Extrapolation Of Curve Research Articles

Mold Filling Simulation Dependence on Material Data Input for Injection Molding Process of Natural Rubber Compound

Abstract The influence of material data input towards the mold filling behavior of a natural rubber compound during an injection molding process was investigated. A commercial injection molding software (Cadmould) was utilized in evaluating the effect of using experimentally obtained material data on the mold filling progression in comparison to the actual injection molding procedure. The experimental rheological data were measured using a capillary rheometer and subsequently, the Carreau and Cross models were used to acquire the rheological parameters by curve fitting and extrapolation procedures. The cure kinetics data were obtained by employing a cure rheometer technique along with utilization of empirical approach through application of mathematical models proposed by Claxton–Liska and Deng–Isayev. It was discovered that the acquired data were able to function as reliable material data input as they were comparable with related data available in the software materials' database. Verification of the simulated filling profiles by experimental short shots specimens showed that the software Rubber Package was able to predict the realistic filling behavior of the formulated natural rubber compound inside the mold cavity when the measured material data were utilized. Whereas, the usage of available material data from the software database failed to model the mold filling progression of the prepared natural rubber compound.

Extrapolation of Creep Curve and Creep Rate by Strain Acceleration Parameter in Al-Mg Solid Solution Alloys

It has been widely accepted that the creep characteristics at high temperatures are mainly evaluated by a minimum creep rate. Although, a shape of creep curve may vary depending on deformation conditions, the apparent steady state or minimum creep rates be the same. Thus,for detailed analysis and prediction of creep behavior, other values which reflect the shape of each creep curve should be considered. For the purpose, authors have proposed Sato’s strain- acceleration-parameter (Strain Acceleration and Transition Objective index, SATO-index) which reflects strain rate change during creep deformation. Based on the concept of SATO-index, the whole creep curve can be represented by a set of small number of numerical parameters, and can be extrapolated from a part of creep curve. In this paper, application of the concept of SATO-index to the creep curves of aluminum-magnesium solid solutions that the creep behavior of the alloys are well investigated and analyzed. The creep curve can be extrapolated by the concept from transient part of creep curve, and the extrapolated creep rates at the minimum creep rate agree well with experiment. Efficiency of the concept of SATO-index to creep experiments is pronounced.

Diesel engine spray characteristics prediction with hybridized artificial neural network optimized by genetic algorithm

ANN (artificial neural network) modeling is adopted along GA (genetic algorithm) optimization method in order to investigate spray behavior as function of nozzle and engine variant parameters such as crank-angle, nozzle tip mass flow rate, turbulence, and nozzle discharge pressure. Spray quality is measured in SMD (Sauter mean diameter) and spray liquid tip penetration prospective. Experimental data were used at limited engine condition and elsewhere requisite data was acquired with the aid of curve fitting and extrapolation of CFD (computational fluid dynamics) numerical simulation results. Engine crank-angle, vapor mass flow rate, turbulence, and nozzle outlet pressure were taken as input layer while spray penetration and SMD were used as output layer. It is found out that Levenburg–Marquardt training algorithm has the least mean square error for ANN and ANN-GA (artificial neural network-genetic algorithm) at 24, 30 neurons in hidden layer with the amount of 0.8994, 0.3348, respectively. The coefficient of determination (R2) for penetration equals 0.994 whereas SMD yields lower amount of 0.992. By application of GA to optimize the network's interconnecting weights, R2 values have been enhanced to 0.999 for SMD and to 0.998 for penetration (both values are close to unity). Results indicate that the ANN-GA improved the spray specification modeling simply and with acceptable accuracy.

Estimation of life expectancy and quality-adjusted life expectancy in non-metastatic nasopharyngeal cancer patients treated by intensity-modulated radiotherapy with or without chemotherapy

