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At least 1,171 records · Page 65

A Bayesian Framework for Spectral Reprojection

Abstract Fourier partial sum approximations yield exponential accuracy for smooth and periodic functions, but produce the infamous Gibbs phenomenon for non-periodic ones. Spectral reprojection resolves the Gibbs phenomenon by projecting the Fourier partial sum onto a Gibbs complementary basis, often prescribed as the Gegenbauer polynomials. Noise in the Fourier data and the Runge phenomenon both degrade the quality of the Gegenbauer reconstruction solution, however. Motivated by its theoretical convergence properties, this paper proposes a new Bayesian framework for spectral reprojection, which allows a greater understanding of the impact of noise on the reprojection method from a statistical point of view. We are also able to improve the robustness with respect to the Gegenbauer polynomials parameters. Finally, the framework provides a mechanism to quantify the uncertainty of the solution estimate.

Li, Tongtong (ORCID:0000000276644764)↗

A composite likelihood approach for inference under photometric redshift uncertainty

ABSTRACT Obtaining accurately calibrated redshift distributions of photometric samples is one of the great challenges in photometric surveys like LSST, Euclid, HSC, KiDS, and DES. We present an inference methodology that combines the redshift information from the galaxy photometry with constraints from two-point functions, utilizing cross-correlations with spatially overlapping spectroscopic samples, and illustrate the approach on CosmoDC2 simulations. Our likelihood framework is designed to integrate directly into a typical large-scale structure and weak lensing analysis based on two-point functions. We discuss efficient and accurate inference techniques that allow us to scale the method to the large samples of galaxies to be expected in LSST. We consider statistical challenges like the parametrization of redshift systematics, discuss and evaluate techniques to regularize the sample redshift distributions, and investigate techniques that can help to detect and calibrate sources of systematic error using posterior predictive checks. We evaluate and forecast photometric redshift performance using data from the CosmoDC2 simulations, within which we mimic a DESI-like spectroscopic calibration sample for cross-correlations. Using a combination of spatial cross-correlations and photometry, we show that we can provide calibration of the mean of the sample redshift distribution to an accuracy of at least 0.002(1 + z), consistent with the LSST-Y1 science requirements for weak lensing and large-scale structure probes.

(cosmology:) large-scale structure of Universe↗

Accurate Efficiency Measurements for Emerging PV: A Comparison of NREL's Steady-State Performance Calibration Protocol Between Conventional and Emerging PV Technologies

Emerging PV technologies (e.g. Perovskite, and Quantum Dot) are commonly known to possess challenges for accurate performance measurement under the existing IEC 60904 series of standards, which were developed for conventional Si solar cells. Potential performance artifacts depending on scan rates and directions and light bias exposure history are often seen in those emerging solar cells. To avoid these artifacts and provide an unbiased and reliable efficiency measurement, NREL's Cell and Module Performance (CMP) Group has developed a steady-state performance calibration protocol - the asymptotic P MAX method. In this paper, we applied this procedure to four PV cell technologies, Si, CIGS, perovskite, and Quantum Dot (QD), and compared their performance variations between the transient and the steady-state conditions. By comparison, we found that the performance parameters ( i.e. V OC , I SC , FF, ..eta..) measured between fast I-V scans (and the asymptotic method (steady-state) change significantly for perovskite and QD cells. These changes do not happen for Si and CIGS cells. Furthermore, the statistical performance analysis on nearly 100 emerging cells received globally (including OPV, Perovskite, and QD) shows that over 70 % of the fast I-V scans have a relative performance deviation larger than 1% compared to those determined using the asymptotic P MAX scan. Given the complex dynamic behavior observed in emerging PV devices, the CMP group at NREL thus only certifies their steady steady-state performance using the Asymptotic P MAX method. We highly recommend similar steady-state performance calibration protocol for all researchers in emerging PV because accuracy in reported efficiencies is critical to the long-term success of those promising new PV technologies.

