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DOE OSTI2019

High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion

A second order interface anchoring method has been developed and used with fast sweeping algorithm for reinitialization of a level set function. The algebraic anchoring formulation ensures that the location of the actual interface is preserved, leading to better mass conservation property. It also provides high order accurate algebraic constraint for solving the Eikonal equation on a finite difference grid. Geometric properties of the interface such as surface normal and curvature are subsequently computed from the reinitialized distance function. Various analytical functions for modeling distortion in level set field are considered and accuracy of reinitialization is evaluated using first and second order anchoring schemes. It is also shown that accurate computation of interface curvature requires a high order anchor in addition to a high order fast sweeping method. Mass conservation property of reinitialization is also analyzed by considering test problems from literature including the classic Rider–Kothe single vortex problem. The formulation is suitable for efficient parallelization for both distributed memory and on-node shared memory parallel systems. In conclusion, scalability and performance of the reinitialization scheme on multiple architectures are demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Signal-to-noise assessment for diffusion tensor imaging with single data set and validation using a difference image method with data from a multicenter study

Purpose: To describe a quantitative method for determination of SNR that extracts the local noise level using a single diffusion data set. Methods: Brain data sets came from a multicenter study (eight sites; three MR vendors). Data acquisition protocol required b = 0, 700 s/mm{sup 2}, fov = 256 × 256 mm{sup 2}, acquisition matrix size 128 × 128, reconstruction matrix size 256 × 256; 30 gradient encoding directions and voxel size 2 × 2 × 2 mm{sup 3}. Regions-of-interest (ROI) were placed manually on the b = 0 image volume on transverse slices, and signal was recorded as the mean value of the ROI. The noise level from the ROI was evaluated using Fourier Transform based Butterworth high-pass filtering. Patients were divided into two groups, one for filter parameter optimization (N = 17) and one for validation (N = 10). Six white matter areas (the genu and splenium of corpus callosum, right and left centrum semiovale, right and left anterior corona radiata) were analyzed. The Bland–Altman method was used to compare the resulting SNR with that from the difference image method. The filter parameters were optimized for each brain area, and a set of “global” parameters was also obtained, which represent an average of all regions. Results: The Bland–Altman analysis on the validation group using “global” filter parameters revealed that the 95% limits of agreement of percent bias between the SNR obtained with the new and the reference methods were −15.5% (median of the lower limit, range [−24.1%, −8.9%]) and 14.5% (median of the higher limits, range [12.7%, 18.0%]) for the 6 brain areas. Conclusions: An FT-based high-pass filtering method can be used for local area SNR assessment using only one DTI data set. This method could be used to evaluate SNR for patient studies in a multicenter setting.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Adaptive immersed isogeometric level-set topology optimization

Here, this paper presents for the first time an adaptive immersed approach for level-set topology optimization using higher-order truncated hierarchical B-spline discretizations for design and state variable fields. Boundaries and interfaces are represented implicitly by the iso-contour of one or multiple level-set functions. An immersed finite element method, the eXtended IsoGeometric Analysis, is used to predict the physical response. The proposed optimization framework affords different adaptively refined higher-order B-spline discretizations for individual design and state variable fields. The increased continuity of higher-order B-spline discretizations together with local refinement enables direct control over the accuracy of the representation of each field while simultaneously reducing computational cost compared to uniformly refined discretizations. A flexible mesh adaptation strategy enables local refinement based on geometric measures or physics-based error indicators. These adaptive discretization and analysis approaches are integrated into gradient-based optimization schemes, evaluating the design sensitivities using the adjoint method. Numerical studies illustrate the features of the proposed framework with static, linear elastic, multi-material, two- and three-dimensional problems. The examples provide insight into the effect of refining the design variable field on the optimization result and the convergence rate of the optimization process. Using coarse higher-order B-spline discretizations for level-set fields promotes the development of smooth designs and suppresses the emergence of small features. Moreover, adaptive mesh refinement for state variable fields results in a reduction of overall computational cost. Higher-order B-spline discretizations are especially interesting when evaluating gradients of state variable fields due to their higher inter-element continuity.

