Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “large system simulation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Catalytic Tar Reduction for Assistance in Thermal Conversion of Space Waste for Energy Production

The Trash to Gas (TtG) project investigates technologies for converting waste generated during spaceflight into various resources. One of these technologies was gasification, which employed a downdraft reactor designed and manufactured at NASA's Kennedy Space Center (KSC) for the conversion of simulated space trash to carbon dioxide. The carbon dioxide would then be converted to methane for propulsion and water for life support systems. A minor byproduct of gasification includes large hydrocarbons, also known as tars. Tars are unwanted byproducts that add contamination to the product stream, clog the reactor and cause complications in analysis instrumentation. The objective of this research was to perform reduction studies of a mock tar using select catalysts and choose the most effective for primary treatment within the KSC downdraft gasification reactor. Because the KSC reactor is operated at temperatures below typical gasification reactors, this study evaluates catalyst performance below recommended catalytic operating temperatures. The tar reduction experimentation was observed by passing a model tar vapor stream over the catalysts at similar conditions to that of the KSC reactor. Reduction in tar was determined using gas chromatography. Tar reduction efficiency and catalyst performances were evaluated at different temperatures.

energy conversion↗
NASA NTRS2016

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

Blonigan, Patrick J.↗
NASA NTRS2010

Simulations of Aerosol Microphysics in the NASA GEOS-5 Model

Aerosol-cloud-chemistry interactions have potentially large but uncertain impacts on Earth's climate. One path to addressing these uncertainties is to construct models that incorporate various components of the Earth system and to test these models against data. To that end, we have previously incorporated the Goddard Chemistry, Aerosol, Radiation, and Transport (GOCART) module online in the NASA Goddard Earth Observing System model (GEOS-5). GEOS-5 provides a platform for Earth system modeling, incorporating atmospheric and ocean general circulation models, a land surface model, a data assimilation system, and treatments of atmospheric chemistry and hydrologic cycle. Including GOCART online in this framework has provided a path for interactive aerosol-climate studies; however, GOCART only tracks the mass of aerosols as external mixtures and does not include the detailed treatments of aerosol size distribution and composition (internal mixtures) needed for aerosol-cloud-chemistry-climate studies. To address that need we have incorporated the Community Aerosol and Radiation Model for Atmospheres (CARMA) online in GEOS-5. CARMA is a sectional aerosol-cloud microphysical model, capable of treating both aerosol size and composition explicitly be resolving the aerosol distribution into a variable number of size and composition groupings. Here we present first simulations of dust, sea salt, and smoke aerosols in GEOS-5 as treated by CARMA. These simulations are compared to available aerosol satellite, ground, and aircraft data and as well compared to the simulated distributions in our current GOCART based system.

Colarco, Peter↗
NASA NTRS1976

Ultrahigh-accuracy body-pointing system for the Large Space Telescope

The Large Space Telescope (LST) is a 3-m diffraction-limited telescope. Pointing stability requirements necessary to assure diffraction-limited images are plus or minus 0.005 arc-sec, over possible experiment observation times of several hours. In order to determine whether these stringent pointing requirements could be met, a complex simulation model was defined which consisted of detailed dynamic representations of control moment gyros (CMGs) and reaction wheels (RWs), including their noise characteristics, dynamic sensor representations with sensor noise, shock mounts for the CMG actuators, a detailed representation of an image motion compensation (IMC) system, and a detailed flexible body structural model with all significant vehicle and solar panel bending modes. On the basis of both stability and performance studies utilizing this model, it was determined that a body-pointing system will meet LST requirements in the presence of CMG vibrational disturbances and sensor noise. The recommended system consists of three orthogonally mounted RWs for primary short-term control, and a cluster of CMG actuators for continuous RW desaturation and vehicle maneuvering.

