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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Development of Integrated Mechanical Pods

This presentation highlights early wins, updated progress, and upcoming developments on ‘national-scale shared development platform’ for rapid prototyping, testing and validation of various integrated Mechanical Pod solutions and form factors. Such pod solutions consist of a set of all-electric heat pump mechanical equipment that have integrated functionalities through built-in controls, with heating, cooling, hot water, ventilation (including energy recovery), electrical management, and battery storage within a single package. The presentation draws inspiration from the success of bathroom pods in the US modular construction industry, UK’s efforts with unitizing mechanical systems as ‘utility cupboards’, and VEIC’s early wins in design-build of all-electric Mechanical Pod solutions in Vermont. The presentation includes researchers and partners involved with NREL in Design for Manufacturing and Assembly (DfMA), Virtual Design and Construction (VDC), and digital twin based process optimization modeling of integrated Mechanical Pod solutions. The presentation aims to highlight early wins from such a platform and how various physical and virtual tools are currently being employed as part of NREL’s ongoing multi-year project funded by US DOE. Streamlined procurement, coordination, installation, and O&M of Mechanical Pods such that the majority of work is delegated to the off-site modular factory implies monetary savings. Such a seemingly basic shift in location of the construction process leads to great reduction in complexity, first cost, lead time, and waste, and greater opportunities for innovative compartmentalization and integration of mechanical systems appropriately sized for each apartment or hotel guest room. However, past studies on unitized combination systems show that high installation costs, maintenance issues, challenges with system integration, limitations in existing electrical infrastructure, and lack of architecturally appealing solutions are key barriers. NREL and partners aim to address key barriers through DfMA approach, rapid prototyping and testing, and digital twin process optimization modeling. The presentation is also a call for interested entities to partner with NREL as part of the national-scale development platform, help drive both product and process innovation, and encourage open source sharing of learnings. Learning objectives include (1) learn about the vision of national-scale shared development platform for process-product innovation on integrated mechanical pod solutions and how to get involved, (2) gain an understanding of the components of an all-electric, high performance home, design characteristics and equipment included in an all-electric mechanical pod, integration of mechanical systems within a modular factories’ assembly line, and the system’s commissioning, operation and maintenance. The pre-planning and coordination with the factory and sub-contractors are also highlighted, (3) gain an understanding of using process modeling tools to quantify resource-constrained performance of operations (such as integration of energy efficiency strategies) to manufacture modules of varying design, (4) gain insights on virtual design, rapid prototyping, and emulated testing of various form factors across different climatic conditions. The need for such preliminary testing with open source sharing of learnings will also be highlighted.

30 DIRECT ENERGY CONVERSION↗
NASA NTRS1971

Rotary relay for space power transfer

The power clutch presented is designed for the transfer of electrical signals and power across rotating joints. Radio noise, friction, and wear are virtually eliminated. The design, construction, and applications are discussed. This clutch eliminates the need of recycling solar arrays once each orbit by recycling only a low-inertia component of the power system.

Haynie, H. T.↗
NASA NTRS1999

Virtual Manufacturing Techniques Designed and Applied to Manufacturing Activities in the Manufacturing Integration and Technology Branch

One of the identified goals of EM3 is to implement virtual manufacturing by the time the year 2000 has ended. To realize this goal of a true virtual manufacturing enterprise the initial development of a machinability database and the infrastructure must be completed. This will consist of the containment of the existing EM-NET problems and developing machine, tooling, and common materials databases. To integrate the virtual manufacturing enterprise with normal day to day operations the development of a parallel virtual manufacturing machinability database, virtual manufacturing database, virtual manufacturing paradigm, implementation/integration procedure, and testable verification models must be constructed. Common and virtual machinability databases will include the four distinct areas of machine tools, available tooling, common machine tool loads, and a materials database. The machine tools database will include the machine envelope, special machine attachments, tooling capacity, location within NASA-JSC or with a contractor, and availability/scheduling. The tooling database will include available standard tooling, custom in-house tooling, tool properties, and availability. The common materials database will include materials thickness ranges, strengths, types, and their availability. The virtual manufacturing databases will consist of virtual machines and virtual tooling directly related to the common and machinability databases. The items to be completed are the design and construction of the machinability databases, virtual manufacturing paradigm for NASA-JSC, implementation timeline, VNC model of one bridge mill and troubleshoot existing software and hardware problems with EN4NET. The final step of this virtual manufacturing project will be to integrate other production sites into the databases bringing JSC's EM3 into a position of becoming a clearing house for NASA's digital manufacturing needs creating a true virtual manufacturing enterprise.

