Non-uniform Parameters Research Articles

The Cubic Spline-Collocation Method for Weakly Singular Integral Equations

It is known (e.g., see [1–10]) that a weak singularity in the kernel of an integral equation of the second kind leads to a singularity in the solution; more precisely, the derivatives of the solution prove to be unbounded near the boundary of the integration domain. This complicates the construction of approximate methods of higher-order accuracy for weakly singular integral equations. It was shown in [3, 4, 8, 10–15] how to condense the grid near points where the solution may prove singular so as to avoid the singularities and construct piecewise polynomial approximations with an arbitrary prescribed accuracy order. A similar approach in the collocation method with cubic splines was considered in [3, 16–18]. The aim of the present paper is to analyze the convergence rate of the collocation method with cubic splines of minimum deficiency for linear weakly singular integral equations of the second kind. Possible singularities of derivatives of the solution of an integral equation are taken into account with the use of a special condensation of the grid, just as in [3]. We generalize and continue the related investigations in [3, 16, 17]. In particular, for integral equations with more general weakly singular kernels, we prove that the use of a special nonuniform grid in the collocation method with cubic splines of minimum deficiency provides the same accuracy order as in a singularity-free problem. We derive new estimates for the error in the approximate solution in the case of a quasiuniform grid as well as in the case of a nonuniform grid depending on the value of the nonuniformity parameter of the grid in question.

Pairing, Crossover and Inhomogeneous Superconductivity in the Attractive Hubbard Model

One- and two-dimensional attractive Hubbard models in the presence of magnetic field h are studied in a wide range of on-site interaction strength U, temperature T and electron concentration n by means of the generalized self-consistent field (GSCF) approach with renormalized chemical potential. Pairing, the smooth crossover from the BCS regime into the Bose condensation state and the inhomogeneous superconductivity with the non-uniform order parameter are investigated. The excitation spectrum, the momentum distribution function and thermodynamic properties, including the concentration of double occupied sites, the kinetic energy, and the chemical potential, are calculated. The numerical calculations are found in a good agreement with the Bethe-ansatz results and quantum Monte-Carlo calculations in a wide range of system parameters U, n and h. The GSCF theory correctly displays the separation of the energy gap from the order parameter (crossover) as n or |U| decrease. The concentration of double occupied sites and the bound electron pairs n pair are calculated and we found a simple relationship between the order parameter and n pair , valid for the arbitrary U and all n in any dimension. The developed GSCF approach in magnetic field suggests a smooth transition into the inhomogeneous superconducting state.

Residual strain in Ge pyramids on Si(111) investigated by x-ray crystal truncation rod scattering

Epitaxial growth of germanium on boron-terminated Si(111) results in the formation of triangular pyramidal Ge islands which are partially relaxed. We show that the termination of the Si(111) surface with 1/3 ML of boron is essential for the formation of faceted islands. We have investigated the residual strain in the Ge islands using x-ray crystal truncation rod scattering, and developed an analytical expression for the scattered intensity from islands with a nonuniform lattice parameter. We compare the measured intensity to x-ray scattering profiles calculated on the basis of different strain models. It is found that the Ge lateral lattice parameter changes linearly from the bottom to the top of the islands.

Kinetics of order-disorder phase transitions for non-uniform order parameters

Phenomenological theories of phase transition kinetics are extended towards initially nonuniform order parameters in the order-disorder limit. The resulting equations predict slowing down of the order parameter kinetics close to the equilibrium state and at low temperatures, T ≫ T c. The extent of the deviations from standard TDGL behaviour depends on the value of the mixing coefficient ε2 c/ε2, which regulates the stability of quenched order parameter fluctuations. Large values of ε2 c/ε2 result in the development of locally saturated order parameters Q(r) in the non-equilibrium state. If the range of interactions falls below the coarse graining length, a transient overshooting of the order parameter above its equilibrium value is predicted.

