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An overview of Equation of State (EOS) theory, some relevant physics, experiments, computational methods, and the SESAME database will be presented. The goal will be to describe what types of data and modeling are required to make an EOS that typically spans up to ~10 9 GPa in pressure and 10 9 K in temperature.
Compliance of member States to the Treaty on the Non-Proliferation of Nuclear Weapons is monitored through nuclear safeguards. The Passive Gamma Emission Tomography (PGET) system is a novel instrument developed within the framework of the International Atomic Energy Agency (IAEA) project JNT 1510, which included the European Commission, Finland, Hungary and Sweden. The PGET is used for the verification of spent nuclear fuel stored in water pools. Advanced image reconstruction techniques are crucial for obtaining high-quality cross-sectional images of the spent-fuel bundle to allow inspectors of the IAEA to monitor nuclear material and promptly identify its diversion. In this work, we have developed a software suite to accurately reconstruct the spent-fuel cross sectional image, automatically identify present fuel rods, and estimate their activity. Unique image reconstruction challenges are posed by the measurement of spent fuel, due to its high activity and the self-attenuation. While the former is mitigated by detector physical collimation, we implemented a linear forward model to model the detector responses to the fuel rods inside the PGET, to account for the latter. The image reconstruction is performed by solving a regularized linear inverse problem using the fast-iterative shrinkage-thresholding algorithm. We have also implemented the traditional filtered back projection (FBP) method based on the inverse Radon transform for comparison and applied both methods to reconstruct images of simulated mockup fuel assemblies. Higher image resolution and fewer reconstruction artifacts were obtained with the inverse-problem approach, with the mean-square-error reduced by 50%, and the structural-similarity improved by 200%. We then used a convolutional neural network (CNN) to automatically identify the bundle type and extract the pin locations from the images; the estimated activity levels finally being compared with the ground truth. The proposed computational methods accurately estimated the activity levels of the present pins, with an associated uncertainty of approximately 5%.
Advanced finite-element discretizations and preconditioners for models of poroelasticity have attracted significant attention in recent years. The equations of poroelasticity offer significant challenges in both areas, due to the potentially strong coupling between unknowns in the system, saddle-point structure, and the need to account for wide ranges of parameter values, including limiting behavior such as incompressible elasticity. This paper was motivated by an attempt to develop monolithic multigrid preconditioners for the discretization developed in [C. Rodrigo et al., Comput. Methods App. Mech. Engrg, 341 (2018), pp. 467--484]; we show here why this is a difficult task and, as a result, we modify the discretization in [Rodrigo et al.] through the use of a reduced-quadrature approximation, yielding a more “solver-friendly” discretization. Local Fourier analysis is used to optimize parameters in the resulting monolithic multigrid method, allowing a fair comparison between the performance and costs of methods based on Vanka and Braess--Sarazin relaxation. Further, numerical results are presented to validate the local Fourier analysis predictions and demonstrate efficiency of the algorithms. Finally, a comparison to existing block-factorization preconditioners is also given.
The Steel Equivalency Spreadsheet was created as a robust, user-friendly method for the following: 1. Determining if it is possible to image an object. 2. Reducing time needed when selecting equipment and preparing for field imaging activities. 3. Reducing the amount of equipment taken for field imaging activities. 4. Determining a starting point for exposure settings prior to imaging an object. 5. Reducing the amount of dose deposited to complete an imaging operation (in the spirit of As Low As Reasonably Achievable, ALARA). The spreadsheet was developed using various physical models to account for different phenomena. Future implementations aim to expand beyond the Digital Radiography and Computed Tomography Single Munition Scanner (DRCT SMS) in standard configuration to include high energy XRGs (Betatrons) and sub-MeV pulsed XRGs (XRS4). Alternative computational methods that compensate for incoherent scattering when calculating relative transmission are also being pursued. Ultimately the spreadsheet exceeded the developmental goal of having less than 10% average error when comparing calculations to real-world images.
