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At least 109 records · Page 6

Streamlining GNC Architecture Development and FSW Integration forthe Mars Ascent Vehicle

The Mars Ascent Vehicle (MAV) will be the first vehicle to perform an ascent from the surface ofanother atmospheric planetary body outside of the Earth-Moon system. Significant light-time delayrequires complete autonomy of flight throughout ascent, and naturally a high level of reliability isdesired in both MAV’s hardware and software subsystems. The MAV Guidance, Navigation and Controls(GNC) team and the MAV Flight Software (FSW) team have partnered together to improve the efficiencyof algorithm integration onto the MAV flight processor, and to increase confidence that said integrationis successful and without human error. An interface architecture is proposed for the GNC suite thatallows both the guidance and navigation subsystems to provide code algorithms directly in C++, and thecontrols subsystem to provide MATLAB Simulink auto-coded algorithms. Several continuous integration/deployment (CI/CD) methodologies have been considered for ease of transition of algorithm code fromthe GNC team to the FSW team. The GNC/FSW teams also worked together to develop a cFS-friendlywrapper which abstracts the integration of the GNC algorithm code into an interface-level API that iscompatible with cFS. Several iterations of vehicle GNC code have been produced between the GNC/FSWteam’s partnership, and this strong interface between these two teams have allowed the GNC/FSWteams to greatly increase confidence of efficient and error-free implementation of the GNC code ontoMAV for a successful flight.

GNC↗

Streamlining GNC Architecture Development and FSW Integration for the Mars Ascent Vehicle

The Mars Ascent Vehicle (MAV) will be the first vehicle to perform an ascent from the surface of another atmospheric planetary body outside of the Earth-Moon system. Significant light-time delay requires complete autonomy of flight throughout ascent, and naturally a high level of reliability is desired in both MAV’s hardware and software subsystems. The MAV Guidance, Navigation and Controls (GNC) team and the MAV Flight Software (FSW) team have partnered together to improve the efficiency of algorithm integration onto the MAV flight processor, and to increase confidence that said integration is successful and without human error. An interface architecture is proposed for the GNC suite that allows both the guidance and navigation subsystems to provide code algorithms directly in C++, and the controls subsystem to provide MATLAB Simulink auto-coded algorithms. Several continuous integration/deployment (CI/CD) methodologies have been considered for ease of transition of algorithm code from the GNC team to the FSW team. The GNC/FSW teams also worked together to develop a cFS-friendly wrapper which abstracts the integration of the GNC algorithm code into an interface-level API that is compatible with cFS. Several iterations of vehicle GNC code have been produced between the GNC/FSW team’s partnership, and this strong interface between these two teams have allowed the GNC/FSW teams to greatly increase confidence of efficient and error-free implementation of the GNC code onto MAV for a successful flight.

Engineering↗

Emulation of Core Flight System Applications for Flight Software Development and Validation

The Mars Sample Return (MSR) campaign is an unprecedented attempt in the return of Martian samples back to Earth. The ascent from the surface will be performed by the Mars Ascent Vehicle (MAV), a critical element in the mission that National Aeronautics and Space Administration (NASA) Marshall Space Flight Center (MSFC) is developing. To this end, innovations in flight software development, verification, and validation are occurring. The MAV flight computer will run Core Flight System (cFS), an open-source software environment developed by NASA Goddard Space Flight Center (GSFC). NASA Marshall’s MAV Mission and Fault Management (M&FM) Team has implemented an emulation of two applications of this architecture: Limit Checker and Stored Command. Using an emulation of the functionalities of these applications allows for rapid prototyping of table-based algorithms. Further, M&FM is leveraging an in-house, low-fidelity but high-throughput State Analysis Model (SAM), an integrated MATLAB Stateflow Plant and Software model. This model is run in parallel with the cFS emulation for full flyout testing of the M&FM algorithms, verification of intent of these algorithms, and for future auto-generation of application-ingestible M&FM tables. The tables can then be delivered to the MAV Flight Software (FSW) team in a seamless process, reducing the cost of traditional FSW development and the risk of starting M&FM FSW development at later points in the NASA program life cycle.

