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846 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry

In numerical dosimetry, the recent advances in high performance computing led to a strong reduction of the required computational time to assess the specific absorption rate (SAR) characterizing the human exposure to electromagnetic waves. However, this procedure remains time-consuming and a single simulation can request several hours. As a consequence, the influence of uncertain input parameters on the SAR cannot be analyzed using crude Monte Carlo simulation. The solution presented here to perform such an analysis is surrogate modeling. This paper proposes a novel approach to build such a surrogate model from a design of experiments. Considering a sparse representation of the polynomial chaos expansions using least-angle regression as a selection algorithm to retain the most influential polynomials, this paper proposes to use the selected polynomials as regression functions for the universal Kriging model. The leave-one-out cross validation is used to select the optimal number of polynomials in the deterministic part of the Kriging model. The proposed approach, called LARS-Kriging-PC modeling, is applied to three benchmark examples and then to a full-scale metamodeling problem involving the exposure of a numerical fetus model to a femtocell device. The performances of the LARS-Kriging-PC are compared to an ordinary Kriging model and to a classical sparse polynomial chaos expansion. The LARS-Kriging-PC appears to have better performances than the two other approaches. A significant accuracy improvement is observed compared to the ordinary Kriging or to the sparse polynomial chaos depending on the studied case. This approach seems to be an optimal solution between the two other classical approaches. A global sensitivity analysis is finally performed on the LARS-Kriging-PC model of the fetus exposure problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Dynamic Event Tree advancements and control logic improvements

The RAVEN code has been under development at the Idaho National Laboratory since 2012. Its main goal is to create a multi-purpose platform for the deploying of all the capabilities needed for Probabilistic Risk Assessment, uncertainty quantification, data mining analysis and optimization studies. RAVEN is currently equipped with three different sampling categories: Forward samplers (Monte Carlo, Latin Hyper Cube, Stratified, Grid Sampler, Factorials, etc.), Adaptive Samplers (Limit Surface search, Adaptive Polynomial Chaos, etc.) and Dynamic Event Tree (DET) samplers (Deterministic and Adaptive Dynamic Event Trees). The main subject of this document is to report the activities that have been done in order to: start the migration of the RAVEN/RELAP-7 control logic system into MOOSE, and develop advanced dynamic sampling capabilities based on the Dynamic Event Tree approach. In order to provide to all MOOSE-based applications a control logic capability, in this Fiscal Year an initial migration activity has been initiated, moving the control logic system, designed for RELAP-7 by the RAVEN team, into the MOOSE framework. In this document, a brief explanation of what has been done is going to be reported. The second and most important subject of this report is about the development of a Dynamic Event Tree (DET) sampler named “Hybrid Dynamic Event Tree” (HDET) and its Adaptive variant “Adaptive Hybrid Dynamic Event Tree” (AHDET). As other authors have already reported, among the different types of uncertainties, it is possible to discern two principle types: aleatory and epistemic uncertainties. The classical Dynamic Event Tree is in charge of treating the first class (aleatory) uncertainties; the dependence of the probabilistic risk assessment and analysis on the epistemic uncertainties are treated by an initial Monte Carlo sampling (MCDET). From each Monte Carlo sample, a DET analysis is run (in total, N trees). The Monte Carlo employs a pre-sampling of the input space characterized by epistemic uncertainties. The consequent Dynamic Event Tree performs the exploration of the aleatory space. In the RAVEN code, a more general approach has been developed, not limiting the exploration of the epistemic space through a Monte Carlo method but using all the forward sampling strategies RAVEN currently employs. The user can combine a Latin Hyper Cube, Grid, Stratified and Monte Carlo sampling in order to explore the epistemic space, without any limitation. From this pre-sampling, the Dynamic Event Tree sampler starts its aleatory space exploration. As reported by the authors, the Dynamic Event Tree is a good fit to develop a goal-oriented sampling strategy. The DET is used to drive a Limit Surface search. The methodology that has been developed by the authors last year, performs a Limit Surface search in the aleatory space only. This report documents how this approach has been extended in order to consider the epistemic space interacting with the Hybrid Dynamic Event Tree methodology.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Effect of noncircularity of experimental beam on CMB parameter estimation

