Fifth-order Polynomial Research Articles

A New Numerical Scheme for Linear Scalar Conservation Laws

In this paper, we develop a numerical scheme with the fifth-order polynomial reconstruction satisfying two conservation laws for the linear advection equation. The scheme is the Godunov type, and has two numerical entities, numerical solution and numerical entropy. Numerical experiments show that the scheme is more robust in long-time behaviors than that of [8].

Sampling interval sensitivity analysis for crack detection by stationary wavelet transform

The purpose of this paper was to analyze the sampling interval sensitivity for crack detection by stationary wavelet transform (SWT) in order to facilitate the identification of crack locations in beam-like structures. SWT is a redundant transform that doubles the number of input samples at each iteration. It has been shown that the SWT decomposition detail coefficient of mode shapes of beam-like structure can provide sensitive crack indication that is useful for damage detection. However, the sampling interval is an important factor that affects the sensitivity of crack detection. Three SWT methods were analyzed, including the method using the SWT of the original mode shape (designated SWT-1), the method using the difference between the detail coefficients of the SWT of the left-half and the reconstructed right-half sets of the mode shapes (designated SWT-2), and the method using the difference between the detail coefficient of the left-half and right-half sets of the interpolated mode shapes (designated SWT-3). The modal responses of damaged beams with single and multiple cracks are computed using the finite element method. The curve of the peak value of SWT detail coefficient versus sampling interval was obtained using a fifth-order polynomial fit method. The effects of crack depth, crack width, and crack locations on the sensitivity of sampling interval on crack detection are investigated. SWT-2 method has a shortcoming in determining whether the cracks are located at the true crack location or its mirror image position at different sampling intervals. In order to overcome this shortcoming, two rules are proposed for the determination of true crack locations and the selection of sampling intervals for single crack or multiple crack detection.

On the optimal symmetric purification scheme of the one-particle density matrix

Density matrix purification is an efficient way of avoiding the expensive cubic scaling diagonalization in self-consistent field calculations. Although there are a number of different algorithms suggested to reduce the number of matrix multiplications for purification, there is no rigorous mathematical proof which scheme is optimal. In this Letter, we show analytically that the repeated application of the fifth-order Holas polynomial throughout all iterations is an optimal scheme that reduces the error symmetrically for both occupied and virtual occupations, and either the use of lower/higher-order polynomials throughout or mixed use of polynomials of different degree at different iteration results in higher cost.

A New Global Set of Downscaled Temperature Scenarios

Abstract A new set of empirical–statistical downscaled seasonal mean temperature scenarios is presented for locations spread across all continents. These results are based on the Coupled Model Intercomparison Project phase 3 (CMIP3) simulations, the Special Report on Emissions Scenarios (SRES) A1B story line, and arguably represent the largest downscaled multimodel ensemble to date in terms of worldwide distribution, length of time interval, and the number of global climate model simulations. The ensemble size of ∼50 members enables a crude uncertainty analysis for simulated future local temperature, and maps have been constructed for Europe, Africa, and the northwestern part of Russia and Scandinavia of the ensemble mean and 95th percentile for seasonal mean temperatures projected for 2100, as well as simulated probabilities for low or high temperatures. The results are stored as matrices of coefficients describing best-fit fifth-order polynomials, used to approximate the long-term trends in the temperature. These results suggest that the 95th percentile of the summer temperature is expected to increase 3°–5°C by 2100 over most of Europe, and that there will be reduced probabilities of winter temperature lower than 0°C for all European locations, with the greatest reduction of ∼60% in areas where the winter temperature presently is around freezing point. A similar analysis for Africa suggests that the June–August mean temperatures may exceed 35°C in isolated regions by 2100. For the northwestern part of Russia and Scandinavia, the analysis yields a 4.5°–7.5°C increase for the ensemble mean December–February temperature, with the most pronounced warming in the northeast, north, and over Finnmark County in Norway.

Development of a Stereo Vision Measurement System for a 3D Three-Axial Pneumatic Parallel Mechanism Robot Arm

In this paper, a stereo vision 3D position measurement system for a three-axial pneumatic parallel mechanism robot arm is presented. The stereo vision 3D position measurement system aims to measure the 3D trajectories of the end-effector of the robot arm. To track the end-effector of the robot arm, the circle detection algorithm is used to detect the desired target and the SAD algorithm is used to track the moving target and to search the corresponding target location along the conjugate epipolar line in the stereo pair. After camera calibration, both intrinsic and extrinsic parameters of the stereo rig can be obtained, so images can be rectified according to the camera parameters. Thus, through the epipolar rectification, the stereo matching process is reduced to a horizontal search along the conjugate epipolar line. Finally, 3D trajectories of the end-effector are computed by stereo triangulation. The experimental results show that the stereo vision 3D position measurement system proposed in this paper can successfully track and measure the fifth-order polynomial trajectory and sinusoidal trajectory of the end-effector of the three- axial pneumatic parallel mechanism robot arm.