41 EE - Solar Energy Technologies Office (EE-4S)↗

Destructive Analysis of TRISO Particles: Crush/Burn/Leach Followed by Davies-Gray Titration and IDMS

The accurate accounting of nuclear materials is a cornerstone of international nuclear safeguards. One emerging challenge in this domain is the fabrication of TRIstructural ISOtropic (TRISO) particle fuels. Although these innovative fuel forms are critical for advanced reactor applications, their robust refractory ceramics and coating compositions present significant obstacles to destructive analysis (DA) methods. Ensuring full and quantitative recovery from these particles is essential for accurate mass accountancy. The current study was initiated to address these challenges, first by validating a previously established destructive method developed by Oak Ridge National Laboratory (ORNL) for the quantitative recovery of uranium from TRISO particles and then following that process with uranium content determination through isotope dilution mass spectrometry (IDMS) and Davies-Gray titration. This study expands on the scope of a digestive method that was developed under the Advanced Gas Reactor Fuel Development and Qualification program and is currently implemented in both the Coated Particle Fuel Development Laboratory and Irradiated Fuels Examination Laboratory at ORNL. The success of the previous Advanced Gas Reactor work relied on developing a DA method to evaluate the fabrication process and reactor experiments. The methodology described in this report was designed to rigorously investigate the efficacy of the crush/burn/leach sample preparation of TRISO particles; it aims to quantify uranium recovery while also assessing the effects of TRISO constituents (e.g., silicon and zirconium) on analytical precision and accuracy. By comparing the results from the titration method and IDMS, we sought to determine whether existing analytical procedures accepted by the International Atomic Energy Agency (IAEA) could be effectively translated to TRISO fuel forms. The team employed an approach that involved processing replicate TRISO samples, optimizing the milling (i.e., crushing) step and performing serial leaches. The elemental composition of the analytical samples was examined to prepare for interference studies in the second year of this project. The integration of gamma spectrometry to verify residual uranium activity further strengthened the validation. Statistical methods were applied to the collected data to evaluate the uncertainties arising from sampling, sample preparation and uranium quantification. These uncertainties were then compared to the IAEA’s international target values (ITVs). Additional data collected in upcoming project work will strengthen the uncertainty estimates. Ultimately, it is hoped that this project will contribute materially to the body of work related to characterization of TRISO based fuels for the purpose of material accountancy and its applications to international safeguards.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Results from the Muon g-2 experiment at Fermilab

The goal of the Muon g-2 experiment at Fermilab is to measure the muon magnetic momentanomaly with a final accuracy of 140 parts per billion (ppb). The experiment has published tworesults based on the data collected in 2018 (Run-1) and 2019-2020 (Run-2/3), respectively. These results confirm the previous measurement performed 20 years ago at Brookhaven National Laboratory, and their combination reaches the unprecedented uncertainty of 200 ppb. This proceeding presents a brief overview of the Standard Model prediction for the muon g-2. It then summarizes the experimental measurement technique and the Run-1 and Run-2/3 measurements, detailing the improvements in their systematic and statistical uncertainties. Finally, it illustrates the comparison between theory and experiment and discusses future prospects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Real-Time Global Flood Estimation Using Satellite-Based Precipitation and a Coupled Land Surface and Routing Model

A widely used land surface model, the Variable Infiltration Capacity (VIC) model, is coupled with a newly developed hierarchical dominant river tracing-based runoff-routing model to form the Dominant river tracing-Routing Integrated with VIC Environment (DRIVE) model, which serves as the new core of the real-time Global Flood Monitoring System (GFMS). The GFMS uses real-time satellite-based precipitation to derive flood monitoring parameters for the latitude band 50 deg. N - 50 deg. S at relatively high spatial (approximately 12 km) and temporal (3 hourly) resolution. Examples of model results for recent flood events are computed using the real-time GFMS (http://flood.umd.edu). To evaluate the accuracy of the new GFMS, the DRIVE model is run retrospectively for 15 years using both research-quality and real-time satellite precipitation products. Evaluation results are slightly better for the research-quality input and significantly better for longer duration events (3 day events versus 1 day events). Basins with fewer dams tend to provide lower false alarm ratios. For events longer than three days in areas with few dams, the probability of detection is approximately 0.9 and the false alarm ratio is approximately 0.6. In general, these statistical results are better than those of the previous system. Streamflow was evaluated at 1121 river gauges across the quasi-global domain. Validation using real-time precipitation across the tropics (30 deg. S - 30 deg. N) gives positive daily Nash-Sutcliffe Coefficients for 107 out of 375 (28%) stations with a mean of 0.19 and 51% of the same gauges at monthly scale with a mean of 0.33. There were poorer results in higher latitudes, probably due to larger errors in the satellite precipitation input.

