Search NASA⌕ Search

SEARCH · Search NASA

Results for “generator parameter estimation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
NASA NTRS2020

Development and Evaluation of the Raindrop Size Distribution Parameters for the NASA Global Precipitation Measurement Mission Ground Validation Program

The National Aeronautics and Space Administration Global Precipitation Measurement (GPM) mission ground validation program uses dual-polarization radar moments to estimate raindrop size distribution (DSD) parameters, the mass-weighted mean drop diameter Dmass, and normalized intercept parameter NW, to validate the GPM Core Observatory–derived DSD parameters. The disdrometer-based Dmass and NW are derived through empirical relationships between Dmass and differential reflectivity ZDR, and between NW, reflectivity ZH, and Dmass. This study employs large datasets collected from two-dimensional video disdrometers (2DVD) during six different field studies to derive the requisite empirical relationships. The uncertainty of the derived Dmass(ZDR) relationship is evaluated through comparisons of 2DVD-calculated and ZDR-estimated Dmass, where ZDR is calculated directly from 2DVD observations. Similarly, the uncertainty of the NW(ZH, Dmass) relationship is evaluated through 2DVD-calculated and Dmass and ZH-estimated NW, where Dmass and ZH are directly calculated from 2DVD observations. This study also presents the sensitivity of Dmass(ZDR) relationships to climate regime and to disdrometer type after developing three additional Dmass(ZDR) relationships from second-generation Particle Size Velocity (PARSIVEL2) disdrometer (P2) observations collected in the Pacific Northwest, in Iowa, and at Kwajalein Atoll in the tropical Pacific Ocean. The application of P2-derived Dmass(ZDR) relationship based on precipitation in the northwestern United States to P2 observations collected over the tropical ocean resulted in the highest error among comparisons of the three datasets.

Ali Tokay↗
DOE OSTI2016

Assessment of Multi-Step CADIS Parameter Sensitivity to Neutron Flux Spectrum in Shutdown Dose Rate Calculations

Shutdown dose rate (SDDR) analysis requires (a) a neutron transport calculation to estimate neutron flux fields, (b) an activation calculation to compute radionuclide inventories and associated photon sources, and (c) a photon transport calculation to estimate final dose rate. In some applications, accurate full-scale Monte Carlo (MC) SDDR simulations are needed for very large systems with massive amounts of shielding materials. For example, SDDR assessments are required throughout the biological shield (bio-shield) of the ITER experimental facility to evaluate the required waiting period after the shutdown of ITER and to identify the locations where human accessibility should be prohibited. The bio-shield is a large cylindrical concrete structure (30 m tall and 34 m in diameter) surrounding the very complex tokamak machine. Determining the effects on SDDR of important factors, such as the cross talk (interactions) between the different ports of ITER, is possible only through full-scale simulations that involve all the complex inner details of the ITER tokamak machine. These simulations are impractical because calculation of space- and energy-dependent neutron fluxes throughout the structural materials is needed to estimate the distribution of radioisotopes causing the SDDR. Determining a good importance function that can be used in biasing a neutron MC calculation for SDDR is complicated because it is difficult to explicitly express the SDDR response function, which depends on subsequent computational steps. The Multi-Step Consistent Adjoint Driven Importance Sampling (MS-CADIS) hybrid MC/deterministic method was developed to speed up the SDDR MC neutron transport calculation using an importance function that represents the neutron importance to the final SDDR. The MS-CADIS method uses the CADIS method, which has been Notice: This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for the United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan). successfully used for more than a decade in radiation shielding applications to generate consistent source biasing and weight window (WW) variance reduction parameters to accelerate continuous-energy MC simulations. However, because MS-CADIS focuses on multi-step shielding calculations such as SDDR calculations, it develops an importance function for the initial radiation transport calculation (e.g., the neutron calculations in SDDR simulations) that represents the importance of particles to the final response of the overall simulation. To develop this importance function, the MS-CADIS method uses an adjoint calculation with a specific neutron adjoint source that represents the neutron's contribution to the final SDDR. Brute force calculation of the MS-CADIS neutron adjoint source requires a deterministic neutron transport calculation coupled with activation calculations in each element of the deterministic mesh. These calculations are needed to determine the MS-CADIS parameter for the neutron interactions that produce radioisotopes contributing to the SDDR. The MS-CADIS parameter is the microscopic cross section of the radioisotope-producing interaction, multiplied by the mass of this radioisotope existing at the end of the irradiation and decay scenario, and divided by the steady-state rate of the interaction. Because the activation calculations are performed for each radionuclide in each mesh element, implementation of the MS-CADIS method can be computationally expensive. However, these neutron transport and activation calculations are not needed if we assume that the radioisotopes are created due to single neutron interactions and their concentrations do not change as a result of burnup by neutron irradiation. The use of this approximation, which renders the MS-CADIS parameter independent of the neutron flux, seems reasonable in calculating the MS-CADIS importance function because this function is needed only to speed up the MC calculation, not to calculate the final SDDR. In this work, we investigate the validity of this approximation by investigating the behavior of the MS-CADIS parameter as a function of the neutron flux spectra in the Fusion Evaluated Nuclear Data Library (FENDL) Neutronics and Shielding Benchmark problem that contains representative isotopes and flux environments of fusion energy systems. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2023

