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At least 289 records · Page 16

Direct statistical simulation of the Lorenz96 system in model reduction approaches

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems. Published by the American Physical Society 2025

Li, Kuan↗

Generalized master equation for particle transport in binary random media with renewal statistics

Particle transport in binary stochastic mixtures is classically modeled assuming Markovian or exponential mixing statistics but in many applications material memory invalidates the Markov assumption. For non-Markovian mixing characterized by alternating renewal processes, a transport-theoretic framework is presented that provides an exact description of transport in nonscattering random binary media with general non-exponential statistics. Our approach is to Markovianize the problem by augmenting the {material type, particle flux} state space with the age or distance from the last interface. A Chapman-Kolmogorov equation is formulated for the joint probability density of the material type, particle flux, and age, and subsequently reduced to a generalized Master equation (GME) in differential form. This constitutes the primary result of this work. A state-updating Monte Carlo algorithm consistent with the GME is developed and benchmarked against analytical solutions for multiple chord-length laws. For purely absorbing renewal statistical media, the GME reproduces analytical benchmarks for the equilibrium age distribution, interior mean/variance of material-conditioned fluxes, and boundary transmittance. Simulations further demonstrate that a Markov (exponential) approximation of non-exponential statistics can introduce large errors in transmittance and interior flux profiles. Lastly, the reintroduction of memory due to scattering is briefly addressed through heuristic considerations.

Fluctuations & noise↗

Edwards statistical mechanics for jammed granular matter

In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium statistical mechanics, despite their inherent athermal features. Since then, the statistical mechanics approach for jammed matter—one of the very few generalizations of Gibbs-Boltzmann statistical mechanics to out-of-equilibrium matter—has garnered an extraordinary amount of attention by both theorists and experimentalists. Its importance stems from the fact that jammed states of matter are ubiquitous in nature appearing in a broad range of granular and soft materials such as colloids, emulsions, glasses, and biomatter. Indeed, despite being one of the simplest states of matter—primarily governed by the steric interactions between the constitutive particles—a theoretical understanding based on first principles has proved exceedingly challenging. Here a systematic approach to jammed matter based on the Edwards statistical mechanical ensemble is reviewed. The construction of microcanonical and canonical ensembles based on the volume function, which replaces the Hamiltonian in jammed systems, is discussed. The importance of approximation schemes at various levels is emphasized leading to quantitative predictions for ensemble averaged quantities such as packing fractions and contact force distributions. An overview of the phenomenology of jammed states and experiments, simulations, and theoretical models scrutinizing the strong assumptions underlying Edwards approach is given including recent results suggesting the validity of Edwards ergodic hypothesis for jammed states. A theoretical framework for packings whose constitutive particles range from spherical to nonspherical shapes such as dimers, polymers, ellipsoids, spherocylinders or tetrahedra, hard and soft, frictional, frictionless and adhesive, monodisperse, and polydisperse particles in any dimensions is discussed providing insight into a unifying phase diagram for all jammed matter. Furthermore, the connection between the Edwards ensemble of metastable jammed states and metastability in spin glasses is established. This highlights the fact that the packing problem can be understood as a constraint satisfaction problem for excluded volume and force and torque balance leading to a unifying framework between the Edwards ensemble of equiprobable jammed states and out-of-equilibrium spin glasses.

97 MATHEMATICS AND COMPUTING↗

Dark Energy Survey Year 3 Results: Cosmological constraints from second- and third-order shear statistics