The Definition of the Tires Limit of Admissible Nonuniformity by Using the Vehicle Vibratory Model

Purpose of this article was to especially emphasize the contribution of tires nonuniformity radial and lateral force variation to vehicles vibrations, within developed nonlinear dynamic model of a vehicle. The tire nonuniformity force variations are introduced in simulations processes by radial and lateral dynamic forces in the area of wheels-road contact. The limits of admissible Peak - to - Peak radial and lateral force variation and Peak - to - Peak first harmonic radial and lateral force variation nonuniformity were defined by using a vehicle vibratory model. The tire nonuniformity parameters were defined from the aspect of vertical seat cushion and the steering wheel rim vibrations using the developed optimization program and the Pentium 90 MHz computer.

Cellular channel modeling and the performance of DS-CDMA systems with antenna arrays

In this paper, a new channel modeling approach incorporating nonuniform propagation environments is introduced, and the bit error rate (BER) of a direct sequence code division multiple access cellular system incorporating antenna arrays for spatial filtering is derived analytically. Specifically, this paper introduces a channel model for, and analyzes the performance of, a system in an environment where the multipath signals on each of the diversity branches of a RAKE receiver have varying fading characteristics. This scenario would typically describe urban environments where a large number of multipath echoes are present, each with different fading statistics resulting from the nonhomogeneous propagation paths seen by each multipath echo. It is shown that nonuniform fading parameters for multipath signals can severely influence the system performance, especially at high E/sub b//N/sub 0/ levels. Furthermore, it is shown that the conventional assumption of identical fading statistics for all RAKE receiver branches provide a lower bound on the system performance.

The Hubble Diagram of Type Ia Supernovae in Non–Uniform Pressure Universes

We use the redshift-magnitude relation, as derived by Dbrowski, for the two exact non-uniform pressure spherically symmetric Stephani universes with the observer positioned at the center of symmetry in order to test the agreement of these models with recent observations of high-redshift Type Ia supernovae (SN Ia's). By a particular choice of model parameters, we show that these models can give an excellent fit to the observed redshifts and (corrected) B-band apparent magnitudes of the data, but for an age of the universe that is typically about 2 Gyr?and may be more than 3 Gyr?greater than in the corresponding Friedmann model, for which nonnegative values of the deceleration parameter appear to be favored by the data. We show that this age increase is obtained for a wide range of the non-uniform pressure parameters of the Stephani models. We claim that this paper is the first attempt to compare inhomogeneous models of the universe with real astronomical data. Several recent calibrations of the Hubble parameter from the Hubble diagram of SN Ia's and other distance indicators indicate a value of H0 65 and a Hubble time of ~15 Gyr. Based on this value for H0 and assuming ? ? 0, the data would imply a Friedmann age of at most 13 Gyr and in fact a best-fit (for q0 = 0.5) age of only 10 Gyr. Our Stephani models, on the other hand, can give a good fit to the data with an age of up to 15 Gyr. The Stephani models considered here could, therefore, significantly alleviate the conflict between recent cosmological and astrophysical age predictions. The choice of model parameters is quite robust: in order to obtain a good fit to the current data, one requires only that the non-uniform pressure parameter a in one of the models be negative and satisfy |a| 3 km2 s-2 Mpc-1. This limit gives a value for the acceleration scalar of order | |0.66?10 -->?10r Mpc-1, where r is the radial coordinate in the model. Thus, although the pressure is not zero at the center of symmetry, r = 0, the effect of acceleration is nondetectable at the center, since the acceleration scalar vanishes there. However, the effect of the nonuniform pressure on the redshift-magnitude relation is clearly seen, since neighboring galaxies are not situated at the center, and they necessarily experience acceleration. By allowing slightly larger negative values of a one may fine-tune the model to give an even better fit to the data.

