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At least 37 records · Page 2

WE-DE-201-05: Evaluation of a Windowless Extrapolation Chamber Design and Monte Carlo Based Corrections for the Calibration of Ophthalmic Applicators

Purpose: To test the validity of a windowless extrapolation chamber used to measure surface dose rate from planar ophthalmic applicators and to compare different Monte Carlo based codes for deriving correction factors. Methods: Dose rate measurements were performed using a windowless, planar extrapolation chamber with a {sup 90}Sr/{sup 90}Y Tracerlab RA-1 ophthalmic applicator previously calibrated at the National Institute of Standards and Technology (NIST). Capacitance measurements were performed to estimate the initial air gap width between the source face and collecting electrode. Current was measured as a function of air gap, and Bragg-Gray cavity theory was used to calculate the absorbed dose rate to water. To determine correction factors for backscatter, divergence, and attenuation from the Mylar entrance window found in the NIST extrapolation chamber, both EGSnrc Monte Carlo user code and Monte Carlo N-Particle Transport Code (MCNP) were utilized. Simulation results were compared with experimental current readings from the windowless extrapolation chamber as a function of air gap. Additionally, measured dose rate values were compared with the expected result from the NIST source calibration to test the validity of the windowless chamber design. Results: Better agreement was seen between EGSnrc simulated dose results and experimental current readings at very small air gaps (<100 µm) for the windowless extrapolation chamber, while MCNP results demonstrated divergence at these small gap widths. Three separate dose rate measurements were performed with the RA-1 applicator. The average observed difference from the expected result based on the NIST calibration was −1.88% with a statistical standard deviation of 0.39% (k=1). Conclusion: EGSnrc user code will be used during future work to derive correction factors for extrapolation chamber measurements. Additionally, experiment results suggest that an entrance window is not needed in order for an extrapolation chamber to provide accurate dose rate measurements for a planar ophthalmic applicator.

07 ISOTOPE AND RADIATION SOURCES↗

Extrapolation of nuclear structure observables with artificial neural networks

Calculations of nuclei are often carried out in finite model spaces. Thus, finite-size corrections enter, and it is necessary to extrapolate the computed observables to infinite model spaces. In this work, we employ extrapolation methods based on artificial neural networks for observables such as the ground-state energy and the point-proton radius. We extrapolate results from no-core shell model and coupled-cluster calculations to very large model spaces and estimate uncertainties. Training the network on different data typically yields extrapolation results that cluster around distinct values. We show that a preprocessing of input data, and the inclusion of correlations among the input data, reduces the problem of multiple solutions and yields more stable extrapolated results and consistent uncertainty estimates. We perform extrapolations for ground-state energies and radii in 4 He, 6 Li, and 16 O, and compare the predictions from neural networks with results from infrared extrapolations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

The importance of round-robin validation when assessing machine-learning-based vertical extrapolation of wind speeds

The extrapolation of wind speeds measured at a meteorological mast to wind turbine rotor heights is a key component in a bankable wind farm energy assessment and a significant source of uncertainty. Industry-standard methods for extrapolation include the power-law and logarithmic profiles. The emergence of machine-learning applications in wind energy has led to several studies demonstrating substantial improvements in vertical extrapolation accuracy in machine-learning methods over these conventional power-law and logarithmic profile methods. In all cases, these studies assess relative model performance at a measurement site where, critically, the machine-learning algorithm requires knowledge of the rotor-height wind speeds in order to train the model. This prior knowledge provides fundamental advantages to the site-specific machine-learning model over the power-law and log profiles, which, by contrast, are not highly tuned to rotor-height measurements but rather can generalize to any site. Furthermore, there is no practical benefit in applying a machine-learning model at a site where winds at the heights relevant for wind energy production are known; rather, its performance at nearby locations (i.e., across a wind farm site) without rotor-height measurements is of most practical interest. To more fairly and practically compare machine-learning-based extrapolation to standard approaches, we implemented a round-robin extrapolation model comparison, in which a random-forest machine-learning model is trained and evaluated at different sites and then compared against the power-law and logarithmic profiles. We consider 20 months of lidar and sonic anemometer data collected at four sites between 50 and 100 km apart in the central United States. We find that the random forest outperforms the standard extrapolation approaches, especially when incorporating surface measurements as inputs to include the influence of atmospheric stability. When compared at a single site (the traditional comparison approach), the machine-learning improvement in mean absolute error was 28 % and 23 % over the power-law and logarithmic profiles, respectively. Using the round-robin approach proposed here, this improvement drops to 20 % and 14 %, respectively. These latter values better represent practical model performance, and we conclude that round-robin validation should be the standard for machine-learning-based wind speed extrapolation methods.