This study was designed to estimate the life expectancy (LE) and quality-adjusted life expectancy (QALE) in non-metastatic nasopharyngeal cancer (NPC) patients. Patients were eligible for the present study if they were diagnosed with NPC and had been treated with intensity-modulated radiotherapy (IMRT) between January 1, 2003 and December 31, 2010. The quality of life (QOL) data were collected using the questionnaires of the European Organization for Research and Treatment of Cancer (EORTC) QLQ-C30 and QLQ-H&N35. The LE of NPC patients was obtained using linear extrapolation of a logit-transformed curve and was adjusted by the corresponding QOL function to calculate the QALE. During the study period, 110 patients met the inclusion criteria, and 53 of these completed questionnaires. The median follow-up was 65.2 months (range 4.0-117.3 months). The average LE and QALE were estimated to be 20.6 years and 11.6 quality-adjusted life years (QALYs) for NPC patients and 24.4 years and 24.4 QALYs for the reference population, respectively. Compared to the reference population, the loss of LE and QALE for NPC patients were 3.8 years and 12.8 QALYs, respectively. This study offers a quick overview of the LE and the QALE of NPC patients treated with IMRT. Moreover, the results appear more understandable than the 5 year survival outcomes when communicating with patients or the general population regarding cancer risk. In the future, evaluating the robustness of comparative assessments for the outcome of NPC patients undergoing different treatment protocols will be possible.

Automatic dynamic depth focusing for NDT

Auto-focusing along with dynamic depth focusing (DDF) would be very valuable to inspect arbitrarily shaped parts when operating with wedges or with other coupling media to avoid the burden of computing and setting the correct focal laws while still getting the best possible resolution at all depths. This work proposes a three-step procedure to perform the auto-focusing function with DDF in real time. First, the part geometry is estimated by the first echo time-of-arrival following one of several possible strategies: pulse-echo, pitch-catch, or plane wave. These are analyzed with regard to their performances and acquisition time, giving closed formulae to get the coordinates of interface points. After a curve fitting and extrapolation process, a virtual array that operates in a homogeneous medium is computed, avoiding the complications of refraction at the interface and allowing operation with already known focusing hardware. This hardware is initialized with the set of focusing parameters adapted to the estimated probe- part geometry, and ensures that all received samples are in focus. Using a standard computer, the auto-focusing procedure currently takes about 2 s to perform. Experiments carried out under different conditions validate the proposed technique.

Troubleshooting in geoelectrical prospecting using real‐coded genetic algorithm with chromosomal extrapolation

SUMMARYThis work presents a genetic operator developed from mathematical methods of curve extrapolation applied in solving problems in geoelectrical prospection. This operator will assist the production of fitter individuals in the population of a genetic algorithm in which inherent patterns of the best individuals of each generation are recognized. The proposed operator in conjunction with a real‐coded genetic algorithm is compared to five alternative optimization techniques known and used in the application to problems in geoelectrical prospection. Copyright © 2014 John Wiley & Sons, Ltd.

Hedging of long term zero-coupon bonds in a market model with reinvestment risk

We present a computational methodology to value and hedge long term zero-coupon bonds trading in short and medium term ones. For this purpose we develop a discrete time stochastic yield curve model with limited availability of maturity dates at a fixed time point and newly issued bonds at future time points. This involves reinvestment risk and there is no perfect hedging strategy available for long term liabilities. We calibrate the model to market data and describe optimal hedging strategies under a given risk tolerance. These considerations provide a natural extrapolation of the yield curve beyond the last liquid maturity date, and a framework which allows to value long term insurance liabilities, for instance, under Solvency 2. Moreover, we determine the optimal trading strategy replicating the liabilities under the given risk tolerance.

Determination of Biaxial Flow Stress Using Frictionless Dome Test

The frictionless dome test can be used to evaluate formability and determine the flow stress curve of sheet materials under biaxial forming conditions. The flow stress curve, obtained from the frictionless dome test can be determined up to larger strains than in tensile test. As a result the need for extrapolation of the stress-strain curve is reduced. The objectives of this study are to (a) for a given sheet material determine K and n values in Hollomon's Law (σ = Kɛn) by using experimental punch force vs. stroke curve and (b) develop the computer program, “PRODOME”, to automate the calculation of K and n values.

2DE‐based approach for estimation of number of protein species in a cell

Insufficient sensitivity of methods for detection of proteins at a single molecule level does not yet allow obtaining the whole image of human proteome. But to go further, we need at least to know the proteome size, or how many different protein species compose this proteome. This is the task that could be at least partially realized by the method described in this article. The approach used in our study is based on detection of protein spots in 2DE after staining by protein dyes with various sensitivities. As the different protein spots contain different protein species, counting the spots opens a way for estimation of number of protein species. The function representing the dependence of the number of protein spots on sensitivity or LOD of protein dyes was generated. And extrapolation of this function curve to theoretical point of the maximum sensitivity (detection of a single smallest polypeptide) allowed to counting the number of different molecules (polypeptide species) at the concentration level of a single polypeptide per proteome. Using this approach, it was estimated that the minimal numbers of protein species for model objects, Escherichia coli and Pirococcus furiosus, are 6200 and 3400, respectively. We expect a single human cell (HepG2) to contain minimum 70 000 protein species.