Rybak, S. C.↗
NASA NTRS2005

Vibration Based Crack Detection in a Rotating Disk: Experimental Results - Part 2

This paper describes the experimental results concerning the detection of a crack in a rotating disk. The goal was to utilize blade tip clearance and shaft vibration measurements to monitor changes in the system's center of mass and/or blade deformation behaviors. The concept of the approach is based on the fact that the development of a disk crack results in a distorted strain field within the component. As a result, a minute deformation in the disk's geometry as well as a change in the system's center of mass occurs. Here, a notch was used to simulate an actual crack. The vibration based experimental results failed to identify the existence of a notch when utilizing the approach described above, even with a rather large, circumferential notch (l.2 in.) located approximately mid-span on the disk (disk radius = 4.63 in. with notch at r = 2.12 in.). This was somewhat expected, since the finite element based results in Part 1 of this study predicted changes in blade tip clearance as well as center of mass shifts due to a notch to be less than 0.001 in. Therefore, the small changes incurred by the notch could not be differentiated from the mechanical and electrical noise of the rotor system. Although the crack detection technique of interest failed to identify the existence ofthe notch, the vibration data produced and captured here will be utilized in upcoming studies that will focus on different data mining techniques concerning damage detection in a disk.

Gyekenyesi, Andrew L.↗
NASA NTRSDate not supplied

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^8 determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

J Wayne Mullinax↗
NASA NTRSDate not supplied

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

Quantum Computing↗
NASA NTRSDate not supplied

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

Quantum Computing↗
NASA NTRS1991

Observing system simulation experiments for the laser atmospheric wind sounder using global spectral model

Fundamental to improving the understanding of the total Earth system are increased and improved observations. In the coming decade several spaceborne instrumented platforms will be constructed and implemented. These platforms will, in large, be housing the NASA Earth Observing System (EOS) instrument suite. One of the proposed instruments is a wind profiling system which is currently referred to as the Laser Atmospheric Wind Sounder (LAWS). This instrument will use a CO2 Doppler lidar wind profiler to give wind measurements with a vertical and horizontal resolution which has yet to be seen globally. The LAWS instrument is now a candidate for launch on a NASA EOS-B platform and is fundamental to increasing our understanding of Earth system science. The LAWS data sets will form an integral component of the temporally continuous data base needed for research of the coupled climate systems. This instrument's observations will aid in giving an improved description of the atmospheric circulation, including the transports of energy, momentum, moisture, trace gases, and aerosols. Also, the wind data will be assimilated and used as the initial state for many global forecast models at various operational centers. Results of system simulation experiments are discussed, and future experiments are described.

Rohaly, Gregg↗
NASA NTRS2001

The Effect of Errors in Snow Assimilation on Land Surface Modeling

The accurate portrayal of the hydrological cycle is extremely important in land surface modeling. Central to this effort is the treatment of snow, as errors in the representation of this quantity can impact practically all other modeled quantities through alterations in the water and energy balances. Although land surface model (LSM) simulations can benefit from the assimilation of snow cover and snow depth observations, they can be negatively impacted if such observations contain errors or if a model bias exists in the simulation of surface or soil temperatures. Both cases may lead to excessive melting or growth of snow packs, and to large alterations in both the energy and water balances. Such problems in the snow assimilation process, made evident by the repeated melting and replenishing of snow pack over significant areas of the United States, exists in the Eta Data Assimilation System and is a product of the EDAS system's direct insertion assimilation of snow data. Occurring on a 24 hour cycle, the repeated melting infuses the soil column with a large quantity of water that upsets the hydrological cycle. In an effort to quantify the impacts of such errors in snow assimilation on water and energy budgets, a series of Mosaic LSM simulations were performed over the 12 month period covering October 1998 to October 1999.

