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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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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

In-flight radiometry of an airborne multispectral sensor

The in-flight radiometric behavior of the NS001 Landsat Thematic Mapper simulator is being reexamined. The absolute radiometric calibration and polarization sensitivity are being analyzed based on data collected in 1990 and 1991. The NS001 has continuously variable gain settings controlled by the aircraft operator. As such, the of in-flight calibration source, an integrating sphere in the solar reflective spectrum, is the only means for calibrating this instrument. Upgrades to the power supply and monitoring circuitry in 1990 improved the in-flight stability. Preliminary results in-flight calibrations of the NS001 indicate no improvement in radiometric accuracy. Laboratory tests have also shown that the NS001 shows strong sensitivity to the degree of polarization and state of the incoming radiations. Simulation studies for typical in-flight conditions have shown that for the NS001 scanning in the principal plane of the sun over a vegetated target, radiance errors reached +/-10 percent in the 0.45-0.52-micron channel and varied with scan angle.

Markham, Brian L.↗
DOE OSTI2020

SICOPOLIS-AD v1: an open-source adjoint modeling framework for ice sheet simulation enabled by the algorithmic differentiation tool OpenAD

We present a new capability of the ice sheet model SICOPOLIS that enables flexible adjoint code generation via source transformation using the open-source algorithmic differentiation (AD) tool OpenAD.The adjoint code enables efficient calculation of the sensitivities of a scalar-valued objective function or quantity of interest (QoI) to a range of important, often spatially varying and uncertain model input variables, including initial and boundary conditions, as well as model parameters.Compared to earlier work on the adjoint code generation of SICOPOLIS, our work makes several important advances:(i) it is embedded within the up-to-date trunk of the SICOPOLIS repository – accounting for 1.5 decades of code development and improvements – and is readily available to the wider community;(ii) the AD tool used, OpenAD, is an open-source tool;(iii) the adjoint code developed is applicable to both Greenland and Antarctica, including grounded ice as well as floating ice shelves, with an extended choice of thermodynamical representations.A number of code refactorization steps were required. They are discussed in detail in an Appendix as they hold lessons for the application of AD to legacy codes at large.As an example application, we examine the sensitivity of the total Antarctic Ice Sheet volume to changes in initial ice thickness, austral summer precipitation, and basal and surface temperatures across the ice sheet.Simulations of Antarctica with floating ice shelves show that over 100 years of simulation the sensitivity of total ice sheet volume to the initial ice thickness and precipitation is almost uniformly positive, while the sensitivities to surface and basal temperature are almost uniformly negative. Sensitivity to austral summer precipitation is largest on floating ice shelves from Queen Maud to Queen Mary Land. The largest sensitivity to initial ice thickness is at outlet glaciers around Antarctica. Comparison between total ice sheet volume sensitivities to surface and basal temperature shows that surface temperature sensitivities are higher broadly across the floating ice shelves, while basal temperature sensitivities are highest at the grounding lines of floating ice shelves and outlet glaciers. A uniformly perturbed region of East Antarctica reveals that, among the four control variables tested here, total ice sheet volume is the most sensitive to variations in austral summer precipitation as formulated in SICOPOLIS.Comparison between adjoint- and finite-difference-derived sensitivities shows good agreement, lending confidence that the AD tool is producing correct adjoint code.The new modeling infrastructure is freely available at http://www.sicopolis.net (last access: 2 April 2020) under the development trunk.

58 GEOSCIENCES↗
DOE OSTI2025

Antihelium-3 sensitivity for the GRAMS experiment

The Gamma-Ray and AntiMatter Survey (GRAMS) is a next-generation balloon/satellite mission utilizing a Liquid Argon Time Projection Chamber (LArTPC) detector to measure both MeV gamma rays and antinuclei produced by dark matter annihilation or decay. The GRAMS can identify antihelium-3 events based on the measurements of X-rays and charged pions from the decay of the exotic atoms, Time of Flight (TOF), energy deposition, and stopping range. This paper shows the antihelium-3 sensitivity estimation using a GEANT4 Monte Carlo simulation. For the proposed long-duration balloon (LDB) flight program (35 days x 3 flights) and future satellite mission (2-year observation/10-year observation), the sensitivities become 1.47 × 10 −7 [m 2 s sr GeV/n] −1 and 1.55 × 10 −9 [m 2 s sr GeV/n] −1 /3.10 x 10 -10 [m 2 s sr GeV/n] −1 , respectively. The results indicate that GRAMS can extensively investigate various dark matter models through the antihelium-3 measurements.