36 MATERIALS SCIENCE↗
DOE OSTI2012

Search for the Decay Modes D0 to e+ e-, D0 to mu+ mu-, and D0 to e+/- mu+/-

We present searches for the rare decay modes D{sup 0} {yields} e{sup +}e{sup -}, D{sup 0} {yields} {mu}{sup +}{mu}{sup -}, and D{sup 0} {yields} e{sup {+-}}{mu}{sup {-+}} in continuum e{sup +}e{sup -} {yields} c{bar c} events recorded by the BABAR detector in a data sample that corresponds to an integrated luminosity of 468 fb{sup -1}. These decays are highly GIM suppressed but may be enhanced in several extensions of the Standard Model. Our observed event yields are consistent with the expected backgrounds. An excess is seen in the D{sup 0} {yields} {mu}{sup +}{mu}{sup -} channel, although the observed yield is consistent with an upward background fluctuation at the 5% level. Using the Feldman-Cousins method, we set the following 90% confidence level intervals on the branching fractions: {Beta}(D{sup 0} {yields} e{sup +}e{sup -}) < 1.7 x 10{sup -7}, {Beta}(D{sup 0} {yields} {mu}{sup +}{mu}{sup -}) within [0.6, 8.1] x 10{sup -7}, and {Beta}(D{sup 0} {yields} e{sup {+-}}{mu}{sup {-+}}) < 3.3 x 10{sup -7}.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

TH-CD-207A-07: Prediction of High Dimensional State Subject to Respiratory Motion: A Manifold Learning Approach

Purpose: The development of high dimensional imaging systems (e.g. volumetric MRI, CBCT, photogrammetry systems) in image-guided radiotherapy provides important pathways to the ultimate goal of real-time volumetric/surface motion monitoring. This study aims to develop a prediction method for the high dimensional state subject to respiratory motion. Compared to conventional linear dimension reduction based approaches, our method utilizes manifold learning to construct a descriptive feature submanifold, where more efficient and accurate prediction can be performed. Methods: We developed a prediction framework for high-dimensional state subject to respiratory motion. The proposed method performs dimension reduction in a nonlinear setting to permit more descriptive features compared to its linear counterparts (e.g., classic PCA). Specifically, a kernel PCA is used to construct a proper low-dimensional feature manifold, where low-dimensional prediction is performed. A fixed-point iterative pre-image estimation method is applied subsequently to recover the predicted value in the original state space. We evaluated and compared the proposed method with PCA-based method on 200 level-set surfaces reconstructed from surface point clouds captured by the VisionRT system. The prediction accuracy was evaluated with respect to root-mean-squared-error (RMSE) for both 200ms and 600ms lookahead lengths. Results: The proposed method outperformed PCA-based approach with statistically higher prediction accuracy. In one-dimensional feature subspace, our method achieved mean prediction accuracy of 0.86mm and 0.89mm for 200ms and 600ms lookahead lengths respectively, compared to 0.95mm and 1.04mm from PCA-based method. The paired t-tests further demonstrated the statistical significance of the superiority of our method, with p-values of 6.33e-3 and 5.78e-5, respectively. Conclusion: The proposed approach benefits from the descriptiveness of a nonlinear manifold and the prediction reliability in such low dimensional manifold. The fixed-point iterative approach turns out to work well practically for the pre-image recovery. Our approach is particularly suitable to facilitate managing respiratory motion in image-guide radiotherapy. This work is supported in part by NIH grant R01 CA169102-02.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

A new background distribution-based active contour model for three-dimensional lesion segmentation in breast DCE-MRI