Measurement of Cosmic Microwave Background (CMB) anisotropies has been playing a lead role in precision cosmology by providing some of the tightest constrains on cosmological models and parameters. However, precision can only be meaningful when all major systematic effects are taken into account. Non-circular beams in CMB experiments can cause large systematic deviation in the angular power spectrum, not only by modifying the measurement at a given multipole, but also introducing coupling between different multipoles through a deterministic bias matrix. Here we add a mechanism for emulating the effect of a full bias matrix to the PLANCK likelihood code through the parameter estimation code SCoPE. We show that if the angular power spectrum was measured with a non-circular beam, the assumption of circular Gaussian beam or considering only the diagonal part of the bias matrix can lead to huge error in parameter estimation. We demonstrate that, at least for elliptical Gaussian beams, use of scalar beam window functions obtained via Monte Carlo simulations starting from a fiducial spectrum, as implemented in PLANCK analyses for example, leads to only few percent of sigma deviation of the best-fit parameters. However, we notice more significant differences in the posterior distributions for some of the parameters, which would in turn lead to incorrect errorbars. These differences can be reduced, so that the errorbars match within few percent, by adding an iterative reanalysis step, where the beam window function would be recomputed using the best-fit spectrum estimated in the first step.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

MONK10: Burnup credit capability - 14596

MONK{sup R} is a Monte Carlo code for nuclear criticality and reactor physics analyses. It has a proven track record of application to the whole of the nuclear fuel cycle and is well established in the UK criticality community. Furthermore it is increasingly being used for reactor physics analysis (as described at ICNC 2011), which makes it an ideal tool for burn-up credit (BUC) calculations. Throughout the paper, example calculations based on a PWR are presented to illustrate the capabilities of the MONK10 code. In order to account for the spatial dependence of material burn-up it has in the past been necessary to design models with multiple regions and materials specifically to allow material burn-up to vary spatially. This is very labour intensive and difficult to change at a later stage. A new code version, MONK10, was released last year which includes the facility to allow a burn-up (BU) mesh to be superimposed on an existing model in order to account for the spatial dependence of the burn-up. This facility is used to consider the effect of radial position of a fuel element in a PWR core on BUC. Additionally, a thermal hydraulics (TH) mesh can be used to specify region dependent temperature. This, coupled with the fact that MONK10 also incorporates an on-the-fly Doppler broadening methodology facilitates the modelling of spatially dependent temperatures for the different components. A TH mesh is used to superimpose a temperature profile on a PWR based model and the effect of this on BUC is considered. The burn-up modelling in MONK has been benchmarked against the ANSWERS WIMS deterministic reactor physics code. Once the burn-up calculation has been completed and the depleted fuel compositions determined the spent fuel compositions can be transferred into a model of a storage facility or transport flask in order to perform burn-up credit analysis. The initial model is usually described as the donor model and the latter model as the receiver model. This transfer is carried out using the COWL option which allows the specification of a material in the receiver model based on the material's composition in a given BU mesh cell from the donor model. This allows compositions and densities to be transferred and also allows user specified adjustments to be made. For example, this could include omitting the fission products in order to estimate their contribution to burn-up credit and provide an actinide-only analysis. The effect of excluding appropriate nuclides is presented. An example of how the ANSWERS SPRUCE code can be used to quantify uncertainty in a BUC calculation is also presented. (authors)

42 ENGINEERING↗
DOE OSTI2019

Development of Critical Experiments to Provide Validation Data for Multiphysics Coupling Methods (Final Report)

Computational simulation has become one of the most important tools in the modern toolbox for nuclear reactor design. Reactor simulations, like the reactors themselves, involve multiple physical processes including neutronics, fluid flow and heat transfer (thermal-hydraulics), thermo-mechanics, fuel behavior, chemistry, and balance of plant. Each process can affect the behavior of the others, and advanced computational tools have been developed that couple separate physics models together to simulate the feedback effects. The objective of this work is to generate experimental data to support the validation of multi-physics reactor codes. It specifically targets the SHARP toolset from the NEAMS Reactor Product Line, but it is intended to be useful in any set of coded that couples thermal-hydraulics with neutronics simulations. The project takes advantage of the inherent flexibility of the RPI Reactor Critical Facility (RCF), a low power open-pool research reactor. The standard configuration of the RCF is used to explore the effects of moderator temperature on neutronic behavior and reactivity. Because the low power of the reactor generates no appreciable temperature change in the moderator, the moderator temperature is artificially changed with two 18 kW electric immersion heaters. The temperature feedback effects can be observed by recording the change in the reactor power as the reactor goes from a supercritical state, to critical, to a subcritical state. To expand the temperature range and temperature rate of change that can be investigated, an experimental apparatus consisting of a heated water loop was designed and installed in the RCF. In this setup, water from a heated reservoir tank is pumped through a pipe placed through the center of the reactor core. The water in the reservoir can be heated to around 70 °C and pumped through the system. The pump has a variable flow rate and electronic control, so a number of scenarios can be developed. A slug of water can be pushed through the system to generate a reasonably fast change in reactivity. The pump speed can be increased or decreased over the course of a measurement, or even oscillated at different periods, to observe the response of the reactor. To complement the experimental data generated by the RCF, a set of computational models have been developed. They are intended to illustrate the usefulness of the experimental data generated in validating coupled multi-physics simulations. A model previously constructed in MCNP has been used in conjunction with safety analysis at the RCF for many years and was modified to support the design of the heated water loop experiment. This model was translated into Serpent 2, a similar Monte Carlo code, which provided the added advantage of being able to produce collapsed cross-section data files for use in the deterministic neutron transport codes that are part of the SHARP toolset. A complete reconstruction of the RCF model, both with and without the heated fluid loop experiment, were necessary for use with the SHARP codes, PROTEUS (neutronics) and Nek5000 (thermal hydraulics), as these require an unstructured mesh format to operate. The computational requirements for fully coupled three dimensional simulations are significant, and challenges to full implementation and comparison with RCF experiments remain. A wide variety of experiments have been conducted for eventual benchmarking and validation of multi-physics reactor codes. A complete database of detailed time- and temperature-dependent measurements have been generated and stored. Several examples of the experimental results are presented here, with refinement and analysis of experiments ongoing. While these experiments still only address a finite range of operating conditions, in particular being limited to water in the sub-boiling regime, they represent a unique (to date) look at the feedback between temperature and neutronic behavior suited for validation of the coupling routines in multi-physics codes. It is hoped that these will be the foundation of future benchmarks that will provide confidence in the tools that will be used to develop the next generation of nuclear reactor systems.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2014