Cody Wheeler↗

Emulation of Core Flight System Applications for Flight Software Development and Validation

The Mars Sample Return (MSR) campaign is an unprecedented attempt in the return of Martian samples back to Earth. The ascent from the surface will be performed by the Mars Ascent Vehicle (MAV), a critical element in the mission that National Aeronautics and Space Administration (NASA) Marshall Space Flight Center (MSFC) is developing. To this end, innovations in flight software development, verification, and validation are occurring. The MAV flight computer will run Core Flight System (cFS), an open-source software environment developed by NASA Goddard Space Flight Center (GSFC). NASA Marshall’s MAV Mission and Fault Management (M&FM) Team has implemented an emulation of two applications of this architecture: Limit Checker and Stored Command. Using an emulation of the functionalities of these applications allows for rapid prototyping of table-based algorithms. Further, M&FM is leveraging an in-house, low-fidelity but high-throughput State Analysis Model (SAM), an integrated MATLAB Stateflow Plant and Software model. This model is run in parallel with the cFS emulation for full flyout testing of the M&FM algorithms, verification of intent of these algorithms, and for future auto-generation of application-ingestible M&FM tables. The tables can then be delivered to the MAV Flight Software (FSW) team in a seamless process, reducing the cost of traditional FSW development and the risk of starting M&FM FSW development at later points in the NASA program life cycle.

Cody Wheeler↗

Mars Ascent Vehicle GNC Targeting Routines with Considerations for Flight Software Development

The Mars Ascent Vehicle (MAV) will be the first vehicle to perform an ascent from the surface of another atmospheric planetary body outside of the Earth-Moon system. Significant light-time delay requires complete autonomy of flight throughout ascent, and naturally a high level of reliability is desired in both MAV’s hardware and software subsystems. The MAV Guidance, Navigation and Controls (GNC) team and the MAV Flight Software (FSW) team have partnered together to improve the efficiency of algorithm integration onto the MAV flight processor, and to increase confidence that said integration is successful and without human error. An interface architecture is proposed for the GNC suite that allows both the guidance and navigation subsystems to provide code algorithms directly in C++, and the controls subsystem to provide MATLAB Simulink auto-coded algorithms. Several continuous integration/deployment (CI/CD) methodologies have been considered for ease of transition of algorithm code from the GNC team to the FSW team. The GNC/FSW teams also worked together to develop a cFS-friendly wrapper which abstracts the integration of the GNC algorithm code into an interface-level API that is compatible with cFS. Several iterations of vehicle GNC code have been produced between the GNC/FSW team’s partnership, and this strong interface between these two teams have allowed the GNC/FSW teams to greatly increase confidence of efficient and error-free implementation of the GNC code onto MAV for a successful flight.

Jason Everett↗

Celestial Navigation in Cislunar Space with autoNGC

Celestial navigation (CelNav) is a source of navigation observables where images of known solar system bodies are used to locate a spacecraft, beneficial within the solar system for both cislunar and deep space missions. CelNav provides a variety of design benefits to support and enable current and new autonomous space operations- using only a camera and a processor to produce in-situ measurements for navigation. This technology reduces subscription to ground-based tracking during all phases of a mission, freeing up resources for other operational needs. This also supports secure navigation since it eliminates the need for ground contact. CelNav enables missions where the light time delay between Earth and the spacecraft is too long (or the Earth to spacecraft line of sight is obscured) to support critical operations. It also enables smaller mission classes, where Deep Space Network (DSN)time is cost prohibitive, to reduce its cost by focusing primarily on data downlink. Finally, it enables the NASA Artemis program and other cislunar human space flight by providing redundant navigation to traditional radiometric tracking. In this presentation, we discuss the implementation of a CelNav app in autonomous Navigation, Guidance, and Control (autoNGC), a comprehensive flight software suite for onboard autonomy that is built on the core Flight System (cFS). The presentation also summarizes the results of flight software-in-the-loop (SIL) and processor-in-the-loop (PIL) demonstrations. Both are high-fidelity simulations with the use of a camera emulator hosted on a GPU server that simulates images that would be captured by the camera. The CelNav app leverages the use of cGIANT (cFS Goddard Image Analysis and Navigation Tool).Previously developed for the autoNGC software suite, cGIANT is an onboard autonomous image processing and optical navigation (OpNav) tool that performs limb-based OpNav and Terrain Relative Navigation. The added CelNav capability of cGIANT generates bearing measurements to multiple known celestial bodies (planets, moons, asteroids, comets, etc.) in monocular (2D) images. These observables are then fed to the Goddard Enhanced Onboard Navigation System (GEONS)navigation filter app, enabling us to navigate the spacecraft autonomously. In early 2025, the autoNGC CelNav capability is planned to be flight tested as part of the onboard autonomy experiment on the Cislunar Autonomous Positioning System Technology Operations and Navigation Experiment(CAPSTONE) spacecraft that is currently in a Lunar Near Rectilinear Halo Orbit(NRHO).