Purpose: To develop and evaluate a computerized semiautomatic segmentation method for accurate extraction of three-dimensional lesions from dynamic contrast-enhanced magnetic resonance images (DCE-MRIs) of the breast. Methods: The authors propose a new background distribution-based active contour model using level set (BDACMLS) to segment lesions in breast DCE-MRIs. The method starts with manual selection of a region of interest (ROI) that contains the entire lesion in a single slice where the lesion is enhanced. Then the lesion volume from the volume data of interest, which is captured automatically, is separated. The core idea of BDACMLS is a new signed pressure function which is based solely on the intensity distribution combined with pathophysiological basis. To compare the algorithm results, two experienced radiologists delineated all lesions jointly to obtain the ground truth. In addition, results generated by other different methods based on level set (LS) are also compared with the authors’ method. Finally, the performance of the proposed method is evaluated by several region-based metrics such as the overlap ratio. Results: Forty-two studies with 46 lesions that contain 29 benign and 17 malignant lesions are evaluated. The dataset includes various typical pathologies of the breast such as invasive ductal carcinoma, ductal carcinomain situ, scar carcinoma, phyllodes tumor, breast cysts, fibroadenoma, etc. The overlap ratio for BDACMLS with respect to manual segmentation is 79.55% ± 12.60% (mean ± s.d.). Conclusions: A new active contour model method has been developed and shown to successfully segment breast DCE-MRI three-dimensional lesions. The results from this model correspond more closely to manual segmentation, solve the weak-edge-passed problem, and improve the robustness in segmenting different lesions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

The backward phase flow method for the Eulerian finite time Lyapunov exponent computations

We propose a simple Eulerian approach to compute the moderate to long time flow map for approximating the Lyapunov exponent of a (periodic or aperiodic) dynamical system. The idea is to generalize a recently proposed backward phase flow method which is specially designed for long time level set propagation. Unlike the original phase flow method or the backward phase flow method, which is applicable only to autonomous systems, the current approach can also be applied to any time-dependent (periodic or aperiodic) flow. We will discuss the stability of the proposed method. Numerical examples will be given to demonstrate the effectiveness of the algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

SU-C-BRA-06: Automatic Brain Tumor Segmentation for Stereotactic Radiosurgery Applications

Purpose: Stereotactic radiosurgery (SRS), which delivers a potent dose of highly conformal radiation to the target in a single fraction, requires accurate tumor delineation for treatment planning. We present an automatic segmentation strategy, that synergizes intensity histogram thresholding, super-voxel clustering, and level-set based contour evolving methods to efficiently and accurately delineate SRS brain tumors on contrast-enhance T1-weighted (T1c) Magnetic Resonance Images (MRI). Methods: The developed auto-segmentation strategy consists of three major steps. Firstly, tumor sites are localized through 2D slice intensity histogram scanning. Then, super voxels are obtained through clustering the corresponding voxels in 3D with reference to the similarity metrics composited from spatial distance and intensity difference. The combination of the above two could generate the initial contour surface. Finally, a localized region active contour model is utilized to evolve the surface to achieve the accurate delineation of the tumors. The developed method was evaluated on numerical phantom data, synthetic BRATS (Multimodal Brain Tumor Image Segmentation challenge) data, and clinical patients’ data. The auto-segmentation results were quantitatively evaluated by comparing to ground truths with both volume and surface similarity metrics. Results: DICE coefficient (DC) was performed as a quantitative metric to evaluate the auto-segmentation in the numerical phantom with 8 tumors. DCs are 0.999±0.001 without noise, 0.969±0.065 with Rician noise and 0.976±0.038 with Gaussian noise. DC, NMI (Normalized Mutual Information), SSIM (Structural Similarity) and Hausdorff distance (HD) were calculated as the metrics for the BRATS and patients’ data. Assessment of BRATS data across 25 tumor segmentation yield DC 0.886±0.078, NMI 0.817±0.108, SSIM 0.997±0.002, and HD 6.483±4.079mm. Evaluation on 8 patients with total 14 tumor sites yield DC 0.872±0.070, NMI 0.824±0.078, SSIM 0.999±0.001, and HD 5.926±6.141mm. Conclusion: The developed automatic segmentation strategy, which yields accurate brain tumor delineation in evaluation cases, is promising for its application in SRS treatment planning.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Prediction of correlation energies using variational subspace valence bond