Polynomial chaos expansions (PCE) provide an efficient approach to uncertainty quantification (UQ) and have been adapted to diverse applications across the spectrum of science and engineering. For situations involving large stochastic parameterizations, the curse of dimensionality renders PCE-based methods computationally prohibitive. A basis adaptation approach for PCE was proposed by Tipireddy and Ghanem (2014) which transforms the input random variables through an isometry such that sufficient probabilistic characterization of specific quantities of interest (QoI) is concentrated in an algebraic manifold embedded in the linear span of the dominant transformed variables. While quite versatile, that original version of the PCE basis adaptation exhibited slow convergence for a number of problems of practical significance. In the present paper, we propose two novel methods to accelerate the convergence of the original basis adaptation approach, thus expanding its reach while also providing insight into its performance. In the first method, information gained from a pilot PCE representation is used to correct the mean and Gaussian coefficients in the adapted space. By taking advantages of probabilistic information in higher dimensional adaptation gleaned from an initial adaptation, the second method updates the rotation matrix used to identify the dominant transformed variables. In this manner, the new rotation matrix concentrates even more probabilistic information in its first few dimensions. These two method can be combined to achieve even better performance, the combined method is referred to as sequentially optimized adaptation method. Here, the methods are demonstrated on an analytical test function and a model of a space structure with several sub-components and a non-smooth quantity of interest representing the maximum acceleration over time. Both methods achieve accelerated convergence of the basis adaptation approach with negligible additional costs.
Hydrogen transfer is a critical component of many chemical and biological processes. The ratio of rate constants for hydrogen and deuterium transfer defines the H/D kinetic isotope effect (KIE), which is a powerful tool for elucidating hydrogen transfer mechanisms. Interpretation of experimental H/D KIEs relies on accurate and affordable computational methods. However, due to their light mass, hydrogen and deuterium can undergo tunneling, which is challenging to describe in multidimensional molecular systems. Herein, we introduce the nuclear–electronic orbital general rate theory (NEO-GRT), which enables the efficient prediction of H/D KIEs based on full-dimensional molecular quantum chemistry calculations. The NEO-GRT approach describes the hydrogen transfer rate constant with a general expression that spans the vibrationally adiabatic and nonadiabatic hydrogen tunneling regimes. The input quantities are computed using NEO density functional theory, which treats the transferring hydrogen or deuterium nucleus quantum mechanically on the same level as the electrons. We investigate two intramolecular proton transfer reactions in organic molecules at temperatures down to 50 K to evaluate the performance of NEO-GRT by comparison to transition state theory and ring-polymer instanton theory. The KIEs computed with NEO-GRT agree with those calculated using ring-polymer instanton theory for the full-dimensional molecular systems at the same level of electronic structure theory. This agreement indicates that NEO-GRT captures the deep hydrogen tunneling effects, in contrast to transition state theory, which neglects such effects. Given its relatively low computational cost, NEO-GRT is a promising approach for predicting H/D KIEs in large organic and organometallic systems.
Single- reference coupled-cluster theory is an accurate and affordable computational method for the nuclear many-body problem. For open-shell nuclei, the reference state typically breaks rotational invariance and angular momentum must be restored as a good quantum number. We perform angular-momentum projection after variation and employ the disentangled coupled-cluster formalism and a Hermitian approach. We compare our results with benchmarks for 8 Be and 20 Ne using a two-nucleon interaction from chiral effective field theory and for pf-shell nuclei within the traditional shell model. We compute the rotational band in the exotic nucleus 34 Mg and find agreement with data.
Understanding the role of oxygen vacancy–induced atomic and electronic structural changes to complex metal oxides during water-splitting processes is paramount to advancing the field of solar thermochemical hydrogen production (STCH). The formulation and confirmation of a mechanism for these types of chemical reactions necessitate a multifaceted experimental approach, featuring advanced structural characterization methods. Synchrotron X-ray techniques are essential to the rapidly advancing field of STCH in part due to properties such as high brilliance, high coherence, and variable energy that provide sensitivity, resolution, and rapid data acquisition times required for the characterization of complex metal oxides during water-splitting cycles. X-ray diffraction (XRD) is commonly used for determining the structures and phase purity of new materials synthesized by solid-state techniques and monitoring the structural integrity of oxides during water-splitting processes (e.g., oxygen vacancy–induced lattice expansion). X-ray absorption spectroscopy (XAS) is an element-specific technique and is sensitive to local atomic and electronic changes encountered around metal coordination centers during redox. While in operando measurements are desirable, the experimental conditions required for such measurements (high temperatures, controlled oxygen partial pressures, and H 2 O) practically necessitate in situ measurements that do not meet all operating conditions or ex situ measurements. Here, we highlight the application of synchrotron X-ray scattering and spectroscopic techniques using both in situ and ex situ measurements, emphasizing the advantages and limitations of each method as they relate to water-splitting processes. The best practices are discussed for preparing quenched states of reduction and performing synchrotron measurements, which focus on XRD and XAS at soft (e.g., oxygen K-edge, transition metal L-edges, and lanthanide M-edges) and hard (e.g., transition metal K-edges and lanthanide L-edges) X-ray energies. The X-ray absorption spectra of these complex oxides are a convolution of multiple contributions with accurate interpretation being contingent on computational methods. The state-of-the-art methods are discussed that enable peak positions and intensities to be related to material electronic and structural properties. Through careful experimental design, these studies can elucidate complex structure–property relationships as they pertain to nonstoichiometric water splitting. A survey of modern approaches for the evaluation of water-splitting materials at synchrotron sources under various experimental conditions is provided, and available software for data analysis is discussed.
