Parabolic Coefficients Research Articles

Growth of Phases and Diffusion of Components in the W-Pt System

Growth kinetics, phase boundary compositions, interdiffusion coefficients and the relative mobilities of the components are determined in the W-Pt system. The measured phase boundary compositions for the γ phase are found to be different from the reported phase diagram. The interdiffusion coefficient and the activation energy decrease in the Pt(W) solid solution with increasing W content. An estimation of the parabolic growth constants and average interdiffusion coefficients in the γ phase indicates that the diffusion process should be explained based on the estimation of diffusion parameters, which otherwise could lead to a wrong conclusion. The estimation of the relative mobilities of the components in the γ phase indicates that Pt has a much higher diffusion rate than W. This is explained with the help of the crystal structure and the possible point defects present on different sublattices.

Three-dimensional Hermite-Bessel solitons in strongly nonlocal media with variable potential coefficients

We solve the three-dimensional nonlinear Schrödinger equation with variable parabolic potential coefficients in strongly nonlocal nonlinear media. Exact analytical solutions in the form of self-similar waves, namely the Hermite-Bessel solitons, are found. Higher-order Hermite-Bessel solitons, which can exist in various forms such as the three-dimensional vortex solitons and the multipole solitons are also discussed. To ascertain the stability of these analytical solutions during evolution, numerical simulations have been performed.

Pointwise convergence of the wavelet solution to the parabolic equation with variable coefficients

We consider the parabolic equationwith variable coefficients k(x)uxx =ut,0,x ≤ 1, t ≥ 0, where 0 < α ≤ k(x) < +∞, the solution on the boundary x = 0 is a given function g and ux(0, t) = 0. We use wavelet Galerkin method with Meyer multi-resolution analysis to obtain a wavelet approximating solution, and also get an estimate between the exact solution and the wavelet approximating solution of the problem.

A fast fingerprint image enhancement algorithm using a parabolic mask

The quality of fingerprint images (FIs) varies depending on the image taking method. The performance of automatic fingerprint recognition systems highly depends on the quality of the fingerprint images. In these images often are distorted areas, where the valleys and ridges are not clear and there are discontinuities at in the ridge flows. To overcome these unwanted defects fingerprint recognition systems employ enhancement algorithms to improve the quality of the images. Following, binarization, feature extraction, and matching algorithms are executed on the enhanced image. In real-time systems, the overall execution time has primary importance and therefore, especially the enhancement algorithm must be fast and effective. In this study, we propose a fast filtering method with a mask of parabolic coefficients based on the directions. The experiments executed on FVC2000 have proved that, the algorithm provides faster and better enhancements from those described in the literature.

A Numerical Study of the Applicability of the Shear Compression Specimen to Parabolic Hardening Materials

This paper addresses quasi-static loading of the shear compression specimen (SCS), that has been especially developed to investigate the shear response of materials at various strain rates. Previous work [4, 5] addressed bi-linear hardening materials, whereas the present work concerns parabolic hardening materials. The investigation is done numerically using three-dimensional elastoplastic finite element simulations. The analyses show that the averaged von Mises stress (\(\widehat{\sigma }_{{eq}} \)) and strain (\(\widehat{\varepsilon }_{{{\text{eq}}}} \)) on a mid-section of the gauge reflect accurately the prescribed parabolic hardening model. A method for finding the parabolic hardening coefficients and reducing the measured load, P, and displacement, d, into equivalent stress \(\widehat{\sigma }_{{eq}} \) and strain \(\widehat{\varepsilon }_{{{\text{eq}}}} \) is introduced and tested. A very good agreement is observed, thus confirming the potential of the technique for large strain testing of parabolic hardening materials.

Time domain analysis of transient propagation in inhomogeneous magnetized plasma using Z-transforms

The electromagnetic propagation through an inhomogeneous magnetized plasma slab is studied using the Z-transform formulation of the Finite-Difference Time-Domain(FDTD) method. The direction of electromagnetic propagation is parallel to the biasing magnetic filed. To validate the Z-transform algorithm, the reflection and transmission coefficients for the right-hand circularly polarized wave of the homogeneous magnetized plasma slab are computed by means of discrete Fourier transform. The comparison between the reflection and transmission coefficients of the homogeneous plasma slab and analytical values indicates that Z-transform algorithm is very accurate. When the plasma frequency varies according to the square root and parabolic relations, the reflection and transmission coefficients of the inhomogeneous magnetized plasma slab are computed.

Analytic study of continuum spectrum pulse dynamics in optical waveguides

It is demonstrated that for femtosecond supercontinuum generation in optical waveguides with nonresonant electronic nonlinearity the squared root-mean-square pulse duration varies near-parabolically with distance, irrespectively of spectrum ultra-broadening scenarios. The derived formulas for parabolic coefficients are applied to find the areas of spectral and energetic parameters of few-cycle pulses propagating in hollow capillaries filled with noble gases, where temporal pulse broadening, compression, or quasi-stationary propagation occur. Each regime is illustrated by the typical changes in the pulse electrical field and spectrum.