celestial navigation↗

Coupled geomechanical investigation of depletion-induced fault reactivation

Fault reactivation during subsurface fluid production pose significant challenges to safe and sustainable resource extraction. Here, this study presents a three-dimensional coupled geomechanical framework to investigate the processes driving fault reactivation, capturing the interactions between reservoir dynamics and geomechanical responses. Verification against theoretical estimations based on linear poroelasticity confirms the model's capacity in representing reservoir background stress responses. However, the study reveals that relying solely on background stress states can underestimate or overestimate fault reactivation potential, emphasizing the importance of including localized stress perturbations such as differential compaction and stress redistribution. Applied to a fault (M1) inspired by the geological characteristics of the Groningen field, the model shows slip initiation at 2965 m depth with 16.0 MPa depletion, aligning with field observations where seismicity occurred at approximately 3 km depth after 15.8 MPa depletion. Parametric studies reveal: (1) inelastic reservoir compaction delays fault reactivation and mitigates fault slip by reducing stress concentration, (2) higher intermediate in-situ stress magnitudes decrease the Coulomb Failure Stress (CFS) increase rate and reduce fault slip, (3) larger fault offsets amplify shear stress near the offset zone, promoting earlier reactivation and longer rupture propagation, and (4) fault permeability significantly influences pressure diffusion, with low-permeability faults leading to sharper stress changes and earlier fault destabilization. These insights highlight the critical role of geological and mechanical parameters in fault reactivation and provide a predictive framework for mitigating induced seismicity risks.

Coupled geomechanical modeling↗

The effect on soot and its gas precursors of doping ethylene with 2,2,4,6,6-pentamethyl-heptane in the nitrogen-fuel stream of a laminar non-premixed Planar Mixing Layer Flame (PMLF)

Synthetic Aviation Turbine Fuels (SATFs) are promising for reducing soot emissions from the aviation sector and diversifying Jet Fuel (JF) sources. Accurately predicting the combustion and emissions behavior of SATFs (and other JFs) necessitates robust experimental databases to elucidate the chemistry of long-chain iso-paraffins, which can compose up to two-thirds of SATF blends and whose behavior is considered to be well-represented by that of iso-dodecane isomers. Here, this study characterizes two laminar non-premixed Planar Mixing Layer Flames (PMLFs) with mild soot loads fueled by nitrogen-diluted ethylene, pure and doped with 2,2,4,6,6-pentamethyl-heptane, respectively. The two PMLFs have the same stoichiometric mixture fraction and total hydrocarbon mole fraction in the fuel stream (X F,F =X C2H4,F +X C12H26,F = 0.260), resulting in nearly the same maximum temperature (T max ≈1800 K) and simple identification of the effects of doping. Importantly, any horizontal PMLF cross-section has a self-similar structure that can be modeled as an equivalent One-Dimensional Counterflow Flame (1D-CF) with vanishingly small strain rate (a). The cross-section at a Height Above the Burner (HAB) of 50 mm is characterized in terms of C 0 -C 18 gas species using capillary sampling followed by GC-MS analyses. Laser-Induced Emission Spectroscopy (LIES) quantifies the soot volume fraction (ƒ v ) profiles at HAB=25 and 50 mm where Elastic Laser Light Scattering (E-LLS) is performed to determine the a of the equivalent 1D-CFs and the profile of the E-LLS equivalent diameter ( d 6,3 ) of soot. The substitution of 1500 ppm of ethylene with 2,2,4,6,6-pentamethyl-heptane causes an increase of ≈1.5 in the concentrations of several polycyclic aromatic hydrocarbons and fv. Concurrently, the measured d 6,3 doubles in the oxidizer stream, yet remains the same in the fuel stream, at HAB=50 mm. Instead, at HAB= 25 mm, the iso-dodecane doping does not affect the d 6,3 profile in either stream. The experimental results partially validate the chemical reactions and soot formation kinetic model developed at Lawrence Livermore National Laboratory and provide directions to further improve its predictions.