In the variational subspace valence bond (VSVB) [G. D. Fletcher, J. Chem. Phys. 142, 134112 (2015)] method, the electronic orbitals comprising the wave function correspond to chemically meaningful objects, such as bonds, lone pairs, atomic cores, and so on. Selected regions of a molecule (for example, a single chemical bond, as opposed to all the bonds) can be modeled with different levels of basis set and possible methods for modeling correlation from the other regions. The interactions between the components of a molecule (say, a bond and a neighboring orbital) can then be studied in detail for their impact on a chemical phenomenon while avoiding the expense of necessarily applying the higher levels and methods to the entire molecule. Here, this work presents the theoretical basis for modeling correlation effects between specific electron pairs by incorporating terms in the inter-electronic coordinates (“r 12 ”) into VSVB. The approach is validated with calculations on small systems using single-reference wave functions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Diesel Generator Model Parameterization for Microgrid Simulation Using Hybrid Box-Constrained Levenberg-Marquardt Algorithm

Existing generator parameterization methods, typically developed for large turbine generator units, are difficult to apply to small kW-level diesel generators in microgrid applications. Here, this article presents a model parameterization method that estimates a complete set of kW-level diesel generator parameters simultaneously using only load-step-change tests with limited measurement points. This method provides a more cost-efficient and robust approach to achieve high-fidelity modeling of diesel generators for microgrid dynamic simulation. A two-stage hybrid box-constrained Levenberg-Marquardt (H-BCLM) algorithm is developed to search the optimal parameter set given the parameter bounds. A heuristic algorithm, namely Generalized Opposition-based Learning Genetic Algorithm (GOL-GA), is applied to identify proper initial estimates at the first stage, followed by a modified Levenberg-Marquardt algorithm designed to fine tune the solution based on the first-stage result. The proposed method is validated against dynamic simulation of a diesel generator model and field measurements from a 16kW diesel generator unit.

42 ENGINEERING↗
DOE OSTI2016

Multilevel segmentation of intracranial aneurysms in CT angiography images

Purpose: Segmentation of aneurysms plays an important role in interventional planning. Yet, the segmentation of both the lumen and the thrombus of an intracranial aneurysm in computed tomography angiography (CTA) remains a challenge. This paper proposes a multilevel segmentation methodology for efficiently segmenting intracranial aneurysms in CTA images. Methods: The proposed methodology first uses the lattice Boltzmann method (LBM) to extract the lumen part directly from the original image. Then, the LBM is applied again on an intermediate image whose lumen part is filled by the mean gray-level value outside the lumen, to yield an image region containing part of the aneurysm boundary. After that, an expanding disk is introduced to estimate the complete contour of the aneurysm. Finally, the contour detected is used as the initial contour of the level set with ellipse to refine the aneurysm. Results: The results obtained on 11 patients from different hospitals showed that the proposed segmentation was comparable with manual segmentation, and that quantitatively, the average segmentation matching factor (SMF) reached 86.99%, demonstrating good segmentation accuracy. Chan–Vese method, Sen’s model, and Luca’s model were used to compare the proposed method and their average SMF values were 39.98%, 40.76%, and 77.11%, respectively. Conclusions: The authors have presented a multilevel segmentation method based on the LBM and level set with ellipse for accurate segmentation of intracranial aneurysms. Compared to three existing methods, for all eleven patients, the proposed method can successfully segment the lumen with the highest SMF values for nine patients and second highest SMF values for the two. It also segments the entire aneurysm with the highest SMF values for ten patients and second highest SMF value for the one. This makes it potential for clinical assessment of the volume and aspect ratio of the intracranial aneurysms.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Multi-Method Characterization of Compression Set in Fluorosilicone O-Rings

Fluorosilicone o-rings with varying levels of compression set were investigated with a variety of methods. Low field NMR experiments were able to elucidate if the sample had taken a compression set; however, this technique did not have the sensitivity to quantify the relative level of compression set of the o-ring. Furthermore, water sorption isotherms probe the interior void structure through void space occupation and while complex, the sorption isotherms indicate a systematic loss of void volume with increasing compression set. Similarly, variable temperature 129 Xe NMR experiments indicate an elimination of macroscopic void space with increasing compression. The NMR techniques, being noninvasive, have a unique ability to assess the service status of an o-ring in real time.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Butterfly, Vinylidene-Like, Monobridged and Trans Structures of Si 2 H 2 + : Comparison to the Well-Characterized Neutral Si 2 H 2