Geomagnetic secular variation 1995–2000

A study was done to determine the difficulty of obtaining a field model for 1995 using magnetic observations taken since that epoch. Ørsted vector data taken from 1999 to 2001 in conjunction with scalar data from all surface ship surveys and secular variation data from magnetic observatories taken since 1995 were utilized. Spherical harmonic models were constructed for the interval from 1995 through early 2001 using selected, magnetically quiet, nighttime intervals. Corrections were made for Dst variations assuming a constant, i.e., ratio (0.28). The data were corrected for magnetic anomalies using Magsat coefficients (m102389) above n = 21. In order to compute secular change data, some observatory hourly values were reduced to remove the annual variations, which ranged up to 40 nT at a few stations. Coefficients were adjusted up to n = 21 in spatial terms, n = 13 in linear secular variation terms, and n = 12 in parabolic secular variation terms. There was also a 30 nT, n = 1 external term. Component maps of this model (f052101) truncated to n = 10 were compared with the IGRF2000 and generally found to be within 20 nT at the surface except for a 110 nT difference in the northern polar region. The model agreed with the OIFM at satellite altitude to within a few nanoteslas except for a few tens of nanoteslas at the poles. Model differences at 1995 from the IGRF1995 peaked over 800 nT in the region west of South America. However, statistical estimates in this region and epoch show model errors up to several hundred nanoteslas. Use of a linear model or one truncated to lower degree is seen to reduce these differences and maximum errors at 1995, but at the expense of less accuracy elsewhere. Besides the large differences from the 1995 IGRF it was also noted that there are a number of areas where the field changes require parabolic coefficients, even over this short a time span.

Legendre sums, Soto–Andrade sums and Kloosterman sums

The three sums named in the title are all known to appear in connection with the complex representation theory of GL(2, q). The first two are incarnations of certain spherical vectors, whereas the third is a matrix coefficient for a parabolic basis. In this work, Legendre and Soto-Andrade sums are shown to occur in a second way, as parabolic Clebsch-Gordan coefficients for the tensor product of two Steinberg representations. This realization connects them with Kloosterman sums, and from it we derive a number of identities.

A New ADI Scheme for Solving Three-Dimensional Parabolic Equations with First-Order Derivatives and Variable Coefficients

An ADI scheme for solving three-dimensional parabolic equations withfirst-order derivatives and variable coefficients has been developed basedon our previous papers and the idea of the modified upwind differencescheme. This ADI scheme is second-order accurate and unconditionallystable. Further, a small parameter can be chosen which makes it suitablefor simulating fast-transient phenomena or for computations on fine spatialmeshes. The method is illustrated with numerical examples.

Interdiffusion in the carbides of the Nb-C system

Interdiffusion coefficients in Nb2C and NbC1−x were measured using bulk diffusion couples in the temperature range from 1400 °C to 1700 °C. Marker experiments were used to show that carbon is the only component undergoing significant diffusion in both carbides. Carbon concentrations were measured by difference using electron probe microanalysis, and interdiffusion coefficients were taken from Boltzmann-Matano analyses of the resulting concentration profiles. This analysis clearly showed that, in NbC1−x, interdiffusion coefficient varies with carbon concentration, and is expressed by $$\tilde D\left( {NbC_{1 - x} } \right) = 3.84 \times 10^{ - 9} \exp \left( {23.24x} \right)\exp \left( { - \frac{{28,450 \pm 850}}{T}} \right)m^2 /s$$ where x is the site fraction of vacancies on the carbon sublattice. The interdiffusion coefficient in Nb2C is given by $$\tilde D\left( {Nb_2 C} \right) = 2.04 \pm 0.57 \times 10^{ - 4} \exp \left( { - \frac{{35,520 \pm 2190}}{T}} \right)m^2 /s$$ Parabolic layer growth coefficients were estimated from the Nb|C diffusion couples as well. They are given by $$\begin{gathered} K_p \left( {NbC} \right) = 2.65_{2.41}^{2.90} \times 10^{ - 5} \exp \left( { - \frac{{37,600 \pm 1400}}{T}} \right)m^2 /s \hfill \\ K_p \left( {Nb_2 C} \right) = 1.57_{1.28}^{1.92} \times 10^{ - 5} \exp \left( { - \frac{{36,400 \pm 3100}}{T}} \right)m^2 /s \hfill \\ \end{gathered} $$ The value of $$\tilde D$$ in NbC1−x was found to be consistent with literature values for the tracer diffusivity of C in NbC1−x via the thermodynamic factor, which was determined in two ways.