Shearrow, Charles A.↗
NASA NTRS2013

Live Virtual Constructive Distributed Test Environment Characterization Report

This report documents message latencies observed over various Live, Virtual, Constructive, (LVC) simulation environment configurations designed to emulate possible system architectures for the Unmanned Aircraft Systems (UAS) Integration in the National Airspace System (NAS) Project integrated tests. For each configuration, four scenarios with progressively increasing air traffic loads were used to determine system throughput and bandwidth impacts on message latency.

UAS↗
NASA NTRS1991

A new active virtual pivot six-degree-of-freedom hand controller for aerospace applications

During 1989 a new six-degree-of-freedom (6-DOF) active hand controller concept was designed and constructed based on the concept of a virtual pivot. This concept, labeled VPHC, was first demonstrated in a 1985 study and a patent was issued in 1990. Operator control input occurs via a force/torque sensor rigidly mounted to the handgrip. Sensed force/torque signals are used by microprocessors to generate motor drive control for each of six independently controlled motors mounted on the three-legged mechanism. The control microprocessor uses input biasing and rate-feedback motor controllers to generate the sensed feel of virtual springs and deadbands found in more conventional designs. An important advantage of this design is that the location of the virtual pivots, reflective forces and torques, breakout force levels, sensed spring rates, and operating modes, can be changed simply by changing the software. This approach yields an autonomous VPHC that can easily adapt itself to an individual operator (by software extension). A proof-of-concept version has been demonstrated, and further improvements are currently being studied and implemented.

Marshall, William C.↗
NASA NTRS2012

Overcoming the Critical Shortage of STEM - Prepared Secondary Students Through Modeling and Simulation

In developing understanding of technological systems - modeling and simulation tools aid significantly in the learning and visualization processes. In design courses we sketch , extrude, shape, refine and animate with virtual tools in 3D. Final designs are built using a 3D printer. Aspiring architects create spaces with realistic materials and lighting schemes rendered on model surfaces to create breathtaking walk-throughs of virtual spaces. Digital Electronics students design systems that address real-world needs. Designs are simulated in virtual circuits to provide proof of concept before physical construction. This vastly increases students' ability to design and build complex systems. We find students using modeling and simulation in the learning process, assimilate information at a much faster pace and engage more deeply in learning. As Pre-Engineering educators within the Career and Technical Education program at our school division's Technology Academy our task is to help learners in their quest to develop deep understanding of complex technological systems in a variety of engineering disciplines. Today's young learners have vast opportunities to learn with tools that many of us only dreamed about a decade or so ago when we were engaged in engineering and other technical studies. Today's learner paints with a virtual brush - scenes that can aid significantly in the learning and visualization processes. Modeling and simulation systems have become the new standard tool set in the technical classroom [1-5]. Modeling and simulation systems are now applied as feedback loops in the learning environment. Much of the study of behavior change through the use of feedback loops can be attributed to Stanford Psychologist Alfred Bandura. "Drawing on several education experiments involving children, Bandura observed that giving individuals a clear goal and a means to evaluate their progress toward that goal greatly increased the likelihood that they would achieve it."

Spencer, Thomas↗
NASA NTRS1989

CCD TV focal plane guider development and comparison to SIRTF applications

It is expected that the SIRTF payload will use a CCD TV focal plane fine guidance sensor to provide acquisition of sources and tracking stability of the telescope. Work has been done to develop CCD TV cameras and guiders at Lick Observatory for several years and have produced state of the art CCD TV systems for internal use. NASA decided to provide additional support so that the limits of this technology could be established and a comparison between SIRTF requirements and practical systems could be put on a more quantitative basis. The results of work carried out at Lick Observatory which was designed to characterize present CCD autoguiding technology and relate it to SIRTF applications is presented. Two different design types of CCD cameras were constructed using virtual phase and burred channel CCD sensors. A simple autoguider was built and used on the KAO, Mt. Lemon and Mt. Hamilton telescopes. A video image processing system was also constructed in order to characterize the performance of the auto guider and CCD cameras.