global flood estimation↗

Flash Optical Energy from the Geostationary Lightning Mapper

The Geostationary Operational Environmental Satellite -16 (GOES-16) Geostationary Lightning Mapper (GLM) is evaluated for many months during the Post Launch Product Test (PLPT) phase in order to ensure that optimal products are available for both the operational forecasting and broader scientific research communities. The emphasis of the PLPT phase is to validate the GLM performance (i.e., lightning flash detection efficiency, geolocation and time-stamp accuracy) using an extensive network of independent ground-based, in-situ, and space-based reference lightning detection systems. However, another essential aspect of the PLPT phase is to obtain benchmarks of the GLM lightning optical amplitude, so that any long-term degradation in the nadir-staring GLM camera system can be realized and quantitatively assessed. This is accomplished in a straight-forward manner by collecting a very large sample of lightning flashes across many geographical regions in the GLM field-of-view so that statistically meaningful benchmarks of lightning optical amplitude (i.e., optical energy in units of femto-joules per flash) are obtained. The benchmarking is particularly important to follow-on studies that will attempt to incorporate the flash optical energy product into new derived products (e.g., energy-weighted lightning "jump" warning algorithms, and lightning nitrogen oxides production estimates).

Lightning↗

Aerosol emissions from water-lean solvents for post-combustion CO 2 capture

Advanced water-lean solvents (WLS) for post-combustion CO 2 capture have been gaining interest due to their ability to reduce the parasitic penalty from energy needed for solvent regeneration. Commercial implementation of these novel CO 2 capture technologies hinges on successful control of amine emissions. RTI conducted a parametric study of fundamental and operational variables influence on overall amine aerosol and vapor emissions from our water-lean solvent eCO 2 Sol™ using our 6-kW equivalent bench-scale gas absorption system. The parametric testing used a simulated flue gas with 15 % CO 2 , 2.3–4.2 % H 2 O, and 0–6 ppm sulfite (SO 3 ) to examine the impact of the presence of aerosols to the capture performance and amine emissions from the system. The SO 3 reacts with water in the flue gas to create H 2 SO 4 , which forms liquid aerosol droplets and provide nucleation sites for growth of aerosols. Scanning Mobility Particle Sizer and Aerodynamic Particle Sizer instruments monitored the aerosol particle size distribution. Parametric testing results suggested that the presence of the aerosols in the flue gas could increase the overall amine emissions by 10X compared to the baseline emissions from WLS’s vapor pressure. Principal component analysis (PCA) and projection to latent squares (PLS) developed models to predict the aerosol-based amine emissions from process data. The predictive PLS model had a correlation coefficient (Q 2 ) of 0.92 and could predict the aerosol-based emissions from the NAS process with ±15 % accuracy (average absolute deviation, AAD). The PLS regression model also identified key variables affecting aerosol-based emissions from WLS.

42 ENGINEERING↗

A stochastic-dynamic model for global atmospheric mass-field statistics

Global atmospheric mass field error correlations based on satellite observations and on numerical forecasts show strong and systematic latitude dependence. A model for the latitude dependent spatial correlation structure of mass field forecast errors is derived from dynamical considerations. Three methods of solution were tested. In the first method, the equation was solved by expansion in spherical harmonics, and the correlation function was computed analytically using the expansion coefficients. In the second method, the finite difference equivalent of the equation was solved using a fast poisson solver. The correlation function was computed using stratified sampling of the individual realizations. In the third method, a higher order equation was derived, and solved directly in finite differences by two successive applications of the fast poisson solver. The three methods were compared for accuracy and efficiency, and the third method was chosen as clearly superior.