A phenomenological approach to ordering kinetics for partially conserved order parameters

The kinetics of cation ordering in complex crystal structures, such as minerals and ceramics, is discussed with regard to the applicability of time-dependent Ginzburg - Landau theory (TDGL). Deviations from the predictions made by TDGL may arise due to partial conservation of continuous and non-uniform order parameters at low temperatures. Under these conditions the movement of areas with large order parameter gradients (`walls') provides a local alternative to the continuous ordering kinetics described by TDGL. A simple phenomenological description of order parameter kinetics taking these constraints into consideration can be obtained. The underlying assumption is that the geometry of spatial order parameter variation close to equilibrium resembles that of a phase-separated system. The resulting kinetics differs substantially from the predicted TDGL behaviour.

The steady laminar flow of an elastico-viscous liquid in a curved pipe of varying elliptic cross section

The fully developed steady laminar flow of an idealized elastico-viscous liquid through a curved tube with elliptic cross section is studied. The axes of the ellipse are placed in an arbitrary position with respect to the radius of curvature, and the cross-sectional area varies slowly with the longitudinal distance. A perturbation scheme in terms of Dean number [1, 2] and a nonuniform curvature parameter is applied to determine the effects of 1. (i) the nonuniformity of the curvature 2. (ii) the shape of the cross section of the curved pipe 3. (iii) the arbitrary positioning of the elliptic cross section relative to the radius of curvature of the curved pipe. It is shown that in a tube of increasing curvature, there will be delay in setting up a secondary motion. The point of maximum shear stress varies with the cross section under consideration. The flow of Newtonian fluid in a curved tube of elliptic cross section is discussed, as a particular case.

A calculation procedure for the nonuniformity parameters of air-jet tempered glass

A procedure based on fundamental works in thermodynamics is proposed for calculating the nonuniformity parameters of air-jet tempered glass. The key factors affecting the nonuniformity coefficient are determined.

Experience with independent radiological review during a topotecan trial in ovarian cancer

The results of phase II clinical trials are usually based on response of tumours to new oncolytic agents as evidenced by radiological imaging techniques. In this trial, all claimed responders were reviewed at a specially convened meeting by the peer group of study investigators and a radiologist, independent of the study institutions. One hundred eleven patients with advanced epithelial ovarian cancer who had previously been treated with a platinum based regimen and had subsequently relapsed and who had measurable disease were treated with topotecan at a dose of 1.5 mg/m2/day i.v. on five consecutive days repeated every 21 days to assess efficacy and tolerability. Ninety-three were considered eligible for the study per protocol and lesions were assessed by either computerised tomography (CT) or ultrasound (US). At the meeting, scans from all 24 (25.8%) claimed responders were reviewed, lesions remeasured by the radiologist and a group discussion led to a final response classification. Ninety-two patients were found to be eligible for the study and 14 (15.2%) were confirmed as responders. Ten were rejected as responders, mainly because the lesion did not decrease in size by < or = 50%, but one patient failed to meet the entry criteria. Remeasurement of CT scans was more objective than US scans. Difficulties were encountered during review of some CT scan sequences because of non-uniform imaging parameters. Independent radiological review in conjunction with the peer review group in this trial enabled rigorous and consistent application of response criteria. This decreased the response rate from 25.8% to 15.2%, but this represents a more objective assessment. CT scanning is an objective technique for assessing response rates in phase II studies whereas US is subjective and dose not necessarily allow accurate lesion assessment on subsequent examinations, nor allows independent review at a later date. For these reasons it should not be used in such studies for accurate lesion assessment. Cross-sectional imaging techniques such as CT and magnetic resonance imaging (MRI) do allow accurate lesion assessment and independent review at a later date, but standard protocols need to be instituted, to allow consistency and a comparison to be made with subsequent studies using the same agent and a broad comparison to be made with other agents.

A general-purpose transmission line model and its interface with an electromagnetic transients programme

The transmission line models implemented in general purpose programs used for the analysis of electromagnetic transients in power systems are not adequate for directly taking into account (a) distributed nonuniform parameters (b) distributed non-linear parameters or (c) distributed sources. However, these features are important in the analysis of many electromagnetic transient problems in power systems. A multiphase transmission line model adequate for taking into account the above-mentioned parameters has been developed. In this paper, application examples of this multi-purpose line model are presented illustrating the solution of various electromagnetic transient problems in power systems. The line model has been implemented as a separate set of Fortran routines that were then connected to EMTP using the standard interface provided by MODELS. This interface allows an external routine to be linked, and to be used in a data case as any regular model. Using a type-94 Thevenin circuit element, this Fortran model is connected directly to the nodes of the data-case, and is included in the simulation without any time-step delay.