This paper investigates four of the constitutional isomers of Si 2 H 2 + , namely the butterfly, vinylidene-like, monobridged, and trans structures. These isomer geometries were all studied using the CCSD(T) method with basis sets as large as cc-pV5Z. Higher level methods CCSDT and CCSDT(Q) were used for final energetics. It is found that the butterfly isomer has the lowest energy, followed by vinylidene-like and monobridged structures; the trans structure has the highest energy of the four. All structures were compared with their neutral counterparts. Partial charges are computed and it is found that all isomers share the positive charge between the silicon atoms. NBO analysis shows that the cation Si-Si bond order is reduced by 0.5 relative to the neutral versions of the same isomer in the case of the butterfly, vinylidene-like, and monobridged; and reduced by 0.6 for the trans isomer. Vibrational frequencies, infrared intensities, and dipole moments are predicted to encourage the spectroscopic identification of Si 2 H 2 + .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Two-color pyrometry based flame to fuel surface radiative heat flux diagnostic using flamelets

In this study, a non-intrusive two-color pyrometry based radiative heat flux diagnostic is presented that accounts for the self-absorption effects. This diagnostic relies on looking up the flame temperature and soot volume fraction using the ratio of color intensities obtained from digital cameras and numerical solutions of 1D steady-state diffusion flames. Virtual two color pyrometry of computed flame show a unique one-to-one mapping of strained flames with intensity ratio; thereby allowing flames to be indexed and creation of a two-color flamelet manifold (TCFM). The TCFM is a function of two variables; the ratio of red to green intensities (flame index) and physical distance to the stoichiometric surface defined using a level-set function. The developed diagnostic is used in upward flame spread experiments where an approximate flame hull reconstruction method is applied to provide the 3D level-set function and intensity ratio for use of TCFM to provide radiative absorption properties for 3D ray tracing. Accounting for self- absorption effects provide improved soot volume fraction estimates. In conclusion, the radiative heat flux estimates are found to be in very good agreement with literature and improved results are obtained near the flame base.

42 ENGINEERING↗
DOE OSTI2025

The Remarkable I 2 O 3 Molecule: A New View from Theory

Atmospheric iodine chemistry has garnered increasing attention as a result of increased iodine emissions. A key subset of this chemistry involves iodine oxides (I 2 O 2–5 ), which serve as precursors to particle formation. Among these, I 2 O 3 is the simplest iodine oxide involved in particle formation, but it has remained undetected in the atmosphere. Previous theoretical studies have characterized this peculiar molecule, primarily using energies to refine geometries obtained at low levels of theory. Due to the reemerging interest in I 2 O 3 , this study presents geometries optimized at the CCSD(T)/aug-cc-pwCVTZ-PP level of theory─marking the first instance, to the best of our knowledge, where this system has been studied exclusively with CCSD(T). Harmonic vibrational frequencies were computed at the same level of theory. Final energetics were obtained using the very high level CCSDT(Q) method with basis sets up to quintuple-zeta cardinality (aug-cc-pwCV5Z-PP) and extrapolated to the CBS limit to yield CCSDT(Q)/CBS//CCSD(T)/aug-cc-pwCVTZ-PP energies. These energies include harmonic zero-point vibrational energy corrections and scalar relativistic energy corrections. Additionally, this study discovers new isomers along the I 2 O 3 potential energy surface, a novel contribution to the field. The performance of different computational methods and DFT functionals commonly used in atmospheric chemistry is also assessed relative to high-level theoretical methods.

basis sets↗
DOE OSTI2014

TU-F-BRF-06: 3D Pancreas MRI Segmentation Using Dictionary Learning and Manifold Clustering

