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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Quantifying magnetic field driven lattice distortions in kagome metals at the femto-scale using scanning tunneling microscopy

A wide array of unusual phenomena has recently been uncovered in kagome solids. The charge density wave (CDW) state in the kagome superconductor AV 3 Sb 5 , in particular, intrigued the community; the CDW phase appears to break the time-reversal symmetry despite the absence of spin magnetism, which has been tied to exotic orbital loop currents possibly intertwined with magnetic field tunable crystal distortions. To test this connection, precise determination of the lattice response to an applied magnetic field is crucial but can be challenging at the atomic scale. We establish a scanning tunneling microscopy (STM) based method to study the evolution of the AV 3 Sb 5 atomic structure as a function of magnetic field. The method substantially reduces the errors of typical STM measurements, which are at the order of 1% when measuring an in-plane lattice constant change. Here, we find that the out-of-plane lattice constant of AV 3 Sb 5 remains unchanged (within 10 —6 ) by the application of both in-plane and out-of-plane magnetic fields. We also reveal that the in-plane lattice response to magnetic field is at most at the order of 0.05%. Our experiments provide further constraints on time-reversal symmetry breaking in kagome metals and establish a tool for higher-resolution extraction of the field-lattice coupling at the nanoscale applicable to other quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Optimal sensing on an asymmetric exceptional surface

We study the connection between exceptional points (EPs) and optimal parameter estimation, in a simple system consisting of two counterpropagating traveling wave modes in a microring resonator. The unknown parameter to be estimated is the strength of a perturbing cross-coupling between the two modes. Partially reflecting the output of one mode into the other creates a non-Hermitian Hamiltonian that exhibits a family of EPs, creating an exceptional surface (ES). We use a fully quantum treatment of field inputs and noise sources to obtain a quantitative bound on the estimation error by calculating the quantum Fisher information (QFI) in the output fields, whose inverse gives the Cramér-Rao lower bound on the mean-squared error of any unbiased estimator. We determine the bounds for two input states, namely, a semiclassical coherent state and a highly nonclassical NOON state. We find that the QFI is enhanced in the presence of an EP for both of these input states and that both states can saturate the Cramér-Rao bound. We then identify idealized yet experimentally feasible measurements that achieve the minimum bound for these two input states. We also investigate how the QFI changes for parameter values that do not lie on the ES, finding that these can have a larger QFI, suggesting alternative routes to optimize the parameter estimation for this problem.

Exceptional points↗
DOE OSTI2015

SU-E-T-508: Internal Organ Motion Effect On Radiation Dose to a Point Under Half-Beam Block Match Line

Purpose Half-beam block is a field matching technique frequently used in radiotherapy. With no setup error, a well calibrated linac, and no internal organ motion, two photon fields can be matched seamlessly dosimetry-wise with their central axes passing the match line. However, in actual clinical situations, internal organ motion is often inevitable. This study was conducted to investigate its influence on radiation dose to patient internal points directly under the matching line. Methods A clinical setting is modeled as two half-space (x<0 and x<0) radiation fields that are turned on sequentially with a time gap of integer times of the patient internal organ motion period (T{sub 0}). Our point of interest moves with patient internal organs periodically and evenly in and out of the radiation fields, resulting in an average location at x=0. When the fields are delivered without any motion management, the initial phase of the point’s movement is unknown. Statistical methods are used to compute the expected value ( ) and variance (σ) of the point dose given the uncertainty. Results Analytical solutions are obtained for and s of dose received by a point directly under the match line. is proportional to the total beam-on time (T1), and σ demonstrates previously unknown periodic behavior. /<Dσ has local maximums (minimums) when T{sub 1} is 2n*T{sub 0} ((2n+1)*T{sub 0}) (n is an integer) with an upper envelope scales as 1/T{sub 1}. Worst case scenario the point dose can be zero or double of the expected value. Conclusion We have analytically analyzed the internal organ motion effect on radiation dose received by a patient internal point directly under a half-beam block match line. Our results help us to better understand this phenomenon and facilitate the reduction of point dosimetric uncertainties in our clinical practice.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Can protein expression be ‘solved’?