Abstract Motivation Millions of protein sequences have been generated by numerous genome and transcriptome sequencing projects. However, experimentally determining the function of the proteins is still a time consuming, low-throughput, and expensive process, leading to a large protein sequence-function gap. Therefore, it is important to develop computational methods to accurately predict protein function to fill the gap. Even though many methods have been developed to use protein sequences as input to predict function, much fewer methods leverage protein structures in protein function prediction because there was lack of accurate protein structures for most proteins until recently. Results We developed TransFun—a method using a transformer-based protein language model and 3D-equivariant graph neural networks to distill information from both protein sequences and structures to predict protein function. It extracts feature embeddings from protein sequences using a pre-trained protein language model (ESM) via transfer learning and combines them with 3D structures of proteins predicted by AlphaFold2 through equivariant graph neural networks. Benchmarked on the CAFA3 test dataset and a new test dataset, TransFun outperforms several state-of-the-art methods, indicating that the language model and 3D-equivariant graph neural networks are effective methods to leverage protein sequences and structures to improve protein function prediction. Combining TransFun predictions and sequence similarity-based predictions can further increase prediction accuracy. Availability and implementation The source code of TransFun is available at https://github.com/jianlin-cheng/TransFun.
The funding enabled the creation of the (University of North) Texas Center for Advanced Scientific Computing and Modeling (CASCaM). Due to its success, CASCaM has continued to grow beyond the initial team focused on the biological and environmental research discussed herein, with investments by the University of North Texas in new faculty and researchers who contribute to CASCaM research. CASCaM is now a sustainable effort, with researchers across multiple fields including chemistry, physics, biology, mechanical engineering, materials science, and other fields, with multiple researchers engaged in a broad variety of research, including other DOE projects. Over 20 PI’s and ~100 researchers are engaged in CASCaM research. The overall goal of the research effort was to provide greater understanding about carbon capture, storage, and utilization. As part of this effort, the development of computational methods and identification of novel strategies to support the CO2 and CO studies were necessary. Three primary themes were investigated: carbon dioxide and CO catalysis; protein- and amino acid-based strategies towards carbon dioxide capture, storage, and utilization; and, finally, the methodology improvements for modeling carbon dioxide chemistry
Abstract The carbon capture, utilization, and storage (CCUS) framework is an essential component in reducing greenhouse gas emissions, with its success hinging on the comprehensive knowledge of subsurface geology and geomechanics. Passive seismic event relocation and fault detection offer vital insights into subsurface structures and the ability to monitor fluid migration pathways. Accurate identification and localization of seismic events, however, face significant challenges, including the necessity for high‐quality seismic data and advanced computational methods. To address these challenges, we introduce a novel deep learning method, , specifically designed for passive seismic source relocation and fault delineating for passive seismic monitoring projects. By leveraging data domain‐adaptation, allows us to train a neural network with labeled synthetic data and apply it directly to field data. Using , the passive seismic sources are automatically clustered based on their recording time and spatial locations, and subsequently, faults and fractures are delineated accordingly. We demonstrate the efficacy of on a field case study involving injection related microseismic data from Decatur, Illinois area. Our approach accurately and efficiently relocated passive seismic events, identified faults and could aid in potential damage induced by seismicity. Our results highlight the potential of as a valuable tool for passive seismic monitoring, emphasizing its role in ensuring CCUS project safety. This research bolsters the understanding of subsurface characterization in CCUS, illustrating machine learning’s capacity to refine these methods. Ultimately, our work has significant implications for CCUS technology deployment, an essential strategy in combating climate change. Plain Language Summary In our quest to tackle climate change, we use a strategy known as carbon capture, utilization, and storage (CCUS) to keep greenhouse gases out of the atmosphere. This strategy relies heavily on our ability to understand what's happening deep under the earth's surface. To make sure we store super critical safely, we need to accurately map out the geological structure, especially faults, but this is tough without high‐quality data and complex computer programs. We've developed a new tool called “DeFault,” which uses advanced machine learning to improve how we find and map these underground features. “DeFault” is smart enough to learn from numerically simulated data and then apply what it’s learned to real‐world situations. It groups together seismic activity—tiny tremors and shifts in the earth—based on when and where they happen, which helps us spot where there might be cracks or faults. We tested “DeFault” in Illinois, where CO 2 is injected underground, and it successfully pinpointed where these tremors occurred and mapped out the faults, helping to prevent accidents accurately in the future. Our study shows that “DeFault” will be a powerful ally in making CCUS safer and more effective, especially for the Illinois Basin Decatur Project. Key Points Faults and fractures introduced by carbon storage can be monitored by passive seismicity DeFault algorithm enables an automatic process for accurate and efficient passive seismic event locating and clustering