Here, we present a cosmological analysis of the third-order aperture mass statistic using Dark Energy Survey Year 3 (DES Y3) data. We perform a complete tomographic measurement of the three-point correlation function of the Y3 weak lensing shape catalog with the four fiducial source redshift bins. Building upon our companion methodology paper, we apply a pipeline that combines the two-point function ξ ± with the mass aperture skewness statistic ⟨ M ap 3 ⟩ , which is an efficient compression of the full shear three-point function. We use a suite of simulated shear maps to obtain a joint covariance matrix. By jointly analyzing ξ ± and ⟨ M ap 3 ⟩ measured from DES Y3 data with a Λ CDM model, we find S 8 = 0.780 ± 0.015 and Ω m = 0.26 6 - 0.040 + 0.039 , yielding 111% of figure-of-merit improvement in the Ω m - S 8 plane relative to ξ ± alone, consistent with expectations from simulated likelihood analyses. With a w CDM model, we find S 8 = 0.74 9 - 0.026 + 0.027 and w 0 = - 1.39 ± 0.31 , which gives an improvement of 22% on the joint S 8 - w 0 constraint. Our results are consistent with w 0 = - 1 . Our new constraints are compared to CMB data from the Planck satellite, and we find that with the inclusion of ⟨ M ap 3 ⟩ the existing tension between the datasets is at the level of 2.3 σ . We show that the third-order statistic enables us to self-calibrate the mean photometric redshift uncertainty parameter of the highest redshift bin with little degradation in the figure of merit. Our results demonstrate the constraining power of higher-order lensing statistics and establish ⟨ M ap 3 ⟩ as a practical observable for joint analyses in current and future surveys.

Gomes, R. C. H. [University of Pennsylvania] (ORCI↗

A unified statistical framework for material decomposition using multienergy photon counting x-ray detectors

Purpose: Material decomposition using multienergy photon counting x-ray detectors (PCXD) has been an active research area over the past few years. Even with some success, the problem of optimal energy selection and three material decomposition including malignant tissue is still on going research topic, and more systematic studies are required. This paper aims to address this in a unified statistical framework in a mammographic environment.Methods: A unified statistical framework for energy level optimization and decomposition of three materials is proposed. In particular, an energy level optimization algorithm is derived using the theory of the minimum variance unbiased estimator, and an iterative algorithm is proposed for material composition as well as system parameter estimation under the unified statistical estimation framework. To verify the performance of the proposed algorithm, the authors performed simulation studies as well as real experiments using physical breast phantom and ex vivo breast specimen. Quantitative comparisons using various performance measures were conducted, and qualitative performance evaluations for ex vivo breast specimen were also performed by comparing the ground-truth malignant tissue areas identified by radiologists.Results: Both simulation and real experiments confirmed that the optimized energy bins by the proposed method allow better material decomposition quality. Moreover, for the specimen thickness estimation errors up to 2 mm, the proposed method provides good reconstruction results in both simulation and real ex vivo breast phantom experiments compared to existing methods.Conclusions: The proposed statistical framework of PCXD has been successfully applied for the energy optimization and decomposition of three material in a mammographic environment. Experimental results using the physical breast phantom and ex vivo specimen support the practicality of the proposed algorithm.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

SU-E-J-82: Intra-Fraction Proton Beam-Range Verification with PET Imaging: Feasibility Studies with Monte Carlo Simulations and Statistical Modeling

Purpose: To study the feasibility of intra-fraction proton beam-range verification with PET imaging. Methods: Two phantoms homogeneous cylindrical PMMA phantoms (290 mm axial length, 38 mm and 200 mm diameter respectively) were studied using PET imaging: a small phantom using a mouse-sized PET (61 mm diameter field of view (FOV)) and a larger phantom using a human brain-sized PET (300 mm FOV). Monte Carlo (MC) simulations (MCNPX and GATE) were used to simulate 179.2 MeV proton pencil beams irradiating the two phantoms and be imaged by the two PET systems. A total of 50 simulations were conducted to generate 50 positron activity distributions and correspondingly 50 measured activity-ranges. The accuracy and precision of these activity-ranges were calculated under different conditions (including count statistics and other factors, such as crystal cross-section). Separate from the MC simulations, an activity distribution measured from a simulated PET image was modeled as a noiseless positron activity distribution corrupted by Poisson counting noise. The results from these two approaches were compared to assess the impact of count statistics on the accuracy and precision of activity-range calculations. Results: MC Simulations show that the accuracy and precision of an activity-range are dominated by the number (N) of coincidence events of the reconstructed image. They are improved in a manner that is inversely proportional to 1/sqrt(N), which can be understood from the statistical modeling. MC simulations also indicate that the coincidence events acquired within the first 60 seconds with 10{sup 9} protons (small phantom) and 10{sup 10} protons (large phantom) are sufficient to achieve both sub-millimeter accuracy and precision. Conclusion: Under the current MC simulation conditions, the initial study indicates that the accuracy and precision of beam-range verification are dominated by count statistics, and intra-fraction PET image-based beam-range verification is feasible. This work was supported by a research award RP120326 from Cancer Prevention and Research Institute of Texas.