Antihelium-3↗
DOE OSTI2023

Validation of turbulence intensity as simulated by the Weather Research and Forecasting model off the US northeast coast

We report turbulence intensity (TI) is often used to quantify the strength of turbulence in wind energy applications and serves as the basis of standards in wind turbine design. Thus, accurately characterizing the spatiotemporal variability in TI should lead to improved predictions of power production. Nevertheless, turbulence measurements over the ocean are far less prevalent than over land due to challenges in instrumental deployment, maintenance, and operation. Atmospheric models such as mesoscale (weather prediction) and large-eddy simulation (LES) models are commonly used in the wind energy industry to assess the spatial variability of a given site. However, the TI derivation from atmospheric models has not been well examined. An algorithm is proposed in this study to realize online calculation of TI in the Weather Research and Forecasting (WRF) model. Simulated TI is divided into two components depending on scale, including sub-grid (parameterized based on turbulence kinetic energy (TKE)) and grid resolved. The sensitivity of sea surface temperature (SST) on simulated TI is also tested. An assessment is performed by using observations collected during a field campaign conducted from February to June 2020 near the Woods Hole Oceanographic Institution Martha's Vineyard Coastal Observatory. Results show that while simulated TKE is generally smaller than the lidar-observed value, wind speed bias is usually small. Overall, this leads to a slight underestimation in sub-grid-scale estimated TI. Improved SST representation subsequently reduces model biases in atmospheric stability as well as wind speed and sub-grid TI near the hub height. Large TI events in conjunction with mesoscale weather systems observed during the studied period pose a challenge to accurately estimating TI from models. Due to notable uncertainty in accurately simulating those events, this suggests summing up sub-grid and resolved TI may not be an ideal solution. Efforts in further improving skills in simulating mesoscale flow and cloud systems are necessary as the next steps.

17 WIND ENERGY↗
NASA NTRS1996

Simulations of light effects on the human circadian pacemaker: implications for assessment of intrinsic period

The sensitivity of the human circadian system to light has been the subject of considerable debate. Using computer simulations of a recent quantitative model for the effects of light on the human circadian system, we investigated these effects of light during different experimental protocols. The results of the simulations indicate that the nonuniform distribution over the circadian cycle of exposure to ordinary room light seen in classical free-run studies, in which subjects select their exposure to light and darkness, can result in an observed period of approximately 25 h, even when the intrinsic period of the subject's endogenous circadian pacemaker is much closer to 24 h. Other simulation results suggest that accurate assessment of the true intrinsic period of the human circadian pacemaker requires low ambient light intensities (approximately 10-15 lx) during scheduled wake episodes, desynchrony of the imposed light-dark cycle from the endogenous circadian oscillator, and a study length of at least 20 days. Although these simulations await further experimental substantiation, they highlight the sensitivity to light of the human circadian system and the potential confounding influence of light on the assessment of the intrinsic period of the circadian pacemaker.

Non-NASA Center↗
NASA NTRS1979

A one-dimensional model describing aerosol formation and evolution in the stratosphere. I - Physical processes and mathematical analogs. II - Sensitivity studies and comparison with observations

A new time-dependent one-dimensional model of the stratospheric sulfate aerosol layer is developed. The model treats atmospheric photochemistry and aerosol physics in detail and includes the interaction between gases and particles explicitly. It is shown that the numerical algorithms used in the model are quite precise. Sensitivity studies and comparison with observations are made. The simulated aerosol physics generates a particle layer with most of the observed properties. The sensitivity of the calculated properties to changes in a large number of aeronomic aerosol parameters is discussed in some detail. The sensitivity analysis reveals areas where the aerosol model is most uncertain. New observations are suggested that might help resolve important questions about the origin of the stratospheric aerosol layer.