Dynamic density functional theory with hydrodynamic interactions and fluctuations

We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, “Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps,” Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, “A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law,” J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Uncertainty quantification of a physics-informed model based on sparse identification of a Thermal Energy Distribution System

Integrated energy systems (IES)s are crucial for enhancing the economy and efficiency of power generation sources (e.g., nuclear energy) necessary to unleash American energy dominance. These systems can be integrated with thermal energy storage (TES) and intermittent renewable energies to optimize overall energy use, peak-load regulation, and demand-side responses. However, the stabilization of energy generation, transport, and utilization introduces operational complexities that exceed the challenges of managing each sub-component individually. Currently, though IESs rely on human operators for efficiency and stability, reducing human error risk and enhancing performance through automation is highly desirable. Recent advances at Idaho National Laboratory have demonstrated successful control of the Thermal Energy Distributed System (TEDS). However, the automatic control system depends on a deterministic Sparse Identification of Nonlinear Dynamics with Control (SINDyC) model, which are trained based on simulation data from physics-based simulations. Because of uncertainties in physics-based simulation, SINDyC model results in large discrepancies against experimental data and cannot be reliably used in automatic control. In this paper, we present an innovative approach to address these discrepancies by quantifying uncertainties and developing a more robust model. We first generated trajectories by using first-principles physics codes to encapsulate the experiment. Next, we trained thousands of models by randomly sampling these trajectories. We then collapsed all those models into one probabilistic SINDyC by fitting a multivariate Gaussian distribution onto the resulting coefficient’s distribution. Despite its simplicity, our approach successfully produced 95% confidence intervals that captured the experimental trajectories. It even did so with a higher probability and better U-pooling score across six of the seven relevant quantities of interest (QoIs), as compared to other classical approaches. In conclusion, ongoing research is focusing on generating new experimental trajectories to validate this approach, and on employing Bayesian calibration to refine parametric uncertainties and guide future model development efforts.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Distributions of the Mean for Lognormally Distributed Data - 19427

In environmental sciences, a distribution of the mean is often needed for right-skewed data. For example, risk assessments are often based on distributions of the mean to obtain upper confidence limits (UCLs) for analyte concentrations, and, in probabilistic performance assessment (PPA) models, parameters are given distributions rather than deterministic values, and they are usually given distributions of their mean rather than the population distributions to account for the large spatial and temporal domains to which they are applied. How this distribution of the mean is developed depends on the characteristics of the parameter's full distribution and how the parameter relates to its use. In this presentation, I will discuss the implications of a right skew in distribution development. Parameters may vary over orders of magnitude and/or may be right-skewed. The material property of saturated hydraulic conductivity, Ks, is a prime example of such a parameter. Right-skewed parameters are often assumed to follow lognormal distributions. If X follows a lognormal distribution, then log(X) follows a normal distribution. For some right-skewed parameters, practitioners go back and forth between the two forms of the data depending on their needs. For example, it may be preferred to use the untransformed version of X in a model or equation, but it is easier to visualize the parameter values on a logarithmic scale. However, distribution development for the average value of the parameter will differ depending on whether X or log(X) is modeled. This difference is due to Jensen's Inequality, a theorem which states that the expected value of a concave function of a variable is less than or equal to the same function of the expected value of the variable; a logarithm is a concave function. In other words, the mean of log(X) is always less than or equal to the log of the mean of X and therefore the mean estimated from a distribution based on log(X) is less than or equal to the mean estimated from a distribution based on X. If a parameter is naturally considered on a log scale by subject matter experts, then distributions developed for the mean of log(X) may be more consistent with the use of the parameters in the literature than distributions developed for X. The statistical decisions of distribution development will be discussed within the context of right-skewed, lognormal data. These issues include method-of-moments versus maximum likelihood estimation of the distribution parameters and the use of bootstrapping to aid in the visualization of a distribution of the mean. The details surrounding Jensen's Inequality will be explained and visualized within the context of distribution development of a right-skewed parameter such as saturated hydraulic conductivity. (authors)

