Third-order Polynomial Equation Research Articles

Determination of Critical Conditions for Dynamic Recrystallization of Commercially Pure Titanium

Abstract Microstructural evolution and mechanical properties are controlled by dynamic recrystallization (DRX) during industrial processing. To identify the critical condition for initiation of DRX, hot isothermal compression tests of commercially pure (CP)-70 titanium were conducted in a temperature range of 750°C–1,100°C and strain rate range of 0.001–10 s−1 to a true strain of 0.69. The critical condition for initiation of DRX can be identified from the inflection point on the strain-hardening rate (θ=∂σ/∂ε) versus flow stress (σ) curve. A third-order polynomial equation was fitted to the experimental θ−σ data to find out the inflection point. The results show that the critical stress (σc) for the initiation of DRX can be expressed as σc=−B/3A, where A and B are the coefficients of the third-order polynomial equation. It was observed that critical stress value depends on the deformation condition. The stress-strain curve was then normalized with respect to the peak stress (U=σ/σp vs.W=ε/εp), leading to a normalized value of critical stress, (Uc)=σc/σp=−B′/3A′, where A′ and B′ are the coefficients of the normalized third-order equation. The value of Uc(≈0.95) is a constant and independent of deformation conditions. These parameters were then used to calculate the DRX fraction, and the relationship between DRX fraction and processing variables was established.

Thermodynamic and transport properties of 2-methoxyaniline with substituted ethanols at various temperatures

Densities (ρ), the speed of sound (u) and viscosities (η) accounted for binary liquid combinations of 2-methoxyaniline with substituted ethanols (2-phenylethanol, 2-chloroethanol and 2-aminoethanol) over the whole arrangement scope of mole fraction at T = 303.15–318.15 K and at ambient pressure were measured. The excess and variable functions have been computed from the measured basic data. Excess and deviation functions have been correlated utilising the Redlich–Kister third-order polynomial equation. The excess partial functions have been figured for the binary systems all through the creation go and at infinite dilutions. The interpretations of these properties with the arrangement of investigated systems suggest the loss of dipolar association, deviation in size and fabrication of the segment molecules and hydrogen bonding between 2-methoxyaniline with substituted ethanols. V E comes out have been anatomised on the part of Prigogine–Flory–Patterson theory.

Dynamic Recrystallization Behavior of AISI 422 Stainless Steel During Hot Deformation Processes

In this work, hot compression tests were performed to investigate the dynamic recrystallization (DRX) process of a martensitic stainless steel (AISI 422) at temperatures of 950, 1000, 1050, 1100 and 1150 °C and strain rates of 0.01, 0.1 and 1 s−1. The dependency of strain-hardening rate on flow stress was used to estimate the critical stress for the onset of DRX. Accordingly, the critical stress to peak stress ratio was calculated as 0.84. Moreover, the effect of true strain was examined by fitting stress values to an Arrhenius type constitutive equation, and then considering material constants as a function of strain by using a third-order polynomial equation. Finally, two constitutive models were used to investigate the competency of the strain-dependent constitutive equations to predict the flow stress curves of the studied steel. It was concluded that one model offers better precision on the flow stress values after the peak stress, while the other model gives more accurate results before the peak stress.

Kinetics and mathematical modeling of infrared thin-layer drying of garlic slices.

Drying of garlic slices in thin-layer have been studied with Infrared (IR) at 0.075, 0.15, 0.225 and 0.3 W cm−2 radiation intensity and 0.75 and 1.25 m s−1 air flow velocity. The results showed increasing in drying rate and decreasing at the time of drying with decreasing air flow velocity and increasing IR radiation intensity. The effective moisture diffusivity (Deff) was obtained using Fick’s diffusion equation and its mean values ranged between 5.83×10−11 and 7.66×10−10 m2 s−1 for all investigated conditions. In addition, a third-order polynomial equation linking the effective moisture diffusivity and moisture content was found. Average activation energy increased with the decrease of IR radiation and increase of air flow velocity. Thirteen different mathematical models were verified with non-linear regression analysis for describing the garlic drying process. Modified Henderson and Pabis model presented the best prediction of the drying of garlic slices.