Machine learning is becoming prevalent in high energy physics, with numerous applications in physics analyses and event reconstruction showing great improvements compared to traditional computing methods. This thesis studies three projects which each propose new avenues for machine learning applications within the high energy physics CMS experiment located at CERN. In the first project, a search for a dark matter signal called “emerging jets” is performed, using graph neural networks to greatly increase sensitivity to the signal’s signature within the data. The result of this dark matter search sets the most stringent exclusion limits to date on theoretical emerging jet models. Motivated by inefficiencies encountered when processing the emerging jet graph neural network at Fermi National Accelerator Laboratory’s computing centers, the second project re-optimizes the computing centers for machine learning inference. This re-optimization uses NVIDIA Triton Inference Servers to process users’ analysis code heterogeneously, therefore achieving high processing throughput and decreasing user time-to-insight. The last project focuses on an upgrade to the CMS experiment’s real-time event selection system which improves physics object reconstruction under harsh processing conditions. A boosted decision tree is used to quickly and efficiently quantify a reconstructed particle’s “track quality” in order to remove particle tracks reconstructed erroneously. In summary, this thesis will not only present examples of how high energy physics can greatly benefit by leveraging machine learning techniques for physics analysis and reconstruction, but will also provide guidance on how the field can prepare for the inevitable increase in machine learning applications.
The total energy consumption in the U.S. has been rising steadily for decades, and it currently amounts to ~98,000 TBtu/yr, with approximately 30% of this total attributable to the industrial sector. Reasonable estimates indicate that 45–55% of total industry energy consumption derives from chemical separations, and for example, over 120 TBtu/yr alone is used in carrying out olefin/paraffin separations via energy-intensive cryogenic distillation. Therefore, the pursuit of new, even radically different approaches to some of the most energy-intensive industrial separations processes is an imperative scientific pursuit for reducing energy consumption toward a more sustainable future. Adsorbent and membrane-based separations can require a fraction of the energy needed for distillation methods, and as such are considered promising solutions for balancing increasing energy demand in the U.S. with the need for a massive reduction in energy consumption. Although considerable research effort has been devoted to the design of materials capable of carrying out various gas separations, usually operating through size-selective, chemisorptive, or physisorptive mechanisms, it remains a great challenge to design materials that function adequately for real-world applications. Indeed, the chemical and physical differences between molecules in gas mixtures of interest are often small, and therefore it is necessary, through the use of nanoscience and synthetic chemistry, to engineer unprecedented molecular-level control in adsorbate–adsorbent interactions. The overarching mission of the Center for Gas Separations (CGS) was to discover fundamental innovations that have the potential to dramatically reduce the energy associated with critical gas separations. In particular, the CGS developed novel synthetic routes, guided by molecular chemistry principles, as well as advanced characterization and computational methods, that have enabled the discovery of new materials and membranes tailor-made to exhibit exceptional performance for a range of gas separations processes, as required in the clean use of fossil fuels and in reducing CO 2 emissions from industry. A challenge of this magnitude required the collaboration and synergy of a large team of researchers with expertise in materials synthesis, characterization, and computations. During the 11-year project period, the CGS created a range of new materials within the family of highly-tunable, porous solids known as metal–organic frameworks (MOFs). These new frameworks demonstrate novel mechanisms for key industrial gas separations, including revolutionary new cooperative adsorption processes that enable low-energy CO 2 and CO capture, and are capable of efficiently separating olefins from paraffins, O 2 from air, and the shape-selective separation of alkane isomers. In addition, the CGS developed new strategies for incorporating these materials into composite membranes toward highly efficient and selective membrane-based separations. As a testament to the success of the CGS, two start-up companies, Mosaic Materials,4 Inc. and Flux Technology, Inc., grew out of these research efforts, and these companies are seeking to commercialize MOF and composite membranes materials for key separations in industry, including large-scale CO 2 capture and hydrocarbon separations, respectively. Another company, framergy, Inc., licensed IP resulting from CGS research toward the commercialization of adsorbents for various energy-relevant applications.