Evaluation of Spray and Combustion Models for Simulating Dilute Combustion in a Direct-Injection Spark-Ignition Engine

Dilute combustion in spark-ignition engines has the potential to improve thermal efficiency by mitigating knock and by reducing throttling and wall heat losses. However, ignition and combustion processes can become unstable for dilute operation due to a lowered laminar flame speed, resulting in excessive cycle-to-cycle variability (CCV) of the combustion process. To compensate for the slower combustion in less reactive mixtures, a modified intake port geometry can be employed to generate a strong tumble flow in the cylinder and elevate turbulence levels around the spark plug, thereby promoting a faster transition to turbulent deflagration. Consequently, optimizing combustion chamber geometry and operating strategy is crucial to maximizing the benefits of using dilute combustion with enhanced in-cylinder turbulence across a wide range of operating conditions. Computational fluid dynamics (CFD) simulations can be utilized for virtual engine optimization tasks, but this would require the models to be truly predictive regarding the impact of changes to the engine design and operational parameters.In this study, multicycle large-eddy simulations (LES) are performed for a direct-injection spark-ignition engine to investigate the model performance in predicting engine combustion characteristics with respect to changes in the intake configuration. A tumble plate that blocks the lower part of the intake port inlet is used to vary the tumble. A set of CFD models that have been recently developed are employed, which takes into account the drag of nonspherical droplets, flash-boiling behavior of liquid sprays, spray-wall interaction, surrogate formulation of a research-grade E10 gasoline, and fast chemical kinetic solvers. Simulation results are compared to experimental engine data in terms of cylinder pressure, apparent heat release rate, mass fraction burned timing, and flame images. It is found that LES employing the state-of-the-art CFD models are capable of properly predicting the spray processes and reproducing the measured mean cylinder pressure for the case with the tumble plate. On the other hand, the LES over-predicts the combustion rate during the early combustion stage and under-estimates the CCV, and these discrepancies become larger when the tumble plate is removed.

computational fluid dynamics simulation↗
DOE OSTI2019

Ecohydrologic separation alters interpreted hydrologic stores and fluxes in a headwater mountain catchment

Recent studies have demonstrated that compartmentalized pools of water preferentially supply either plant transpiration (poorly mobile water) or streamflow and groundwater (highly mobile water) in some catchments, a phenomenon referred to as ecohydrologic separation. Additionally, the omission of processes accounting for ecohydrologic separation in standard applications of hydrological models is expected to influence estimates of water residence times and plant water availability. However, few studies have tested this expectation or investigated how ecohydrologic separation alters interpretations of stores and fluxes of water within a catchment. In this study, we compare two rainfall-runoff models that integrate catchment-scale representations of transport, one that incorporates ecohydrologic separation and one that does not. The models were developed for a second-order watershed at the H.J. Andrews Experimental Forest (Oregon, USA), the site where ecohydrologic separation was first observed, and calibrated against multiple years of stream discharge and chloride concentration. Model structural variations caused mixed results for differences in calibrated parameters and differences in storage between reservoirs. However, large differences in catchment storage volumes and fluxes arise when considering only mobile water. These changes influence interpreted residence times for streamflow-generating water, demonstrating the importance of ecohydrologic separation in catchment-scale water and solute transport.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Life cycle greenhouse gas emissions of hydrogen fuel production from chlor-alkali processes in the United States