Rank, David M.↗
NASA NTRS2013

Virtual Construction of Space Habitats: Connecting Building Information Models (BIM) and SysML

Current trends in design, construction and management of complex projects make use of Building Information Models (BIM) connecting different types of data to geometrical models. This information model allow different types of analysis beyond pure graphical representations. Space habitats, regardless their size, are also complex systems that require the synchronization of many types of information and disciplines beyond mass, volume, power or other basic volumetric parameters. For this, the state-of-the-art model based systems engineering languages and processes - for instance SysML - represent a solid way to tackle this problem from a programmatic point of view. Nevertheless integrating this with a powerful geometrical architectural design tool with BIM capabilities could represent a change in the workflow and paradigm of space habitats design applicable to other aerospace complex systems. This paper shows some general findings and overall conclusions based on the ongoing research to create a design protocol and method that practically connects a systems engineering approach with a BIM architectural and engineering design as a complete Model Based Engineering approach. Therefore, one hypothetical example is created and followed during the design process. In order to make it possible this research also tackles the application of IFC categories and parameters in the aerospace field starting with the application upon the space habitats design as way to understand the information flow between disciplines and tools. By building virtual space habitats we can potentially improve in the near future the way more complex designs are developed from very little detail from concept to manufacturing.

space architecture↗
NASA NTRS2019

NASA Centennial Challenge: 3D Printed Habitat, Phase 3 Final Results

NASA's Centennial Challenges program uses prize competitions with the goal of accelerating innovation in the aerospace industry. Competitions in the Centennial Challenges portfolio have previously focused on advancements in space robotics, regolith excavation, bio-printing, astronaut suit design, small satellites, and solar-powered vehicles. NASA's Three Dimensional (3D) Printed Habitat Centennial Challenge represents a partnership between NASA and the non-profit partner: Bradley University, with co-sponsors Caterpillar, Bechtel, Brick and Mortar Ventures, the American Concrete Institute, and the United States Army Corps of Engineers (USACE) Engineer Research and Development Center (ERDC) to spur development in automated additive construction technologies. The challenge asks teams to design and construct a scaled and simulated Martian habitat using indigenous materials and large scale 3D automated printing systems. Phase 1 of the competition, held in 2015, was an architectural design competition for habitat concepts that could be 3D printed. Phase 2, completed in 2017, asked teams to develop feedstocks from indigenous materials and hydrocarbon polymer recyclables, and demonstrate automated printing systems to manufacture these feedstocks into test specimens to assess mechanical strength. This paper will discuss the Phase 3 competition, focusing on technology outcomes that can potentially be infused into both terrestrial and planetary construction applications. The Phase 3 competition was divided into two sub-competitions: 1) virtual construction, where teams created a high fidelity building information model (BIM) of their 3D-printed habitat design and 2) the construction competition, which required teams to 3D print a structural foundation and subject materials samples to freeze/thaw testing and impact testing (level 1), produce a habitat element and complete a hydrostatic test (level 2), and additively manufacture a 1:3 scale habitat onsite in a head to head competition at Caterpillar, inc.'s Edwards Demonstration & Learning Center near Peoria, Illinois over the course of three days (level 3). While the Phase 2 competition focused primarily on the development of novel feedstocks and robotic printing systems, Phase 3 emphasized the scale-up of these systems and autonomous operation (demonstrating the capability to operate systems on precursor missions prior to the arrival of crew, or terrestrially in field operation settings where human tending of a manufacturing system may be limited). The Phase 3 virtual construction levels yielded a number of novel habitat designs, including both modular habitats and vertically-oriented habitat concepts. The Phase 3 construction competition also challenged teams to autonomously place penetrations and interfacing elements in additively manufactured structures. The paper will emphasize potential applications for the new materials and technologies developed under the umbrella of the competition within NASA's portfolio and in Earth-based applications such as disaster response and infrastructure improvement.