Prediction of the elastic strain limit of tendons

The elastic strain limit (ESL) of tendons is the point where maximum elastic modulus is reached, after which micro-damage starts. Study of damage progression in tendons under repetitive (fatigue) loading requires a priori knowledge about ESL. In this study, we propose three different approaches for predicting ESL. First, one single value is assumed to represent the ESL of all tendon specimens. Second, different extrapolation curves are used for extrapolating the initial part of the stress–strain curve. Third, a method based on comparing the shape of the initial part of the stress–strain curve of specimens with a database of stress–strain curves is used. A large number of porcine tendon explants (97) were tested to examine the above-mentioned approaches. The variants of the third approach yielded significantly (p<0.05) smaller error values as compared to the other approaches. The mean absolute percentage error of the best-performing variant of the shape-based comparison was between 8.14±6.44% and 9.96±9.99% depending on the size of the initial part of the stress–strain curves. Interspecies generalizability of the best performing method was also studied by applying it for prediction of the ESL of horse tendons. The ESL of horse tendons was predicted with mean absolute percentage errors ranging between 10.53±7.6% and 19.16±14.31% depending on the size of the initial part of the stress–strain curves and the type of normalization. The results of this study suggest that both ESL and the shape of stress–strain curves may be highly different between different individuals and different anatomical locations.

Gamma geometry dependency of efficiency functions in the 4πβ-γ coincidence measurements of complex decaying nuclides

In order to clarify the γ-efficiency dependency of 4πβ-γ efficiency functions, a series of 4πβ-γ efficiency extrapolation measurements of a 134Cs source were carried out for a wide variety of γ-geometries using a 4πβ(PS)-4πγ detector configuration. As the source is situated in the plastic scintillator (PS) β-detector, the γ-efficiency of the system can be readily changed by extracting the β-detector from the well-hole in a series of stages. For data acquisition and analyses, a list-mode two-parameter data acquisition system was employed. The forms of the extrapolation curves were monitored with decreasing γ-geometry, eventually exhibiting a similar behavior to those obtained in a usual 4πβ-γ coincidence counting system. The experimental results and considerations suggested that the γ-geometry dependency of the efficiency functions were due to summing effects in the γ-channel, and some qualitative remarks on the form of the extrapolation functions are given.

Standardisation of 64Cu using a software coincidence counting system

The activity of the radionuclide 64Cu was determined by the efficiency extrapolation method applied to 4π(PC)−γ coincidence counting. The standardisation was performed by software coincidence counting—a digital method for primary activity measurement that simplifies the setting of optimal coincidence parameters. The γ-ray-energy window, characterised by identical gamma detection efficiency related to the sum of EC and to the sum of beta decay branches, was found. This setting ensured a linear and zero slope extrapolation curve.

Standardization of Tc-99 by two methods and participation at the CCRI(II)-K2. Tc-99 comparison

The work accomplished within the participation at the 2012 key comparison of Tc-99 is presented. The solution was standardized for the first time in IFIN-HH by two methods: LSC-TDCR and 4π(PC)β-γ efficiency tracer. The methods are described and the results are compared. For the LSC-TDCR method, the program TDCR07c, written and provided by P. Cassette, was used for processing the measurement data. The results are 2.1% higher than when applying the TDCR06b program; the higher value, calculated with the software TDCR07c, was used for reporting the final result in the comparison. The tracer used for the 4π(PC)β-γ efficiency tracer method was a standard 60Co solution. The sources were prepared from the mixture 60Co+99Tc solution and a general extrapolation curve, type: NβTc−99/(M)Tc−99=f [1−εCo−60], was drawn. This value was not used for the final result of the comparison. The difference between the values of activity concentration obtained by the two methods was within the limit of the combined standard uncertainty of the difference of these two results.