17 WIND ENERGY↗

An experimental extrapolation technique using the Gafchromic EBT3 film for relative output factor measurements in small x-ray fields

Purpose: An experimental extrapolation technique is presented, which can be used to determine the relative output factors for very small x-ray fields using the Gafchromic EBT3 film. Methods: Relative output factors were measured for the Brainlab SRS cones ranging in diameters from 4 to 30 mm{sup 2} on a Novalis Trilogy linear accelerator with 6 MV SRS x-rays. The relative output factor was determined from an experimental reducing circular region of interest (ROI) extrapolation technique developed to remove the effects of volume averaging. This was achieved by scanning the EBT3 film measurements with a high scanning resolution of 1200 dpi. From the high resolution scans, the size of the circular regions of interest was varied to produce a plot of relative output factors versus area of analysis. The plot was then extrapolated to zero to determine the relative output factor corresponding to zero volume. Results: Results have shown that for a 4 mm field size, the extrapolated relative output factor was measured as a value of 0.651 ± 0.018 as compared to 0.639 ± 0.019 and 0.633 ± 0.021 for 0.5 and 1.0 mm diameter of analysis values, respectively. This showed a change in the relative output factors of 1.8% and 2.8% at these comparative regions of interest sizes. In comparison, the 25 mm cone had negligible differences in the measured output factor between zero extrapolation, 0.5 and 1.0 mm diameter ROIs, respectively. Conclusions: This work shows that for very small fields such as 4.0 mm cone sizes, a measureable difference can be seen in the relative output factor based on the circular ROI and the size of the area of analysis using radiochromic film dosimetry. The authors recommend to scan the Gafchromic EBT3 film at a resolution of 1200 dpi for cone sizes less than 7.5 mm and to utilize an extrapolation technique for the output factor measurements of very small field dosimetry.

60 APPLIED LIFE SCIENCES↗

Constrained Extrapolation Problem and Order-Dependent Mappings

In this work, we consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP) the goal is to find classes of approximants that give well converged results already for low perturbative truncation orders. First, we show that standard Padé and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so-called Maximum Entropy extrapolation method (MaxEnt). However, we show that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is thus not practical for the CEP in this case. Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple, practical, and general method for the CEP. Here, we find that the ODME approximants for the ground-state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Adaptive stratified importance sampling: hybridization of extrapolation and importance sampling Monte Carlo methods for estimation of wind turbine extreme loads

Wind turbine extreme load estimation is especially difficult because turbulent inflow drives nonlinear turbine physics and control strategies; thus there can be huge differences in turbine response to essentially equivalent environmental conditions. The two main current approaches, extrapolation and Monte Carlo sampling, are both unsatisfying: extrapolation-based methods are dangerous because by definition they make predictions outside the range of available data, but Monte Carlo methods converge too slowly to routinely reach the desired 50-year return period estimates. Thus a search for a better method is warranted. We introduce an adaptive stratified importance sampling approach that allows for treating the choice of environmental conditions at which to run simulations as a stochastic optimization problem that minimizes the variance of unbiased estimates of extreme loads. Furthermore, the framework, built on the traditional bin-based approach used in extrapolation methods, provides a close connection between sampling and extrapolation, and thus allows the solution of the stochastic optimization (i.e., the optimal distribution of simulations in different wind speed bins) to guide and recalibrate the extrapolation. Results show that indeed this is a promising approach, as the variance of both the Monte Carlo and extrapolation estimates are reduced quickly by the adaptive procedure. We conclude, however, that due to the extreme response variability in turbine loads to the same environmental conditions, our method and any similar method quickly reaches its fundamental limits, and that therefore our efforts going forward are best spent elucidating the underlying causes of the response variability.

17 WIND ENERGY↗

Nonlinear force-free extrapolation of the coronal magnetic field based on the magnetohydrodynamic relaxation method

We develop a nonlinear force-free field (NLFFF) extrapolation code based on the magnetohydrodynamic (MHD) relaxation method. We extend the classical MHD relaxation method in two important ways. First, we introduce an algorithm initially proposed by Dedner et al. to effectively clean the numerical errors associated with ∇ · B . Second, the multigrid type method is implemented in our NLFFF to perform direct analysis of the high-resolution magnetogram data. As a result of these two implementations, we successfully extrapolated the high resolution force-free field introduced by Low and Lou with better accuracy in a drastically shorter time. We also applied our extrapolation method to the MHD solution obtained from the flux-emergence simulation by Magara. We found that NLFFF extrapolation may be less effective for reproducing areas higher than a half-domain, where some magnetic loops are found in a state of continuous upward expansion. However, an inverse S-shaped structure consisting of the sheared and twisted loops formed in the lower region can be captured well through our NLFFF extrapolation method. We further discuss how well these sheared and twisted fields are reconstructed by estimating the magnetic topology and twist quantitatively.