By-product hydrogen from chlor-alkali processes can help meet the increasing demand for hydrogen fuel in early fuel cell electric vehicle markets (e.g., California) in the U.S. Hydrogen produced from chlor-alkali plants is typically combusted for process heat on site, vented to the atmosphere (i.e., wasted), or sold to the external merchant hydrogen market. Whether it is combusted, vented, or sold as a commodity, relevant information is lacking as to the life-cycle environmental benefits or trade-offs of using by-product hydrogen from chlor-alkali plants. A life-cycle analysis framework was employed to evaluate well-to-gate greenhouse gas (GHG) emissions associated with by-product hydrogen from chlor-alkali processes in comparison with hydrogen from the conventional centralized natural gas steam methane reforming (central SMR) pathway. U.S.-specific, plant-by-plant, and up-to-date chlor-alkali production characteristics were incorporated into the analysis. In addition to the venting and combustion scenarios, to deal with the multi-functionality of the chlor-alkali processes that simultaneously produce chlorine, sodium hydroxide, and hydrogen, two different co-product allocation strategies were adopted mass allocation and market value allocation. It was estimated that by-product hydrogen production from chlor-alkali processes creates 1.3-9.8 kg CO 2 e/kg H 2 of life-cycle GHG emissions on average, which is 20-90% less than the conventional central SMR pathway. The results vary with co-product treatment scenarios, regional electric grid characteristics, on-site power generation, product prices, and hydrogen yield. Despite the variations in the results, it was concluded that the life-cycle GHG emission reduction benefits of using by-product hydrogen from chlor-alkali processes are robust. In conclusion, with a diverse set of scenario analyses, the study developed a comprehensive and detailed life-cycle GHG emissions inventory of the chlor-alkali by-product hydrogen pathway and quantified sensitivity indices in the context of different assumptions and input parameter values.

08 HYDROGEN↗
NASA NTRS1994

Electron injection and acceleration at nonlinear shocks: Results of numerical simulations

We present results of numerical simulations of electron injection and acceleration at nonlinear high Mach number shocks. The electrons are assumed to be heated at the thermal subshock to an energy E(sub inj), which is treated as a free parameter, above which they are injected by self-generated whistlers to momentum m(sub p) x V(sub A). This injection mechanism requires Mach numbers greater than (43/(beta(sub -)))(((k T(sub e))/(E(sub inj)))(exp 1/2)), where T(sub e) and beta (sub -) are the upstream electron temperature and plasma beta parameter. Above m(sub p) x V(sub A) electrons are trapped in the shock by Alfven waves. In the proton precursor region the Alfven waves are assumed to be generated by protons accelerated at the shock, and have nonlinear intensities. Below GeV, however, electrons of a given rigidity propagate faster than protons with a similar rigidity and therefore diffuse to regions ahead of the proton precursor. In those regions the Alfven waves are generated by the electrons themselves. The diffusion coefficient appears to increase with decreasing acceleration efficiency. As a result, the number of electrons accelerated to energies GeV and above and, hence, the electron to proton ratio, depend only weakly on the extent of electron heating at the subshock. The negative feedback also renders the electron spectra insensitive to shock compression ratio and smoothing length scale. The estimated e/p ratio at GeV is between approximately 1%-10%.

Levinson, Amir↗
NASA NTRS2015

Assessing Air-Sea Interaction in the Evolving NASA GEOS Model

In order to understand how the climate responds to variations in forcing, one necessary component is to understand the full distribution of variability of exchanges of heat and moisture between the atmosphere and ocean. Surface heat and moisture fluxes are critical to the generation and decay of many coupled air-sea phenomena. These mechanisms operate across a number of scales and contain contributions from interactions between the anomalous (i.e. non-mean), often extreme-valued, flux components. Satellite-derived estimates of the surface turbulent and radiative heat fluxes provide an opportunity to assess results from modeling systems. Evaluation of only time mean and variability statistics, however only provides limited traceability to processes controlling what are often regime-dependent errors. This work will present an approach to evaluate the representation of the turbulent fluxes at the air-sea interface in the current and evolving Goddard Earth Observing System (GEOS) model. A temperature and moisture vertical profile-based clustering technique is used to identify robust weather regimes, and subsequently intercompare the turbulent fluxes and near-surface parameters within these regimes in both satellite estimates and GEOS-driven data sets. Both model reanalysis (MERRA) and seasonal-to-interannual coupled GEOS model simulations will be evaluated. Particular emphasis is placed on understanding the distribution of the fluxes including extremes, and the representation of near-surface forcing variables directly related to their estimation. Results from these analyses will help identify the existence and source of regime-dependent biases in the GEOS model ocean surface turbulent fluxes. The use of the temperature and moisture profiles for weather-state clustering will be highlighted for its potential broad application to 3-D output typical of model simulations.