Iso-dodecane (2,2,4,6,6-Pentamethyl-Heptane)↗

Interplay of superconducting, metallic, and crystalline states of composite fermions at 𝜈 = $\frac{1}{6}$ in wide quantum wells

Evidence for developing fractional quantum Hall effect (FQHE) at filling fraction 𝜈 = 1/6 and 1/8 was recently reported in wide GaAs quantum wells [Wang et al., Phys. Rev. Lett. 134, 046502 (2025)]. In this article, we theoretically investigate the nature of the state at 𝜈 = 1/6 as a function of the quantum well width and the density by considering composite-fermion (CF) crystals, CF Fermi sea, and various kinds of paired CF states. The 𝑓-wave paired state has the lowest energy among the paired CF states. However, for parameters of interest, the energies of the CF crystal, the CF Fermi liquid, and the 𝑓-wave paired CF state are too close to distinguish. We, therefore, predict that 𝑖𝑓 the FQHE at 𝜈 = 1/6 is experimentally confirmed, this state would be an 𝑓-wave paired state of CFs, which can be verified by measurement of its thermal Hall conductance. Exact diagonalization studies on clean systems with up to eight electrons show that the ground states at 𝜈 = 𝑛/(6⁢𝑛 ± 1) are incompressible for all widths and densities we have considered, and are well described by the corresponding Laughlin and Jain states. We propose a phase diagram for large quantum well widths and densities in which at zero disorder, incompressible FQHE states are stabilized at 𝜈 = 𝑛/(6⁢𝑛 ± 1) and 𝜈 = 1/6, but in between these fillings the CF crystal is stabilized. We also present a qualitative discussion on the effects of disorder and propose a schematic phase diagram based on it. With disorder, which creates a spatial variation in the filling factor, two regimes are identified: (i) for small disorder, when the incompressible states percolate at the special fillings, FQHE with quantized Hall plateaus and vanishing longitudinal resistance should occur; and (ii) for larger disorder, when the CF crystal percolates, the longitudinal resistance rises with decreasing temperature but the domains of FQHE liquid produce minima at the special filling factors. Here, experiments are consistent with the latter scenario. We also mention a possible connection of the phase diagram presented here to a puzzling behavior observed for the fractional quantum anomalous Hall effect in pentalayer graphene.

Composite fermions↗

Splitting of the Girvin-MacDonald-Platzman Density Wave and the Nature of Chiral Gravitons in the Fractional Quantum Hall Effect

A fundamental manifestation of the nontrivial correlations of an incompressible fractional quantum Hall (FQH) state is that an electron added to it disintegrates into more elementary particles, namely fractionally-charged composite fermions (CFs). We show here that the Girvin-MacDonald-Platzman (GMP) density-wave excitation of the 𝜈=𝑛/(2⁢𝑝⁢𝑛±1) FQH states also splits into more elementary single CF excitons. In particular, the GMP graviton, which refers to the recently observed spin-2 neutral excitation in the vanishing wave vector limit [Liang et al., Nature 628, 78 (2024)], remains undivided for 𝜈 =𝑛/(2⁢𝑛 ±1) but splits into two gravitons at 𝜈 =𝑛/(4⁢𝑛 ±1) with 𝑛 >1. Here, a detailed experimental confirmation of the many observable consequences of the splitting of the GMP mode should provide a unique window into the correlations underlying the FQH effect.

Composite fermions↗

Magnetic Bearing Pumps for Molten Salt Fusion Energy Devices

The Commonwealth Fusion Systems (CFS) ARC reactor will employ a novel liquid immersion blanket design that uses a molten lithium salt as both the tritium-breeding material and the vacuum vessel coolant. fluoride lithium beryllium (FLiBe) (a lithium fluoride–beryllium difluoride mixture) is currently the leading salt candidate. Its low-Z components provide good moderation, it has adequate heat transfer properties and low electrical conductivity, and it has good neutron multiplication properties, which further enhance tritium production.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Oxide Dispersion Strengthened Ferritic Steel Wire Feedstock Development for Larger Format Additive Manufacturing (CRADA Final Report)