Recombinant protein expression is central to biotechnology’s application in academic exploration as well as human health, climate applications and the bioeconomy in general. However, not all proteins can be expressed in all organisms, and the field lacks a predictive model of soluble protein overexpression that could replace laborious experimental trial-and-error. Here, we discuss the state of the field and identify the lack of large, high-fidelity datasets as the primary bottleneck to progress. We review possible assays that could be used for data collection to identify a path toward an extensible experimental platform for collecting soluble recombinant protein overexpression data across organisms. We suggest that the resulting dataset should be used to train increasingly generalizable predictive models of protein expression to answer the question: “How can predictive protein expression be solved?”.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

Efficient Lossy Compression for Scientific Data Based on Pointwise Relative Error Bound

An effective data compressor is becoming increasingly critical to today's scientific research, and many lossy compressors are developed in the context of absolute error bounds. Based on physical/chemical definitions of simulation fields or multiresolution demand, however, many scientific applications need to compress the data with a pointwise relative error bound (i.e., the smaller the data value, the smaller the compression error to tolerate). To this end, we propose two optimized lossy compression strategies under a state-of-the-art three-staged compression framework (prediction + quantization + entropy-encoding). The first strategy (called block-based strategy) splits the data set into many small blocks and computes an absolute error bound for each block, so it is particularly suitable for the data with relatively high consecutiveness in space. The second strategy (called multi-threshold-based strategy) splits the whole value range into multiple groups with exponentially increasing thresholds and performs the compression in each group separately, which is particularly suitable for the data with a relatively large value range and spiky value changes. We implement the two strategies rigorously and evaluate them comprehensively by using two scientific applications which both require lossy compression with point-wise relative error bound. Experiments show that the two strategies exhibit the best compression qualities on different types of data sets respectively. In conclusion, the compression ratio of our lossy compressor is higher than that of other state-of-the-art compressors by 17.2-618 percent on the climate simulation data and 30-210 percent on the N-body simulation data, with the same relative error bound and without degradation of the overall visualization effect of the entire data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Characterization of ultrasound elevation beamwidth artifacts for prostate brachytherapy needle insertion

Purpose: Ultrasound elevation beamwidth leads to image artifacts and uncertainties in localizing objects (such as a surgical needle) in ultrasound images. The authors examined the clinical significance of errors caused by elevation beamwidth artifacts and imaging parameters in needle insertion procedures. Methods: Beveled prostate brachytherapy needles were inserted through all holes of a grid template under real-time transrectal ultrasound (TRUS) guidance. The needle tip position as indicated by the TRUS image was compared to their observed physical location. A new device was developed to measure the ultrasound elevation beamwidth. Results: Imaging parameters of the TRUS scanner have direct impact on the localization error ranging from 0.5 up to 4 mm. The smallest localization error was observed laterally close to the center of the grid template and axially within the beam's focal zone. Largest localization error occurs laterally around both sides of the grid template and axially within the beam's far field. The authors also found that the localization errors vary with both lateral and elevation offsets. Conclusions: The authors found properly adjusting the TRUS imaging settings to lower the ultrasound gain and power effectively minimized the appearance of elevation beamwidth artifacts and in turn reduced the localization errors of the needle tip.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1992

Inverse design of a proper number, shapes, sizes, and locations of coolant flow passages

