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At least 361 records · Page 20

Usability and Optimization Improvements in MOOSE

The Multiphysics Object-Oriented Simulation Environment (MOOSE) framework is a foundational capability used by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to create over 15 different simulation tools for advanced nuclear reactors. Due to MOOSE’s broad use, improvements to the framework in support of modeling and simulation goals are critical to the program. Such improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and new capabilities. The work described in this report was conducted in direct support of the simulation tools and has already been deployed. The capabilities were implemented in the same order as they are covered in this report: multiple nonlinear systems in the same input file, implementation of generic field transfers and other transfer system enhancements, support for stateful material property redistribution for adaptivity and distributed meshes, and dynamic linking and loading of individually compiled applications. These four additions are fundamental capabilities that will be leveraged by many NEAMS applications.

97 MATHEMATICS AND COMPUTING↗

Development of a MOOSE thermal model of the MPC-32 canister and HI-STORM overpack

Nuclear power is a significant source of electricity in the United States, but the average age of nuclear power plants is around 40 years old. Safe management of spent nuclear fuel (SNF) is a key aspect of the back end of the nuclear fuel cycle, and SNF dry storage systems are becoming a popular, effective solution in this area, given the absence of a final disposal system. The spent fuel cask system (dry cask method) provides a feasible solution for maintaining SNF (~60 years) prior to final disposal. This project aims to develop a thermal model of the MPC-32 canister and HI-STORM overpack, using the Multiphysics Object-Oriented Simulation Environment (MOOSE). MOOSE is an open-source framework developed by Idaho National Laboratory (INL) for multiscale, multiphysics simulations. This study will investigate and demonstrate the thermal-hydraulics capabilities of the MOOSE framework, including natural circulation, heat transfer, porous flows, etc. The ultimate goal of the project is to verify whether MOOSE tools (including Pronghorn) can be used to study the thermal performance of the SNF dry cask storage system. This study provides reliable and inclusive solving strategy for dry cask problems. The detailed information about the solving scheme and the governing equations related to the physics of the system is provided in the report. The results for thermal-hydraulic analysis of the HI-STORM system is produced with using open source modules of the MOOSE framework. This results highlights the flexibility and modularity of the MOOSE which makes it a unique candidate for the frameworks and code packages. Therefore, integration of the MOOSE to UNF ST&DARDS will improve the thermal-hydraulic capability of the system while providing distinctive features to users.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NEAMS Technical Area Support in MOOSE

The Multiphysics Object-Oriented Simulation Environment (MOOSE) framework is a foundational capability used by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program to create over 15 different simulation tools for advanced nuclear reactors. Due to this ubiquity, improvements to the framework in support of modeling and simulation goals are critical to the program. These improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and other new capabilities. The work described in this report was conducted in direct support of the simulation tools and has already been deployed. The capabilities outlined in this report include implementing hash table matrix assembly for efficient sparsity pattern construction for contact in BISON, developing re-step testing infrastructure for ensuring the viability of overlapping domain coupling between SAM and Pronghorn, allowing unique preconditioners for single-input multi-system solves, supporting multi-system in MOOSE’s workhorse executioners, and many more smaller feature enhancements and bug fixes.

97 - MATHEMATICS AND COMPUTING↗

High Performance Object-Oriented Scientific Programming in Fortran 90

We illustrate how Fortran 90 supports object-oriented concepts by example of plasma particle computations on the IBM SP. Our experience shows that Fortran 90 and object-oriented methodology give high performance while providing a bridge from Fortran 77 legacy codes to modern programming principles. All of our object-oriented Fortran 90 codes execute more quickly thatn the equeivalent C++ versions, yet the abstraction modelling capabilities used for scentific programming are comparably powereful.

Scientific Programming↗

Electromagnetic Interactions GenERalized (EIGER): Applications at Johnson Space Center

This slide presentation reviews the software framework for the analysis and design of complex electromagnetic systems. The system called Electromagnetic Interactions GenERalized (EIGER) is a hybrid finite element solution for wave equations and deru=ives boundary element solutions for integral equation formulations. Written in Fortran 90 Eiger uses object-oriented design methods to abstract key analysis components. EIGER has been applied to higher order modeling for analysis of antennas to assist in the design of the antennas of a mini-AERCam. EIGER might also be used to model the Ion Cyclotron Resonant heating stage for the VAriable Specific Impulse Magnetoplasma Rocket (VASIMR).