This CRADA project funded through DOE’s INFUSE program sought to demonstrate the viability of fabricating large, complex parts from oxide dispersion strengthened (ODS) steel with advanced manufacturing. Exhibiting excellent radiation tolerance and high mechanical performance at elevated temperatures, ODS steel is a promising structural material candidate for near-plasma components in fusion energy systems. Its use, however, has been limited by a lack of manufacturability. This project sought to produce ODS steel wire through a solid-state shear assisted extrusion process and then demonstrate that the wire can undergo controlled local melting while being welded with the final part sufficiently retaining the beneficial properties of ODS steel. This would allow the use of wire-arc additive manufacturing (WAAM) to manufacture large-scale ODS parts, even though ODS is currently only available as a powder. WAAM is a promising technique for producing components like the replaceable ARC vacuum vessel in CFS’ fusion reactor design. Meanwhile, this project will also expand PNNL’s capability in producing custom wire feedstock with friction extrusion, enabling downstream large-scale manufacturing with WAAM and solid-state based additive manufacturing. The project achieved its goals of developing tooling and fixturing to produce ODS wire at smaller diameters than previous projects. Several small lengths of wire of 1.5 mm and 2.5 mm diameter in the range of 2.5-30 mm long were produced at tool temperatures that are known to cause ODS particle coarsening (~1200 °C). Fixtures and tooling for longer (>1 m) wires were developed but further process development is needed reduce tool temperature during extrusions and to increase wire length needed for WAAM testing and development.

36 MATERIALS SCIENCE↗

PPPL Report on Reduced Modeling of Fusion Alpha Transport in ARC Burning Plasmas

We are reporting on the modeling of fusion alpha particle transport in the planned ARC fusion device being designed by the CFS (Commonwealth Fusion Systems: https://cfs.energy). The ARC tokamak is designed to operate in a burning-plasma regime characterized by a substantial population of fusion-born alpha particles. Alfvén eigenmode (AE) stability is assessed both analytically and numerically, incorporating alpha-particle drive, ion Landau, and radiative damping from thermal species and collisional damping from trapped electrons. Regions of unstable and near-threshold AE activity are mapped across ARC’s operational parameter space. Linear stability analysis with NOVA indicates multiple, often marginally unstable AEs, extending to toroidal mode numbers up to n= 30. The present report focuses on the ARC flat-top operating point prior to the sawtooth event. Alpha-particle transport on timescales exceeding the neoclassical slowing-down time is assessed using the NUBEAM module [1][2] of the TRANSP code [3], employing transport coefficients derived from the RBQ quasilinear modeling (cf. Appendix B). These global simulations identify favorable and unfavorable operating regimes with respect to alpha confinement, pressure redistribution, and overall alpha-heating efficiency. We also evaluate additional transport mechanisms—including neoclassical tearing mode (TM)–induced stochasticity, sawtooth-driven redistribution, and toroidal-field ripple using the kick model (cf. Appendix C) which makes use of the guiding-center code ORBIT, see Section 5. The kick model is integrated into TRANSP to enable self-consistent predictions of alpha-driven current formation and sustainment within the ARC scenario. Sensitivity scans are performed over the mode frequency, rational-surface alignment, island width, mode amplitude, and proximity of the limiter to the plasma. Our study provides an initial, physics-based guidance for machine design, operational planning, and equilibrium control, ensuring adequate alpha confinement and robust self-heating performance in ARC. Our simulations mostly targeted worst case scenarios, e.g. for TMs and sawteeth. Overall, we expect benign effects for the ARC scenario investigated in this work on fusion alpha confinement and losses in the presence of AEs, tearing modes and sawteeth. This report addresses three thrusts identified at the outset. The first thrust focuses on analytic estimates of the parametric dependencies of EP relaxation based on local AE stability simulations (Section 3). The second thrust involves global evaluations of AE stability using the NOVA, RBQ, and NUBEAM codes (Section 4). Finally, we investigate alpha-particle transport driven by low-frequency instabilities associated with sawteeth and tearing modes (Section 5).

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

High-resolution continuum observations of the Sun

The aim of the PFI or photometric filtergraph instrument is to observe the Sun in the continuum with as high resolution as possible and utilizing the widest range of wavelengths. Because of financial and political problems the CCD was eliminated so that the highest photometric accuracy is only obtainable by comparison with the CFS images. Presently there is a limitation to wavelengths above 2200 A due to the lack of sensitivity of untreated film below 2200 A. Therefore the experiment at present consists of a film camera with 1000 feet of film and 12 filters. The PFI experiments are outlined using only two cameras. Some further problems of the experiment are addressed.