During the past several years we have developed an inverse method that allows a thermal cooling system designer to determine proper sizes, shapes, and locations of coolant passages (holes) in, say, an internally cooled turbine blade, a scram jet strut, a rocket chamber wall, etc. Using this method the designer can enforce a desired heat flux distribution on the hot outer surface of the object, while simultaneously enforcing desired temperature distributions on the same hot outer surface as well as on the cooled interior surfaces of each of the coolant passages. This constitutes an over-specified problem which is solved by allowing the number, sizes, locations and shapes of the holes to adjust iteratively until the final internally cooled configuration satisfies the over-specified surface thermal conditions and the governing equation for the steady temperature field. The problem is solved by minimizing an error function expressing the difference between the specified and the computed hot surface heat fluxes. The temperature field analysis was performed using our highly accurate boundary integral element code with linearly varying temperature along straight surface panels. Examples of the inverse design applied to internally cooled turbine blades and scram jet struts (coated and non-coated) having circular and non-circular coolant flow passages will be shown.

George S. Dulikravich↗
DOE OSTI2012

Optimized pulses for the control of uncertain qubits

The construction of high-fidelity control fields that are robust to control, system, and/or surrounding environment uncertainties is a crucial objective for quantum information processing. Using the two-state Landau-Zener model for illustrative simulations of a controlled qubit, we generate optimal controls for π/2 and π pulses and investigate their inherent robustness to uncertainty in the magnitude of the drift Hamiltonian. Next, we construct a quantum-control protocol to improve system-drift robustness by combining environment-decoupling pulse criteria and optimal control theory for unitary operations. By perturbatively expanding the unitary time-evolution operator for an open quantum system, previous analysis of environment-decoupling control pulses has calculated explicit control-field criteria to suppress environment-induced errors up to (but not including) third order from π/2 and π pulses. We systematically integrate this criteria with optimal control theory, incorporating an estimate of the uncertain parameter to produce improvements in gate fidelity and robustness, demonstrated via a numerical example based on double quantum dot qubits. For the qubit model used in this work, postfacto analysis of the resulting controls suggests that realistic control-field fluctuations and noise may contribute just as significantly to gate errors as system and environment fluctuations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Stillwater Hybrid Geo-Solar Power Plant Optimization Analyses

Solar field and power plant models have been developed to predict the performance of the Stillwater geothermal / solar-thermal hybrid power plant. The models have been validated using operational data from the Stillwater plant. The validated models will be used to optimize performance of the Stillwater hybrid plant and explore next-generation hybrid plant design concepts. A preliminary effort to improve performance of the Stillwater hybrid plant using optical characterization of the solar field has been completed. The Stillwater solar field optical characterization involved measurement of mirror reflectance, mirror slope error, and receiver position error. Subsequent analyses of the optical characterization results indicate that the solar field is currently operating at approximately 90% of the manufacturer’s performance specifications. Control system and hardware modifications expected to improve solar array performance by XX% have been identified.

14 SOLAR ENERGY↗
NASA NTRS1993

A variational method for finite element stress recovery and error estimation

A variational method for obtaining smoothed stresses from a finite element derived nonsmooth stress field is presented. The method is based on minimizing a functional involving discrete least-squares error plus a penalty constraint that ensures smoothness of the stress field. An equivalent accuracy criterion is developed for the smoothing analysis which results in a C sup 1-continuous smoothed stress field possessing the same order of accuracy as that found at the superconvergent optimal stress points of the original finite element analysis. Application of the smoothing analysis to residual error estimation is also demonstrated.

Tessler, A.↗
DOE OSTI2016

SU-F-T-273: Using a Diode Array to Explore the Weakness of TPS DoseCalculation Algorithm for VMAT and Sliding Window Techniques