Determination of the Whiteside line on femur surface models by fitting high-order polynomial functions to cross-section profiles of the intercondylar fossa

Innovative methods for morphological and functional analysis of bones have become a primary objective in the development of planning systems for total knee replacement (TKR). These methods involve the interactive identification of clinical landmarks (reference points, distances, angles, and functional axes of movement) and the determination of the optimal implant size and positioning. Among the functional axes used to estimate the correct alignment of the femoral component, the Whiteside line, namely, the anterior-posterior (AP) direction, is one of the most common. In this paper, we present a computational framework that allows automatic identification of the Whiteside line.The approach is based on geometric analysis of the saddle shape of the intercondylar fossa to extract the principal line in the AP direction. A plane parallel to the frontal plane is moved in the AP direction to obtain the 2D profiles of the intercondylar fossa. Each profile is fitted to a fifth-order polynomial curve and its maximum curvature point computed. The point set collected across all the profiles is then processed to compute the principal direction. The 2D profile-fitting and 3D line-fitting residual errors were analyzed to study the relationship between the intercondylar fossa aspect and the nominal saddle surface. The method was validated using femur specimens from elderly subjects reconstructed from CT scans. The repeatability of the method was evaluated across five different femur surface resolutions.For comparison, three expert orthopaedic surgeons identified, by virtual palpation, the Whiteside line on the same 3D femur models. The repeatability (median angular error) of the Whiteside lines computed by the automated method and by manual virtual palpation, was approximately 1.0° and 3.5°, respectively. The angular skew error between the two axes, measured on the axial plane, averaged approximately 4.00° (SD: 2.64°) with no statistical difference. The automated method therefore proved more reproducible and was in agreement with the manual method. We conclude that operator-independent methods, such the one presented in this paper, can be favorably introduced into orthopaedic surgical planning systems.

Prediction of Critical Properties of Normal Alkanes Using Pakmakar−Ivan Topological Index

For the first time Pakmakar−Ivan (PI) topological index has been applied for prediction of various critical properties of normal alkanes from methane to eicosane. A general fifth-order polynomial as a function of just a single variable of PI index has been proposed for this prediction. Predicted critical properties of normal alkanes based on this method were compared with the other well-known predictive methods as well as the experimental data, and excellent agreement was obtained.

Dynamic analysis algorithm for a micro-robot for surgical applications

The applications of robotics in medical field have increased extensively in the last two decades. The purpose of this paper is to present an algorithm for a complete dynamic analysis for a six degrees of freedom micro-robot intended for surgical applications. The algorithm consists of five modules and it can easily draw the torque history for each joint provided that the homogeneous transformation matrices and the robot and joint parameters are known. The kinematic equations of motion were obtained using Denavit–Hartenberg notations. The workspace of the robot can be drawn through the solution of the inverse kinematic equations considering the physical limit of each joint. The trajectory planning was derived in the joint space using two different techniques; fifth-order polynomial, and soft motion trajectory. The dynamic equations of motion were derived using the Lagrangian–Euler technique which is appropriate for numerical simulation. The standard inverse dynamics computation method was used to calculate the required hub torque, to move each joint according to a prescribed trajectory. A simulation analysis was carried out to choose the most suitable method that gives the smooth torque profile its best performance for the robot under investigation.The simulation results were obtained using MATLAB Symbolic Toolbox.

Evaluation of egg production in layers using random regression models

The objectives of this study were to estimate genetic parameters for egg production over the age trajectory in 3 layer lines, which represent different biotypes for egg production, and to validate the use of breeding values for slope as a measure of persistency to be used in the selection program. Egg production of more than 26,000 layers per line from 6 consecutive generations were analyzed with a random regression model with a within-hatch-nested fifth-order fixed-regression polynomial and linear polynomials for random additive genetic and permanent environmental effects. Daily records were cumulated into biweekly periods. In all lines, a nonzero genetic variance for mean and slope and a positive genetic correlation between mean and slope were estimated. Genetic variance of egg production by 2-wk period was low at the beginning of lay and increased as the birds aged for all 3 lines, which resulted in heritability estimates increasing with age. Breeding values for slope reflected the shape of the egg production curve well and can be used to directly select for persistency of egg production.