Zirin, Harold↗

Diskoseismology: Probing accretion disks. II - G-modes, gravitational radiation reaction, and viscosity

A scalar potential is used to derive a single partial differential equation governing the oscillation of a disk. The eigenfunctions and eigenfrequencies of a variety of disk models are found to fall into two main classes which are analogous to the p-modes and g-modes in the sun. Specifically, the eigenfunctions and eigenfrequencies of isothermal disks are computed, and the way in which these results can be generalized to other disk models is indicated. The (assumed) relatively small rates of growth or damping of the modes due to various mechanisms, in particular gravitational radiation reaction and parameterized models of viscosity are also computed. It is found that for certain parameters the p-modes are unstable to gravitational radiation reaction (CFS instability), while both the p-modes and g-modes are unstable to viscosity unless highly anisotropic viscosity models are considered.

Nowak, Michael A.↗

Requirements for a network storage service

Sandia National Laboratories provides a high performance classified computer network as a core capability in support of its mission of nuclear weapons design and engineering, physical sciences research, and energy research and development. The network, locally known as the Internal Secure Network (ISN), was designed in 1989 and comprises multiple distributed local area networks (LAN's) residing in Albuquerque, New Mexico and Livermore, California. The TCP/IP protocol suite is used for inner-node communications. Scientific workstations and mid-range computers, running UNIX-based operating systems, compose most LAN's. One LAN, operated by the Sandia Corporate Computing Directorate, is a general purpose resource providing a supercomputer and a file server to the entire ISN. The current file server on the supercomputer LAN is an implementation of the Common File System (CFS) developed by Los Alamos National Laboratory. Subsequent to the design of the ISN, Sandia reviewed its mass storage requirements and chose to enter into a competitive procurement to replace the existing file server with one more adaptable to a UNIX/TCP/IP environment. The requirements study for the network was the starting point for the requirements study for the new file server. The file server is called the Network Storage Services (NSS) and is requirements are described in this paper. The next section gives an application or functional description of the NSS. The final section adds performance, capacity, and access constraints to the requirements.

Kelly, Suzanne M.↗

Requirements for a network storage service

Sandia National Laboratories provides a high performance classified computer network as a core capability in support of its mission of nuclear weapons design and engineering, physical sciences research, and energy research and development. The network, locally known as the Internal Secure Network (ISN), comprises multiple distributed local area networks (LAN's) residing in New Mexico and California. The TCP/IP protocol suite is used for inter-node communications. Scientific workstations and mid-range computers, running UNIX-based operating systems, compose most LAN's. One LAN, operated by the Sandia Corporate Computing Computing Directorate, is a general purpose resource providing a supercomputer and a file server to the entire ISN. The current file server on the supercomputer LAN is an implementation of the Common File Server (CFS). Subsequent to the design of the ISN, Sandia reviewed its mass storage requirements and chose to enter into a competitive procurement to replace the existing file server with one more adaptable to a UNIX/TCP/IP environment. The requirements study for the network was the starting point for the requirements study for the new file server. The file server is called the Network Storage Service (NSS) and its requirements are described. An application or functional description of the NSS is given. The final section adds performance, capacity, and access constraints to the requirements.

Kelly, Suzanne M.↗

Electromagnetic scattering calculations on the Intel Touchstone Delta

During the first year's operation of the Intel Touchstone Delta system, software which solves the electric field integral equations for fields scattered from arbitrarily shaped objects has been transferred to the Delta. To fully realize the Delta's resources, an out-of-core dense matrix solution algorithm that utilizes some or all of the 90 Gbyte of concurrent file system (CFS) has been used. The largest calculation completed to date computes the fields scattered from a perfectly conducting sphere modeled by 48,672 unknown functions, resulting in a complex valued dense matrix needing 37.9 Gbyte of storage. The out-of-core LU matrix factorization algorithm was executed in 8.25 h at a rate of 10.35 Gflops. Total time to complete the calculation was 19.7 h-the additional time was used to compute the 48,672 x 48,672 matrix entries, solve the system for a given excitation, and compute observable quantities. The calculation was performed in 64-b precision.

Cwik, Tom↗