Turco, R. P.↗
NASA NTRS1991

Numerical and experimental investigations of rarefied nozzle and plume flows of nitrogen

Numerical and experimental investigations are performed for the rarefied flow of nitrogen through a small nozzle which is expanded into near-vacuum conditions. Two different numerical studies are undertaken: the first employs a continuum approach in solving the Navier-Stokes equations, and the second employs a particle approach through use of the direct simulation Monte Carlo method (DSMC). The experimental investigation concerns the measurement of pressure, using a Pitot tube, in the nozzle exit plane and near-field of the plume. Comparison of the experimental and numerical data at the nozzle exit reveals that the DSMC technique provides the more accurate description of the expanding flow. It is discovered that the DSMC solutions are quite sensitive to the model employed to simulate the interaction between the gas and the nozzle wall surface. It is concluded that the simplistic fully diffuse model is quite satisfactory for the present application.

Boyd, Iain D.↗
DOE OSTI2021

Time Evolution and Diurnal Variability of the Parametric Sensitivity of Turbine-Height Winds in the MYNN-EDMF Parameterization

The Mellor-Yamada-Nakanishi-Niino (MYNN) parameterization applied in the Weather Research and Forecasting (WRF) model has been augmented to include the Eddy-Diffusion Mass-Flux (EDMF) approach to better represent transport by boundary-layer eddies. This change includes the addition of new parameters associated with convective updrafts and boundary-layer clouds. These additions lead to new parametric sensitivities in the hub-height wind speed compared to simulations using the standard MYNN parameterization that were explored previously. This work builds on efforts focused on WRF’s MYNN parameterization by examining the sensitivity of hub-height wind speed to parameters in the MYNN-EDMF parameterization as a function of simulation lead time. Summer and winter periods were selected from the second Wind Forecast Improvement Project (WFIP2). Five sets of simulations were completed for each season, with lead times ranging from 2 to 6 days. The results show that the sensitivity to the new parameters associated with the EDMF scheme is generally small compared to other parameters, with the largest impact in convective boundary layers. The spread in the perturbed parameter ensembles was found to grow quickly over the first 8 to 19 hours in the summer simulations and 17 to 24 hours in the winter simulations with little change after that, regardless of the simulation length. A strong diurnal cycle in the parameter sensitivity was also found associated with changes in the atmospheric stability, as well as an increase in the sensitivity to the entrainment parameter used in the EDMF parameterization that is associated with increasing fractional areas covered by plumes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Optimization of a High Pressure Turbine Blade and Sector-Based Annular Rig Design for Supercritical CO2 Power Cycle Representative Testing

Abstract As part of the ongoing research into the design of hardware for zero emission cycles, a first-stage high-pressure turbine (HPT) blade is optimized for a 300 MWe supercritical CO2 (sCO2) power cycle using the surrogate-assisted genetic algorithm optimizer in Numeca FINE/Design three-dimensional with objectives of increasing efficiency and decreasing heat load to the blade. Supercritical CO2 property tables are constructed from NIST REFPROP data for the condensable gas simulation in FINE/Turbo. A detailed mesh sensitivity study is performed for a baseline design to identify the proper-grid refinement and efficiently allocate resources for the optimization. Seventy design variables are selected for the initial population generation. Self-organizing maps are then used to focus the design variables on the most important ones affecting the objective functions. The optimization results in approximately 3000 three-dimensional Reynolds Averaged Navier Stokes simulations of different blade shapes with increases in efficiency of up to 0.85% and decreases in heat load of 14%. Families of blade shapes are identified for experimental testing in an annular rig at the Purdue Experimental Turbine Aerothermal Laboratory. A design to adapt the annular cascade for testing optimized geometries is introduced, which features eccentric radius sectors allowing for scaled-up geometries of sCO2 optimized blade profiles to be tested at design cycle representative conditions at high Reynolds numbers in dry air. Analysis into the effects of Reynolds number, working fluid, and geometric relations are presented to prove the efficacy of the test method.