Construction↗
NASA NTRS2019

Nasa Centennial Challenge: Three Dimensional (3d) Printed Habitat, Phase 3

NASA's Centennial Challenges program uses prize competitions with the goal of accelerating innovation in the aerospace industry. Competitions in the Centennial Challenges portfolio have previously focused on advancements in space robotics, regolith excavation, bio-printing, astronaut suit design, small satellites, and solar-powered vehicles. NASA's Three Dimensional (3D) Printed Habitat Centennial Challenge represents a partnership between NASA and the non-profit partner: Bradley University, with co-sponsors Caterpillar, Bechtel, Brick and Mortar Ventures, the American Concrete Institute, and the United States Army Corps of Engineers (USACE) Engineer Research and Development Center (ERDC) to spur development in automated additive construction technologies. The challenge asks teams to design and construct a scaled and simulated Martian habitat using indigenous materials and large scale 3D automated printing systems. Phase 1 of the competition, held in 2015, was an architectural design competition for habitat concepts that could be 3D printed. Phase 2, completed in 2017, asked teams to develop feedstocks from indigenous materials and hydrocarbon polymer recyclables, and demonstrate automated printing systems to manufacture these feedstocks into test specimens to assess mechanical strength. This paper will discuss the Phase 3 competition, focusing on technology outcomes that can potentially be infused into both terrestrial and planetary construction applications. The Phase 3 competition was divided into two sub-competitions: 1) virtual construction, where teams created a high fidelity building information model (BIM) of their 3D-printed habitat design and 2) the construction competition, which required teams to 3D print a structural foundation and subject materials samples to freeze/thaw testing and impact testing (level 1), produce a habitat element and complete a hydrostatic test (level 2), and additively manufacture a 1:3 scale habitat onsite in a head to head competition at Caterpillar, inc.'s Edwards Demonstration & Learning Center near Peoria, Illinois over the course of three days (level 3). While the Phase 2 competition focused primarily on the development of novel feedstocks and robotic printing systems, Phase 3 emphasized the scale-up of these systems and autonomous operation (demonstrating the capability to operate systems on precursor missions prior to the arrival of crew, or terrestrially in field operation settings where human tending of a manufacturing system may be limited). The Phase 3 virtual construction levels yielded a number of novel habitat designs, including both modular habitats and vertically-oriented habitat concepts. The Phase 3 construction competition also challenged teams to autonomously place penetrations and interfacing elements in additively manufactured structures. The paper will emphasize potential applications for the new materials and technologies developed under the umbrella of the competition within NASA's portfolio and in Earth-based applications such as disaster response and infrastructure improvement.

Centennial challenge↗
NASA NTRS1996

Using Virtual Simulations in the Design of 21st Century Space Science Environments

Space Technology has been rapidly increasing in the past decade. This can be attributed to the future construction of the International Space Station (ISS). New innovations must constantly be engineered to make ISS the safest, quality, research facility in space. Since space science must often be gathered by crew members, more attention must be geared to the human's safety and comfort. Virtual simulations are now being used to design environments that crew members can live in for long periods of time without harmful effects to their bodies. This paper gives a few examples of the ergonomic design problems that arise on manned space flights, and design solutions that follow NASA's strategic commitment to customer satisfaction. The conclusions show that virtual simulations are a great asset to 21st century design.

Hutchinson, Sonya L.↗
DOE OSTI2022

The Virtual Test Bed (VTB) repository: a library of multiphysics reference reactor models using NEAMS tools

With the next generation of nuclear reactors under development, modeling and simulation (MS) tools are being developed by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in order to support their design, licensing, and future operation. Mirroring the physical test beds currently under construction (i.e., EBR-II and ZPPR), the Virtual Test Bed (VTB) was launched by the National Reactor Innovation Center (NRIC) in collaboration with NEAMS to support the advanced reactor community. This collaborative effort, which involves multiple teams at both Idaho National Laboratory and Argonne National Laboratory aims to use NEAMS tools to model a wide range of reactor designs. Those models are automatically tested to ensure their continued functionality as the tools are further developed. Examples are extensively documented, each acting as a tutorial for applying the relevant NEAMS tools to that reactor design. Currently, five advanced reactor types (with a total of eight specific design variants) are simulated by a variety of different models. These models range from steady-state, core multiphysics simulations to integrated plant analysis during loss-of flow transients. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

The Virtual Test Bed (VTB) Repository: A Library of Multiphysics Reference Reactor Models using NEAMS Tools