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Examples of Use of SINBAD Database for Nuclear Data and Code Validation

Benchmark experiments can serve several purposes and the availability of suitable experimental data is fundamental to ensure that modelling tools meet the requirements of nuclear industry and licensing needs. Essentially, they are used for: - validation of nuclear cross-section data, - validation of nuclear codes and models used, - qualification and training of users through benchmarking and code comparison exercises. The Shielding Integral Benchmark Archive and Database (SINBAD) project was started in the early 1990's at the OECD Nuclear Energy Agency Data Bank (NEA DB) and the Radiation Safety Information Computational Center (RSICC) as a collection of quality experiments for validating and benchmarking computer codes and data for radiation transport and shielding applications. Currently, the SINBAD database comprises over 100 benchmark compilations and evaluations of relevance to: - reactor shielding, pressure vessel dosimetry (48); - fusion blanket neutronics (31); - accelerator shielding (23). In order to facilitate their use, the data are organized in the standardized format structure. The index and the master document (called abstract) use the Hyper Text Markup Language (HTML) format with links to text files, figures, Portable Document Format (pdf) documents and computer code inputs. The format allows easy access and forward/backward navigation among the data and has proved to be suitable, general enough and above all easy (and low-cost) to maintain. In addition to the characterization of the radiation source, description of the shielding set-up, the instrumentation and the relevant detector measurements, most sets in SINBAD contain also the deterministic or Monte Carlo radiation transport computer model used for the interpretation of the experiment and, where available, results from uncertainty analysis. The set of primary documents used for the benchmark compilation and evaluation are provided in computer readable form. The database is intended for different types of users, including nuclear data evaluators, computer code developers, experiment designers and university students. SINBAD is available from the NEA Data Bank and RSICC (see https://www.oecdnea.org/science/wprs/shielding/sinbad/). Up to now several hundreds of SINBAD packages were distributed from the NEA DB and RSICC. Since 2011 the maintenance and further development of the database is coordinated in the scope of the OECD NEA Nuclear Science Committee (NSC) Working Party on Scientific Issues of Reactor Systems (WPRS) Expert Group on Radiation Transport and Shielding (EGRTS). A key objective of the group is to identify, evaluate and preserve experimental data on shielding benchmarks. The Expert Group maintains close links with the International Reactor Physics Experiment Evaluation (IRPhE) and International Criticality Safety Benchmark Evaluation (ICSBEP) projects, as well as in co-ordination with the JEFF and EFF NEA Data Bank projects and with the SATIF community of accelerator shielding specialists. In the last years, much effort was devoted to the quality review of the available benchmark information.

42 ENGINEERING↗
DOE OSTI2019

The Photometric LSST Astronomical Time-series Classification Challenge PLAsTiCC: Selection of a Performance Metric for Classification Probabilities Balancing Diverse Science Goals

Classification of transient and variable light curves is an essential step in using astronomical observations to develop an understanding of the underlying physical processes from which they arise. However, upcoming deep photometric surveys, including the Large Synoptic Survey Telescope (LSST), will produce a deluge of low signal-to-noise data for which traditional type estimation procedures are inappropriate. Probabilistic classification is more appropriate for such data but is incompatible with the traditional metrics used on deterministic classifications. Furthermore, large survey collaborations like LSST intend to use the resulting classification probabilities for diverse science objectives, indicating a need for a metric that balances a variety of goals. We describe the process used to develop an optimal performance metric for an open classification challenge that seeks to identify probabilistic classifiers that can serve many scientific interests. The Photometric LSST Astronomical Time-series Classification Challenge (PLASTICC) aims to identify promising techniques for obtaining classification probabilities of transient and variable objects by engaging a broader community beyond astronomy. Using mock classification probability submissions emulating realistically complex archetypes of those anticipated of PLASTICC, we compare the sensitivity of two metrics of classification probabilities under various weighting schemes, finding that both yield results that are qualitatively consistent with intuitive notions of classification performance. We thus choose as a metric for PLASTICC a weighted modification of the cross-entropy because it can be meaningfully interpreted in terms of information content. Finally, we propose extensions of our methodology to ever more complex challenge goals and suggest some guiding principles for approaching the choice of a metric of probabilistic data products.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