Engineering↗
DOE OSTI2024

Tropical dry forest response to nutrient fertilization: a model validation and sensitivity analysis

Abstract. Soil nutrients, especially nitrogen (N) and phosphorus (P), regulate plant growth and hence influence carbon fluxes between the land surface and atmosphere. However, how forests adjust biomass partitioning to leaves, wood, and fine roots in response to N and/or P fertilization remains puzzling. Recent work in tropical forests suggests that trees increase fine root production under P fertilization, but it is unclear whether mechanistic models can reproduce this dynamic. In order to better understand mechanisms governing nutrient effects on plant allocation and improve models, we used the nutrient-enabled ED2 model to simulate a fertilization experiment being conducted in a secondary tropical dry forest in Costa Rica. We evaluated how different allocation parameterizations affected model performance. These parameterizations prescribed a linear relationship between relative allocation to fine roots and soil P concentrations. The slope of the linear relationship was allowed to be positive, negative, or zero. Some parameterizations realistically simulated leaf, wood, and fine root production, and these parameterizations all assumed a positive relationship between relative allocation to fine roots and soil P concentration. Model simulations of a 30-year timeframe indicated strong sensitivity to parameterization and fertilization treatment. Without P fertilization, the simulated aboveground biomass (AGB) accumulation was insensitive to the parameterization. With P fertilization, the model was highly sensitive to the parameterization and the greatest AGB accumulation occurred when relative allocation to fine roots was independent of soil P. Our study demonstrates the need for simultaneous measurements of leaf, wood, and fine root production in nutrient fertilization experiments and for longer-term experiments. Models that do not accurately represent allocation to fine roots may be highly biased in their simulations of AGB, especially on multi-decadal timescales.

Environmental Sciences & Ecology↗
DOE OSTI2021

Attribution of Snowpack Errors to Simulated Temperature and Precipitation in E3SMv1 Over the Contiguous United States

Abstract Snow water equivalent (SWE), temperature, and precipitation biases and trends are evaluated in the atmosphere‐land simulations of the Energy Exascale Earth System Model version 1 (E3SMv1) in comparison to the Community Earth System Model version 2 (CESM2) and two other models using the ground measurement‐based University of Arizona (UA) snow product. SWE, temperature, and precipitation biases are highest in magnitude in the Western contiguous United States (CONUS). SWE errors are attributed to temperature and precipitation through multiple linear regressions of normalized errors, the coefficients of which represent the sensitivities to temperature and precipitation errors. SWE errors are more sensitive to temperature errors throughout the CONUS. Model SWE and temperature trends are generally opposite from UA product trends in the Western CONUS. SWE trend errors are also attributed to temperature and precipitation trend errors using multiple linear regressions of normalized trend errors. SWE trend errors are more sensitive to those of precipitation at higher elevations (>1,500 m) in the Western CONUS in these simulations. Thus, the sensitivity to temperature and precipitation differ for SWE errors and its trend errors. Furthermore, the SWE trend errors are more sensitive to temperature and precipitation in the atmosphere‐ocean coupled simulations in which the atmosphere‐land is coupled to an active ocean model. These results suggest that both errors in simulated temperature and precipitation contribute to SWE errors.

Meteorology & Atmospheric Sciences↗
DOE OSTI2025

Linear and Nonlinear X-ray Spectra of Chiral Molecules: X-ray Circular Dichroism, Sum- and Difference-Frequency Generation of Fenchone and Cysteine