60 APPLIED LIFE SCIENCES↗

SU-E-J-261: Statistical Analysis and Chaotic Dynamics of Respiratory Signal of Patients in BodyFix

Purpose: To quantify respiratory signal of patients in BodyFix undergoing 4DCT scan with and without immobilization cover. Methods: 20 pairs of respiratory tracks recorded with RPM system during 4DCT scan were analyzed. Descriptive statistic was applied to selected parameters of exhale-inhale decomposition. Standardized signals were used with the delay method to build orbits in embedded space. Nonlinear behavior was tested with surrogate data. Sample entropy SE, Lempel-Ziv complexity LZC and the largest Lyapunov exponents LLE were compared. Results: Statistical tests show difference between scans for inspiration time and its variability, which is bigger for scans without cover. The same is for variability of the end of exhalation and inhalation. Other parameters fail to show the difference. For both scans respiratory signals show determinism and nonlinear stationarity. Statistical test on surrogate data reveals their nonlinearity. LLEs show signals chaotic nature and its correlation with breathing period and its embedding delay time. SE, LZC and LLE measure respiratory signal complexity. Nonlinear characteristics do not differ between scans. Conclusion: Contrary to expectation cover applied to patients in BodyFix appears to have limited effect on signal parameters. Analysis based on trajectories of delay vectors shows respiratory system nonlinear character and its sensitive dependence on initial conditions. Reproducibility of respiratory signal can be evaluated with measures of signal complexity and its predictability window. Longer respiratory period is conducive for signal reproducibility as shown by these gauges. Statistical independence of the exhale and inhale times is also supported by the magnitude of LLE. The nonlinear parameters seem more appropriate to gauge respiratory signal complexity since its deterministic chaotic nature. It contrasts with measures based on harmonic analysis that are blind for nonlinear features. Dynamics of breathing, so crucial for 4D-based clinical technologies, can be better controlled if nonlinear-based methodology, which reflects respiration characteristic, is applied. Funding provided by Varian Medical Systems via Investigator Initiated Research Project.

60 APPLIED LIFE SCIENCES↗

WE-G-18A-04: 3D Dictionary Learning Based Statistical Iterative Reconstruction for Low-Dose Cone Beam CT Imaging

Purpose: To develop a 3D dictionary learning based statistical reconstruction algorithm on graphic processing units (GPU), to improve the quality of low-dose cone beam CT (CBCT) imaging with high efficiency. Methods: A 3D dictionary containing 256 small volumes (atoms) of 3x3x3 voxels was trained from a high quality volume image. During reconstruction, we utilized a Cholesky decomposition based orthogonal matching pursuit algorithm to find a sparse representation on this dictionary basis of each patch in the reconstructed image, in order to regularize the image quality. To accelerate the time-consuming sparse coding in the 3D case, we implemented our algorithm in a parallel fashion by taking advantage of the tremendous computational power of GPU. Evaluations are performed based on a head-neck patient case. FDK reconstruction with full dataset of 364 projections is used as the reference. We compared the proposed 3D dictionary learning based method with a tight frame (TF) based one using a subset data of 121 projections. The image qualities under different resolutions in z-direction, with or without statistical weighting are also studied. Results: Compared to the TF-based CBCT reconstruction, our experiments indicated that 3D dictionary learning based CBCT reconstruction is able to recover finer structures, to remove more streaking artifacts, and is less susceptible to blocky artifacts. It is also observed that statistical reconstruction approach is sensitive to inconsistency between the forward and backward projection operations in parallel computing. Using high a spatial resolution along z direction helps improving the algorithm robustness. Conclusion: 3D dictionary learning based CBCT reconstruction algorithm is able to sense the structural information while suppressing noise, and hence to achieve high quality reconstruction. The GPU realization of the whole algorithm offers a significant efficiency enhancement, making this algorithm more feasible for potential clinical application. A high zresolution is preferred to stabilize statistical iterative reconstruction. This work was supported in part by NIH(1R01CA154747-01), NSFC((No. 61172163), Research Fund for the Doctoral Program of Higher Education of China (No. 20110201110011), China Scholarship Council.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Global Sensitivity Analysis for Statistical Model Parameters