The FREYA project at VENUS-F - the next step towards MYRRHA

The VENUS-F reactor is a fast, zero-power research reactor. Since 2009 it has used 30% wt. metallic uranium as fuel and solid lead as reflector and coolant simulator. It can also be coupled to a particle accelerator with a neutron producing target and make up a subcritical Accelerator Driven System (ADS). Within the currently ongoing FREYA project, the main tasks being investigated are the validation of online reactivity monitoring of an ADS, the validation of nuclear data and neutronic codes, and the experimental characterization of fast critical and subcritical cores representative for MYRRHA. MYRRHA will be an ADS demonstrator with the option to be operated in critical mode too. So far the only critical core at VENUS-F was assembled using 97 fuel assemblies, each of them consisting of 9 U and 16 Pb rodlets. The core was thoroughly characterized: flux traverses, spectral indices, control rod worth, delayed neutron parameters were measured and compared with Monte Carlo and deterministic calculations. A sensitivity study was also performed focusing on the influence of material impurities, positioning uncertainties, structures and detectors around the core. It was a simple core without any perturbations in the active zone. In the next critical cores that are planned to be investigated in 2015 and 2016, additional elements will be introduced in order to become more representative for MYRRHA. As MYRRHA will use MOX fuel, oxygen will be added into the following core. This will be done by introducing Al{sub 2}O{sub 3} into the fuel assemblies. New fuel assemblies have been already made and are ready to be loaded. Each consists of 13 U, 8 Pb, and 4 Al{sub 2}O{sub 3} rodlets. The new critical core will consist of approximately 40 such fuel assemblies and will be loaded in January 2015. The first results of the characterization measurements will be presented. Additionally, it is planned to investigate coolant void effects. As MYRRHA will be a rather complex system using a number of in-pile sections and heterogeneous elements inside and around the active zone, the next cores will be step by step modified by loading new materials and perturbations with the aim to assemble a MYRRHA mock-up. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Reassessment of uncertainties for the PU-MET-INTER-002 benchmark - 14432

Uncertainty for the PU-MET-INTER-002 benchmark of ZPR-6/10 was unusually large for a ZPR assembly and was dominated by the uncertainties in matrix tube pitch and composition uncertainties for plutonium, graphite and stainless steel plates. The original uncertainty analysis for PU-MET-INTER-002 was limited by computer resources, software and the nuclear data available in 2002, all of which have been improved since. An as-built Monte Carlo model of ZPR-6/10 was used to quantify components of the transformation from the detailed model to a simplified RZ benchmark in 2002. Compositional uncertainties were estimated based upon TWODANT calculations of the RZ benchmark model (20 group, S{sub 8} - P{sub 1}). MC{sup 2}-2 was used with END/B-V.2 data to generate homogenized cross section data for TWODANT. The MC{sup 2}-2 calculations did not account for lattice cell spatial heterogeneity which was driven by the manual process required to generate ∼80 modifications to the deterministic model and by the software limitations of MC{sup 2}-2. Improvements to DIF3D-VARIANT, development of the MC{sup 2}-3 and BuildZPRModel codes, and better computer resources make accurate 3D transport calculations of reactivity changes practical today. BuildZPRModel imports the as-built geometry and creates a 'drawer' homogenized DIF3D model where each radial DIF3D mesh is the exact size of a single ZPR matrix tube and drawer. A MC{sup 2}-3 input is constructed for each drawer to produce homogenized cross section data where the spatial cell heterogeneity is captured by solving a 1D MOC transport calculation on the ultrafine energy group level. Collapsing 3D drawers into 1D MC{sup 2}-3 drawer models follows conventional procedures and is done by BuildZPRModel. MCNP6 was used to re-compute relevant geometry components of the uncertainty using ENDF/B-VII.0 data with the as-built model. Changes in the geometry components compared with earlier results are insignificant. DIF3D calculations of the compositional uncertainties were performed using 33, 70, 116, 230, 425, and 703 group energy structures and selectively combined with P{sub 3}-P{sub 7} transport approximations and P{sub 1} and P{sub 3} scattering kernels. 3D diffusion theory calculations were also performed for comparison. Many composition uncertainty components were essentially unchanged with the updated methodology. However, the dominant experimental uncertainty for PU-MET-INTER-002 is the composition of stainless steel. The new calculations reduce the stainless steel uncertainty from ∼115 pcm to ∼70 pcm which significantly reduces the total uncertainty for PU-MET-INTER-002. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2019