Ghil, M.↗

CADIS and FW-CADIS Variance Reduction in Gamma Transport for Predicting Prompt Forensics Signatures

The goal of prompt nuclear forensics is to determine the characteristics of a nuclear detonation based on the signatures available almost immediately after the explosion. An important characteristic is the reaction time history (RTH), a measure of the device’s rate of neutron multiplication. The RTH can be estimated by observation of the gamma radiation emitted from the detonation, which can be detected directly or observed indirectly as Teller light. Gamma transport simulations used to predict these radiation fields are often modeled stochastically using the Monte Carlo N-Particle (MCNP) code, which can be a computationally demanding task due to the number of particle histories needed to achieve statistical convergence. In an attempt to improve the efficiency of these calculations, we evaluate two variance reduction techniques: Consistent Adjoint-Driven Importance Sampling (CADIS) and Forward-Weighted Consistent Adjoint-Driven Importance Sampling (FW-CADIS). These methods use a deterministically calculated adjoint flux to create weight windows and source biasing that guide MCNP sampling. We study the utility of CADIS and FW-CADIS for their use in MCNP gamma transport for nuclear forensics prediction simulations. Furthermore, the results demonstrate that both CADIS and FW-CADIS improve the accuracy for forensics-focused simulations, with CADIS being most beneficial in direct detection and FW-CADIS being ideal for computing a global Teller light source.

CADIS↗

Estimating Vegetation Parameters from Interferometric and Polarimetric Radar Using Physical Scattering Models

Radar data from vegetated land surfaces depend on many structural and compositional parameters describing the terrain. Because early, noninterferometric radar systems usually constituted an insufficient observation set from which to estimate parameters of the terrain, statistical regression techniques were used which incorporated some level of apriori knowledge or field measurements. With the advent of radar interferometry and polarimetric interferometry, potentially at multiple baselines, the observation set is now approaching that required to quantitatively estimate the parameters describing a vegetated land surface. Quantitative estimation entails formulating a physical scattering model relating the radar observations to the vegetation and surface parameters on which they depend. This paper describes the physics of candidate scattering models, and shows how the models determine the estimable parameter set. It also indicates the measurement accuracy of parameters such as vegetation height, height-to-base-of-live-crown, and surface topography with multibaseline polarimetric interferometry.

Treuhaft, Robert N.↗

Convolutional neural network identification of galaxy post-mergers in UNIONS using IllustrisTNG

ABSTRACT The Canada–France Imaging Survey (CFIS) will consist of deep, high-resolution r-band imaging over ∼5000 deg2 of the sky, representing a first-rate opportunity to identify recently merged galaxies. Because of the large number of galaxies in CFIS, we investigate the use of a convolutional neural network (CNN) for automated merger classification. Training samples of post-merger and isolated galaxy images are generated from the IllustrisTNG simulation processed with the observational realism code RealSim. The CNN’s overall classification accuracy is 88 per cent, remaining stable over a wide range of intrinsic and environmental parameters. We generate a mock galaxy survey from IllustrisTNG in order to explore the expected purity of post-merger samples identified by the CNN. Despite the CNN’s good performance in training, the intrinsic rarity of post-mergers leads to a sample that is only ∼6 per cent pure when the default decision threshold is used. We investigate trade-offs in purity and completeness with a variable decision threshold and find that we recover the statistical distribution of merger-induced star formation rate enhancements. Finally, the performance of the CNN is compared with both traditional automated methods and human classifiers. The CNN is shown to outperform Gini–M20 and asymmetry methods by an order of magnitude in post-merger sample purity on the mock survey data. Although the CNN outperforms the human classifiers on sample completeness, the purity of the post-merger sample identified by humans is frequently higher, indicating that a hybrid approach to classifications may be an effective solution to merger classifications in large surveys.

Bickley, Robert W.↗

A hybrid data–model approach to map soil thickness in mountain hillslopes

Abstract. Soil thickness plays a central role in the interactions between vegetation, soils, and topography, where it controls the retention and release of water, carbon, nitrogen, and metals. However, mapping soil thickness, here defined as the mobile regolith layer, at high spatial resolution remains challenging. Here, we develop a hybrid model that combines a process-based model and empirical relationships to estimate the spatial heterogeneity of soil thickness with fine spatial resolution (0.5 m). We apply this model to two aspects of hillslopes (southwest- and northeast-facing, respectively) in the East River watershed in Colorado. Two independent measurement methods – auger and cone penetrometer – are used to sample soil thickness at 78 locations to calibrate the local value of unconstrained parameters within the hybrid model. Sensitivity analysis using the hybrid model reveals that the diffusion coefficient used in hillslope diffusion modeling has the largest sensitivity among all input parameters. In addition, our results from both sampling and modeling show that, in general, the northeast-facing hillslope has a deeper soil layer than the southwest-facing hillslope. By comparing the soil thickness estimated between a machine-learning approach and this hybrid model, the hybrid model provides higher accuracy and requires less sampling data. Modeling results further reveal that the southwest-facing hillslope has a slightly faster surface soil erosion rate and soil production rate than the northeast-facing hillslope, which suggests that the relatively less dense vegetation cover and drier surface soils on the southwest-facing slopes influence soil properties. With seven parameters in total for calibration, this hybrid model can provide a realistic soil thickness map with a relatively small amount of sampling dataset comparing to machine-learning approach. Integrating process-based modeling and statistical analysis not only provides a thorough understanding of the fundamental mechanisms for soil thickness prediction but also integrates the strengths of both statistical approaches and process-based modeling approaches.