79 ASTRONOMY AND ASTROPHYSICS↗

How accurate is a machine learning-based wind speed extrapolation under a round-robin approach?

As the size of commercial wind turbines keeps increasing, having accurate ways to vertically extrapolate wind speed is essential to obtain a precise characterization of the wind resource for wind energy production. Recently, machine learning has been proposed and applied to extrapolate wind speed to hub heights. However, previous studies trained and tested the machine learning methods at the same site, giving them an unfair advantage over the conventional extrapolation techniques, which are instead more universal. Here, we use data from four sites in Oklahoma to test a round-robin validation approach for machine learning, under which we train a random forest at a site, and test it at a different site, where the model has no prior knowledge of the wind resource. We quantify how the accuracy of this technique varies with distance from the training site, and we find that it outperforms conventional techniques for wind extrapolation at all the considered spatial separations. We then assess how the accuracy of the machine-learning based approach varies when it is used to predict wind speed in a wind farm far wake. Finally, we explore as case study the performance of the random forest in extrapolating winds during a low-level jet event.

17 WIND ENERGY↗

Resurgent extrapolation: rebuilding a function from asymptotic data. Painlevé I

Extrapolation is a generic problem in physics and mathematics: how to use asymptotic data in one parametric regime to learn about the behavior of a function in another parametric regime. For example: extending weak coupling expansions to strong coupling, or high temperature expansions to low temperature, or vice versa. Such extrapolations are particularly interesting in systems possessing dualities. Here we study numerical procedures for performing such an extrapolation, combining ideas from resurgent asymptotics with well-known techniques of Borel summation, Padé approximants and conformal mapping. We illustrate the method with the concrete example of the Painlevé I equation, which has applications in many branches of physics and mathematics. Starting solely with a finite number of coefficients from asymptotic data at infinity on the positive real line, we obtain a high precision extrapolation of the function throughout the complex plane, even across the phase transition into the pole region. The precision far exceeds that of state-of-the-art numerical integration methods along the real axis. Furthermore, the methods used are both elementary and general, not relying on Painlevé integrability properties, and so are applicable to a wide class of extrapolation problems.

97 MATHEMATICS AND COMPUTING↗

SU-E-J-145: Geometric Uncertainty in CBCT Extrapolation for Head and Neck Adaptive Radiotherapy

Purpose: One primary limitation of using CBCT images for H'N adaptive radiotherapy (ART) is the limited field of view (FOV) range. We propose a method to extrapolate the CBCT by using a deformed planning CT for the dose of the day calculations. The aim was to estimate the geometric uncertainty of our extrapolation method. Methods: Ten H'N patients, each with a planning CT (CT1) and a subsequent CT (CT2) taken, were selected. Furthermore, a small FOV CBCT (CT2short) was synthetically created by cropping CT2 to the size of a CBCT image. Then, an extrapolated CBCT (CBCTextrp) was generated by deformably registering CT1 to CT2short and resampling with a wider FOV (42mm more from the CT2short borders), where CT1 is deformed through translation, rigid, affine, and b-spline transformations in order. The geometric error is measured as the distance map ||DVF|| produced by a deformable registration between CBCTextrp and CT2. Mean errors were calculated as a function of the distance away from the CBCT borders. The quality of all the registrations was visually verified. Results: Results were collected based on the average numbers from 10 patients. The extrapolation error increased linearly as a function of the distance (at a rate of 0.7mm per 1 cm) away from the CBCT borders in the S/I direction. The errors (μ±σ) at the superior and inferior boarders were 0.8 ± 0.5mm and 3.0 ± 1.5mm respectively, and increased to 2.7 ± 2.2mm and 5.9 ± 1.9mm at 4.2cm away. The mean error within CBCT borders was 1.16 ± 0.54mm . The overall errors within 4.2cm error expansion were 2.0 ± 1.2mm (sup) and 4.5 ± 1.6mm (inf). Conclusion: The overall error in inf direction is larger due to more large unpredictable deformations in the chest. The error introduced by extrapolation is plan dependent. The mean error in the expanded region can be large, and must be considered during implementation. This work is supported in part by Varian Medical Systems, Palo Alto, CA.