Astroparticle Physics Tests of Lorentz Invariance Violation

Testing Lorentz invariance is essential as it is one of the pillars of modern physics. Moreover, its violation is foreseen in several popular Quantum Gravity models. Several authors study the effects of Lorentz invariance violation (LIV) in the propagation of ultra-high energy cosmic rays. These particles are the most energetic events ever detected and therefore represent a promising framework to test LIV. In this work we present an analytic calculation of the inelasticity for any a + b → c + d interaction using first order perturbation in the dispersion relation that violates Lorentz invariance. The inelasticity can be calculated by solving a third-order polynomial equation containing: a) the kinematics of the interaction, b) the LIV term for each particle and c) the geometry of the interaction. We use the inelasticity we calculate to investigate the proton propagation in the intergalactic media. The photopion production of the proton interaction with the CMB is taken into account using the inelasticity and the attenuation length in different LIV scenarios. We show how the allowed phase space for the photopion production changes when LIV is considered for the interaction. The calculations presented here are going to be extended in order to calculated the modified ultra-high energy cosmic rays spectrum and compare it to the data.

General calibration of TDR to assess the moisture of tropical soils using artificial neural networks

Summary Determinations of soil moisture are important for various agricultural, environmental and hydrological applications, and accurate assessments are required. Artificial neural networks (ANNs) were applied in the present study to conduct general calibrations of time-domain reflectometry (TDR) probes using the physical characteristics of soil to estimate the moisture. The ANNs were trained and tested using data from five different soils. All of the combinations of physical properties, including the bulk density and sand, silt, clay and organic matter contents, were tested, and the inclusion of at least one of those network variables along with the apparent dielectric constant ( K a ), which was assessed using the TDR device, were sufficient to calibrate all five of the soils simultaneously. The ANN selected for the general calibration has a hidden layer with 13 neurons and tan-sigmoid-type transfer function. The analysis of the statistical indexes values indicates that the ANNs were slightly better than the third-order polynomial equations (Topp-like equations), which were specifically fitted to each soil. The tests were conducted to assess the performance of the general calibrations that were applied to estimate the moisture of the soils excluded from the training process, although the ANNs have such a potential; the most representative variables in descending order of importance were as follows: organic matter, sand, clay, and bulk density. The soil silt content failed to stand out in this analysis and showed a lower performance. Based on the results, the organic matter content was the preferred variable for use along with the K a in the ANNs applied to the general calibration of TDR (RMSE ranging from 0.0126 to 0.0237 g/g and r 2 ranging from 0.9083 to 0.9891). The sand content was also considered an advantageous variable because it was more easily assessed. The variables clay content and bulk density or the combination of several variables may also be used when available. As found by previous studies, the TDR calibration using ANN were better to sandy soils.

First-principles investigation of bowing parameter in zinc-blende ScxGa1−xN

We present first-principles calculations of the structural and electronic properties of binary GaN, ScN and alloys in the zinc-blende structure using pseudopotential plane-wave method within the density functional theory. The alloys are described by considering configurations in 16-atom supercells, corresponding to conventional cubic cells. The lattice parameter, bulk modulus, bulk modulus derivation, the energy band gap and bowing parameter are obtained as a function of Sc concentration for ternary alloys . Our studies focus on the concentration dependence of the electronic band structure and bowing parameter of these alloys. We found that composition affects strongly bowing parameter and the band gap increases with increasing Sc concentration for in the zinc-blende structure. The results also show that the energy band gap and bowing parameter of the alloys can be obtained by a third-order polynomial equation, and , respectively.

Continuous cervical spine kinematics during in vivo dynamic flexion-extension

Background contextA precise and comprehensive definition of “normal” in vivo cervical kinematics does not exist due to high intersubject variability and the absence of midrange kinematic data. In vitro test protocols and finite element models that are validated using only end range of motion data may not accurately reproduce continuous in vivo motion. PurposeThe primary objective of this study was to precisely quantify cervical spine intervertebral kinematics during continuous, functional flexion-extension in asymptomatic subjects. The advantages of assessing continuous intervertebral kinematics were demonstrated by comparing asymptomatic controls with patients with single-level anterior arthrodesis. Study designCervical spine kinematics were determined during continuous in vivo flexion-extension in a clinically relevant age group of asymptomatic controls and a group of patients with C5–C6 arthrodesis. Patient sampleThe patient sample consisted of 6 patients with single-level (C5–C6) anterior arthrodesis (average age: 48.8±6.9 years; 1 male, 5 female; 7.6±1.2 months postsurgery) and 18 asymptomatic control subjects of similar age (average age: 45.6±5.8 years; 5 male, 13 female). Outcome measuresOutcome measures included the physiologic measure of continuous kinematic motion paths at each cervical motion segment (C2–C7) during flexion-extension. MethodsParticipants performed flexion-extension while biplane radiographs were collected at 30 images per second. A previously validated tracking process determined three-dimensional vertebral positions with submillimeter accuracy. Continuous flexion-extension rotation and anterior-posterior translation motion paths were adjusted for disc height and static orientation of each corresponding motion segment. ResultsIntersubject variability in flexion-extension angle was decreased 15% to 46% and intersubject variability in anterior-posterior translation was reduced 14% to 33% after adjusting for disc height and static orientation angle. Average intersubject variability in continuous motion paths was 1.9° in flexion-extension and 0.6 mm in translation. Third-order polynomial equations were determined to precisely describe the continuous flexion-extension and anterior-posterior translation motion path at each motion segment (all R2>0.99). ConclusionsA significant portion of the intersubject variability in cervical kinematics can be explained by the disc height and the static orientation of each motion segment. Clinically relevant information may be gained by assessing intervertebral kinematics during continuous functional movement rather than at static, end range of motion positions. The fidelity of in vitro cervical spine mechanical testing protocols may be evaluated by comparing in vitro kinematics to the continuous motion paths presented.