Purpose: To identify the weakness of dose calculation algorithm in a treatment planning system for volumetric modulated arc therapy (VMAT) and sliding window (SW) techniques using a two-dimensional diode array. Methods: The VMAT quality assurance(QA) was implemented with a diode array using multiple partial arcs that divided from a VMAT plan; each partial arc has the same segments and the original monitor units. Arc angles were less than ± 30°. Multiple arcs delivered through consecutive and repetitive gantry operating clockwise and counterclockwise. The source-toaxis distance setup with the effective depths of 10 and 20 cm were used for a diode array. To figure out dose errors caused in delivery of VMAT fields, the numerous fields having the same segments with the VMAT field irradiated using different delivery techniques of static and step-and-shoot. The dose distributions of the SW technique were evaluated by creating split fields having fine moving steps of multi-leaf collimator leaves. Calculated doses using the adaptive convolution algorithm were analyzed with measured ones with distance-to-agreement and dose difference of 3 mm and 3%.. Results: While the beam delivery through static and step-and-shoot techniques showed the passing rate of 97 ± 2%, partial arc delivery of the VMAT fields brought out passing rate of 85%. However, when leaf motion was restricted less than 4.6 mm/°, passing rate was improved up to 95 ± 2%. Similar passing rate were obtained for both 10 and 20 cm effective depth setup. The calculated doses using the SW technique showed the dose difference over 7% at the final arrival point of moving leaves. Conclusion: Error components in dynamic delivery of modulated beams were distinguished by using the suggested QA method. This partial arc method can be used for routine VMAT QA. Improved SW calculation algorithm is required to provide accurate estimated doses.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2017

Role of Forcing Uncertainty and Background Model Error Characterization in Snow Data Assimilation

Accurate specification of the model error covariances in data assimilation systems is a challenging issue. Ensemble land data assimilation methods rely on stochastic perturbations of input forcing and model prognostic fields for developing representations of input model error covariances. This article examines the limitations of using a single forcing dataset for specifying forcing uncertainty inputs for assimilating snow depth retrievals. Using an idealized data assimilation experiment, the article demonstrates that the use of hybrid forcing input strategies (either through the use of an ensemble of forcing products or through the added use of the forcing climatology) provide a better characterization of the background model error, which leads to improved data assimilation results, especially during the snow accumulation and melt-time periods. The use of hybrid forcing ensembles is then employed for assimilating snow depth retrievals from the AMSR2 (Advanced Microwave Scanning Radiometer 2) instrument over two domains in the continental USA with different snow evolution characteristics. Over a region near the Great Lakes, where the snow evolution tends to be ephemeral, the use of hybrid forcing ensembles provides significant improvements relative to the use of a single forcing dataset. Over the Colorado headwaters characterized by large snow accumulation, the impact of using the forcing ensemble is less prominent and is largely limited to the snow transition time periods. The results of the article demonstrate that improving the background model error through the use of a forcing ensemble enables the assimilation system to better incorporate the observational information.

assimilation↗
DOE OSTI2019

Improving Vertical Velocity Retrievals from Doppler Radar Observations of Convection Field Campaign Report

Our National Science Foundation (NSF)-supported project was designed to address two longstanding challenges in radar-, meso-scale-, and hydro-meteorology: (1) mitigating the effects of non-simultaneous data collection on radar data-based analysis products, and (2) improving estimates of the vertical velocity (w) field in dual-Doppler wind analyses. Errors associated with the non-simultaneous data collection introduce errors in all Doppler analyses, and impose a lower limit on the time and space scales that can be studied. For many investigations the w field is of prime meteorological importance, but it is the velocity component most difficult to accurately synthesize from dual-Doppler wind observations. Our original plan proposed for short field campaigns at the Atmospheric Radiation Measurement (ARM) user facility Southern Great Plains (SGP) Central Facility (CF) was to use multiple-Doppler radial wind data from the scanning ARM X-band radars to test and refine our multiple-Doppler wind analysis algorithms. An important part of our plan was the use of high-temporal-resolution w observations to verify the analyses. In our original plan, these data would be obtained from Doppler lidars, 915 MhZ profilers and Ka-band ARM Zenith Radar (KAZR) zenith-pointing radars at the CF and nearby ARM facilities in north-central Oklahoma. Using the data, we planned to test the utility of new spatially variable advection-correction/analysis procedures, the utility of the anelastic vertical vorticity equation as a constraint in variational multiple-Doppler wind analysis, and other Doppler wind analysis procedures. Idealized tests with numerically-simulated supercell data had suggested the vorticity constraint could help improve the vertical velocity field if the data were gathered with sufficiently high temporal resolution (e.g., volume scans completed in 30-60 sec), so we were interested in exploring the use of rapid-scan data from the X-band Scanning ARM Precipitation Radars (XSAPRs).