With the next generation of nuclear reactors under development, modeling and simulation (M&S) tools are being developed by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in order to support their design, licensing, and future operation. Mirroring the physical test beds currently under construction (i.e., EBR-II and ZPPR), the Virtual Test Bed (VTB) was launched by the National Reactor Innovation Center (NRIC) in collaboration with NEAMS to support the advanced reactor community. This collaborative effort, which involves multiple teams at both Idaho National Laboratory and Argonne National Laboratory aims to use NEAMS tools to model a wide range of reactor designs. Those models are automatically tested to ensure their continued functionality as the tools are further developed. Examples are extensively documented, each acting as a tutorial for applying the relevant NEAMS tools to that reactor design. Currently, five advanced reactor types (with a total of eight specific design variants) are simulated by a variety of different models. These models range from steady-state, core multiphysics simulations to integrated plant analysis during loss-of-flow transients.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS2016

Additive Manufacturing, Design, Testing, and Fabrication: A Full Engineering Experience at JSC

I worked on several projects this term. While most projects involved additive manufacturing, I was also involved with two design projects, two testing projects, and a fabrication project. The primary mentor for these was Richard Hagen. Secondary mentors were Hai Nguyen, Khadijah Shariff, and fabrication training from James Brown. Overall, my experience at JSC has been successful and what I have learned will continue to help me in my engineering education and profession long after I leave. My 3D printing projects ranged from less than a 1 cubic centimeter to about 1 cubic foot and involved several printers using different printing technologies. It was exciting to become familiar with printing technologies such as industrial grade FDM (Fused Deposition Modeling), the relatively new SLA (Stereolithography), and PolyJet. My primary duty with the FDM printers was to model parts that came in from various sources to print effectively and efficiently. Using methods my mentor taught me and the Stratasys Insight software, I was able to minimize imperfections, hasten build time, improve strength for specific forces (tensile, shear, etc...), and reduce likelihood of a print-failure. Also using FDM, I learned how to repair a part after it was printed. This is done by using a special kind of glue that chemically melts the two faces of plastic parts together to form a fused interface. My first goal with SLA technology was to bring the printer back to operational readiness. In becoming familiar with the Pegasus SLA printer, I researched the leveling, laser settings, and different vats to hold liquid material. With this research, I was successfully able to bring the Pegasus back online and have successfully printed multiple sample parts as well as functional parts. My experience with PolyJet technology has been focused on an understanding of the abilities/limits, costs, and the maintenance for daily use. Still upcoming will be experience with using a composite printer that uses FDM technology to print plastic while laying an internal filament of Kevlar or carbon-fiber inside the printed material. It has been incredible being exposed to this range of technologies and I feel very fortunate to be ready for virtually any kind of printing technology I come across in the future. Design work played a part in my internship this term as well. Working with Hai Nguyen, I was able to design a set of testing tips and a test frame for use with an Arcjet. The testing tips will be made of several different materials that will possibly be used in the heat shield of the Orion space craft. These designs included technical drawings that were presented to the fabrication shop. The frame design was created from 80/20 (a popular brand of frame construction equipment) and included an order form with pricing for fabrication. An independent design was also done for the virtual reality lab. This design was to create a hand-controller based on a previous design. This final design was sent directly to a 3D printer without technical drawings. Overall, my design work has given me experience with using 80/20, helped improve my CAD (Computer Aided Design) proficiency, and increased my knowledge of how to set up technical drawings for fabrication. The final role I have played in this internship has been to assist with testing of the inflatable technology materials working Khadijah Shariff. I began the internship assisting with permeability testing with the initial plan to continue the testing independently after training. Unfortunately, the testing apparatus suffered a technical failure and had funding pulled which cancelled that portion of the project. Further testing with inflatable technology continued with tensile testing of various stitching methods. This testing took place over a two-days and concluded successfully. Final testing was to be more tensile testing but of straps used to connect various inflatable sections. Unfortunately, the needed grips for the tensile tests could not be located and put the testing on hold. It is possible this round of testing will still take place by the end of the internship if the grips can be found. Overall, this portion of the internship has helped me become familiar with one kind of permeability test as well as a popular tensile/compression testing machine. Finally, I also had the chance to be trained using a metal lathe for making very small tips for a soldering iron. These tips will be used to melt threaded brass inserts into 3D printed plastic. Working with James Brown, I was able to successfully machine a brass rod down to as little as 0.064 inches plus or minus 0.001 inches. It was very rewarding to learn how to best use the machine and become familiar with a skill that will undoubtedly be used again in the future. I have been told by several professional engineers that learning to use a lathe and mill will be invaluable skills in the field. This knocks 50 percent of that goal off and I look forward to learning the mill at some point in the future. As is apparent with this list of projects, my internship was not focused on a single over-arching goal. Instead, I was able to gain experience in a myriad of very different areas. I feel like my time here was spent bouncing from one project to the next. Though sometimes difficult to switch gears, it was very rewarding to be a part of so much in so little time. My career and education will be positively impacted by what I have learned at JSC. My experience with 3D printing has improved my ability to handle many issues that may come up in the future with multiple different technologies. The design work I took part in, especially creating technical drawings, will help me better present designs to any engineer or shop I will encounter. My testing experience has helped me become familiar with a popular kind of tensile test machine that will likely be similar to the kinds I will encounter in the future. Finally, my experience with fabrication has given me a rare opportunity, as an engineer, to take part in the fabrication of a part. This experience will help me better tailor my future designs for the manufacturing process and has given me an appreciation for detailed/delicate machining work. My experience at JSC has been successful and will continue to assist me for a long time within the engineering field.