Ponatinib—A Step Forward in Overcoming Resistance in Chronic Myeloid Leukemia

With the current therapy, the improvement in survival of patient with early chronic phase chronic myelogenous leukemia (CML) is unrivaled by that of any other leukemia. In fact, extrapolation of the survival curves may suggest that life expectancy of patients who achieve and maintain predetermined milestones may not differ from that of the age-matched healthy adults. The main reasons for such success are the presence of a well-defined molecular target, the BCR-ABL oncogene, necessary and sufficient for the initiation and propagation of CML, and the powerful and selective agents that inhibit it. Five U.S. Food and Drug Administration (FDA)-approved tyrosine kinase inhibitors (TKI), each with unique activities and toxicity profiles, allow for individualized patient care. Despite the remarkable responses of most patients, a small but significant fraction of patients develops clinical resistance to the TKIs, some of which is attributed to the BCR-ABL kinase domain mutations affecting TKI binding and activity. The recently approved third-generation TKI ponatinib showed remarkable activity in the patients with multi-TKI-resistant disease. Particularly impressive was its efficacy in patients with T315I mutation that is resistant to all other TKIs. In lieu of the current emphasis on achieving earlier and more profound responses and excellent activity of ponatinib in the refractory setting, its optimal position among the available armamentarium of agents is being established.

Entropy and the species accumulation curve: a novel entropy estimator via discovery rates of new species

Summary Estimating Shannon entropy and its exponential from incomplete samples is a central objective of many research fields. However, empirical estimates of Shannon entropy and its exponential depend strongly on sample size and typically exhibit substantial bias. This work uses a novel method to obtain an accurate, low‐bias analytic estimator of entropy, based on species frequency counts. Our estimator does not require prior knowledge of the number of species. We show that there is a close relationship between Shannon entropy and the species accumulation curve, which depicts the cumulative number of observed species as a function of sample size. We reformulate entropy in terms of the expected discovery rates of new species with respect to sample size, that is, the successive slopes of the species accumulation curve. Our estimator is obtained by applying slope estimators derived from an improved Good‐Turing frequency formula. Our method is also applied to estimate mutual information. Extensive simulations from theoretical models and real surveys show that if sample size is not unreasonably small, the resulting entropy estimator is nearly unbiased. Our estimator generally outperforms previous methods in terms of bias and accuracy (low mean squared error) especially when species richness is large and there is a large fraction of undetected species in samples. We discuss the extension of our approach to estimate Shannon entropy for multiple incidence data. The use of our estimator in constructing an integrated rarefaction and extrapolation curve of entropy (or mutual information) as a function of sample size or sample coverage (an aspect of sample completeness) is also discussed.

Re-evaluation of Evans blue dye dilution method of plasma volume measurement.

To simplify the method of plasma volume measurement by Evans blue dye dilution we used, for the first time, the same venous site for injection of dye and collection of samples. In a series of 49 studies the dye decay between 10 and 35 min after injection was highly linear (r = 0.991 +/- 0.01), indicating that contamination of samples is very unlikely. We repeated the measurements after eight weeks in nine patients; the mean difference was 16.4 +/- 19.6 ml, indicating a high degree of reproducibility. We found that extrapolation of the dye decay curve to time zero is required for accurate estimates of plasma volume. There was good agreement between the estimates of plasma volume obtained by extrapolation from only three samples taken at 10, 20 and 30 min after dye injection with the results obtained using all six samples. We also found good agreement between the estimates of plasma volume obtained by using standard curves constructed from four standard dilutions of 1.25, 2.5, 5 and 10 mg/l and those obtained by the use of standard curves constructed from the blank and only one standard dilution of 10 mg/l. We therefore conclude that the Evans blue technique can be simplified with minimal loss of accuracy, by using only one venous site for injection and withdrawal, withdrawing only three samples between 10 and 30 min after injection and using a two point calibration line.

A technique to improve the accuracy of Earth orientation prediction algorithms based on least squares extrapolation

We present a technique to improve the least squares (LS) extrapolation of Earth orientation parameters (EOPs), consisting of fixing the last observed data point on the LS extrapolation curve, which customarily includes a polynomial and a few sinusoids. For the polar motion (PM), a more sophisticated two steps approach has been developed, which consists of estimating the amplitude of the more stable one of the annual (AW) and Chandler (CW) wobbles using data of longer time span, and then estimating the other parameters using a shorter time span. The technique is studied using hindcast experiments, and justified using year-by-year statistics of 8 years. In order to compare with the official predictions of the International Earth Rotation and Reference Systems Service (IERS) performed at the U.S. Navy Observatory (USNO), we have enforced short-term predictions by applying the ARIMA method to the residuals computed by subtracting the LS extrapolation curve from the observation data. The same as at USNO, we have also used atmospheric excitation function (AEF) to further improve predictions of UT1-UTC. As results, our short-term predictions are comparable to the USNO predictions, and our long-term predictions are marginally better, although not for every year. In addition, we have tested the use of AEF and oceanic excitation function (OEF) in PM prediction. We find that use of forecasts of AEF alone does not lead to any apparent improvement or worsening, while use of forecasts of AEF+OEF does lead to apparent improvement.