Southern Great Plains, convection, KAZR, XSAPR, ve↗
DOE OSTI2016

From plane waves to local Gaussians for the simulation of correlated periodic systems

Here, we present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller–Plesset perturbation theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

TH-C-12A-08: New Compact 10 MV S-Band Linear Accelerator: 3D Finite-Element Design and Monte Carlo Dose Simulations

Purpose: To design a new compact S-band linac waveguide capable of producing a 10 MV x-ray beam, while maintaining the length (27.5 cm) of current 6 MV waveguides. This will allow higher x-ray energies to be used in our linac-MRI systems with the same footprint. Methods: Finite element software COMSOL Multiphysics was used to design an accelerator cavity matching one published in an experiment breakdown study, to ensure that our modeled cavities do not exceed the threshold electric fields published. This cavity was used as the basis for designing an accelerator waveguide, where each cavity of the full waveguide was tuned to resonate at 2.997 GHz by adjusting the cavity diameter. The RF field solution within the waveguide was calculated, and together with an electron-gun phase space generated using Opera3D/SCALA, were input into electron tracking software PARMELA to compute the electron phase space striking the x-ray target. This target phase space was then used in BEAM Monte Carlo simulations to generate percent depth doses curves for this new linac, which were then used to re-optimize the waveguide geometry. Results: The shunt impedance, Q-factor, and peak-to-mean electric field ratio were matched to those published for the breakdown study to within 0.1% error. After tuning the full waveguide, the peak surface fields are calculated to be 207 MV/m, 13% below the breakdown threshold, and a d-max depth of 2.42 cm, a D10/20 value of 1.59, compared to 2.45 cm and 1.59, respectively, for the simulated Varian 10 MV linac and brehmsstrahlung production efficiency 20% lower than a simulated Varian 10 MV linac. Conclusion: This work demonstrates the design of a functional 27.5 cm waveguide producing 10 MV photons with characteristics similar to a Varian 10 MV linac.

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRS2021

Sky-Scanning Sun-Tracking Airborne Radiometer (3STAR): Instrument Design, Flight Testing, and Tracking Performance

The Sky-Scanning, Sun-Tracking Airborne Radiometer (3STAR) adapts commercial radiometer technology developed for the ocean color research community to airborne measurement of spectrally resolved solar irradiance and sky radiance. These atmospheric observations are used to derive aerosol optical depth (AOD), supporting localized AOD inputs for atmospheric correction of satellite and airborne data over terrestrial and aquatic (including optically dark) targets. The ability to regionally “tune” atmospheric correction schemes with relevant spatial AOD supports constraining atmospheric correction of remote sensing reflectance. Very wide dynamic range has been achieved for multi-channel band-pass-filter-radiometers originally designed for deployment into the water column. By actively tracking and directly pointing to the Sun, the light attenuation by aerosol particles in the atmospheric column can be quantified. These measurements improve knowledge of atmospheric constituents and the atmospheric corrections required to improve remote sensing capabilities for interpreting reflectance measurements from the Earth surface. 3STAR incorporates a custom Sun-tracking/sky-scanning pointing head, a Sun-tracking camera, and a commercially available, cylindrical, 19-channel radiometer tube assembly. An accurate and responsive mount and tracking system has been developed and certified to NASA and Naval Air Systems Command (NAVAIR) airworthiness standards for deployment into the aircraft slipstream. Ground and flight testing indicate typical tracking errors of less than 0.1 degrees, well within the field of view of the radiometer as required to minimize measurement uncertainty from alignment error. Preliminary AOD measurements compare to within 0.013 with 15 measurements from an Aerosol Robotic Network (AERONET) Cimel instrument at 500 nm wavelength and low solar angle.