Recent advancements in X-ray light sources enable element-sensitive nonlinear spectroscopies for probing molecular chirality. We simulate X-ray absorption spectroscopy, X-ray circular dichroism (XCD), and nonlinear optical/X-ray SFG and DFG (OX SFG/DFG) signals for two prototypical chiral molecules, fenchone and cysteine. Furthermore, our multireference simulations reproduce experimental data and reveal how novel X-ray spectroscopies exploit the site- and element-sensitivity of X-rays to uncover molecular asymmetry. The XCD spectra show strong asymmetries at chiral centers, while distant atoms contribute weaker signals. The OX SFG/DFG signals, under fixed resonant optical excitation, strongly depend on the core and valence excitations. This allows us to introduce two-dimensional (2D) chirality-sensitive valence-core spectroscopy, which provides insight into the overlap between valence orbitals and local molecular asymmetry. Finally, our estimates using realistic laser and X-ray pulse parameters demonstrate that such nonlinear experiments are feasible at XFELs, offering a promising tool for investigating chiral molecules.

Circular dichroism spectroscopy↗
DOE OSTI2023

Physical Regime Sensitivity

Abstract This work presents a novel sensitivity approach that quantifies sensitivity to regimes of a model’s state variables rather than constitutive model parameters. This Physical Regime Sensitivity (PRS) determines which regimes of a model’s independent variables have the biggest influence on an experiment or application. PRS analysis is demonstrated on a strength model used in the simulation of a copper Taylor cylinder. In a series of simulations, the strength model was perturbed sequentially in local regimes of plastic strain, plastic strain rate, temperature and pressure, and then the prediction of cylinder shape was compared to unperturbed calculations. Results show, for example, that the deformed length of the cylinder was most sensitive to strength at a strain rate of 1.0 × 10 4 /sec., but the deformed footprint radius was most sensitive to strength at a strain rate of about 4.0 × 10 4 /sec. Compared to current histogram approaches, PRS can be used to design or interpret integrated experiments by identifying not just which regimes are accessed somewhere in the experiment but the causality question of which regimes actually affect the measured data. PRS should allow one to focus experimental and modeling efforts where they are most needed and to better interpret experiments.

36 MATERIALS SCIENCE↗
NASA NTRS1988

Flight simulation of a wide-body transport aircraft to evaluate MLS-RNAV procedures

In a collaborative effort between the Federal Aviation Administration (FAA) NASA and the U.S. Air Force, a piloted simulation was conducted to look at the issues involved with flying a large, wide-body aircraft in the airport terminal area using Microwave Landing System Area Navigation (MLS)-RNAV procedures. A variety of approach paths, departure paths, and holding patterns were evaluated during the course of the study for operational use, flight technical errors, and safety. In addition, several methods for driving the horizontal situation indicator and flight director instruments were investigated along with needle sensitivity. The ultimate goal of the simulation was to develop and verify candidate paths and procedures prior to flight tests conducted in 1986/87. Subject pilots for the simulation study were provided by the FAA, NASA, the U.S. Air Force, and the airline industry.

Branstetter, James R.↗
NASA NTRS2010

Exploring Discretization Error in Simulation-Based Aerodynamic Databases

This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.

Aftosmis, Michael J.↗
NASA NTRS2002

Sensitivity of Stratocumulus Optical Depths to Droplet Concentrations: Satellite Observations and Large-Eddy Simulations

A number of observations and simulations have shown that increased droplet concentrations in ship tracks increase their total cross-sectional area, thereby enhancing cloud albedo and providing a negative (cooling) radiative forcing at the surface and the top of the atmosphere. In some cases cloud water has been found to be enhanced in ship tracks, which has been attributed to suppression of drizzle and implies an enhanced susceptibility of cloud albedo to droplet concentrations. However, observations from aircraft and satellite indicate that on average cloud water is instead reduced in daytime ship tracks. Such a reduction in liquid water may be attributable to cloud-burning caused by solar heating by soot within the ship exhaust, or by increased precipitation resulting from giant nuclei in the ship exhaust. We will summarize the observational evidence and present results from large-eddy simulations that evaluate these mechanisms. Along the way we will present our insights into the interpretation of satellite retrievals of cloud microphysical properties.