Clayson, Carol Anne↗
NASA NTRS2019

Improving the AVHRR Long Term Data Record BRDF Correction

The Long Term Data Record (LTDR) project has the goal of developing a quality and consistent surface reflectance product from coarse resolution optical sensors. This paper focuses on the Advanced Very High Resolution Radiometer (AVHRR) part of the record, using the Moderate Resolution Imaging Spectrometer (MODIS) instrument as a reference. When a surface reflectance time series is acquired from satellites with variable observation geometry, the directional variation generates an apparent noise which can be corrected by modeling the bidirectional reflectance distribution function (BRDF). The VJB (Vermote, Justice and Bréon, 2009) method estimates a target’s BRDF shape using 5 years of observation and corrects for directional effects maintaining the high temporal resolution of the measurement using the instantaneous Normalized Difference Vegetation Index (NDVI). The method was originally established on MODIS data but its viability and optimization for AVHRR data have not been fully explored. In this study we analyze different approaches to find the most robust way of applying the VJB correction to AVHRR data, considering that high noise in the red band (B1) caused by atmospheric effect makes the VJB method unstable. Firstly, our results show that for coarse spatial resolution, where the vegetation dynamics of the target don’t change significantly, deriving BRDF parameters from 15+ years of observations reduces the average noise by up to 7% in the Near Infrared (NIR) band and 6% in the NDVI, in comparison to using 3-year windows. Secondly, we find that the VJB method can be modified for AVHRR data to improve the robustness of the correction parameters and decrease the noise by an extra 8% and 9% in the red and NIR bands with respect to using the classical VJB inversion. We do this by using the Stable method, which obtains the volumetric BRDF parameter (V) based on its NDVI dependency, and then obtains the geometric BRDF parameter (R) through the inversion of just one parameter.

LTDR↗
DOE OSTI2024

Uncertainty Propagation from Experiment Measurements to Modeling Approaches: A Case for SMR Steam Entrainment Testing

To license new and advanced reactor designs, regulators must be convinced that their unique safety cases—relative to existing large scale reactors—have been adequately addressed by the designed reactor protection systems. In water cooled small modular reactors (SMRs), droplet entrainment in steam flow has significant implications on the progression of accident scenarios due to its compact design features, which requires representative test data applicable to SMR designs. Computer code, modeling and simulation (M&S) tools and models require adequate verification, assessment, and qualification. This includes M&S results validation against scaled empirical data within allowable uncertainty bands to gain regulatory approvals during the various stages of reactor system design, demonstration, and commercialization. However, measurement uncertainty within the empirical datasets and test data applicability ranges requires careful consideration of M&S inputs (i.e., boundary conditions, and initial conditions), and verification and validation efforts. This study focuses on uncertainty quantification in designing scaled test facilities for SMR applications with appropriate measurements and a standard data-reduction method to estimate thermal hydraulics characteristics parameters that incorporate physics phenomena of interest. In addition, this study supports the evaluation model development and assessment process using M&S that interfaces with advanced computing tools and digital twin capabilities. This will allow synchronization between experiment and modeling approaches for droplet entrainment testing and analysis, improving diagnostics, prognostics, and decision-making to accelerate regulatory approval.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Assessing the nature of large language models: A caution against anthropocentrism.