Purpose: The recent advent of MRI guided radiotherapy machines has lent an exciting platform for soft tissue target localization during treatment. However, tools to efficiently utilize MRI images for such purpose have not been developed. Specifically, to efficiently quantify the organ motion, we develop an automated segmentation method using dictionary learning and manifold clustering (DLMC). Methods: Fast 3D HASTE and VIBE MR images of 2 healthy volunteers and 3 patients were acquired. A bounding box was defined to include pancreas and surrounding normal organs including the liver, duodenum and stomach. The first slice of the MRI was used for dictionary learning based on mean-shift clustering and K-SVD sparse representation. Subsequent images were iteratively reconstructed until the error is less than a preset threshold. The preliminarily segmentation was subject to the constraints of manifold clustering. The segmentation results were compared with the mean shift merging (MSM), level set (LS) and manual segmentation methods. Results: DLMC resulted in consistently higher accuracy and robustness than comparing methods. Using manual contours as the ground truth, the mean Dices indices for all subjects are 0.54, 0.56 and 0.67 for MSM, LS and DLMC, respectively based on the HASTE image. The mean Dices indices are 0.70, 0.77 and 0.79 for the three methods based on VIBE images. DLMC is clearly more robust on the patients with the diseased pancreas while LS and MSM tend to over-segment the pancreas. DLMC also achieved higher sensitivity (0.80) and specificity (0.99) combining both imaging techniques. LS achieved equivalent sensitivity on VIBE images but was more computationally inefficient. Conclusion: We showed that pancreas and surrounding normal organs can be reliably segmented based on fast MRI using DLMC. This method will facilitate both planning volume definition and imaging guidance during treatment.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

Novel multimodality segmentation using level sets and Jensen-Rényi divergence

Purpose: Positron emission tomography (PET) is playing an increasing role in radiotherapy treatment planning. However, despite progress, robust algorithms for PET and multimodal image segmentation are still lacking, especially if the algorithm were extended to image-guided and adaptive radiotherapy (IGART). This work presents a novel multimodality segmentation algorithm using the Jensen-Rényi divergence (JRD) to evolve the geometric level set contour. The algorithm offers improved noise tolerance which is particularly applicable to segmentation of regions found in PET and cone-beam computed tomography. Methods: A steepest gradient ascent optimization method is used in conjunction with the JRD and a level set active contour to iteratively evolve a contour to partition an image based on statistical divergence of the intensity histograms. The algorithm is evaluated using PET scans of pharyngolaryngeal squamous cell carcinoma with the corresponding histological reference. The multimodality extension of the algorithm is evaluated using 22 PET/CT scans of patients with lung carcinoma and a physical phantom scanned under varying image quality conditions. Results: The average concordance index (CI) of the JRD segmentation of the PET images was 0.56 with an average classification error of 65%. The segmentation of the lung carcinoma images had a maximum diameter relative error of 63%, 19.5%, and 14.8% when using CT, PET, and combined PET/CT images, respectively. The estimated maximal diameters of the gross tumor volume (GTV) showed a high correlation with the macroscopically determined maximal diameters, with aR{sup 2} value of 0.85 and 0.88 using the PET and PET/CT images, respectively. Results from the physical phantom show that the JRD is more robust to image noise compared to mutual information and region growing. Conclusions: The JRD has shown improved noise tolerance compared to mutual information for the purpose of PET image segmentation. Presented is a flexible framework for multimodal image segmentation that can incorporate a large number of inputs efficiently for IGART.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2021

Chemical vapor infiltration of additively manufactured preforms: Pore-resolved simulations and experimental validation

The densification of additively manufactured porous preforms by chemical vapor infiltration (CVI) is studied using pore-resolved simulations and experiments. Experimentally, 3D printed silicon carbide (SiC) preforms are subject to CVI synthesis using methyltrichlorosilane (MTS) precursor to obtain high purity SiC/SiC composites. Optical images of the cross sections of the processed preforms are analyzed to obtain the spatial porosity distribution. The numerical method is based on a level set formulation to capture the spatial distribution and time evolution of the pore scale microstructural characteristics. The coupled transport and kinetic effects are represented using a dimensionless Thiele modulus. Simulations are initialized using representative synthetic preform geometries comprising of packed particles based on the size distribution of the powder used for 3D printing. The simulation results are validated against the experimental observations in terms of total density and the distribution of residual porosity. The densification characteristics, porosity classification, concentration profiles, and structure functions are analyzed as functions of processing temperature and Thiele modulus.

36 MATERIALS SCIENCE↗