Cosgrove, Brian A.↗
NASA NTRS2014

NASA Tech Briefs, June 2014

Topics include: Real-Time Minimization of Tracking Error for Aircraft Systems; Detecting an Extreme Minority Class in Hyperspectral Data Using Machine Learning; KSC Spaceport Weather Data Archive; Visualizing Acquisition, Processing, and Network Statistics Through Database Queries; Simulating Data Flow via Multiple Secure Connections; Systems and Services for Near-Real-Time Web Access to NPP Data; CCSDS Telemetry Decoder VHDL Core; Thermal Response of a High-Power Switch to Short Pulses; Solar Panel and System Design to Reduce Heating and Optimize Corridors for Lower-Risk Planetary Aerobraking; Low-Cost, Very Large Diamond-Turned Metal Mirror; Very-High-Load-Capacity Air Bearing Spindle for Large Diamond Turning Machines; Elevated-Temperature, Highly Emissive Coating for Energy Dissipation of Large Surfaces; Catalyst for Treatment and Control of Post-Combustion Emissions; Thermally Activated Crack Healing Mechanism for Metallic Materials; Subsurface Imaging of Nanocomposites; Self-Healing Glass Sealants for Solid Oxide Fuel Cells and Electrolyzer Cells; Micromachined Thermopile Arrays with Novel Thermo - electric Materials; Low-Cost, High-Performance MMOD Shielding; Head-Mounted Display Latency Measurement Rig; Workspace-Safe Operation of a Force- or Impedance-Controlled Robot; Cryogenic Mixing Pump with No Moving Parts; Seal Design Feature for Redundancy Verification; Dexterous Humanoid Robot; Tethered Vehicle Control and Tracking System; Lunar Organic Waste Reformer; Digital Laser Frequency Stabilization via Cavity Locking Employing Low-Frequency Direct Modulation; Deep UV Discharge Lamps in Capillary Quartz Tubes with Light Output Coupled to an Optical Fiber; Speech Acquisition and Automatic Speech Recognition for Integrated Spacesuit Audio Systems, Version II; Advanced Sensor Technology for Algal Biotechnology; High-Speed Spectral Mapper; "Ascent - Commemorating Shuttle" - A NASA Film and Multimedia Project DVD; High-Pressure, Reduced-Kinetics Mechanism for N-Hexadecane Oxidation; Method of Error Floor Mitigation in Low-Density Parity-Check Codes; X-Ray Flaw Size Parameter for POD Studies; Large Eddy Simulation Composition Equations for Two-Phase Fully Multicomponent Turbulent Flows; Scheduling Targeted and Mapping Observations with State, Resource, and Timing Constraints;

Source record↗
NASA NTRS2021

Impacts of Fully Coupling Land Surface and Flood Models on the Simulation of Large Wetlands’ Water Dynamics: The Case of the Inner Niger Delta

It is known that representing wetland dynamics in land surface modeling improves models ‘capacity to reproduce fluxes and land surface boundary conditions for atmospheric modeling in general circulation models. This study presents the development of the full coupling between the Noah-MP land surface model (LSM) and the HyMAP flood model in the NASA Land Information System and its application over the Inner Niger Delta (IND), a well-known hot-spot of strong land surface-atmosphere interactions in West Africa. Here, we define two experiments at 0.02o spatial resolution over 2002-2018 to quantify the impacts of the proposed developments on simulating IND dynamics. One represents the one-way approach for simulating land surface and flooding processes (1-WAY), i.e., Noah-MP neglects surface water availability, and the proposed two-way coupling (2-WAY), where Noah-MP takes surface water availability into account in the vertical water and energy balance. Results show that accounting for two-way interactions between Noah- MP and HyMAP over IND improves simulations of all selected hydrological variables. Compared to 1-WAY, evapotranspiration derived from 2-WAY over flooding zones doubles, increased by 0.8mm/day, resulting in an additional water loss rate of ~18,900km(exp 3)/year, ~40% drop of wetland extent during wet seasons and major improvement in simulated water level variability at multiple locations. Significant soil moisture increase and surface temperature drop were also observed. Wetland outflows decreased by 35%, resulting in a substantial a Nash-Sutcliffe coefficient improvement, from -0.73 to 0.79. It is anticipated that future developments in water monitoring and water-related disaster warning systems will considerably benefit from these findings.