60 APPLIED LIFE SCIENCES↗

Patient-bounded extrapolation using low-dose priors for volume-of-interest imaging in C-arm CT

Purpose: Three-dimensional (3D) volume-of-interest (VOI) imaging with C-arm systems provides anatomical information in a predefined 3D target region at a considerably low x-ray dose. However, VOI imaging involves laterally truncated projections from which conventional reconstruction algorithms generally yield images with severe truncation artifacts. Heuristic based extrapolation methods, e.g., water cylinder extrapolation, typically rely on techniques that complete the truncated data by means of a continuity assumption and thus appear to be ad-hoc. It is our goal to improve the image quality of VOI imaging by exploiting existing patient-specific prior information in the workflow. Methods: A necessary initial step prior to a 3D acquisition is to isocenter the patient with respect to the target to be scanned. To this end, low-dose fluoroscopic x-ray acquisitions are usually applied from anterior–posterior (AP) and medio-lateral (ML) views. Based on this, the patient is isocentered by repositioning the table. In this work, we present a patient-bounded extrapolation method that makes use of these noncollimated fluoroscopic images to improve image quality in 3D VOI reconstruction. The algorithm first extracts the 2D patient contours from the noncollimated AP and ML fluoroscopic images. These 2D contours are then combined to estimate a volumetric model of the patient. Forward-projecting the shape of the model at the eventually acquired C-arm rotation views gives the patient boundary information in the projection domain. In this manner, we are in the position to substantially improve image quality by enforcing the extrapolated line profiles to end at the known patient boundaries, derived from the 3D shape model estimate. Results: The proposed method was evaluated on eight clinical datasets with different degrees of truncation. The proposed algorithm achieved a relative root mean square error (rRMSE) of about 1.0% with respect to the reference reconstruction on nontruncated data, even in the presence of severe truncation, compared to a rRMSE of 8.0% when applying a state-of-the-art heuristic extrapolation technique. Conclusions: The method we proposed in this paper leads to a major improvement in image quality for 3D C-arm based VOI imaging. It involves no additional radiation when using fluoroscopic images that are acquired during the patient isocentering process. The model estimation can be readily integrated into the existing interventional workflow without additional hardware.

60 APPLIED LIFE SCIENCES↗

SU-D-204-02: BED Consistent Extrapolation of Mean Dose Tolerances

Purpose: The safe use of radiotherapy requires the knowledge of tolerable organ doses. For experimental fractionation schemes (e.g. hypofractionation) these are typically extrapolated from traditional fractionation schedules using the Biologically Effective Dose (BED) model. This work demonstrates that using the mean dose in the standard BED equation may overestimate tolerances, potentially leading to unsafe treatments. Instead, extrapolation of mean dose tolerances should take the spatial dose distribution into account. Methods: A formula has been derived to extrapolate mean physical dose constraints such that they are mean BED equivalent. This formula constitutes a modified BED equation where the influence of the spatial dose distribution is summarized in a single parameter, the dose shape factor. To quantify effects we analyzed 14 liver cancer patients previously treated with proton therapy in 5 or 15 fractions, for whom also photon IMRT plans were available. Results: Our work has two main implications. First, in typical clinical plans the dose distribution can have significant effects. When mean dose tolerances are extrapolated from standard fractionation towards hypofractionation they can be overestimated by 10–15%. Second, the shape difference between photon and proton dose distributions can cause 30–40% differences in mean physical dose for plans having the same mean BED. The combined effect when extrapolating proton doses to mean BED equivalent photon doses in traditional 35 fraction regimens resulted in up to 7–8 Gy higher doses than when applying the standard BED formula. This can potentially lead to unsafe treatments (in 1 of the 14 analyzed plans the liver mean dose was above its 32 Gy tolerance). Conclusion: The shape effect should be accounted for to avoid unsafe overestimation of mean dose tolerances, particularly when estimating constraints for hypofractionated regimens. In addition, tolerances established for a given treatment modality cannot necessarily be applied to other modalities with drastically different dose distributions.