Global sensitivity analysis (GSA) is typically used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical models. Such analyses may enable reduced or parsimonious modeling and greater predictive capability. Yet, difficulties such as parameter correlation, model stochasticity, multivariate model output, and unknown parameter distributions prohibit a direct application of GSA tools to statistical models. By leveraging a loss function associated with the statistical model, we introduce a novel framework to address these difficulties and enable efficient GSA for statistical model parameters. Theoretical and computational properties are considered and hihglighted on a synthetic example. The framework is applied to a Gaussian process model from the literature, which depends on 95 parameters. Noninfluential parameters are discovered through GSA, and a reduced model with equal or stronger predictive capability is constructed by using only 79 parameters.

97 MATHEMATICS AND COMPUTING↗

Convective Transition Statistics over Tropical Oceans for Climate Model Diagnostics: Observational Baseline

Convective transition statistics, which describe the relation between column-integrated water vapor (CWV) and precipitation, are compiled over tropical oceans using satellite and ARM site measurements to quantify the temperature and resolution dependence of the precipitation–CWV relation at fast time scales relevant to convection. At these time scales, and for precipitation especially, uncertainties associated with observational systems must be addressed by examining features with a variety of instrumentation and identifying robust behaviors versus instrument sensitivity at high rain rates. Here the sharp pickup in precipitation as CWV exceeds a certain critical threshold is found to be insensitive to spatial resolution, with convective onset occurring at higher CWV but at lower column relative humidity as bulk tropospheric temperature increases. Mean tropospheric temperature profiles conditioned on precipitation show vertically coherent structure across a wide range of temperature, reaffirming the use of a bulk temperature measure in defining the convective transition statistics. The joint probability distribution of CWV and precipitation develops a peak probability at low precipitation for CWV above critical, with rapidly decreasing probability of high precipitation below and near critical, and exhibits systematic changes under spatial averaging. The precipitation pickup with CWV is reasonably insensitive to time averaging up to several hours but is smoothed at daily time scales. This work demonstrates that CWV relative to critical serves as an effective predictor of precipitation with only minor geographic variations in the tropics, quantifies precipitation-related statistics subject to different spatial–temporal resolution, and provides a baseline for model comparison to apply these statistics as observational constraints on precipitation processes.

54 ENVIRONMENTAL SCIENCES↗

Convective Transition Statistics over Tropical Oceans for Climate Model Diagnostics: GCM Evaluation

To assess deep convective parameterizations in a variety of GCMs and examine the fast-time-scale convective transition, a set of statistics characterizing the pickup of precipitation as a function of column water vapor (CWV), PDFs and joint PDFs of CWV and precipitation, and the dependence of the moisture–precipitation relation on tropospheric temperature is evaluated using the hourly output of two versions of the GFDL Atmospheric Model, version 4 (AM4), NCAR CAM5 and superparameterized CAM (SPCAM). The 6-hourly output from the MJO Task Force (MJOTF)/GEWEX Atmospheric System Study (GASS) project is also analyzed. Contrasting statistics produced from individual models that primarily differ in representations of moist convection suggest that convective transition statistics can substantially distinguish differences in convective representation and its interaction with the large-scale flow, while models that differ only in spatial–temporal resolution, microphysics, or ocean–atmosphere coupling result in similar statistics. Most of the models simulate some version of the observed sharp increase in precipitation as CWV exceeds a critical value, as well as that convective onset occurs at higher CWV but at lower column RH as temperature increases. While some models quantitatively capture these observed features and associated probability distributions, considerable intermodel spread and departures from observations in various aspects of the precipitation–CWV relationship are noted. For instance, in many of the models, the transition from the low-CWV, nonprecipitating regime to the moist regime for CWV around and above critical is less abrupt than in observations. Additionally, some models overproduce drizzle at low CWV, and some require CWV higher than observed for strong precipitation. For many of the models, it is particularly challenging to simulate the probability distributions of CWV at high temperature.

54 ENVIRONMENTAL SCIENCES↗

Development and testing of improved statistical wind power forecasting methods.