Nanoindentation of Micrograins in Polycrystals under Multiaxial Stress: Control of Abrupt & Stochastic Plastic Events

Deforming objects in the world of the small has proven a much more complex task than just bending a common-sized object like a spoon. Over the last decade, it has become clear that the application of stress on micron-sized objects, such as micropillars, leads to abrupt and stochastic plastic strain jumps that do not satisfy Weibull statistics (as expected for uncorrelated defect yielding) but instead seem to follow highly wide, power-law distributions, pointing towards cooperative dislocation plasticity. Are power-law distributed plastic events the rule or the exception in crystals? If the rule, can we design protocols to control and suppress them in order to achieve deterministic and smooth microforming processes? We propose to combine experiments and theory to unravel the mysteries of abrupt microplastic deformation in a natural dislocation environment: micron-sized grains (\micrograins") of polycrystals. We propose a novel experimental design that utilizes nanoindentation and 4-point bending techniques on the substrate of polycrystalline thin films of two typical FCC metals (Al and Cu), and make concrete theoretical conjectures, based on intuition built from previous theoretical and experimental efforts in micropillar compression and nanoindentation. Based on a wide set of observations over the last decade, we put forward two distinct hypotheses that we propose to investigate in both theory and experiments: Our first conjecture is that crystal plasticity in the central region of micron-sized grains has micropillar-like stochastic features: power-law plastic strain jumps at stresses above the macroscale yield strength, displaying strong size and rate effects. We will demonstrate this similarity in spherical nanoindentation experiments in the central-region of multi-orientation grains of Al and Cu thin films. Al and Cu are selected for their disparity in stacking fault energy and consequently, their different propensity for cross-slip relaxation; however, our protocol may be applied to any crystalline material of technological interest. We will test our hypothesis by performing two-dimensional extended discrete dislocation plasticity (2.5D-DDP) simulations, inspired by comparable successful studies of micropillar plasticity, and extended to model nanoindentation with two slip systems and on a surface of a bicrystal with microhard grain-boundaries (GB), ie. not allowing dislocation absorption (116). Our model will include effective three dimensional dislocation mechanisms such as dislocation multiplication and double-cross-slip assisted glide. Second, we hypothesize that the application of uniform in-plane stress on our thin films below the yield point can smoothen the micrograin plastic response during nanoindentation. On a technological level, we propose that indentation-induced localization (sink-in) may be diminished by the application of concurrent in-plane stress that activates slow, viscoplastic relaxations near GBs. We aim to demonstrate our hypothesis through a 4-point bending apparatus that introduces a homogeneous in-plane stress state before indentation. We will perform simulations of a coarse-grained mesoscale theory of plasticity in a system with microhard GBs, benchmarked through 2.5D-DDP simulations, which will capture the effects of slow viscoplastic relaxations. Our nanoindentation abrupt event statistics studies, either in the micrograin interior or near GBs, will be correlated to direct observations of induced surface dislocation microstructures. For we will use TEM-based methods (PACOM/TKD) in combination with EBSD. Indents placed in the center of grains will be analyzed based on the orientation of the grain, while those near to GBs will be analyzed based on the orientation of each grain, the distance from the GB and the 5 degrees of freedom of the GB.

36 MATERIALS SCIENCE↗
DOE OSTI2023

The Influence of Soil Properties on Sea-Breeze Circulations in the Southeast U.S.