Recent advances in cryo-electron microscopy (cryo-EM) have enabled modeling macromolecular complexes that are essential components of the cellular machinery. The density maps derived from cryo-EM experiments are often integrated with manual, knowledge or artificial intelligence driven, and physics-guided computational methods to build, fit, and refine molecular structures. Going beyond a single stationary- structure determination scheme, it is becoming more common to interpret the experimental data with an ensemble of models, which contributes to an average observation. Hence, there is a need to decide on the quality of an ensemble of protein structures on-the-fly, while refining them against the density maps. Here, we introduce such an adaptive decision making scheme during the molecular dynamics flexible fitting (MDFF) of biomolecules. Using RADICAL-Cybertools, and the new RADICAL augmented MDFF implementation (R-MDFF) is examined in high-performance computing environments for refinement of two protein systems, Adenylate Kinase and Carbon Monoxide Dehydrogenase. For the test cases, use of multiple replicas in flexible fitting with adaptive decision making in R-MDFF improves the overall correlation to the density by 40% relative to the refinements of the brute-force MDFF. The improvements are particularly significant at high, 2 - 3 Å, map resolutions. More importantly, the ensemble model captures key features of biologically relevant molecular dynamics that is inaccessible to a single-model interpretation. Finally, the pipeline is applicable to systems of growing sizes, which is demonstrated using ensemble refinement of capsid proteins from Chimpanzee adenovirus. The overhead for decision making remaining low and robust to computing environments. The software is publicly available on GitHub and includes a short user guide to install the R-MDFF on different computing environments, from local Linux based workstations to High Performance Computing (HPC) environments.
Deposits in commercial uranium processing facilities of interest to nuclear safeguards are predominantly low enriched uranium (LEU). The shapes and sizes of holdup deposits can vary significantly, thus making it difficult to model the deposits accurately for calibration purposes. This presents a challenge to currently employed methods such as the Generalized Geometry Holdup (GGH) that rely on quantifying 235U mass by simplifying deposit shapes as a point, a line, or an area. In this work, gamma ray imaging using high energy resolution Germanium Gamma Imagers (GeGI™) is employed to determine the distribution of uranium inside the source containment. Two types of imaging methods are employed; coded-aperture imaging and Compton imaging. Gamma-ray emissions seen in different regions of the image are quantified using an inverse gamma-ray transport solver being developed at ORNL. Using measured data, the inverse method will be used to solve for unknown source parameters such as source matrix thickness, density, and attenuation due to container wall and shielding. The intrinsic efficiency of the detector is determined based on a library of built-in response functions and key dimensions of the detector (e.g., thickness and radius of the detector crystal). Measurements are performed in both imaging modalities using uranium sources of well-known masses and enrichments configured inside mocked-up holdup fixtures. Results from the two imaging modalities are intercompared. The paper presents preliminary results of the imaging measurements and the progress made in the computational methods to quantify uranium mass.