60 APPLIED LIFE SCIENCES↗

SU-F-T-579: Extrapolation Techniques for Small Field Dosimetry Using Gafchromic EBT3 Film

Purpose: The purpose of this project is to test an experimental approach using an extrapolation technique for Gafchromic EBT3 film for small field x-ray dosimetry. Methods: Small fields from a Novalis Tx linear accelerator with HD Multileaf Collimators with 6 MV was used. The field sizes ranged from 5 × 5 to 50 × 50 mm2 MLC fields and a range of circular cones of 4 to 30 mm2 diameters. All measurements were performed in water at an SSD of 100 cm and at a depth of 10 cm. The relative output factors (ROFs) were determined from an extrapolation technique developed to eliminate the effects of partial volume averaging in film scan by scanning films with high resolution (1200 DPI). The size of the regions of interest (ROI) was varied to produce a plot of ROFs versus ROI which was then extrapolated to zero ROI to determine the relative output factor. The results were compared with other solid state detectors with proper correction, namely, IBA SFD diode, PTW 60008 and PTW 60012 diode. Results: For the 4 mm cone, the extrapolated ROF had a value of 0.658 ± 0.014 as compared to 0.642 and 0.636 for 0.5 mm and 1 mm2 ROI analysis, respectively. This showed a change in output factor of 2.4% and 3.3% at this comparative ROI sizes. In comparison, the 25 mm cone had a difference in measured output factor of 0.3% and 0.5% between 0.5 and 1.0 mm, respectively compared to zero volume. For the fields defined by MLCs a difference of up to 2% for 5×5 mm2 was observed. Conclusion: A measureable difference can be seen in ROF based on the ROI when radiochromic film is used. Using extrapolation technique from high resolution scanning a good agreement can be achieved.

60 APPLIED LIFE SCIENCES↗

Decreasing wind speed extrapolation error via domain-specific feature extraction and selection

Abstract. Model uncertainty is a significant challenge in the wind energy industry and can lead to mischaracterization of millions of dollars' worth of wind resources. Machine learning methods, notably deep artificial neural networks (ANNs), are capable of modeling turbulent and chaotic systems and offer a promising tool to produce high-accuracy wind speed forecasts and extrapolations. This paper uses data collected by profiling Doppler lidars over three field campaigns to investigate the efficacy of using ANNs for wind speed vertical extrapolation in a variety of terrains, and it quantifies the role of domain knowledge in ANN extrapolation accuracy. A series of 11 meteorological parameters (features) are used as ANN inputs, and the resulting output accuracy is compared with that of both standard log-law and power-law extrapolations. It is found that extracted nondimensional inputs, namely turbulence intensity, current wind speed, and previous wind speed, are the features that most reliably improve the ANN's accuracy, providing up to a 65 % and 52 % increase in extrapolation accuracy over log-law and power-law predictions, respectively. The volume of input data is also deemed important for achieving robust results. One test case is analyzed in depth using dimensional and nondimensional features, showing that the feature nondimensionalization drastically improves network accuracy and robustness for sparsely sampled atmospheric cases.

17 WIND ENERGY↗

Projecting species’ vulnerability to climate change: Which uncertainty sources matter most and extrapolate best?

Species distribution models (SDMs) are commonly used to assess potential climate change impacts on biodiversity, but several critical methodological decisions are often made arbitrarily. We compare variability arising from these decisions to the uncertainty in future climate change itself. We also test whether certain choices offer improved skill for extrapolating to a changed climate and whether internal cross-validation skill indicates extrapolative skill.We compared projected vulnerability for 29 wetland-dependent bird species breeding in the climatically dynamic Prairie Pothole Region, USA. For each species we built 1,080 SDMs to represent a unique combination of: future climate, class of climate covariates, collinearity level, and thresholding procedure. We examined the variation in projected vulnerability attributed to each uncertainty source. To assess extrapolation skill under a changed climate, we compared model predictions with observations from historic drought years. Uncertainty in projected vulnerability was substantial, and the largest source was that of future climate change. Large uncertainty was also attributed to climate covariate class with hydrological covariates projecting half the range loss of bioclimatic covariates or other summaries of temperature and precipitation. We found that choices based on performance in cross-validation improved skill in extrapolation. Qualitative rankings were also highly uncertain. Given uncertainty in projected vulnerability and resulting uncertainty in rankings used for conservation prioritization, a number of considerations appear critical for using bioclimatic SDMs to inform climate change mitigation strategies. Our results emphasize explicitly selecting climate summaries that most closely represent processes likely to underlie ecological response to climate change. For example, hydrological covariates projected substantially reduced vulnerability, highlighting the importance of considering whether water availability may be a more proximal driver than precipitation. However, because cross-validation results were correlated with extrapolation results, the use of cross-validation performance metrics to guide modeling choices where knowledge is limited was supported.