Sea-breeze circulations (SBCs) are common weather phenomena at and near coastal regions. They form because of a thermal gradient between the land surface at the coast and the sea surface. In a mid-day regime, a “thermal low” generated at the warm coast will lead to rising air motion, creating a wind shift coming from the sea near the surface displacing the coastal air. A “return flow” moving back towards the sea is generated by upper-level divergence because of the rising motion from the thermal low. SBCs propagate and serve as a method of urban pollutant dispersion in the Los Angeles region of California and are constrained to the coast due to the topography of surrounding mountains serving as a boundary for further inland propagation. Within the northeast U.S. SBCs are seen in the warm season but tend to remain coastally bound due to Coriolis distortion over long distances. Within the southeast U.S. (SEUS), the paradigmatic example of SBCs occurs over the Florida peninsula, where thunderstorms form on a nearly daily occurrence due to the convergence of SBCs from the east and west sides of the peninsula. However, there are further examples of sea-breezes in the SEUS that warrant study. Within the region bordering the SEUS and the Mid-Atlantic, just east of the southern Appalachian Mountains, warm-season SBCs form at the coast of Georgia and the Carolinas. Relatively flat topography ~150-200km inland allows for mostly unimpeded inland SBC propagation. Through visual analysis, Viner et al. catalogued several SBCs that propagated as far inland as the Central Savannah River Area surrounding Augusta, Georgia. Wermter et al. found that while the land-sea thermal gradient at the coast can influence coastal SBC genesis, the inland-coastal thermal gradient over the land is the primary influencer on the speed and depth of inland propagation of SBCs in this region. Additionally, soil moisture itself is a known correlative factor to sea-breeze formation, as it influences the soil temperature and the thermal gradient needed for SBC genesis and inland penetration. Physick determined that higher latent heat fluxes associated with wetter soil dampen the land-sea thermal gradient and suppress the formation of a SBC. Physick determined that higher latent heat fluxes associated with wetter soil dampen the land-sea thermal gradient and suppress the formation of a SBC. Conversely, drier soil enhances the thermal gradient and promotes SBC formation. However, while there is an inverse relationship between soil moisture and SBCs, higher soil moisture can actually promote more convective rainfall following a SBC if it does not significantly impact the thermal gradient. While the relationship between soil moisture and SBC formation has been conceptually explored and modeled numerically, there is a research gap in observed connections. The Soil Moisture Active Passive (SMAP) satellite mission has been operational since 2015 and has been used to create high-resolution re-analytical Level 4 (L4) datasets of soil moisture and soil temperature at different soil depths: the surface (0-5cm) and rootzone (0-1m). The surface soil temperature effectively acts as the “skin temperature” of the surface at these levels, and a spatial map of the land-sea as well as the coastal-inland thermal gradients can be represented. SMAP data are also assimilated in some atmospheric models such at the High Resolution Rapid Refresh (HRRR) mesoscale model. We propose leveraging the use of SMAP products to fill in spatial gaps left by weather and mesonet stations within the SEUS region, as well as assessing the effectiveness of utilizing SMAP products towards SBC forecasting in both deterministic and machine learning (ML) models.

58 GEOSCIENCES↗
DOE OSTI2017

Testing Nesting DXTRAN Spheres for Neutron Transport in Air

The deterministic transport sphere (DXTRAN sphere) is a technology that can be utilized in MCNP for improving sampling in the vicinity of a particular geometry, when the solid angle, between the source and particular geometry, is small. At a collision event, a DXTRAN particle is created and deterministically transported to the DXTRAN sphere, while the colliding particle (NONDXTRAN particle) continues transporting as if no DXTRAN event had occurred. Weight is balanced by killing the NONDXTRAN particle when traversing the DXTRAN sphere. If set up correctly, the DXTRAN particle placed on the DXTRAN sphere has a high probability of interacting with the geometry within the DXTRAN sphere. The Central Limit Theorem (CLT) states that the estimated mean approaches a normal distribution with known variance as the number of random samples grows sufficiently large. In reality the variance is seldom known and therefore must be estimated. In a Monte Carlo calculation, one must determine when the number of random samples is sufficiently large for the CLT to be satisfied. For the CLT to be satisfied, the first two moments (mean and variance) must exist. The second moment, the variance of a normal distribution is estimated. The slope test, which uses the largest 201 history scores of each tally fluctuation chart (TFC) bin fit to a Pareto function, is used to determine if the largest history scores decrease faster than 1/x{sup 3}. If the slope is less than 3, then enough histories have not yet been sampled such to meet the second moment existence requirement of the CLT. Usually, a slope of less than 3 indicates that the effects of high weight scores have not been satisfactorily sampled; such a consequence can also be manifested in examining trends in the 4. moment, the variance of the variance (VOV). For example, when examining the TFC, if the VOV is monotonically decreasing for a few sets of histories and then drastically increases for the next set of histories, chances are a rare high weight score, significantly greater than the average score, was encountered. As a result of the 1/R{sup 2} term, a point detector can achieve an extremely high weight, much greater than the average, as the distance from collision to point detector approaches zero. To remedy this difficulty, a 'radius of exclusion' is applied, where within the radius of exclusion 'the point detector estimate is assumed to be the average flux uniformly distributed'. A DXTRAN sphere can suffer from the same weight fluctuation as collisions in the vicinity of the DXTRAN sphere produce much larger weights than collisions happening far from the DXTRAN sphere. If the rare large weight put on the DXTRAN sphere then scores in a tally, there will be a significant increase in the VOV and the slope may drop below 3. To compliment that analysis, here we utilize an air composition and density that varies as a function of altitude, detailing the trials and tribulations of attempting to pass the 10 statistical checks for a variety of single and nested DXTRAN sphere approaches. The objective here is to illuminate important considerations for radiation transport problems with small solid angles in a scatter medium of few mean free paths (MFPs)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Modified Closures in Monte Carlo Algorithms for Diffusive Binary Stochastic Media Transport Problems