Estimates of genetic parameters for scrotal circumference using random regression models in Nelore cattle

A total of 15,901 scrotal circumference (SC) records from 5300 Nelore bulls, ranging from 229 to 560days of age, were used with the objective of estimating (co)variance functions for SC, using random regression models. Models included the fixed effects of contemporary group and age of dam at calving as covariable (linear and quadratic effects). To model the population mean trend, a third order Legendre polynomial on animal age was utilized. The direct additive genetic and animal permanent environmental random effects were modeled by Legendre polynomials on animal age, with orders of fit ranging from 1 to 5. Residual variances were modeled considering 1 (homogeneity of variance) or 4 age classes. Results obtained with the random regression models were compared to multi-trait analysis. (Co)variance estimates using multi-trait and random regression models were similar. The model considering a third- and fifth-order Legendre polynomials for additive genetic and animal permanent environmental effects, respectively, was the most adequate to model changes in variance of SC with age. Heritability estimates for SC ranged from 0.24 (229days of age) to 0.47 (300days of age), remained almost constant until 500days of age (0.52), decreasing thereafter (0.44). In general, the genetic correlations between measures of scrotal circumference obtained from 229 to 560days of age decreased with increasing distance between ages. For genetic evaluation scrotal circumference could be measured between 400 and 500days of age.

Boundary slip dependency on surface stiffness

The paper investigates the effects of surface stiffness on the slip process aiming to obtain a better insight of the momentum transfer at nanoscale. The surface stiffness is modeled through the stiffness, κ, of spring potentials, which are employed to construct the thermal walls. It is shown that variations of stiffness, κ, influence the slip mechanism either toward slip or stick conditions. Increasing the values of κ alters the oscillation frequency and the mean displacement of the wall particles toward higher and lower values, respectively. Our results suggest that the amount of slip produced as a function of stiffness follows a common pattern that can be modeled through a fifth-order polynomial function.

Scaled Polynomial Expression for Self-Diffusion Coefficients for Water, Benzene, and Cyclohexane over a Wide Range of Temperatures and Densities

Self-diffusion coefficients D for water, benzene, and cyclohexane were determined in high-temperature conditions along the liquid branch of the coexistence curve and in supercritical conditions including an extremely low density region. The diffusion data available in literature were compared and evaluated. A fifth-order polynomial for ln D with the single variable T−1 (ln(D/10−9 m2·s−1) = a0+ a1x + a2x2 + a3x3 + a4x4 + a5x5 with x = 1000/(T/K)) was found to provide good fitting along the liquid branch of the coexistence curve. A single polynomial function for the scaled quantity ρD/T1/2 with the two variables, density ρ and temperature T−1 (third-order polynomial of ρ and T−1 and the cross terms), can universally represent the diffusion data over a wider range including both the gas−liquid coexistence and the extremely low density conditions. The function gives a reliable and reasonable behavior of D in the medium-density supercritical states in which the experimental uncertainty is rather large due to t...

Silicon Raman Amplifiers With Ring-Resonator-Enhanced Pump Power

In this paper, design rules for optimal silicon Raman amplifiers operating at standard telecommunications wavelengths are formulated. For given material and waveguide parameters, and a specified upper pump-power limit, explicit expressions are derived for the optimal length and maximum possible gain of single-pass-pumped amplifiers. For ring-resonator (RR) amplifiers, the optimization problem is reduced to finding a zero of a fifth-order polynomial. Due to resonant pump-power enhancement, RR amplifiers with positive gain can be realized for any pump power, however small it is. Finally, for small pump powers, the maximum possible gain is most effectively increased by reducing the linear waveguide losses as opposed to the effective area or the effective free-carrier lifetime.

Solubility of SO2 in Caprolactam Tetrabutyl Ammonium Bromide Ionic Liquids

To explore environmentally benign solvents for absorbing SO2, a series of caprolactam tetrabutyl ammonium bromide ionic liquids were synthesized, the solubilities of SO2 in which were measured at (298.2 to 403.2) K and atmospheric pressure. The solubilities of SO2 in these ionic liquids were 0.680 at 298.2 K and ambient pressure and decreased sharply as temperature increased and increased with the increasing mole ratio of caprolactam. A fifth-order polynomial was proposed and verified by experimental solubility data. The absorption and desorption of SO2 were practically reversible in the synthesized ionic liquids.

Numerical solution of curved pipes submitted to in-plane loading conditions

An alternative formulation to current meshes dealing with finite shell elements is presented to solve the problem of stress analysis of curved pipes subjected to in-plane bending forces. The solution is based on finite curved elements, where displacements are defined from a total set of trigonometric functions or a fifth-order polynomial, combined with Fourier series. Global shell displacements are achieved through the one associated with curved arch bending and the other referred to the toroidal thin-walled shell distortion. Beam-type displacement and in-plane rotation are uncoupled and separately formulated, using trigonometric shape functions, as in Timoshenko or Mindlin beam theory. To build up the solution, a simple deformation model was adopted, based on the semi-membrane concept of the doubly curved shells behaviour. Several studies are presented and compared with experimental and numerical analyses reported by other authors.