thresholds↗

Improving in vitro to in vivo extrapolation by incorporating toxicokinetic measurements: A case study of lindane-induced neurotoxicity

Approaches for extrapolating in vitro toxicity testing results for prediction of human in vivo outcomes are needed. The purpose of this case study was to employ in vitro toxicokinetics and PBPK modeling to perform in vitro to in vivo extrapolation (IVIVE) of lindane neurotoxicity. Lindane cell and media concentrations in vitro, together with in vitro concentration-response data for lindane effects on neuronal network firing rates, were compared to in vivo data and model simulations as an exercise in extrapolation for chemical-induced neurotoxicity in rodents and humans. Time- and concentration-dependent lindane dosimetry was determined in primary cultures of rat cortical neurons in vitro using “faux” (without electrodes) microelectrode arrays (MEAs). In vivo data were derived from literature values, and physiologically based pharmacokinetic (PBPK) modeling was used to extrapolate from rat to human. The previously determined EC{sub 50} for increased firing rates in primary cultures of cortical neurons was 0.6 μg/ml. Media and cell lindane concentrations at the EC{sub 50} were 0.4 μg/ml and 7.1 μg/ml, respectively, and cellular lindane accumulation was time- and concentration-dependent. Rat blood and brain lindane levels during seizures were 1.7–1.9 μg/ml and 5–11 μg/ml, respectively. Brain lindane levels associated with seizures in rats and those predicted for humans (average = 7 μg/ml) by PBPK modeling were very similar to in vitro concentrations detected in cortical cells at the EC{sub 50} dose. PBPK model predictions matched literature data and timing. These findings indicate that in vitro MEA results are predictive of in vivo responses to lindane and demonstrate a successful modeling approach for IVIVE of rat and human neurotoxicity. - Highlights: • In vitro to in vivo extrapolation for lindane neurotoxicity was performed. • Dosimetry of lindane in a micro-electrode array (MEA) test system was assessed. • Cell concentrations at the MEA EC{sub 50} equaled rat brain levels associated with seizure. • PBPK-predicted human brain levels at seizure also equaled EC{sub 50} cell concentrations. • In vitro MEA results are predictive of lindane in vivo dose–response in rats/humans.

60 APPLIED LIFE SCIENCES↗

Use of the Wilshire Equations to Correlate and Extrapolate Creep Data of Inconel 617 and Nimonic 105

Advanced power plant alloys must endure high temperatures and pressures for durations at which creep data are often not available, necessitating the extrapolation of creep life. A recently developed creep life extrapolation method is the Wilshire equations, with which multiple approaches can be used to increase the goodness of fit of available experimental data and improve the confidence level of calculating long-term creep strength at times well beyond the available experimental data. In this article, the Wilshire equation is used to extrapolate the creep life of Inconel 617 and Nimonic 105 to 100,000 h. The use of (a) different methods to determine creep activation energy, (b) region splitting, (c) heat- and processing-specific tensile strength data, and (d) short-duration test data were investigated to determine their effects on correlation and extrapolation. For Inconel 617, using the activation energy of lattice self-diffusion as Q C * resulted in a poor fit with the experimental data. Additionally, the error of calculated rupture times worsened when splitting regions. For Nimonic 105, the error was reduced when heat- and processing-specific tensile strengths were used. Extrapolating Inconel 617 creep strength to 100,000 h life gave conservative results when compared to values calculated by the European Creep Collaborative Committee.

36 MATERIALS SCIENCE↗

Melting of “non-magic” argon clusters and extrapolation to the bulk limit

The melting of argon clusters Ar{sub N} is investigated by applying a parallel-tempering Monte Carlo algorithm for all cluster sizes in the range from 55 to 309 atoms. Extrapolation to the bulk gives a melting temperature of 85.9 K in good agreement with the previous value of 88.9 K using only Mackay icosahedral clusters for the extrapolation [E. Pahl, F. Calvo, L. Koči, and P. Schwerdtfeger, “Accurate melting temperatures for neon and argon from ab initio Monte Carlo simulations,” Angew. Chem., Int. Ed. 47, 8207 (2008)]. Our results for argon demonstrate that for the extrapolation to the bulk one does not have to restrict to magic number cluster sizes in order to obtain good estimates for the bulk melting temperature. However, the extrapolation to the bulk remains a problem, especially for the systematic selection of suitable cluster sizes.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