58 GEOSCIENCES↗

Virtual Fit Assessment: Validation using Historical Spacesuit Fit Data

Virtual fit tests using 3D body scans have provided a cost-effective means to predictively assess spacesuit fit for the current and future astronaut population. However, fit is a complex issue influenced by physical interferences, subjective preference, and many other factors. Fit can substantially differ between the type of hardware, environmental conditions, and tasks being performed. Namely, fit changes across different contexts, such as 3D printed mockup evaluations, pressurized one-g suited test events, neutral buoyancy and other training events, and flight extravehicular activities (EVA). These challenges make it difficult to validate virtual fit frameworks to physical suit sizing. This study proposes a new method of validation using the wealth of historically archived suit fit data. Physically Assessed Fit (PAF) data was assessed from astronauts and test volunteers who wore the legacy Extravehicular Mobility Unit (EMU). The data was collected during the past decades at NASA and considered to be most reliable and dependable. Each participant was 3D scanned for body shape and spacesuit-critical dimensions were measured per NASA guidelines. The participants’ size preference for hard upper torso (HUT) assembly was retrieved from their pressurized suit fit check records. Fit assessments were also updated after one-g EVA training, neutral buoyancy training, and EVA flights. Virtually Assessed Fit (VAF) was done by overlaying the CAD model of a HUT with the 3D body scans of the PAF participants. Each body scan was iteratively adjusted for the position inside the HUT to minimize the suit-to-body contact interference while satisfying a set of prescribed requirements. Then the residual contact area, depth, and volume were quantified as VAF metrics. This process was repeated for the different HUT sizes, including medium, large, and extra-large. Statistical modeling is currently in progress and will be presented at the conference. A statistical classifier will be developed to predict a fit probability for different HUT sizes as a function of the corresponding person’s VAF metrics. The HUT size with the highest fit probability will constitute the most likely size selection for the person, and the prediction will be compared against the corresponding PAF data. The participant data will be randomly pre-grouped into either a model development or validation subset. While the model development subset will be used to build the probability model, the validation subset will be used to assess the model accuracy. Also, the locations and magnitudes of suit-body-contacts will be estimated from VAF. This information can identify the critical suit geometry and body shape features that influence suit fit. The variations found in PAF size selections by subjects with similar VAF metrics will allow for investigations into subjective preferences, for example, tight versus loose fit. Overall, this study is expected to provide a structured validation of a virtual suit fit framework, which has not been possible in the past. The outcome can also provide useful insights and potential limitations for interpreting virtual fit tests for future spacesuit designs and population accommodation.

Han Kim↗

Statistical and Machine Learning Approaches to Analyzing Pipeline Incidents in the United States (2010–2024)

This study applies machine learning methods to analyze natural gas pipeline incidents in the United States using the Pipeline and Hazardous Materials Safety Administration (PHMSA) Gas Distribution Incident Dataset (2010–2024). The dataset includes over 600 variables describing incident characteristics, infrastructure attributes, and contributing factors associated with unintentional gas releases. The objective is to assess whether these features can reliably predict the underlying cause of pipeline failures. Multinomial logistic regression and Random Forest models were developed to classify incident causes, including excavation damage, corrosion, equipment failure, and natural forces. Results show that excavation damage is both the most frequent and most predictable cause, with models achieving strong performance for this category. However, when excavation damage is excluded, model accuracy declines significantly, with some models performing near random levels. Across all approaches, severe class imbalance and limited variability in key predictors constrain predictive performance. Pipeline age and diameter emerge as the most influential variables, but they provide insufficient discriminatory power to distinguish among less frequent failure types. These findings indicate that non-excavation-related incidents are rare, heterogeneous, and weakly represented in the dataset, limiting the effectiveness of machine learning classification. Overall, this study highlights the structural limitations of the PHMSA dataset for predictive modeling and underscores the need for improved data balance and feature enrichment. The results reinforce excavation damage prevention as the most impactful strategy for reducing pipeline incidents.