Generative AI models garnered a large amount of public attention and speculation with the release of OpenAI’s chatbot, ChatGPT in November of 2022. At least two opinion camps exist – one that is excited about the possibilities these models offer for fundamental changes to human tasks, and another that is highly concerned about the power these models seem to have – especially since the release of GPT-4, which was trained on multimodal data and has ~1.7 trillion (T) parameters. We evaluated some concerns regarding these models’ power by assessing GPT-3.5 using standard, normed, and validated cognitive and personality measures. These measures come from the tradition of psychometrics in experimental psychology and have a long history of providing valuable insights and predictive distinctions in humans. For this seedling project, we developed a battery of tests that allowed us to estimate the boundaries of some of these models’ capabilities, how stable those capabilities are over a short period of time, and how they compare to humans.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Assessing the nature of large language models: A caution against anthropocentrism

Generative AI models garnered a large amount of public attention and speculation with the release of OpenAI’s chatbot, ChatGPT in November of 2022. At least two opinion camps exist – one that is excited about the possibilities these models offer for fundamental changes to human tasks, and another that is highly concerned about the power these models seem to have – especially since the release of GPT-4, which was trained on multimodal data and has ~1.7 trillion (T) parameters. We evaluated some concerns regarding these models’ power by assessing GPT 3.5 using standard, normed, and validated cognitive and personality measures. These measures come from the tradition of psychometrics in experimental psychology and have a long history of providing valuable insights and predictive distinctions in humans. For this seedling project, we developed a battery of tests that allowed us to estimate the boundaries of some of these models’ capabilities, how stable those capabilities are over a short period of time, and how they compare to humans.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

Parametric Study of Three-Stringer-Panel Compression-After-Impact Strength

Damage tolerance requirements for integrally-stiffened composite wing skins are typically met using design allowables generated by testing impact-damaged subcomponents, such as three-stringer stiffened panels. To improve these structures, it is necessary to evaluate the critical design parameters associated with three-stringer stiffened-panel compressive behavior. During recent research and development programs, four structural parameters were identified as sources for strength variation: (a) material system, (b) stringer configuration, (c) skin layup, and (d) form of axial reinforcement (tape versus pultruded carbon rods). Relative effects of these parameters on damage resistance and damage tolerance were evaluated numerically and experimentally. Material system and geometric configuration had the largest influence on damage resistance; location and extent of the damage zone influenced the sublaminate buckling behavior, failure initiation site, and compressive ultimate strength. A practical global-local modeling technique captured observed experimental behavior and has the potential to identify critical damage sites and estimate failure loads prior to testing. More careful consideration should be given to accurate simulation of boundary conditions in numerical and experimental studies.

Rousseau, Carl Q.↗
NASA NTRS2019

Coordinated Turn Trajectory Generation and Tracking Control for Multi-rotors Operating in Urban Environment

The paper presents an efficient trajectory generation and tracking approach for multi-rotor air vehicles operating in urban environment, which takes into account uncertainties in the urban wind field and in the vehicle's parameters. Generated trajectories are sufficiently smooth, based on the differential flatness of the vehicle's dynamics and optimal in the sense of minimum agility and time. They pass through given set of way points, guarantee flight without a side-slip, and satisfy vehicle's dynamics and actuator constraints. In addition, an algorithm is presented to compute the required power to traverse the generated trajectory. Presented algorithms are implementable in real time using on-board computers. They do not take into account the vehicle's existing flight controller, hence there is no guarantee that the controller will be able to provide acceptable tracking of the generated trajectory, especially in the presence of atmospheric disturbances. To this end, we propose an adaptive augmentation algorithm to improve vehicle's performance by taking into account the effects of disturbances and on-line estimates of vehicle's existing flight controller's gains. The algorithms have been verified by simulations using DJI S1000 octocopter's model.

Stepanyan, Vahram↗
NASA NTRS2019

Coordinated Turn Trajectory Generation and Tracking Control for Multi-Rotors Operating in Urban Environment

The paper presents an efficient trajectory generation and tracking approach for multi-rotor air vehicles operating in urban environment, which takes into account uncertainties in the urban wind field and in the vehicle's parameters. Generated trajectories are sufficiently smooth, based on the differential flatness of the vehicle's dynamics and optimal in the sense of minimum agility and time. They pass through given set of way points, guarantee flight without a side-slip, and satisfy vehicle's dynamics and actuators constraints. In addition, an algorithm is presented to compute the required power to traverse the generated trajectory. Presented algorithms are implementable in real time using on-board computers. They do not take into account the vehicle's existing flight controller, hence there is no guarantee that the controller will be able to provide acceptable tracking of the generated trajectory, especially in the presence of atmospheric disturbances. To this end, we propose an adaptive augmentation algorithm to improve vehicle's performance by taking into account the effects of disturbances and on-line estimates of vehicle's existing flight controller's gains. The algorithms have been verified by simulations using DJI S1000 octocopter's model.