Ackerman, A. S.↗
DOE OSTI2021

Techno-Economic Analysis of a Concentrating Solar Power Plant Using Redox-Active Metal Oxides as Heat Transfer Fluid and Storage Media

We present results for a one-dimensional quasi-steady-state thermodynamic model developed for a 111.7 MW e concentrating solar power (CSP) system using a redox-active metal oxide as the heat storage media and heat transfer agent integrated with a combined cycle air Brayton power block. In the energy charging and discharging processes, the metal oxide CaAl 0.2 Mn 0.8 O 2.9-δ (CAM28) undergoes a reversible, high temperature redox cycle including an endothermic oxygen-releasing reaction and exothermic oxygen-incorporation reaction. Concentrated solar radiation heats the redox-active oxide particles under partial vacuum to drive the reduction extent deeper for increased energy density at a fixed temperature, thereby increasing storage capacity while limiting the required on sun temperature. Direct counter-current contact of the reduced particles with compressed air from the Brayton compressor releases stored chemical and sensible energy, heating the air to 1,200°C at the turbine inlet while cooling and reoxidizing the particles. The cool oxidized particles recirculate through the solar receiver subsystem for another cycle of heating and reduction (oxygen release). We applied the techno-economic model to 1) size components, 2) examine intraday operation with varying solar insolation, 3) estimate annual performance characteristics over a simulated year, 4) estimate the levelized cost of electricity (LCOE), and 5) perform sensitivity analyses to evaluate factors that affect performance and cost. Simulations use hourly solar radiation data from Barstow, California to assess the performance of a 111.7 MW e system with solar multiples (SMs) varying from 1.2 to 2.4 and storage capacities of 6–14 h. The baseline system with 6 h storage and SM of 1.8 has a capacity factor of 54.2%, an increase from 32.3% capacity factor with no storage, and an average annual energy efficiency of 20.6%. Calculations show a system with an output of 710 GWh e net electricity per year, 12 h storage, and SM of 2.4 to have an installed cost of $329 million, and an LCOE of 5.98 ¢/kWh e . This value meets the U.S. Department of Energy’s SunShot 2020 target of 6.0 ¢/kWh e ( U. S Department of Energy, 2012 ), but falls just shy of the 5.0 ¢/kWh e 2030 CSP target for dispatchable electricity ( U. S Department of Energy, 2017 ). The cost and performance results are minimally sensitive to most design parameters. However, a one-point change in the weighted annual cost of capital from 8 to 7% (better understood as a 12.5% change) translates directly to an 11% decrease (0.66 ¢/kWhe) in the LCOE.

Gorman, Brandon T.↗
DOE OSTI2021

Evaluating Safeguards Statistical Assumptions via Stochastic Simulation

Herein, the authors built and tested a stochastic simulation to estimate achieved detection probabilities (DPs) on a stratum basis, over a tailorable range of diverted amounts from 0 to 2 SQ, using typical IAEA inspection data: i.e., SQ in stratum, number of items, number of gross/partial/bias defect measurements conducted, and realistic relative standard deviation (RSD) values for typical IAEA verification measurements. For bulk strata, the model calculates achieved DP at 0.01 SQ diversion increments; for item strata, the model calculates DP using the smallest realistic diversion increment (e.g., a plate, pin, or coupon). After successfully benchmarking against IAEA deterministic models, the simulation was used to test the sensitivity of DP to certain standard assumptions and selected input parameters. First, the equal defect assumption was tested; the results suggest significant complexity in the effectiveness of partial defect measurements. Next, the authors explored the sensitivity of DP to the assumed RSD of attribute tests. Then, the authors compared non-normal models for instrument performance (e.g., logistic, step, or arbitrary functions) to the typical results from a normal distribution (characterized by RSD). This last comparison was supplemented with experimentally derived performance data for an HM-5. The HM-5 was used to make enrichment measurements on both LEU and HEU MTR fuel elements as plates were removed, and the results fit with logistic and step curves and applied in the simulation. These stochastic DP results were compared to DP estimates from a deterministic model assuming a normal curve and typical RSD, yielding insights that could improve effectiveness in the field. These early results illustrate the potential of stochastic models to better understand achieved DP and to improve safeguards effectiveness.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