Technical Basis for Application of Weight Function Method for Calculation of Stress Intensity Factor for Surface Flaws Proposed for ASME Section XI Appendix A

Analytical evaluation procedures for determining the acceptability of flaws detected during in-service inspection of nuclear power plant components are provided in Section XI of the ASME Boiler and Pressure Vessel Code. Linear elastic fracture mechanics based evaluation procedures in ASME Section XI require calculation of the stress intensity factor. A method for calculating the stress intensity factor is provided in Appendix A of ASME Section XI. This method consists of a two-step process. In the first step, the stress distribution, as calculated in the absence of the flaw, is obtained at the flaw location. For a surface flaw, the stress distribution at the flaw location is then fitted to a third-order polynomial equation. In the second step, the fitted polynomial representation of the stress distribution is used with standardized influence coefficients to calculate the stress intensity factor. An alternate method for calculation of the stress intensity factor for a surface flaw that makes explicit use of the universal weight function method and does not require a polynomial fit to the actual stress distribution is proposed in this paper for implementation into Appendix A of ASME Section XI. Universal weight function coefficients are determined from standardized influence coefficients through closed-form equations. Closed-form equations for calculation of the stress intensity factor are provided. The technical basis and verification for this alternate method for calculation of the stress intensity factor are described in this paper.

라이다 측정을 이용한 나셀 풍속계 보정식 제안

The nacelle anemometer mounted behind the blade roots of a wind turbine measures distorted wind speed comparable with free-stream wind because of the wake effects caused dependent upon the operation of the wind turbine and the rotation of its blades. The field campaign was carried out to measure free-stream wind speed at a height identical to the height of the nacelle anemometer by deploying a ground-based remote-sensing equipment, LIDAR. It is derived that a third-order polynomial equation for correcting wind speed measured by the nacelle anemometer to undistorted free-stream wind speed incident to a wind turbine. It is anticipated that the derived correction equation enables wind speed measured by the nacelle anemometer to be used as a precise input for a wind turbine performance test and for developing an active control logic.

Third-order polynomial equations of municipal urban low-volume pavement for the most common distress types

The estimation of the distress mechanism change for low-volume pavements with the help of third-order polynomial equations is the subject of discussion in this study. In the literature, various models are available, but their complex structure has restricted their application for real-life situations. This study is an attempt to provide suitable models for the estimation of pavement deterioration based on pavement distress mechanism changing individually with time. Three models, for the most distress types existing on the network, have been developed using a survey data of 10 years for overlaid sections on the roads network of Riyadh and Dammam, Saudi Arabia.

THE COMPOSITION EFFECT ON THE BOWING PARAMETER IN THE CUBIC TlxAl1-xAs

The band gap bowing parameter of the new semiconductor Tl x Al 1-x As alloys are investigated numerically based on first-principles calculations and the local density approximation. A 16-atom supercell is used to model for the ternary Tl x Al 1-x As alloys. The alloy's lattice constants obey Vegard's law well. Band gap bowing coefficients show very strong composition dependence. The results suggest that the unstrained band gap bowing parameter of the ternary Tl x Al 1-x As alloys is b = 1.9754 eV. The results also suggest that the composition-dependent band gap energy of the zincblende alloys can be expressed by a third-order polynomial equation, Eg(x) = -7.2064x3 + 14.8397x2-10.016x + 2.2217 eV .