Nonequilibrium macroparticle charging in low-density discharge plasmas

Nonequilibrium macroparticle (MP) charging was studied theoretically in the case of small MP radius to the Debye length ratio. The different cases were considered: 1) nonstationary MP charging in plasmas with large MP density to the ion density ratio /spl kappa/ and 2) MP charging in nonuniform plasmas. In the first case, the large fraction of plasma charges captured by MP's was taken into account. In the second case, the charging of MP's moving in plasmas with nonuniform density distributions was considered. It was obtained that the MP charge decreases with parameter /spl kappa/ and increases and saturates with radius (for MP radii larger than some critical radius R/sub cr/) and these effects strongly depend on the MP residence time in the discharge plasma. In the case of plasma density N/sub i/=10/sup 12/ m/sup -3/ and for /spl kappa/ in the range 10/sup -4/-10/sup -1/, the value of R decreases from 30 to 0.4 /spl mu/m if the MP residence time is t/spl sim/0.1 ms, and R/sub cr/ decreases from 20 to 0.1 /spl mu/m if t/spl sim/10 ms, while in the steady-state case, R/sub cr/ changes more significantly from 10 to 10/sup -2/ /spl mu/m. Qualitative agreement with experiments of MP charge behavior with the MP radius and the effect of MP charge saturation with the radius was obtained. MP's traveling through a nonuniform plasma, when the plasma density changed as N/sub i//spl sim/1/x/sup m/ (where m is the nonuniformity parameter) were considered. It was obtained that if the distance during which charging occurred is larger than the characteristic linear scale of the plasma density changes, the MP's may not have time to reach their equilibrium charge value at any location that they pass through. In the case of MP traveling in the plasma jet, the MP does not reach the equilibrium charge if m/spl ges/2 and /spl sim/1 cm.

Absence of persistent magnetic oscillations in type-II superconductors.

We report on a numerical study intended to examine the possibility that magnetic oscillations persist in type-II superconductors beyond the point where the pairing self-energy exceeds the normal state Landau level separation. Our work is based on the self-consistent numerical solution for model superconductors of the Bogoliubov--de Gennes equations for the vortex lattice state. In the regime where the pairing self-energy is smaller than the cyclotron energy, magnetic oscillations resulting from Landau level quantization are suppressed by the broadening of quasiparticle Landau levels due to the nonuniform order parameter of the vortex lattice state and by splittings of the quasiparticle bands. Plausible arguments that the latter effect can lead to a sign change of the fundamental harmonic of the magnetic oscillations when the pairing self-energy is comparable to the cyclotron energy are shown to be flawed. Our calculations indicate that magnetic oscillations are strongly suppressed once the pairing self-energy exceeds the Landau level separation. \textcopyright{} 1996 The American Physical Society.

Computation of electromagnetic transients on nonuniform transmission lines

A nonuniform power transmission line model is presented, based on a finite-differences algorithm to solve the wave equations for any space variation of the line parameters. This line model is interfaced with EMTP and used for representing transmission line towers. Results are obtained for comparison with other solution methods, showing a good performance of the proposed model. Computer simulation of experimental tests is performed, and a good agreement between the simulation results and the published experimental results is found, the tower losses being considered as a frequency-constant nonuniform parameter.

Molecular electronegativity in density functional theory (I)——Direct calculation of atomic charges in a molecule via electronegativity equalization principle

On the basis of electronegativity expressed in density functional theory and electronegativity equalization principle, a new scheme for calculating the atomic charges in a molecule has been proposed and designed, which gives a new scale of the atomic electronegativity and hardness in a certain molecular environment and takes the harmonic mean electronegativity as a reference value of the molecular electronegativity so that the multiple-regression and nonuniform parameters in the original method are avoided. This approach can be easily and widely applied to the calculation of atomic charges for a big molecule and quite good results of atomic charges in some illustrated molecules are obtained as compared with those from the ab initio STO-3G SCF calculations.

