Based on the experimental results, this behaviour is discussed in some detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

Synthesis and MALDI-TOF-MS of PS-PMA and PMA-PS block copolymers

The synthesis of well-defined block copolymers from styrene and methyl acrylate via ATRP is discussed in this contribution. Kinetic studies on these block copolymerizations as well as characterization studies were performed to investigate the monomer composition in the respective PS and PMA blocks. MALDI-TOF-MS was performed to clarify the exact number of repeating units of each block and the total number of units in the block copolymer. Block copolymers up to 22 kDa could be analyzed by MALDI-TOF-MS, whereby polymers with PMA as first block showed a large second distribution corresponding to PMA homopolymers. However, SEC demonstrated that only a small amount of homopolymer was present indicating that care needs to be taken with interpreting MALDI-TOF-MS data, which is a qualitative rather than a quantitative technique.     

Hazardous metal geochemistry of sedimentary phosphate rock used for fertilizer (Maz?dag, SE Anatolia, Turkey)

Composition of phosphate rocks mostly depend on their type and origin. Sedimentary rocks contain high concentration of heavy metals. Phosphate rocks are mainly used for the manufacturing of phosphate fertilizers. The contents of heavy metals Cd, Co, Cu, Fe, Mn, Ni, Pb and Zn, as well as rare earth elements Ce, La, and Th were determined in sedimentary phosphate rock used for production of fertilizer in Turkey. The Kasrik-Semikan, Mazidag (Mardin, SE Anatolia, Turkey) high-grade phosphate rock used in this study is situated near the border with Syria and was deposited during the Turonian and Senonian (Cretaceous) ages. Total phosphorus (P) concentration in the rock is 18.5% on the average. Microwave acid digestion (MW-AD) followed by ?nductively Coupled Plasma-Optical Emission Spectrophotometry (ICP-OES) was carried out for the determination of all the elements of interest in phosphate rock. The results revealed that hazardous metal content of the phosphate rock was lower in Mazidag phosphate than that in samples imported from other countries and were within the safety limits.     

Numerical solution of ordinary differential equations by Fluctuationlessness theorem

This paper presents a numerical method based on Fluctuationlessness Theorem for the solution of Ordinary Differential Equations over appropriately defined Hilbert Spaces. We focus on the linear differential equations in this work. The approximated solution is written in the form of an nth degree polynomial of the independent variable. The unknown coefficients are obtained by setting up a system of linear equations which satisfy the initial or boundary conditions and the differential equation at the grid points, which are constructed as the independent variable’s matrix representation restricted to an n dimensional subspace of the Hilbert Space. An error comparison of the numerical solution and the MacLaurin series with the analytical solution is performed. The results show that the numerical solution obtained here converges to the analytical solution without using too many mesh points.     

On the lattice Boltzmann method for phonon transport

The lattice Boltzmann method is a discrete representation of the Boltzmann transport equation that has been employed for modeling transport of particles of different nature. In the present work, we describe the lattice Boltzmann methodology and implementation techniques for the phonon transport modeling in crystalline materials. We show that some phonon physical properties, e.g., mean free path and group velocity, should be corrected to their effective values for one- and two-dimensional simulations, if one uses the isotropic approximation. We find that use of the D2Q9 lattice for phonon transport leads to erroneous results in transient ballistic simulations, and the D2Q7 lattice should be employed for two-dimensional simulations. Furthermore, we show that at the ballistic regime, the effect of direction discretization becomes apparent in two dimensions, regardless of the lattice used. Numerical methodology, lattice structure, and implementation of initial and different boundary conditions for the D2Q7 lattice are discussed in detail.     

Characterization of chemically deposited ZnSe/SnO2/glass films: Influence of annealing in Ar atmosphere on physical properties

The Zinc Selenide (ZnSe) thin films have been deposited on SnO₂/glass substrates by a simple and inexpensive chemical bath deposition (CBD). The structural, optical and electrical properties of ZnSe films have been characterized by X-ray diffraction (XRD), Energy Dispersive X-ray Analysis (EDAX), optical absorption spectroscopy, and four point probe techniques, respectively. The films have been subjected to different annealing temperature in Argon (Ar) atmosphere. An increase in annealing temperature does not cause a complete phase transformation whereas it affects the crystallite size, dislocation density and strain. The optical band gap (E_g) of the as-deposited film is estimated to be 3.08 eV and decreases with increasing annealing temperature down to 2.43 eV at 773 K. The as-deposited and annealed films show typical semiconducting behaviour, dρ/dT > 0. Interestingly, the films annealed at 373 K, 473 K, and 573 K show two distinct temperature dependent regions of electrical resistivity; exponential region at high temperature, linear region at low temperature. The temperature at which the transition takes place from exponential to linear region strongly depends on the annealing temperature.     

Dual Reciprocity Boundary Element Method for Magnetohydrodynamic Flow Using Radial Basis Functions

A dual reciprocity boundary element method is given to obtain the solution in terms of velocity and induced magnetic field for the study of MHD (magnetohydrodynamic) flow through a rectangular duct having insulating walls. The equations are transformed to two types of nonlinear Poisson equations and the right-hand sides in these equations are approximated using combinations of two classes of radial basis functions (the value of the function and its normal derivatives are utilized for approximation). Computations are carried out for several values of the Hartman number (0 h M h 10) by using constant boundary elements. Comparisons are made for two types of formulations and for traditional and osculatory type approximations of the right-hand side functions. It is found that osculatory interpolation gives better results than traditional interpolation and the type of the Poisson equation, which contains derivative of the unknown function, is better than the other type, which contains unknown function only. The results for velocity and induced magnetic field are illustrated by some selected graphs.