Dobbins, Justin A.↗

pyCRTM: A Python Interface for the Community Radiative Transfer Model

The Community Radiative Transfer Model (CRTM) is a powerful and versatile scalar radiative transfer model for satellite data assimilation and remote sensing applications. It is implemented as an object-oriented Fortran library, enabling flexible code development and optimal runtime performance on clusters. The downsides of the Fortran interface are a steep learning curve for students and the reduced productivity of users that is typical for static compiled languages, in contrast to dynamic interpreted languages like Python. pyCRTM is a new software framework that directly interfaces the CRTM Fortran data structures and procedures in Python, leveraging both the simplicity and ease of use of Python syntax as well as the flexibility arising from the vast contemporary Python ecosystem. The goal of pyCRTM is to lower the barrier of entry for university students to learn and use the CRTM and to boost the productivity of researchers seeking to create new methods in radiative transfer and data assimilation, or seeking to apply the CRTM to study atmospheric phenomena without having to go through the pre-existing complexity of the CRTM Fortran interface.

Python↗

Integrated Modeling and Development of Component-Based Embedded Software in Scala

Programming of embedded systems is challenging due to the low-level design patterns normally applied in the implementation of such systems. Furthermore, programming languages normally considered suitable for this level of programming, such as C and C++, are themselves low-level compared to more modern programming languages. We report on an effort exploring modeling and programming of embedded systems in modern high-level programming languages combining object-oriented and functional programming. We present an integration of four separate internal DSLs (libraries), considered useful for embedded program- ming, in the Scala programming language, for programming and testing component-based systems. These include a DSL for defining components and their connections, and a DSL for programming the individual components as hierarchical state machines. Two additional DSLs support testing, and include a DSL for writing temporal logic flavored test oracles for monitoring program executions, and a DSL for rule-based test input generation. The paper discusses the gap between Scala as used here and the needs for embedded systems programming.

Bocchino, Robert↗

Modeling Tool Development and Validation for Solar Industry Process Heat Using Particle Thermal Energy Storage

U.S. industry sectors used 26.2 quadrillion Btu and accounted for 33% of total energy consumption in 2021 according to the Energy Information Agency. Industrial process heat accounts for 70% of industrial energy use with application temperatures ranging from 60 degrees -1100 degrees C. Industry processes, heavily relying on fossil fuels of cheap coal or natural gas, differ widely in operating conditions and load requirements which makes them difficult to standardize and imposes great challenges in decarbonization. Industry processes require reliable energy supply and vary widely in temperature ranges. Storing energy from renewable sources is necessary to improve reliability and to mitigate renewable intermittency when replacing carbon fuel-based heat supplies to achieve energy savings and reduce emissions. To this end, we have developed a particle-based thermal energy storage (TES) technology using low-cost and highly stable silica sand as a storage medium. The economic and performance-based analysis is key for renewable energy sources to reliably supply industry process heat and ultimately displace fossil fuels for decarbonization. The diversified industrial processes need case-by-case analysis and design. Therefore, an adaptive modeling tool is key for renewable power with energy storage to meet industry demands. Thus, a modeling tool to simulate a solar industry process heat system using the particle TES has been developed using the object-oriented equation-based language Modelica and the commercial platform of Modelon Impact. The Modelica-based software tool provides a general simulation environment for the design of reliable solar energy sources integrated with TES for various industrial process applications at different temperatures for economic competence with fossil fuels such as coal and natural gases. It uses both customized and standard component modeling modules in Modelon libraries for the flexibility to be adapted to a specific energy demand application. The particle TES system establishes a uniform energy supply platform with an efficient heat exchanger and particle thermal energy reservoir integrated with renewable powers. The particle TES system can provide a wide temperature range and can have a large storage temperature difference that increases storage energy density; therefore, it can be an adaptable energy storage system integrated with renewable power to supply 24/7 heat for industry decarbonization.

concentrated solar thermal↗

The generation and use of numerical shape models for irregular Solar System objects