03 NATURAL GAS↗

A hybrid calibration approach to Hertz-type contact parameters for discrete element models

This study aims at providing a hybrid calibration framework to estimate Hertz-type contact parameters (particle-scale shear modulus and Poisson ratio) for both two-dimensional and three-dimensional discrete element modelling (DEM). On the basis of statistically isotropic granular packings, a set of analytical formulae between macroscopic material parameters (Young modulus and Poisson ratio) and particle-scale Hertz-type contact parameters for granular systems are derived under small-strain isotropic stress conditions. However, the derived analytical solutions are only estimated values for general models. By viewing each DEM modelling as an implicit mathematical function taking the particle-level parameters as independent variables and employing the derived analytical solutions as the initial input parameters, an automatic iterative scheme is proposed to obtain the calibrated parameters with higher accuracies. Considering highly nonlinear features and discontinuities of the macro-micro relationship in Hertz-based discrete element models, the adaptive moment estimation algorithm is adopted in this study because of its capacity of dealing with noise gradients of cost functions. Here, the proposed method is validated with several numerical cases including randomly distributed monodisperse and polydisperse packings. Noticeable improvements in terms of calibration efficiency and accuracy have been made.

Constitutive law↗

Wavelength Calibration of the Full-sun Ultraviolet Rocket SpecTrograph (FURST)

The Sun has a well-known periodicity in sunspot number and magnetic field variation. The underlying cause of this 11-year cycle is not fully understood and has yet to be connected with those processes in other stellar objects. The Full-sun Ultraviolet Rocket SpecTrograph (FURST) is a sounding rocket payload being developed by Montana State University (MSU) alongside the Marshall Space Flight Center(MSFC) solar physics group. Scheduled to launch from White Sands Missile Range (WSMR) in 2022, this instrument is unique in that it will provide the connection between stellar observatories with measurements of our Sun. It will achieve this through measuring high-resolution full-disk spectral irradiance. We aim to obtain a wavelength resolution R>10,000 in the 120 - 181 nm UltraViolet (UV) range, on par with that of the Hubble (HST) Space Telescope Imaging Spectrograph (STIS). This resolution goal will allow us to study the relatively low-temperature plasma in the chromosphere and lower corona with spectral accuracy down to 0.1 Å (a Doppler-shift of about±30 km/s). In addition, the Lyman Alpha(121 nm) line is known to saturate most CCD electronics. These factors illustrate the particular challenge of precise wavelength calibration for this spectral range. We are building a collimator in order to calibrate the FURST instrument under these strict spectral requirements. This paper will present the results of our simulation of the diagnostic lamp signal to be used for wavelength calibration. The simulation allows us to begin to account for photon noise, electronic readout noise, and statistical error. These in turn lead to the development of our pre- and post-launch calibration plans. Future work includes absolute radiometric and wavelength calibration with this new collimator. In addition, the ability of FURST to measure small Doppler-shifts will provide capabilities for planetary atmospheric scientists. This impact is coupled with the diverse international partnership created by the closely-knit Sounding Rocket teams around the globe. Sounding Rockets like FURST have an even broader impact, as they encourage future satellite missions under the prospect of long-term observations

FURST↗

A hierarchical Bayesian model for background variation in radiation source localization

In this paper, we apply a new model to account for varying background radiation in radiological source localization. We present a hierarchical Bayesian model that simultaneously infers background and source location parameters without requiring separate estimation of the background radiation at each detector location. We employ a simplified photon transport model to reduce the computational expense of Bayesian model calibration. Furthermore, we demonstrate the model accuracy by localizing a cesium-137 source in a simulated city block, and we analyze experimental field measurements with varying background. In both cases, the model provides sufficient fidelity that we can locate the source while simultaneously estimating background radiation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