In this work, theoretical and computational methods for simulating the creation of ionization tracks by fast ions in solids were applied to the passage of a-particles in CsI, an inorganic scintillator commonly used for radiation detection. The methods were implemented in a Monte Carlo program to simulate the interaction of $\alpha$-particles, with incident energies of up to 1 MeV, with CsI. The simulations followed the fate of individual electron-hole pairs and thus allowed for a detailed description of the microscopic structure of ionization tracks created by incident radiation. Simulations were also performed with $\gamma$-rays of the same energy to compare and contrast the ionization tracks obtained with both types of particle. Intrinsic properties such as the mean energy per electron-hole pair, Fano factor, maximum theoretical light yield, and spatial distributions of electron-hole pairs were computed for both $\alpha$-particles and $\gamma$-rays. $\alpha$-particles created cylindrical tracks that were initially aligned with the incident direction and with initial radii of a few nanometers, whereas $\gamma$-rays showed significant scattering, resulting in probability distributions with lower intensities and much greater radial extents.
The deployment of liquid chromatography-mass spectrometry-based plasma proteomics experiments in a large cohort is sparse, leading to a lack of data available for benchmarking, method development or validation. Comprised of 6,426 plasma analyses, The Environmental Determinants of Diabetes in the Young (TEDDY) proteomics validation study constitutes one of the largest targeted proteomics experiments in the literature to date. The proteomics data from this study were generated over the course of 2.5 years from over 900 study subjects, each providing up to 29 longitudinal samples. The data also includes 916 quality control samples. The targeted mass spectrometry assay was comprised of 694 peptides mapping to 167 proteins and the panel was measured in each subject and QC sample. The targeted proteomic dataset presented here can be used as a resource for new computational method development, such as for batch correction, as well as for benchmarking and comparing the performance of different methods/tools.
Metal Additive Manufacturing (AM) is a promising method for cost-efficient fabrication of complex shape structures for applications in harsh environment, such as in a nuclear reactor. However, internal defects (pores) occur in high-strength AM alloys, which are manufactured with Laser Powder Bed Fusion (LPBF) AM method. Pulsed Infrared Thermography (PIT) is an efficient nondestructive evaluation (NDE) method to examine actual structures, because this method offers one-sided non-contact measurements, and fast processing of large sample areas. However, imaging of material defects, particularly defects with sizes at microscopic level, is challenging. In this report, we benchmark the performance of several Unsupervised Learning (UL) algorithms designed to enhance imaging of microscopic defects in metals with PIT. UL aims to learn the latent principal patterns (dictionaries) in PIT data to detect defects with minimal human supervision. Performance of Independent Component Analysis (ICA), Sparse Coding (SC), Principal Component Analysis (PCA) and Exploratory Factor Analysis (EFA) was compared using F-score, UL model training time and defects reconstruction time. We obtained the average F-score of 0.75, and a highest F-score of 0.89 for the EFA algorithm. Overall, EFA outperforms other UL algorithms considered in this study. In another approach, we investigate Thermal Tomography (TT), which is a computational method for reconstruction of depth profile of internal material defects from PIT nondestructive evaluation (NDE). TT algorithm obtains depth reconstructions of thermal effusivity, which has been shown to provide visualization of subsurface internals defects in metals. In many applications, one needs to determine the defect shape and orientation from reconstructed effusivity images. Interpretation of TT images is non-trivial because of blurring, which increases with depth due to heat diffusion-based nature of image formation. We have developed a deep learning convolutional neural network (CNN) to classify size and orientation of subsurface material defects in TT images. CNN was trained with TT images produced with computer simulations of 2D metallic structures (thin plates) containing elliptical subsurface voids. Performance of CNN was investigated using test TT images developed with computer simulations of plates containing elliptical defects, and defects with shape imported from scanning electron microscopy (SEM) images. CNN demonstrated the ability to classify radii and angular orientation of elliptical defects in previously unseen test TT images. We have also demonstrated that CNN trained on TT images of elliptical defects is capable of classifying shape and orientation of irregular defects. Training the CNN on irregular defect shapes instead of on elliptical shapes would make the resulting classifications more descriptive of actual defect shapes. However, this requires a much higher volume of SEM images of material defects, which are difficult to obtain because of random occurrence of defects in LPBF. To address this challenge, we developed a generative adversarial network (GAN) to augment the existing dataset of SEM defect images. The GAN model is demonstrated to create novel yet realistic defect shapes that can be used as input for simulated PTT images to train CNN. We also investigate several approaches based on Gaussian Random Circle and Bezier Curves for constructing parametric models of irregular-shape defects.