In a stochastic medium, the material properties at a given spatial location are known only statistically. The most common approach to solving particle transport problems involving binary stochastic media (BSM) is to use the atomic mix approximation in which the transport problem is solved using homogenized (volume-averaged) material properties. A common deterministic model developed for solving BSM particle transport problems is the Levermore-Pomraning (LP) model. Zimmerman and Adams proposed a Monte Carlo algorithm (Algorithm A) that solves the LP equations and another Monte Carlo algorithm (Algorithm B) that locally preserves the sampled material realization; we refer to these Monte Carlo algorithms as the LP and LPLRP (LP local realization preserving) algorithms, respectively. One-dimensional (1D) planar geometry benchmark studies have shown that the LPLRP algorithm is often significantly more accurate than the LP algorithm for problems with an incident angular flux as well as for problems with an interior source. The LPLRP algorithm implementation in these benchmark comparisons made explicit use of the one-dimensional nature of the problem. The LP model is derived by assuming an 'upwind' closure in the coupling term relating the two materials in a binary stochastic medium. Su and Pomraning developed a modified form of this closure by considering the small correlation length limit and requiring the modified closure to produce the correct exponential decay for a source-free half-line albedo problem in rod geometry. They concluded that the modified closure is generally not inferior to the LP closure and in some cases is significantly better. Brantley investigated the use of the Su-Pomraning (SP) closure in the Monte Carlo LP algorithm (LP-SP) for the suite of benchmark problems and concluded that 1) the LP-SP algorithm was somewhat more accurate overall than the LP algorithm and somewhat less accurate overall than the LPLRP algorithm for an incident angular flux benchmark suite, and 2) the LP-SP algorithm was generally the least accurate of the algorithms for an interior source benchmark suite. Larsen et al. performed an asymptotic analysis of the transport equation in 1D planar geometry for the situation in which the physical system is 1) a random binary stochastic medium with material macroscopic total cross sections and mean slab width values of O(1) or smaller and 2) optically thick with weak absorption and sources at each spatial point and therefore globally diffusive. The asymptotic analysis demonstrates that, under these assumptions, the transport equation limits to the conventional diffusion equation with atomically-mixed (volume-averaged) material properties. Larsen et al. also demonstrate that, under these same assumptions, the LP equations asymptotically limit to an atomically-mixed diffusion equation with a diffusion coefficient that is too large, leading to an unphysical flattening of the ensemble-averaged scalar flux distribution. Vasques and Yadav recently performed an asymptotic analysis of an adjusted Levermore-Pomraning closure in which the Markovian transition functions are rescaled such that the equations asymptotically limit to the correct atomically-mixed diffusion equation; we refer to this model as LP-VY. In this paper, we demonstrate that the adjusted LP closure proposed by Vasques and Yadav is a special case of the SP closure obtained by assuming that the absorption cross sections in the two materials are equal. We further demonstrate that the Su-Pomraning closure has the correct asymptotic limit for the diffusive physical system and is therefore an appropriate closure for these problems. We also describe how to incorporate these various closures into the Monte Carlo LP and LPLRP particle transport algorithms, and we present numerical results comparing the accuracy of the Monte Carlo LP, LP-VY, LP-SP, LPLRP, and LPLRP-SP algorithms for the set of diffusive benchmark problems. We demonstrated that the SP closure has the correct asymptotic limit for the diffusive physical system under investigation in this paper and that the VY closure is a special case of the SP closure obtained by assuming equal absorption in the two materials. Both of these closures are readily implemented in the Monte Carlo LP and LPLRP algorithms for particle transport in BSM. Through numerical comparisons to a diffusive benchmark suite, we confirmed that 1) the LP and LPLRP algorithms do not limit to the appropriate diffusion solution and 2) the LP-VY, LP-SP, and LPLRP-SP algorithms limit to the appropriate diffusion solution and are of comparable accuracy. The LPLRP algorithm has been shown to be generally more accurate than the LP algorithm for non-diffusive problems. However, the numerical results in this paper indicate that the LPLRP algorithm does not limit to the correct diffusion equation for the asymptotic limit under consideration. The work in this paper demonstrates that the SP algorithm does limit to the correct diffusion equation for the asymptotic limit considered. Future work will investigate the possibility of whether the LPLRP-SP algorithm is accurate for both diffusive and non-diffusive problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