Atmosphere↗
DOE OSTI2024

Solving the Orszag–Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks

We study the 2D Orszag–Tang vortex magnetohydrodynamics (MHD) problem through the use of physics-constrained convolutional neural networks (PCNNs) for forecasting the density, ρ, and the magnetic field, B, as well as the prediction of B given the velocity field v of the fluid. In addition to translation equivariance from the convolutional architecture, other physics constraints were embedded: absence of magnetic monopoles, non-negativity of ρ, use of only relevant variables, and the periodic boundary conditions of the problem. The use of only relevant variables and the hard constraint of non-negative ρ were found to facilitate learning greatly. The divergenceless condition ∇·B=0 was implemented as a hard constraint up to machine precision through the use of a magnetic potential to define B=∇×A. Residual networks and data augmentation were also used to improve performance. This allowed for some of the residual models to function as surrogate models and provide reasonably accurate simulations. For the prediction task, the PCNNs were evaluated against a physics-informed neural network, which had the ideal MHD induction equation as a soft constraint. Several models were able to generate highly accurate fields, which are visually almost indistinguishable and have low mean squared error. Only methods with built-in hard constraints produced physical fields with ∇·B=0. The use of PCNNs for MHD has the potential to produce physically consistent real-time simulations to serve as virtual diagnostics in cases where inferences must be made with limited observables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Uncertainty quantification for radiation measurements: Bottom-up error variance estimation using calibration information

One example of top-down uncertainty quantification (UQ) involves comparing two or more measurements on each of multiple items. One example of bottom-up UQ expresses a measurement result as a function of one or more input variables that have associated errors, such as a measured count rate, which individually (or collectively) can be evaluated for impact on the uncertainty in the resulting measured value. In practice, it is often found that top-down UQ exhibits larger error variances than bottom-up UQ because some error sources are present in the fielded assay methods used in top-down UQ that are not present (or not recognized) in the assay studies used in bottom-up UQ One would like better consistency between the two approaches in order to claim understanding of the measurement process. The purpose of this paper is to refine bottom-up uncertainty estimation by using calibration information so that if there are no unknown error sources, the refined bottom-up uncertainty estimate will agree with the top-down uncertainty estimate to within a specified tolerance. Then, in practice, if the top-down uncertainty estimate is larger than the refined bottom-up uncertainty estimate by more than the specified tolerance, there must be omitted sources of error beyond those predicted from calibration uncertainty. The paper develops a refined bottom-up uncertainty approach for four cases of simple linear calibration: (1) inverse regression with negligible error in predictors, (2) inverse regression with non negligible error in predictors, (3) classical regression followed by inversion with negligible error in predictors, and (4) classical regression followed by inversion with non-negligible errors in predictors. Our illustrations are of general interest, but are drawn from our experience with nuclear material assay by non-destructive assay. The main example we use is gamma spectroscopy that applies the enrichment meter principle. Previous papers that ignore error in predictors have shown a tendency for inverse regression to have lower error variance than classical regression followed by inversion. Our paper supports that tendency both with and without error in predictors. Furthermore, the paper shows that calibration parameter estimates using error in predictor methods perform worse than without using error in predictor methods in the case of inverse regression, but perform better than without using error in predictor methods in the case of classical regression followed by inversion. Both inverse and classical regression involve the ratio of dependent random variables; therefore, the assumed error distribution(s) will matter in parameter estimation and in uncertainty calculations. Mainly for that reason, calibration using a single predictor is distinct from simple regression, and it has not been thoroughly treated in the literature, nor in the ISO Guide to the Expression of Uncertainty in Measurements (GUM). This refined approach is based on simulation, because we illustrate that analytical approximations are not adequate when there are, for example, 10 or fewer calibration measurements, which is common in calibration applications, each consisting of measured responses from known quantities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