We describe a procedure that allows the efficient generation of numerical shape models for irregular Solar System objects, where a numerical model is simply a table of evenly spaced body-centered latitudes and longitudes and their associated radii. This modeling technique uses a combination of data from limbs, terminators, and control points, and produces shape models that have some important advantages over analytical shape models. Accurate numerical shape models make it feasible to study irregular objects with a wide range of standard scientific analysis techniques. These applications include the determination of moments of inertia and surface gravity, the mapping of surface locations and structural orientations, photometric measurement and analysis, the reprojection and mosaicking of digital images, and the generation of albedo maps. The capabilities of our modeling procedure are illustrated through the development of an accurate numerical shape model for Phobos and the production of a global, high-resolution, high-pass-filtered digital image mosaic of this Martian moon. Other irregular objects that have been modeled, or are being modeled, include the asteroid Gaspra and the satellites Deimos, Amalthea, Epimetheus, Janus, Hyperion, and Proteus.

Simonelli, Damon P.↗

3D Position and Velocity Vector Computations of Objects Jettisoned from the International Space Station Using Close-Range Photogrammetry Approach

Measurement of the jettisoned object departure trajectory and velocity vector in the International Space Station (ISS) reference frame is vitally important for prompt evaluation of the object s imminent orbit. We report on the first successful application of photogrammetric analysis of the ISS imagery for the prompt computation of the jettisoned object s position and velocity vectors. As post-EVA analyses examples, we present the Floating Potential Probe (FPP) and the Russian "Orlan" Space Suit jettisons, as well as the near-real-time (provided in several hours after the separation) computations of the Video Stanchion Support Assembly Flight Support Assembly (VSSA-FSA) and Early Ammonia Servicer (EAS) jettisons during the US astronauts space-walk. Standard close-range photogrammetry analysis was used during this EVA to analyze two on-board camera image sequences down-linked from the ISS. In this approach the ISS camera orientations were computed from known coordinates of several reference points on the ISS hardware. Then the position of the jettisoned object for each time-frame was computed from its image in each frame of the video-clips. In another, "quick-look" approach used in near-real time, orientation of the cameras was computed from their position (from the ISS CAD model) and operational data (pan and tilt) then location of the jettisoned object was calculated only for several frames of the two synchronized movies. Keywords: Photogrammetry, International Space Station, jettisons, image analysis.

Papanyan, Valeri↗

Massively Parallel Bayesian Model Calibration and Uncertainty Quantification with Applications to Nuclear Fuels and Materials

The U.S. Department of Energy (DOE)’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering-scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. Fuel behavior in a nuclear reactor is governed by a complex network of mechanisms interacting with various other physics aspects in the reactor system. Any model developed to represent the fuel behavior will likely be idealized resulting in uncertainties in their predictions compared to the observed data. As such, this report was motivated by the need to identify the sources of uncertainties and quantify and propagate them through the fuel model outputs. Such quantification of uncertainties will establish a level of model trustworthiness, identify approaches to improve the model trustworthiness, and even guide optimal experiment design for maximal information gain. To accomplish the uncertainty quantification for computational models, this report has relied on the Bayesian framework which provides probabilistic treatment of models their inputs and outputs. The current state-of-the-art on performing Bayesian Uncertainty Quantification (UQ) for nuclear engineering models using High Performance Computing (HPC) resources have been reviewed. Implementation of capabilities for massively parallel Bayesian UQ in Multiphysics Object-Oriented Simulation Environment (MOOSE) is discussed. Several verification cases are discussed to verify the accuracy of the quantified uncertainties using the developed computational capabilities in MOOSE. Then, the problem of quantifying the uncertainties in TRI-Structural isOtropic (TRISO) fuel silver release is addressed. For the first time, the uncertainties arising from the TRISO Fission Gas Release (FGR) model due to model inadequacy and experimental noise are quantified. Also, the Bayesian capabilities are applied to the calibration of the MATPRO creep model, a widely used model in several fuel assessment cases. The impact of the prediction uncertainties in the MATPRO model on the fuel cladding behavior as part of the TRIBULATION assessment case (which is an integral effects case) is investigated. This report concludes with a discussion on the future work for the UQ for computational models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Global Reference Atmospheric Model (GRAM) Advancements and Additions