Cell loss analysis and design trade-offs of nonblocking ATM switches with nonuniform traffic

In practical ATM switch design, a proper dimensioning of buffer sizes and a cost effective selection of speed-up factor should be considered to guarantee a specified cell loss requirement for a given traffic. Although a larger speed-up factor provides better throughput for the switch, increasing the speed-up factor involves greater complexity and cost. Hence, it may not be cost effective to increase the speed-up factor for 100% throughput. Moreover, with a given buffer budget, an increase in the speed-up factor beyond a certain value only adds to the cell loss. The paper addresses design trade-offs existing between finite input/output buffer sizes and speed-up factor in a nonblocking ATM switch. Another important issue is the adverse effect on cell loss performance caused by nonuniform traffic (different traffic intensity and unevenly distributed routing). The paper analyzes cell loss performance of ATM switches with nonuniform traffic, and examines the effect of each nonuniform traffic parameter. The authors also provide an algorithm for effective buffer sharing that alleviates the performance degradation caused by traffic nonuniformity.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Surface Grid Generation in a Parameter Space

A robust and efficient technique is discussed for surface-grid generation on a general curvilinear surface. This technique is based on a non-uniform parameter space and allows for the generation of surface grids on highly skewed and nonuniform spaced background surface-grids. This method has been successfully integrated into the GRIDGEN software system.

Solutions for transients in arbitrarily branching cables: IV. Nonuniform electrical parameters

Solutions for transients in arbitrarily branching passive cable neurone models with a soma are extended to models with nonuniform electrical parameters and multiple dendritic shunts. The response to an injected current can again be represented as an infinite series of exponentially decaying components with system time constants obtained from the roots of a recursive transcendental equation. The reciprocity relations and global parameter dependencies are the same as for uniform models. Infinitely many "raw" electro-morphological models map onto a given "core" electrotonic model; local as well as global raw parameter trade-offs are now possible. The solutions are illustrated by means of biologically relevant examples: (i) the effects of nonuniform electrical parameters in a two-cylinder + soma cortical pyramidal cell model, (ii) the errors that can occur when uniformity is incorrectly assumed in a single cylinder model, (iii) nonsumming interactions between cells and electrodes that can dramatically increase the duration of the effective capacitative electrode artefact, and (iv) shunting inhibition and double impalements in a hippocampal CA1 pyramidal cell "cartoon" representation. These solutions should complement compartmental modelling techniques.

Crossed-field (trochoidal) electron monochromators and their optimization

In electron spectroscopy a wide variety of methods using the dispersive properties of both magnetic and electric fields are applied to analyse the energies of charged particles moving in a longitudinal magnetic field. Retarding potential analysers where a uniform magnetic field is used, however, possess a disadvantage: an integral characteristic (retarding curve) must be differentiated in order to determine the energy spectrum. In analysers with a non-uniform magnetic field (which is increased or decreased in the retarding region), electrons are analysed by both the longitudinal and total components of electron velocity. The method of using a Wien filter with non-uniform transverse fields, immersed in a weak longitudinal magnetic field, has also been reported. A complicated system of magnetic field formation of these analysers is coupled with restrictions on the magnetic field alteration rate. Trochoidal electron monochromators (TEMs) have a favourable advantage-principle simplicity-enabling low-energy electron beams to be obtained. Since being created, the TEM has been used in a series of studies of electron scattering by atoms and molecules and solid surfaces. The monochromator theory has been considered in detail in the literature where the principal parameters of the TEM were calculated. Here we consider the influence of transverse potential drop at the entrance slit and suggest the minimization of beam distortion at the exit by means of the proper choice of non-uniform transverse electric field parameters.