The piecewise parabolic finite analytic method. Part I: Theory

To meet both the qualitative and quantitative requirements of the convective diffusion process, a numerical scheme, called the piecewise parabolic finite analytic method, is established by using a piecewise parabolic function as a boundary condition. This scheme incorporates the local analytic solution of the convective diffusion equation into the numerical scheme. It is free from numerical diffusion and automatically incorporates the convective diffusion effects. In this first part, a detailed study of the piecewise parabolic finite analytic scheme is presented. Initially, the maximum and minimum principle of the convective diffusion equation is used to determine the properties of the piecewise parabolic finite analytic coefficients. Then, based upon the truncation error and properties of the coefficients, the existence, uniqueness, stability, convergence, and error estimates of the numerical solution are obtained. For nonlinear problems the existence and error estimates are also obtained.

Lead‐Ion Stability in Soda–Lime Lead Silicate Glasses

Sodium‐calcium‐lead silicate glass compositions were prepared over a wide compositional range by conventional glass‐melting methods. The acid chemical stability of the glass structure was studied by corroding samples of glass in 4% acetic acid solution at 22°C for periods up to 24 h. Lead corrosion stability was evaluated by measuring lead concentrations in the corrosion solution. At short times, parabolic time dependence was observed and the parabolic time coefficients were regressed against composition, yielding a simple additive relationship. A similar model was fitted to 24‐h release data, which showed compositional effects similar to the 2‐h data. Of the oxides studied, sodium was the most detrimental to durability, and the coefficients of the oxides decreased in the series: Na2O, PbO, CaO, SiO2. The effects of the oxides could be partially explained by the number of nonbridging oxygens expected in the glass structure, and the residual effect was attributed to cation characteristics. Small phosphate additions to the glass greatly increased the lead‐ion stability under nearly all experimental conditions examined.

Effect of ion implantation on the oxidation kinetics of WSix

Abstract The oxidation characteristics of LPCVD tungsten silicide deposited on phosphorus doped polycrystalline silicon have been investigated. Thermal treatments in the temperature range of 600–1000°C, both in inert (dry N2) and oxidizing atmosphere (dry O2), and ion implantation into silicide with different ions (As, BF2, P and Ar) were considered. The oxidation behaviour was found to be very different, both in terms of oxide thickness and composition, depending on the annealing temperature and on the implanted species. At low temperature (⩽ 700°C), unimplanted tungsten silicide was found to be very sensitive to the oxygen content in the annealing atmosphere, and an anomalous oxidation, with metal-silicon oxide formation, was noticed also for thermal treatments in nominally pure nitrogen. On the contrary, at higher temperature (800–1000°C) and in dry oxygen, a pure SiO2 layer grows at the silicide surface. The kinetics for thermal oxide growth on tungsten silicide, has been studied as a function of the different implanted species and the rate of silicon oxide growth was analyzed in terms of both linear and parabolic coefficients.

Interface effects in the formation of silicon oxide on metal silicide layers over silicon substrates

Samples of several metal silicides grown over silicon substrates and samples of pure silicon were oxidized at the same time in an atmosphere of wet oxygen. The rates of silicon oxide growth were analyzed in terms of both linear and parabolic coefficients. The biggest difference is seen between the linear coefficients for metallic silicides on the one hand and pure silicon on the other, with a semiconducting silicide occupying an intermediate position. While the question of why metallic oxides are not always generated simultaneously with SiO2 remains a mystery, the results suggest a possible interpretation.

Some Applications of a Computer-Controlled X-Ray Spectrometer in a Steel Research Laboratory

The U. S. Steel Research x-ray spectrometric laboratory performs between 7,000 and 10,000 analytical determinations each month for alloying elements in all types of steels and raw -materials. The spectrometer is automatically controlled by a DEC PDP 8/1 minicomputer utilizing vari ations of software packages provided by Siemens Corporation. As many as 256 individual analytical measurements can be sequentially performed. The minimal interelemental effects encountered in low-alloy steel analyses are corrected in a separate program written in FOCAL language. Correction coefficients for the program were established by multiple linear regression analyses.Stainless and multialloy steels are analyzed with a two-part control and correction program. The control program controls all functions of the spectrometer automatically and stores parabolic calibration coefficients. Following a sequential determination of the alloying elements control is switched to a correction program written in FOCAL. The correction program prints a tabular listing of the elements determined, followed by a listing of the corrected concentrations of elements adjusted for interelemental effects. Orthogonal polynomial analyses were performed to determine σ values for all constituents determined.For analysis of raw materials, the samples are fused prior to analysis by use of a flux and heavy absorber technique that essentially eliminates interelement effects and permits linear calibrations up to 100 percent. Samples are ground and pelletized after fusion for better reproducibility. Single sets of calibration standards are used regardless of raw materials mineralogical history. Synthetic standards can be produced for ranges where no calibration standards exist.