Introduction:The Global Reference Atmospheric Model (GRAM) is one of the most widely used engineering models of the atmosphere. GRAM development and maintenance has been led by NASA Marshall Space Flight Center (MSFC). The NASA Science Mission Directorate (SMD) has provided funding support to upgrade the GRAMs since Fiscal Year 2018. NASA Langley Research Center has been working with MSFC on the upgrades.This presentation will provide details regarding the upgrades that have been made to the existing GRAMs, the development of new GRAMs, as well as the ongoing objectives, tasks, and milestones re-lated to the GRAM upgrades funded by NASA SMD. GRAM: The GRAMs are engineering-oriented atmospheric models that estimate mean values and statistical variations of the atmospheric properties for numerous planetary destinations.They provide mean values and variability for any point in the atmosphere as well as seasonal, geographic, and altitude variations. GRAM outputs include atmospheric density, temperature, pressure, winds, and chemical composition along a user-defined path.Theyhave been widely used by the engineering community because of their ability to create realistic dispersions. GRAMs have been integrated into high fidelity flight dynamic simulations of launch, entry, descent and landing (EDL), aerobraking and aerocapture. MSFC has been developing and updating GRAMs since 1974; GRAMs are currently available for Earth, Mars, Venus, Neptune, and Titan. GRAM Upgrade Status: Code Moderization.The planetary GRAMs are being rearchitected from Fortran to a common object-ori-entedC++ framework called the GRAM Suite. This new architecture creates a common GRAM library of data models and utilities. The first C++ releases of the existing planetary GRAMs (Mars, Venus, Neptune, and Titan-GRAM) in the GRAM Suite are straight conversions from the latest Fortran version. Model Upgrades.The focus of the model upgrade task is to improve the atmosphere models in the existing GRAMs and to establish a foundation for developing GRAMs for additional destinations. The GRAM ephemerishas been upgraded to the NASA Navigation and Ancillary Information Facility (NAIF) SPICE toolkit (version N0066). The calculation of the speed of sound has also been improved in the GRAMs. The GRAM team has received updated Mars General Circulation Model (MGCM) datasets from NASA Ames Research Center. Mars Global Ionosphere-Thermosphere Model (M-GITM) data is being obtained toreplace the Mars Thermospheric General Circulation Model (MTGCM) data in legacy Mars-GRAM. M-GITM and updated MGCM data will be incorporated into a future GRAM Suite release.Twoprojects that will improve the atmospheric model data in the GRAMs have been funded by the GRAM team since Fiscal Year 2020. Sanjay Limaye and Patrick Fry at the University of Wisconsin are reanalyzing the Venus Express radio occultation observations and analyzing the Akatsukiradio occultation observations.This will lead tothe calculation of number density, temperature, and pressure profiles for the 40-90 km altitude range. Kunio Sayanagi, Justin Garland, and Ryan McCabeat Hampton University are developing empirical global models for Venus,Jupiter, Saturn, Uranus, Neptune, and Titan that incorporates the latest data available for each of these planetary destinations. Upgraded GRAM Releases. GRAM Suite Version 1.0 was released in May 2020 and contains the rearchitected Neptune-GRAM, including the common GRAM framework and planet–specific code. GRAM Suite Version 1.1 was released in September 2020 and addedthe rearchitected Titan-GRAM to the GRAM Suite. A User Guide and Programmer’s Manualarereleased with all GRAMs. The rearchitected Mars and Venus-GRAMs will be released in upcomingversions of the GRAM Suite. New GRAM Releases. New GRAMs have been de-veloped for Uranus and Jupiter. Uranus-GRAM is based on an individual profile generated by Gary Allen (ARC) from Voyager 2 occultation data and will be released in GRAM Suite Version 1.2. Jupiter-GRAM is based on individual profile produced from Al Seiff’s Ju-piter model[1].Jupiter-GRAM will be released in GRAM Suite Version 1.3. Saturn-GRAM is currently under development and will be released in a future version of the GRAM Suite. Conclusions: GRAMs are vital and frequently used toolsets. Releases of the GRAM Suite, upgrades of the existing planetary GRAMs, and development of new planetary GRAMs are ongoing. NASA SMD funding has been essential to addressing current limitations and accomplishing GRAM developmental goals. Continua-tion ofSMD fundingwill ensure the development, up-grades, and maintenance of the GRAMs. References: [1] Seiff, A., et al. (1998) JGR, 103, 22,857-22,889. Acknowledgments: The authors gratefully acknowledge support from the NASA SMD

atmospheric models↗

Applying Fortran 90 and Object-Oriented Techniques to Scientific Applications

High-performance parallel computing is having a profound impact on the size and complexity of physical problems which can be modeled. This impact has been a long time in coming, because the learning curve in adapting to this new world of computing is steeper than was imagined.