Augusto Getirana↗
NASA NTRS2011

Non-Venting Thermal and Humidity Control for EVA Suits

Future EVA suits need processes and systems to control internal temperature and humidity without venting water to the environment. This paper describes an absorption-based cooling and dehumidification system as well as laboratory demonstrations of the key processes. There are two main components in the system: an evaporation cooling and dehumidification garment (ECDG) that removes both sensible heat and latent heat from the pressure garment, and an absorber radiator that absorbs moisture and rejects heat to space by thermal radiation. This paper discusses the overall design of both components, and presents recent data demonstrating their operation. We developed a design and fabrication approach to produce prototypical heat/water absorbing elements for the ECDG, and demonstrated by test that these elements could absorb heat and moisture at a high flux. Proof-of-concept tests showed that an ECDG prototype absorbs heat and moisture at a rate of 85 W/ft under conditions that simulate operation in an EVA suit. The heat absorption was primarily due to direct absorption of water vapor. It is possible to construct large, flexible, durable cooling patches that can be incorporated into a cooling garment with this system. The proof-of-concept test data was scaled to calculate area needed for full metabolic loads, thus showing that it is feasible to use this technology in an EVA suit. Full-scale, lightweight absorber/radiator modules have also been built and tested. They can reject heat at a flux of 33 W/ft while maintaining ECDG operation at conditions that will provide a cool and dry environment inside the EVA suit.

Izenson, Mike↗
NASA NTRS2021

System Analysis and Generative Design for Icenode, a Buoyant Vehicle for Measuring Melt Rate Under Ice Shelves

Antarctic ice shelves buttress the Antarctic Ice Sheet from sliding into the ocean, and their collapse could trigger a meter or more of global sea level rise by the end of the century. Current state-of-the-art predictions for ice shelf behavior in a warming climate have large uncertainty, significantly hindered by a lack of in situ melt rate observations under ice shelves, especially near grounding zones. IceNode is a novel robotic vehicle under development at the NASA Jet Propulsion Laboratory to acquire such measurements, but presents a complex design problem owing to the large design space and conflicting performance requirements. Evaluating a preliminary design requires several types of tedious analysis which prevents rapid iteration and exploration of the design space. We present the implementation of a custom system analysis framework which was used to automate analysis such as resource budgeting, mission simulation, mass and buoyancy balancing, and static landing stability analysis of a given design configuration. Using this framework, we selected parameters which had the largest effects on design success and conducted a generative design study in which we programmatically varied a handful of parameters to generate 1540 different design candidates and test them across 160 different environmental scenarios. The custom built system analysis tool enabled rapid development of critical analysis and automated exploration of a large design space to guide preliminary design of the IceNode vehicle.

Gebara, Christine↗
NASA NTRS2016

Coupled Aerosol-Cloud Systems over Northern Vietnam during 7-SEAS BASELInE: A Radar and Modeling Perspective

The 2013 7-SEASBASELInE campaign over northern Southeast Asia (SEA) provided, for the first time ever, comprehensive ground-based W-band radar measurements of the low-level stratocumulus (Sc) systems that often exist during the spring over northern Vietnam in the presence of biomass-burning aerosols. Although spatially limited, ground-based remote sensing observations are generally free of the surface contamination and signal attenuation effects that often hinder space-borne measurements of these low-level cloud systems. Such observations permit detailed measurements of structures and lifecycles of these clouds as part of a broader effort to study potential impacts of these coupled aerosol-cloud systems on local and regional weather and air quality. Introductory analyses of the W-band radar data show these Sc systems generally follow a diurnal cycle, with peak occurrences during the nighttime and early morning hours, often accompanied by light precipitation. Preliminary results from idealized simulations of Sc development over land based on the observations reveal the familiar response of increased numbers and smaller sizes of cloud droplets, along with suppressed drizzle formation, as aerosol concentrations increase. Slight reductions in simulated W-band reflectivity values also are seen with increasing aerosol concentrations and result primarily from decreased droplet sizes. As precipitation can play a large role in removing aerosol from the atmosphere, and thereby improving air quality locally, quantifying feedbacks between aerosols and cloud systems over this region are essential, particularly given the negative impacts of biomass burning on human health in SEA. Such an endeavor should involve improved modeling capabilities along with comprehensive measurements of time-dependent aerosol and cloud profiles.

aerosol cloud interactions↗
NASA NTRS1994

Numerical simulation of helicopter engine plume in forward flight

Flowfields around helicopters contain complex flow features such as large separated flow regions, vortices, shear layers, blown and suction surfaces and an inherently unsteady flow imposed by the rotor system. Another complicated feature of helicopters is their infrared signature. Typically, the aircraft's exhaust plume interacts with the rotor downwash, the fuselage's complicated flowfield, and the fuselage itself giving each aircraft a unique IR signature at given flight conditions. The goal of this project was to compute the flow about a realistic helicopter fuselage including the interaction of the engine air intakes and exhaust plume. The computations solve the Think-Layer Navier Stokes equations using overset type grids and in particular use the OVERFLOW code by Buning of NASA Ames. During this three month effort, an existing grid system of the Comanche Helicopter was to be modified to include the engine inlet and the hot engine exhaust. The engine exhaust was to be modeled as hot air exhaust. However, considerable changes in the fuselage geometry required a complete regriding of the surface and volume grids. The engine plume computations have been delayed to future efforts. The results of the current work consists of a complete regeneration of the surface and volume grids of the most recent Comanche fuselage along with a flowfield computation.