Zusack, Steven↗
NASA NTRS1985

PISCES: An environment for parallel scientific computation

The parallel implementation of scientific computing environment (PISCES) is a project to provide high-level programming environments for parallel MIMD computers. Pisces 1, the first of these environments, is a FORTRAN 77 based environment which runs under the UNIX operating system. The Pisces 1 user programs in Pisces FORTRAN, an extension of FORTRAN 77 for parallel processing. The major emphasis in the Pisces 1 design is in providing a carefully specified virtual machine that defines the run-time environment within which Pisces FORTRAN programs are executed. Each implementation then provides the same virtual machine, regardless of differences in the underlying architecture. The design is intended to be portable to a variety of architectures. Currently Pisces 1 is implemented on a network of Apollo workstations and on a DEC VAX uniprocessor via simulation of the task level parallelism. An implementation for the Flexible Computing Corp. FLEX/32 is under construction. An introduction to the Pisces 1 virtual computer and the FORTRAN 77 extensions is presented. An example of an algorithm for the iterative solution of a system of equations is given. The most notable features of the design are the provision for several granularities of parallelism in programs and the provision of a window mechanism for distributed access to large arrays of data.

Pratt, T. W.↗
NASA NTRS2015

RUMS - Realtime Visualization and Evaluation of Live, Virtual, Constructive Simulation Data

This paper describes the tools and display capabilities being developed to visualize aircraft flight and trajectory information that is produced during a distributed Live, Virtual, Constructive (LVC) simulation events involving a mix of manned and unmanned aircraft. This paper discusses the design approach and general software architecture of the Remote User Monitor Service (RUMS) application. The simulations and flight tests are conducted over a nationwide network with components communicating via software gateways that translate the messages and provide a location to access and collect data. The data collected is not only archived for post-processing and analysis, but also processed in real-time by RUMS, which allows dynamic viewing of the information via a web browser. This real-time dynamic viewing of the data allows test conductors and researchers to monitor the health of the distributed system and of the data being collected not only in situ where tests are conducted but also at remote locations.

distributed simulation↗
DOE OSTI2025

Scan2Sim: Software to Convert Network Scans to Emulations

Within operational technology (OT) systems design, the construction of testing environments for simulation is often a tedious, manual process that slows down safety and security evaluations. This document details the design and functionality of Scan2Sim, a program designed to construct high-fidelity topological schematics for OT systems without significant manual human input. Scan2Sim may take as input a detailed network scan of a system, and produces an instruction set to re-create the original scanned network within a virtualized simulation network. This construction is achieved via heuristic methods of machine template selection, which allows for a fast, performant approach to automated environment construction. The current tool is designed to produce topology schematics compatible with the Minimega, a tool designed by Sandia National Laboratories for repeatable experimentation management.

97 MATHEMATICS AND COMPUTING↗