Overview of the Mg Corrosion Mechanism

Our recently developed plug-in specimens allow direct comparison between corrosion rates measured by weight loss, hydrogen evolution and from Tafel extrapolation of polarization curves. These have allowed identification of some of the reasons why Tafel extrapolation has previously not provided a good measure of steady state corrosion for Mg, because: (i) of crevice corrosion in the specimen mount, (ii) of decoupling of the Mg corrosion from the electrochemical measurements; and (iii) Tafel extrapolation has often been used to study Mg corrosion soon after specimen insertion into the solution, despite the fact that it is well known that Mg alloy corrosion is often non-linear, the corrosion rate accelerates to a steady state rate after an initial period of low corrosion rate

Economic Evaluation of Fulvestrant 500 mg Versus Generic Nonsteroidal Aromatase Inhibitors in Patients With Advanced Breast Cancer in the United Kingdom

ObjectiveThe goal of this study was to examine the cost-effectiveness of fulvestrant 500 mg for the treatment of first progression or recurrence of advanced breast cancer in postmenopausal patients compared with generic nonsteroidal aromatase inhibitors (anastrozole and letrozole) in the United Kingdom. MethodsA cost-utility model based on a time-in-state approach was used. Clinical effectiveness estimates used in the model were derived from a network meta-analysis for overall survival and serious adverse events. Overall survival was extrapolated by using a Weibull distribution, and progression-free survival (PFS) estimates were derived from a simultaneous network meta-analysis and extrapolation of PFS curves by using the log-normal distribution. Data on resource use, costs, and utilities were based on various sources, including expert opinion and published data. To explore uncertainty, 1-way and probability sensitivity analyses were conducted. The study was conducted from the perspective of the UK National Health Service, and costs are reported in 2010/2011 British pounds. ResultsThe base case incremental cost-effectiveness ratio (ICER) for fulvestrant 500 mg versus letrozole was £34,528, with incremental costs of £14,383 and an incremental quality-adjusted life-year (QALY) of 0.417. Extended dominance occurred for anastrozole because the ICER for anastrozole versus letrozole was higher than the ICER for fulvestrant 500 mg versus anastrozole. Based on the probability sensitivity analyses, the probability that fulvestrant 500 mg was the most cost-effective treatment option was 3%, 20%, and 53% at a willingness-to-pay threshold of £20,000, £30,000, and £40,000 per QALY, respectively. According to the 1-way sensitivity analyses, the PFS estimates were the key drivers of the model results. ConclusionsAlthough fulvestrant 500 mg was found not to be a cost-effective option at a standard UK threshold of £20,000 to £30,000 per QALY, it may be relevant to apply a higher threshold due to the poor prognosis of patients with advanced breast cancer and the limited number of hormonal treatment options available for this stage of treatment. Certain subgroups may also benefit from fulvestrant as a treatment option; however, limited data are currently available to identify these subgroups.

Assessment of forming limit stress curves as failure criterion for non-proportional forming processes

The forming limit stress curve (FLSC) is often recommended as failure criterion for the virtual tryout of forming processes which include non-proportional loading. However, parameters influencing position and shape of the forming limit stress curve are not fully known. Up to today it has not been proved if the forming limit curve is strain path-independent, or at least approximately path-independent. In this study the influence of the parameters yield criterion, flow curve extrapolation and level of pre-stretching on the applicability of the FLSC as failure criterion are assessed. The work is performed using the aluminum alloy AA6014 based on forming limit curves for proportional and non-proportional loading published in Werber et al. Key Eng Mater 502–506:71–76, (2012). FLSCs are generated for yield criteria according to von Mises and Hill’48, for flow curve extrapolations according to Ghosh and Hockett-Sherby as well as for an experimentally measured flow curve. In order to be able to assess the influence of the described parameters on the failure criterion based on the FLSC the application of a mean forming limit stress curve (MFLSC) is used. This method is based on the assumption that all FLSCs gained for proportional as well as non-proportional loading map to one single curve. The influence of yield criterion and flow curve approximation on the FLSCs is addressed; the strain path dependency of FLSCs is proved and the forming limit curves for non-linear loading calculated with an assumed mean forming limit stress curve are compared to the experimentally gained forming limit curves.