Liquid–Liquid Equilibria of Polyvinylpyrrolidone + Several Ammonium Salts + Water Aqueous Two-Phase Systems: Experimental and Correlation

Phase equilibrium behaviors of polyvinylpyrrolidone (PVP) + (NH4)2HPO4, (NH4)2SO4, (NH4)2CO3, (NH4)2C4H4O6, and (NH4)2HC6H5O7 + H2O aqueous two-phase systems (ATPS's) were determined at 298.15 K. A series of common phase-forming ammonium salts and the corresponding anions were discussed. Meanwhile, the temperature effect on phase equilibrium behavior for PVP (K30) + (NH4)2HPO4 + H2O ATPS was investigated at (288.15, 298.15, and 308.15) K. It was found that phase-forming abilities of the salts are in the order: (NH4)2HPO4 > (NH4)2SO4 > (NH4)2C4H4O6 > (NH4)2HC6H5O7 > (NH4)2CO3. Furthermore, a third-order polynomial equation was used to correlate the binodal data, while a simple two-parameter equation along with the Othmer–Tobias and Bancroft equations was used to correlate the tie-lines data. All equations used above were proved to be valid for the experimental data. At last, the data of critical points were obtained by an extrapolation method.

Influence of regression model and incremental test protocol on the relationship between lactate threshold using the maximal-deviation method and performance in female runners

This study examined the influence of the regression model and initial intensity of an incremental test on the relationship between the lactate threshold estimated by the maximal-deviation method and the endurance performance. Sixteen non-competitive, recreational female runners performed a discontinuous incremental treadmill test. The initial speed was set at 7 km · h−1, and increased every 3 min by 1 km · h−1 with a 30-s rest between the stages used for earlobe capillary blood sample collection. Lactate-speed data were fitted by an exponential-plus-constant and a third-order polynomial equation. The lactate threshold was determined for both regression equations, using all the coordinates, excluding the first and excluding the first and second initial points. Mean speed of a 10-km road race was the performance index (3.04 ± 0.22 m · s−1). The exponentially-derived lactate threshold had a higher correlation (0.98 ≤ r ≤ 0.99) and smaller standard error of estimate (SEE) (0.04 ≤ SEE ≤ 0.05 m · s−1) with performance than the polynomially-derived equivalent (0.83 ≤ r ≤ 0.89; 0.10 ≤ SEE ≤ 0.13 m · s−1). The exponential lactate threshold was greater than the polynomial equivalent (P < 0.05). The results suggest that the exponential lactate threshold is a valid performance index that is independent of the initial intensity of the incremental test and better than the polynomial equivalent.

Development of a Simple Reference Evapotranspiration Model for Irrigation of Woody Ornamentals

Rooted cuttings of Rhaphiolepis indica, a low slow-growing evergreen shrub, were grown outdoors in weighing lysimeters to market size in 11.4-L containers. Actual evapotranspiration (ETA) and evaporation from containers shaded with plastic foliage was determined daily. The first 60 days after transplanting, substrate evaporation accounted for most of ETA and was the major component through the first 127 days. ETA generally followed variations in reference evapotranspiration (ETo). Mean cumulative ETA to produce 90% of measured plants to market size was 101 L or 1.99-m depth per plant based on container surface area. Water need indices, similar to crop coefficients, were highly correlated with percent canopy closure using an exponential decay equation (r2 = 0.898), but a more precise estimate at higher canopy closures was achieved using a third-order inverse polynomial equation (r2 = 0.907). When combined with similar previous data from Viburnum odoratissimum and Ligustrum japonicum, the inverse polynomial equation correlation was 0.802 for all three shrubs. This implies the %Closure model provides a good general base for ETo-based irrigation of woody evergreen shrub species based on canopy size and spacing with improved precision when individual equations are derived by species.

Optimization of Process Parameters of Hot-Dip Aluminized Coating

The hot-dip aluminized process parameters with respect to the thickness and microstructure of intermetalic layer were investigated using a uniform design of experiments. The measured thickness of intermetalic layer was regressed as first- to third-order polynomial equations of four related parameters, i.e. hot-dip temperature, hot-dip time, diffusion treatment temperature and diffusion treatment time. It was found that the third-order regressed equation was acceptable and appropriate to identify the influences of the investigated parameters on the thickness of intermetalic layer. Comprehensive analysis of the results based on the regressed equation and microstructure could supply believable and optimized process parameters.