Wind power forecasting (WPF) provides important inputs to power system operators and electricity market participants. It is therefore not surprising that WPF has attracted increasing interest within the electric power industry. In this report, we document our research on improving statistical WPF algorithms for point, uncertainty, and ramp forecasting. Below, we provide a brief introduction to the research presented in the following chapters. For a detailed overview of the state-of-the-art in wind power forecasting, we refer to [1]. Our related work on the application of WPF in operational decisions is documented in [2]. Point forecasts of wind power are highly dependent on the training criteria used in the statistical algorithms that are used to convert weather forecasts and observational data to a power forecast. In Chapter 2, we explore the application of information theoretic learning (ITL) as opposed to the classical minimum square error (MSE) criterion for point forecasting. In contrast to the MSE criterion, ITL criteria do not assume a Gaussian distribution of the forecasting errors. We investigate to what extent ITL criteria yield better results. In addition, we analyze time-adaptive training algorithms and how they enable WPF algorithms to cope with non-stationary data and, thus, to adapt to new situations without requiring additional offline training of the model. We test the new point forecasting algorithms on two wind farms located in the U.S. Midwest. Although there have been advancements in deterministic WPF, a single-valued forecast cannot provide information on the dispersion of observations around the predicted value. We argue that it is essential to generate, together with (or as an alternative to) point forecasts, a representation of the wind power uncertainty. Wind power uncertainty representation can take the form of probabilistic forecasts (e.g., probability density function, quantiles), risk indices (e.g., prediction risk index) or scenarios (with spatial and/or temporal dependence). Statistical approaches to uncertainty forecasting basically consist of estimating the uncertainty based on observed forecasting errors. Quantile regression (QR) is currently a commonly used approach in uncertainty forecasting. In Chapter 3, we propose new statistical approaches to the uncertainty estimation problem by employing kernel density forecast (KDF) methods. We use two estimators in both offline and time-adaptive modes, namely, the Nadaraya-Watson (NW) and Quantilecopula (QC) estimators. We conduct detailed tests of the new approaches using QR as a benchmark. One of the major issues in wind power generation are sudden and large changes of wind power output over a short period of time, namely ramping events. In Chapter 4, we perform a comparative study of existing definitions and methodologies for ramp forecasting. We also introduce a new probabilistic method for ramp event detection. The method starts with a stochastic algorithm that generates wind power scenarios, which are passed through a high-pass filter for ramp detection and estimation of the likelihood of ramp events to happen. The report is organized as follows: Chapter 2 presents the results of the application of ITL training criteria to deterministic WPF; Chapter 3 reports the study on probabilistic WPF, including new contributions to wind power uncertainty forecasting; Chapter 4 presents a new method to predict and visualize ramp events, comparing it with state-of-the-art methodologies; Chapter 5 briefly summarizes the main findings and contributions of this report.

17 WIND ENERGY↗

Statistical Mechanics Modeling of Mesoscale Deformation in Metals

The research under this project focused on a theoretical and computational modeling of dislocation dynamics of mesoscale deformation of metal single crystals. Specifically, the work aimed to implement a continuum statistical theory of dislocations to understand strain hardening and cell structure formation under monotonic loading. These aspects of crystal deformation are manifestations of the evolution of the underlying dislocation system under mechanical loading. The project had three research tasks: 1) Investigating the statistical characteristics of dislocation systems in deformed crystals. 2) Formulating kinetic equations of dislocations and coupling these kinetics equations and crystal mechanics. 3) Computational solution of coupled crystal mechanics and dislocation kinetics. Comparison of dislocation dynamics predictions with experimental results in the area of statistical properties of dislocations and their field was also a part of the proposed effort. In the first research task, the dislocation dynamics simulation method was used to investigate the spatial, orientation, velocity, and temporal statistics of dynamical dislocation systems, and on the use of the results from this investigation to complete the kinetic description of dislocations. The second task focused on completing the formulation of a kinetic theory of dislocations that respects the discrete nature of crystallographic slip and the physics of dislocation motion and dislocation interaction in the crystal. Part of this effort also targeted the theoretical basis for establishing the connection between discrete and continuum representation of dislocations and the analysis of discrete dislocation simulation results within the continuum framework. This part of the research enables the enrichment of the kinetic description with information representing the discrete dislocation systems behavior. The third task focused on the development of physics-inspired numerical methods of solution of the coupled dislocation kinetics and crystal mechanics framework. To a large extent, this task has also been successfully started. We have developed a custom finite-element approach with mesh points being a subset of the underlying crystal structure. When used to predict the evolution of the dislocation system, the planar motion of dislocations is naturally captured for all slip systems, thus minimizing numerical errors and providing simple ways to investigate cross slip and dislocation reactions. Preliminary results in this direction show that we are closer than ever in building a predictive framework for dislocation dynamics and mesoscale plasticity based on the first principles of dislocation dynamics. The rest of the report gives and overview of the research performed under this project and highlights the key results and open questions left for future investigations.