Dimanlig, Arsenio C. B.↗
NASA NTRS2013

Scalable Adaptive Graphics Environment (SAGE) Software for the Visualization of Large Data Sets on a Video Wall

The use of collaborative scientific visualization systems for the analysis, visualization, and sharing of "big data" available from new high resolution remote sensing satellite sensors or four‐dimensional numerical model simulations is propelling the wider adoption of ultra‐resolution tiled display walls interconnected by high speed networks. These systems require a globally connected and well‐integrated operating environment that provides persistent visualization and collaboration services. This abstract and subsequent presentation describes a new collaborative visualization system installed for NASA's Shortterm Prediction Research and Transition (SPoRT) program at Marshall Space Flight Center and its use for Earth science applications. The system consists of a 3 x 4 array of 1920 x 1080 pixel thin bezel video monitors mounted on a wall in a scientific collaboration lab. The monitors are physically and virtually integrated into a 14' x 7' for video display. The display of scientific data on the video wall is controlled by a single Alienware Aurora PC with a 2nd Generation Intel Core 4.1 GHz processor, 32 GB memory, and an AMD Fire Pro W600 video card with 6 mini display port connections. Six mini display‐to‐dual DVI cables are used to connect the 12 individual video monitors. The open source Scalable Adaptive Graphics Environment (SAGE) windowing and media control framework, running on top of the Ubuntu 12 Linux operating system, allows several users to simultaneously control the display and storage of high resolution still and moving graphics in a variety of formats, on tiled display walls of any size. The Ubuntu operating system supports the open source Scalable Adaptive Graphics Environment (SAGE) software which provides a common environment, or framework, enabling its users to access, display and share a variety of data‐intensive information. This information can be digital‐cinema animations, high‐resolution images, high‐definition video‐teleconferences, presentation slides, documents, spreadsheets or laptop screens. SAGE is cross‐platform, community‐driven, open‐source visualization and collaboration middleware that utilizes shared national and international cyberinfrastructure for the advancement of scientific research and education.

Jedlovec, Gary↗
NASA NTRS1992

A domain-specific design architecture for composite material design and aircraft part redesign

Advanced composites have been targeted as a 'leapfrog' technology that would provide a unique global competitive position for U.S. industry. Composites are unique in the requirements for an integrated approach to designing, manufacturing, and marketing of products developed utilizing the new materials of construction. Numerous studies extending across the entire economic spectrum of the United States from aerospace to military to durable goods have identified composites as a 'key' technology. In general there have been two approaches to composite construction: build models of a given composite materials, then determine characteristics of the material via numerical simulation and empirical testing; and experience-directed construction of fabrication plans for building composites with given properties. The first route sets a goal to capture basic understanding of a device (the composite) by use of a rigorous mathematical model; the second attempts to capture the expertise about the process of fabricating a composite (to date) at a surface level typically expressed in a rule based system. From an AI perspective, these two research lines are attacking distinctly different problems, and both tracks have current limitations. The mathematical modeling approach has yielded a wealth of data but a large number of simplifying assumptions are needed to make numerical simulation tractable. Likewise, although surface level expertise about how to build a particular composite may yield important results, recent trends in the KBS area are towards augmenting surface level problem solving with deeper level knowledge. Many of the relative advantages of composites, e.g., the strength:weight ratio, is most prominent when the entire component is designed as a unitary piece. The bottleneck in undertaking such unitary design lies in the difficulty of the re-design task. Designing the fabrication protocols for a complex-shaped, thick section composite are currently very difficult. It is in fact this difficulty that our research will address.

Punch, W. F., III↗