Stepanyan, Vahram↗
DOE OSTI2024

Prognostic model and failure mechanisms of steam generators in Sodium-Cooled fast reactors

This paper presents a prognostic model for sodium-cooled fast reactor (SFR) steam generators (SGs). Here, the purpose of the model is to estimate the remaining useful life of SFR SGs and thus to support the decision-making of autonomous control. SFR SGs are of great interest for plant integrity due to their harsh operation environment. They operate at higher temperatures and higher coolant-to-steam pressure differences than those of current light water reactors (LWR). The severity of the SFR SG failure consequences, which include water-sodium contact, is another reason. Understanding its failure mechanisms is important for the development of its prognostic model. Based on our literature review and physics-based analysis, we concluded that creep would be a dominant degradation mode of SFR SGs due to SFR’s high-temperature and high-pressure environment. Thus, creep is the focus of the prognostic model. Various other failure modes were also investigated in this study. The mechanical fatigue due to flow-induced vibration is usually observed in early developmental phases and would not be an important issue during normal operation. The thermal fatigue due to thermal stripping is occasionally observed in other components in SFRs but does not affect SG integrity. Pure water stress corrosive crack, fretting, and so on are commonly observed in LWR SGs but are significantly less important in SFR SGs because of the high temperatures, high pressure differences, and chemical properties of liquid sodium. Based on these investigations, a prognostic model focusing on creep failures was developed. It estimates the failure probability profile by sampling the Larson-Miller parameter (LMP) and temperature and associated uncertainties through Monte Carlo methods. Two case studies were presented. The first one demonstrated the model’s capability to calculate the failure probability for a new specimen within a given time. If the tube is working under temperatures of 500C ± 3 and pressures of 15.2 MPa, which leads to LMP of 20,100 ± 50, the failure probabilities within 50, 70, and 90 years are approximately 0.1 %, 3.2 %, and 17.5 %. The second demonstrated how adjusting the workload can help to protect the integrity of the component. For an old tube reaching 99 % of its lifespan, continuing to run at temperatures of 500C ± 3 and LMP of 20,100 ± 50 leads to a failure probability of about 29.0 % within a year. If the temperature is reduced by 5C, the failure probability can be reduced to 2.5 %, and, if the pressure is also reduced such that the LMP is increased by 100, the failure probability can further be reduced to 0.12 %.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Implications of Grain-Scale Mineralogical Heterogeneity for Radionuclide Transport in Fractured Media

The geological disposal of nuclear waste is based on the multi-barrier concept, comprising various engineered and natural barriers, to confine the radioactive waste and isolate it from the biosphere. Some of the planned repositories for high-level nuclear waste will be hosted in fractured crystalline rock formations. The potential of these formations to act as natural transport barriers is related to two coupled processes: diffusion into the rock matrix and sorption onto the mineral surfaces available in the rock matrix. Different in situ and laboratory experiments have pointed out the ubiquitous heterogeneous nature of the rock matrix: mineral surfaces and pore space are distributed in complex microstructures and their distribution is far from being homogeneous (as typically assumed by Darcy-scale coarse reactive transport models). We use a synthetically generated fracture–matrix system to assess the implications of grain-scale physical and mineralogical heterogeneity on cesium transport and retention. The resulting grain-scale reactive transport model is solved using high-performance computing technologies, and the results are compared with those derived from two alternative models, denoted as upscaled models, where mineral abundance is averaged over the matrix volume. In the grain-scale model, the penetration of cesium into the matrix is faster and the penetration front is uneven and finger-shaped. The analysis of the cesium breakthrough curves computed at two different points in the fracture shows that the upscaled models provide later first-arrival time estimates compared to the grain-scale model. The breakthrough curves computed with the three models converge at late times. These results suggest that spatially averaged upscaled parameters of sorption site distribution can be used to predict the late-time behavior of breakthrough curves but could be inadequate to simulate the early behavior.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong↗