36 MATERIALS SCIENCE↗

In-Situ Statistical Analysis of Autotune Simulation Data using Graphical Processing Units

Developing accurate building energy simulation models to assist energy efficiency at speed and scale is one of the research goals of the Whole-Building and Community Integration group, which is a part of Building Technologies Research and Integration Center (BTRIC) at Oak Ridge National Laboratory (ORNL). The aim of the Autotune project is to speed up the automated calibration of building energy models to match measured utility or sensor data. The workflow of this project takes input parameters and runs EnergyPlus simulations on Oak Ridge Leadership Computing Facility’s (OLCF) computing resources such as Titan, the world’s second fastest supercomputer. Multiple simulations run in parallel on nodes having 16 processors each and a Graphics Processing Unit (GPU). Each node produces a 5.7 GB output file comprising 256 files from 64 simulations. Four types of output data covering monthly, daily, hourly, and 15- minute time steps for each annual simulation is produced. A total of 270TB+ of data has been produced. In this project, the simulation data is statistically analyzed in-situ using GPUs while annual simulations are being computed on the traditional processors. Titan, with its recent addition of 18,688 Compute Unified Device Architecture (CUDA) capable NVIDIA GPUs, has greatly extended its capability for massively parallel data processing. CUDA is used along with C/MPI to calculate statistical metrics such as sum, mean, variance, and standard deviation leveraging GPU acceleration. The workflow developed in this project produces statistical summaries of the data which reduces by multiple orders of magnitude the time and amount of data that needs to be stored. These statistical capabilities are anticipated to be useful for sensitivity analysis of EnergyPlus simulations

accelerators↗

Summary Statistics for LC_TA03_130719: Micro-CT Data Acquired at LLNL, Specimen 3 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, lithium carbonate (LC). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, LC_TA03_130719, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images 2 . The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗

Summary Statistics for TA_MP03_130620: Micro-CT Data Acquired at LLNL, Specimen 3 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_MP03_130620, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images 2 . The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗

Summary Statistics for TA_MH03_130828: Micro-CT Data Acquired at LLNL, Specimen 3 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_MH03_130828, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗

Summary Statistics for TA_MH01_130826: Micro-CT Data Acquired at LLNL, Specimen 1 of 3

Using x-ray micro computed tomography (MicroCT), we have characterized the linear attenuation coefficients (LAC), μ, of a sample of a dry powder material, tartaric acid (TA). The specimen was prepared at Lawrence Livermore National Laboratory (LLNL), loaded into a 60mL low density polyethylene (LDPE) bottle. After completed packing, the specimen was scanned following the protocol for MicroCT measurements under Test Plan 79. This particular specimen, TA_MH01_130826, recorded the bulk packing density (mass of sample divided by volume of sample) shown above. Two additional preparations were made and analyzed. We used the computer program IMGREC to reconstruct the CT images. The values of the key parameters used in the x-ray data capture and image reconstruction are given in this report. Additional experimental details may be found in the SOP and a separate document. To characterize the statistical distribution of LAC values in each CT image, we first isolated an ~80% region or segment of volume elements (“voxels”) lying completely within the sample, away from the walls of the container. We then calculated the mean value, standard deviation and entropy for (a) the high and low energy image segments and for (b) their digital gradient images. The statistics of the initial image of LAC values are called “first order statistics;” those of the gradient image, “second order statistics.” See Seetho for details of the analysis used to obtain the numbers reported in this document.

42 ENGINEERING↗