Fortran 90 parallel computing C++↗

An Object-oriented Computer Code for Aircraft Engine Weight Estimation

Reliable engine-weight estimation at the conceptual design stage is critical to the development of new aircraft engines. It helps to identify the best engine concept amongst several candidates. At NASA Glenn (GRC), the Weight Analysis of Turbine Engines (WATE) computer code, originally developed by Boeing Aircraft, has been used to estimate the engine weight of various conceptual engine designs. The code, written in FORTRAN, was originally developed for NASA in 1979. Since then, substantial improvements have been made to the code to improve the weight calculations for most of the engine components. Most recently, to improve the maintainability and extensibility of WATE, the FORTRAN code has been converted into an object-oriented version. The conversion was done within the NASA s NPSS (Numerical Propulsion System Simulation) framework. This enables WATE to interact seamlessly with the thermodynamic cycle model which provides component flow data such as airflows, temperatures, and pressures, etc. that are required for sizing the components and weight calculations. The tighter integration between the NPSS and WATE would greatly enhance system-level analysis and optimization capabilities. It also would facilitate the enhancement of the WATE code for next-generation aircraft and space propulsion systems. In this paper, the architecture of the object-oriented WATE code (or WATE++) is described. Both the FORTRAN and object-oriented versions of the code are employed to compute the dimensions and weight of a 300- passenger aircraft engine (GE90 class). Both versions of the code produce essentially identical results as should be the case. Keywords: NASA, aircraft engine, weight, object-oriented

Tong, Michael T.↗

An Object-Oriented Computer Code for Aircraft Engine Weight Estimation

Reliable engine-weight estimation at the conceptual design stage is critical to the development of new aircraft engines. It helps to identify the best engine concept amongst several candidates. At NASA Glenn Research Center (GRC), the Weight Analysis of Turbine Engines (WATE) computer code, originally developed by Boeing Aircraft, has been used to estimate the engine weight of various conceptual engine designs. The code, written in FORTRAN, was originally developed for NASA in 1979. Since then, substantial improvements have been made to the code to improve the weight calculations for most of the engine components. Most recently, to improve the maintainability and extensibility of WATE, the FORTRAN code has been converted into an object-oriented version. The conversion was done within the NASA's NPSS (Numerical Propulsion System Simulation) framework. This enables WATE to interact seamlessly with the thermodynamic cycle model which provides component flow data such as airflows, temperatures, and pressures, etc., that are required for sizing the components and weight calculations. The tighter integration between the NPSS and WATE would greatly enhance system-level analysis and optimization capabilities. It also would facilitate the enhancement of the WATE code for next-generation aircraft and space propulsion systems. In this paper, the architecture of the object-oriented WATE code (or WATE++) is described. Both the FORTRAN and object-oriented versions of the code are employed to compute the dimensions and weight of a 300-passenger aircraft engine (GE90 class). Both versions of the code produce essentially identical results as should be the case.

Tong, Michael T.↗

Systems Level Fuel Cycle Modeling in TMAP8 - A Demonstration

The tritium migration analysis program (TMAP) has been used for tritium inventory tracking and analysis for several years, and the Multiphysics Object Oriented Simulation Environment (MOOSE)-based TMAP8 has several improvements over TMAP4 and TMAP7, such as support for multiple dimensions and non-cartesian coordinate systems, as well as interoperability with sub-apps at higher and lower length scales. We demonstrate that TMAP8 has the additional capacity to solve systems-level problems using zero-dimensional ordinary differential equations by reproducing a literature model which describes a systems-level fuel-cycle of tritium inventory in a hypothetical fusion power plant. The capacity to run several coupled multi-scale physics calculations as part of a single package will be necessary for accurate blanket and fuel-cycle design.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