THE STABILITY OF OPTICALLY THIN REACTING PLASMAS: EFFECTS OF THE BULK VISCOSITY

The thermochemical stability of reacting plasmas is analyzed by taking into account the change in the thermodynamical equilibrium values during the fluctuation. This shift in the equilibrium produces two main effects: a change in the four instability criteria for reacting gases resulting when the above effect is neglected and adds a fifth instability criterion due to the fact that the corresponding secular equation becomes a fifth-order polynomial. The above results are applied to several plasma models, in particular, to a photoionized hydrogen plasma for which the bulk viscosity can be more important than the dynamic viscosity and the thermometric conductivity. Therefore, the bulk viscosity may quench thermochemical instabilities were the thermal conduction is unable of stabilizing. This occurs for low values of the photoionizing energy E. The implications of the above results in explaining the formation of clump structures in different regions of the interstellar medium are outlined.

Design and Manufacture of Spiral Bevel Gears With Reduced Transmission Errors

A method for the determination of the optimal polynomial functions for the conduction of machine-tool setting variations in pinion teeth finishing in order to reduce the transmission errors in spiral bevel gears is presented. Polynomial functions of order up to 5 are applied to conduct the variation in the cradle radial setting and in the cutting ratio in the process for pinion teeth generation. Two cases were investigated: In the first case, the coefficients of the polynomial functions are constant throughout the whole generation process of one pinion tooth-surface; in the second case, the coefficients are different for the generation of the pinion tooth-surface on the two sides of the initial contact point. The obtained results have shown that by the use of two different fifth-order polynomial functions for the variation in the cradle radial setting for the generation of the pinion tooth-surface on the two sides of the initial contact point, the maximum transmission error can be reduced by 81%. By the use of the optimal modified roll, this reduction is 61%. The obtained results have also shown that by the optimal variation in the cradle radial setting, the influence of misalignments inherent in the spiral bevel gear pair and of the transmitted torque on the increase in transmission errors can be considerably reduced.

Kinetic Rate Laws of Cd, Pb, and Zn Vaporization during Municipal Solid Waste Incineration

The kinetic rate laws of heavy metal (HM) vaporization from municipal solid waste during its incineration were studied. Realistic artificial waste (RAW) samples spiked with Pb, Zn, and Cd were injected into a fluidized bed reactor. Metal vaporization wastracked by continuous measure ofthe above metals in exhaust gases. An inverse model of the reactor was used to calculate the metal vaporization rates from the concentration vs time profiles in the outlet gas. For each metal, experiments were carried out at several temperatures in order to determine the kinetic parameters and to obtain specific rate laws as functions of temperature. Temperature has a strong influence on the HM vaporization dynamics, especially on the vaporization kinetics profile. This phenomenon was attributed to internal diffusion control of the HM release. Two types of kinetic rate laws were established based on temperature: a fourth- or fifth-order polynomial rate law (r(x) = k0e(-E(A)/RT)p(x)) for temperatures lower than 740 degrees C and a first-order polynomial (r(x) = k0e(-E(A)/ RT(q-q(f) for temperatures higher than 740 degrees C.

Autonomous parallel parking of a car-like mobile robot by a neuro-fuzzy sensor-based controller

In this paper, a neuro-fuzzy model has been developed for autonomous parallel parking of a car-like mobile robot. In our approach we have focused on the most difficult case of parallel parking which is the case when the parking space dimensions cannot be identified. The proposed model uses the data from three sonar sensors mounted in the front left corner of the car to decide on the turning angle. Fifth-order polynomial reference paths for three different size parking dimensions have been used to generate the training data. The fuzzy model has been identified by subtractive clustering algorithm and trained by ANFIS. The simulation results show that the model can successfully decide about the motion direction at each sampling time without knowing the parking space width, based on the direct sonar readings which serve as inputs. The results which are based on real dimensions of a typical car demonstrate the feasibility and effectiveness of the proposed controller in parallel parking.

A first-principles-derived method for computing the piezoelectric coefficients of complex semiconductor Sc1−xGaxN alloys

Abstract We use direct first-principles techniques and Keating's semiempirical valence force field (VFF) approach to develop a first-principles-derived method to calculate the piezoelectric coefficients e ij of semiconductor heterostructures and alloys. This technique is applied to study the effect of the atomic arrangement and composition on e 33 piezoelectric coefficients of hexagonal ordered and disordered Sc 1− x Ga x N alloys. Our results on ordered structures are in excellent agreement with local density approximation (LDA) first-principles calculations. Our results reveal that atomic ordering can have a large effect on piezoelectricity and that e 33 of ordered and disordered Sc 1− x Ga x N alloys as a function of Ga concentration can be fitted into a fourth-order and a fifth-order polynomial, respectively. Results of this work are predicted to have a large impact on improving the quality of Sc 1− x Ga x N alloys and heterostructures grown on ScN substrates. The microscopic origins for these effects are discussed and explained in detail.