Decentralized output feedback polynomial control of seismically excited structures using genetic algorithm

This paper presents novel decentralized output feedback control strategy for the active and semi-active controls of the highway bridge benchmark phases I and II problems subjected to earthquake ground motions. The control force is calculated using two third-order polynomial equations expressing a direct relationship between displacement and velocity of the control device and the control force. An advanced implicit redundant representation genetic algorithm is utilized to determine optimal coefficients of the two polynomial equations by minimizing the sum of three evaluation criteria for six prescribed earthquakes. The performance of the proposed controller is evaluated in terms of a set of prescribed 21 evaluation criteria and is compared with the other several control strategies published in the special issue of the benchmark problem. The results show that the proposed decentralized output feedback polynomial control strategy can achieve significant response reductions in the bridge system, and it is evidently superior to sample control strategies and other suggested active and semi-active controls for the phase I problem and is quite competitive with respect to the sample and other semi-active control approaches for the fully isolated phase II problem. Copyright © 2011 John Wiley & Sons, Ltd.

Influence of the pressure holding time on strain generation in fuel injection lines

An influence of the pressure holding time on residual strain generation during the autofrettage process was studied experimentally for the first time in the present work. It is the state of the art that fuel injection lines are held at the autofrettage pressure for only a few seconds in an industrial production. In doing so, it is assumed that a desirable residual stress–strain pattern is generated. However, the results of the experimental investigations outlined in this work indicated that completion of the plastic deformation caused by the autofrettage process and generation of the desirable stress–strain pattern require a much longer period. As shown, a third-order polynomial equation best described the interdependence between the time required for the completion of the process, the corresponding autofrettage pressure and the generated strain state. The method presented can be used as a tool for the determination of the optimal autofrettage process parameters in industrial production of fuel injection lines.

Characterization of glucose-insulin responsiveness and impact of fetal number and sex difference on insulin response in the sheep fetus

GSIS is often measured in the sheep fetus by a square-wave hyperglycemic clamp, but maximal β-cell responsiveness and effects of fetal number and sex difference have not been fully evaluated. We determined the dose-response curve for GSIS in fetal sheep (0.9 of gestation) by increasing plasma glucose from euglycemia in a stepwise fashion. The glucose-insulin response was best fit by curvilinear third-order polynomial equations for singletons (y = 0.018x(3) - 0.26x(2) + 1.2x - 0.64) and twins (y = -0.012x(3) + 0.043x(2) + 0.40x - 0.16). In singles, maximal insulin secretion was achieved at 3.4 ± 0.2 mmol/l glucose but began to plateau after 2.4 ± 0.2 mmol/l glucose (90% of maximum), whereas the maximum for twins was reached at 4.8 ± 0.4 mmol/l glucose. In twin (n = 18) and singleton (n = 49) fetuses, GSIS was determined with a square-wave hyperglycemic clamp >2.4 mmol/l glucose. Twins had a lower basal glucose concentration, and plasma insulin concentrations were 59 (P < 0.01) and 43% (P < 0.05) lower in twins than singletons during the euglycemic and hyperglycemic periods, respectively. The basal glucose/insulin ratio was approximately doubled in twins vs. singles (P < 0.001), indicating greater insulin sensitivity. In a separate cohort of fetuses, twins (n = 8) had lower body weight (P < 0.05) and β-cell mass (P < 0.01) than singleton fetuses (n = 7) as a result of smaller pancreata (P < 0.01) and a positive correlation (P < 0.05) between insulin immunopositive area and fetal weight (P < 0.05). No effects of sex difference on GSIS or β-cell mass were observed. These findings indicate that insulin secretion is less responsive to physiological glucose concentrations in twins, due in part to less β-cell mass.

Nutrient concentration variations during Oenanthe javanica growth and decay in the ecological floating bed system

The ecological floating bed system is a natural alternative to technical methods of wastewater treatment and involves complex processes induced by plants or microorganisms in the wastewater. This study aimed to identify nutrient concentration variations during Oenanthe javanica (Blume) DC growth and decay in the ecological floating bed system. Results showed that the third-order polynomial equation was suitable to describe pollutant concentration changes, showing that the effect of O. javanica ecological floating bed system on polluted water could be divided into the purification phase and decay phase. During the purification phase, nutrient concentrations rapidly decreased because O. javanica influenced water microbial communities and water physical parameters (i.e., dissolved oxygen, pH, and temperature), and had a direct uptake of nutrients. However, during the decay phase, nitrogen and phosphorus concentrations in the plant tissues decreased, and these lost nutrients ultimately transferred to water and led to water quality deterioration. Results also showed that the uptake and storage of O. javanica in nutrients were temporary and the plant served only as media of the nutrients removed from the water. Under these circumstances, harvesting was an appropriate intervention to improve the treatment efficiency of O. javanica ecological floating bed system.