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At least 19 records

LLNL contributions to MPD thrusters for SEI

Some of the topics covered with respect to the Lawrence Livermore National Laboratory's (LLNL's) contributions to Magnetoplasmadynamic (MPD) Thrusters for the Space Exploration Initiative (SEI) include: an IR camera, plasma-induced erosion/redeposition, the Mirror Fusion Test Facility-B (MFTF-B), the Thruster Lifetime Test Facility, the RACE Compact Torus Accelerator Facility, and a RACE program summary. Some of the other topics addressed include: flux contours for HAM simulation, comparison of RACE data of plasma ring formation with the HAM 2-D magnetohydrodynamic code, and the 2-D Ring Acceleration Code (TRAC).

Hooper, Edwin Bickford↗

Effects of stratospheric aerosol surface processes on the LLNL two-dimensional zonally averaged model

We have investigated the effects of incorporating representations of heterogeneous chemical processes associated with stratospheric sulfuric acid aerosol into the LLNL two-dimensional, zonally averaged, model of the troposphere and stratosphere. Using distributions of aerosol surface area and volume density derived from SAGE II satellite observations, we were primarily interested in changes in partitioning within the Cl- and N- families in the lower stratosphere, compared to a model including only gas phase photochemical reactions. We have considered the heterogeneous hydrolysis reactions N2O5 + H2O(aerosol) yields 2 HNO3 and ClONO2 + H2O(aerosol) yields HOCl + HNO3 alone and in combination with the proposed formation of nitrosyl sulfuric acid (NSA) in the aerosol and its reaction with HCl. Inclusion of these processes produces significant changes in partitioning in the NO(y) and ClO(y) families in the middle stratosphere.

Connell, Peter S.↗

Laboratory Astrophysics at the LLNL Electron Beam Ion Traps: EBIT-I and EBIT-II

In order to provide a complete, accurate set of atomic data for interpreting spectra provided by missions such as XMM-Newton, the Chandra X-Ray Observatory, and Astro-E2, we have harnessed the Lawrence Livermore National Laboratory's electron beam ion traps EBIT-I. EBIT-II, and Super-EBIT for laboratory astrophysics. In support of this work we have developed a number of unique techniques, including the ability to experimentally simulate a Maxwellian distribution of electron energies and measuring low-energy charge exchange cross sections using the magnetic trapping mode. We have also built and operated a full suite of spectrometers spanning the 1-7000 Angstrom wavelength band, the most recent being a spectrometer based on a spare Astro-E (6 x 6) microcalorimeter array. Results of our efforts include a complete list of wavelengths of the Fe L-shell transitions, measurements of absolute and relative cross sections for direct impact, dielectronic, and resonance excitation, and measurements of low energy charge transfer reactions. A brief overview of the LLNL ebit facility, its capabilities, and some results will be discussed.

Brown, G. V.↗

The EBIT Calorimeter Spectrometer: A New, Permanent User Facility at the LLNL EBIT

The EBIT Calorimeter Spectrometer (ECS) has recently been completed and is currently being installed at the EBIT facility at the Lawrence Livermore National Laboratory. The ECS will replace the smaller XRS/EBIT spectrometer that has been in almost continuous operation since 2000. The XRS/EBIT was based on a spare laboratory cryostat and an engineering model detector system from the Suzaku/XRS observatory. The new ECS spectrometer was built from the ground up to be a low maintenance, high performance microcalorimeter spectrometer with 4 eV resolution at 6 keV, 32 detector channels, 10 us event timing, and capable of uninterrupted acquisition sessions of over 70 hours at 50 mK. The XRSIEBIT program has been extremely successful, producing over two-dozen refereed publications on topics such as laboratory astrophysics, atomic physics, nuclear physics, and calibration of the spectrometers for the National Ignition Facility, with many more publications in preparation. The ECS spectrometer will continue this work into the future with improved spectral resolution, integration times, and ease-of-use. We designed the ECS instrument with TES detectors in mind by using the same highly successful magnetic shielding as our laboratory TES cryostats. This design will lead to a future TES instrument at the LLNL EBIT. This proposed future instrument would include a hybrid detector system with 0.8 eV resolution in the band from 0.1-1.0 keV, 2 eV from 0.1-10 keV, and 30 eV from 0.5-100 keV, with high quantum efficiency in each band. Here we discuss the legacy of the XRS/EBIT program, the performance of the new ECS spectrometer, and plans for a future TES spectrometer.

Porter, S.↗

Development of a Point of Care Technology for Military Medical Applications in Austere Environments

NASA, Lawrence Livermore National Laboratory (LLNL) and the Department of Defense (DoD) share a common interest in compact medical diagnostic technologies—also known as “point of care testing” (POCT) technologies. For NASA, the need is to take care of astronauts on deep space missions. For LLNL, the focus is on technologies needed to support homeland security applications. For DoD, the need is to support warfighters in military theaters of operation, especially for prolonged field care and en route care. A recently patented technology, “Portable Medical Diagnosis Instrument” (U.S. Patent 9824870), co-invented by NASA and LLNL, is being developed further in a partnership between NASA, LLNL and Travis Air Force Base, with a focus on military applications. This instrument, the NASA-LLNL Medical Tricorder, can be used for a wide range of clinical samples including breath, saliva and blood. One component of the Tricorder is the NASA E-Nose, a carbon nanotube-based chemical sensor, integrated into a hand-held smart phone, that can detect and measure “breath biomarkers” in the gas phase of exhaled breath. The response of the NASA E-Nose is rapid, which makes it possible to detect various gas-phase substances in real time. The NASA E-Nose, with modification, can also be used for breath condensate analysis. Another component of the Tricorder is a miniaturized microfluidic analyzer, under development by LLNL, that does not require any pumps. The microfluidic analyzer can detect and measure biomarkers in liquid samples, such as blood, saliva and breath condensate. This microfluidic system requires small quantities of liquid sample and can perform analysis very rapidly (seconds to minutes), which makes it possible to detect relevant biomarkers in near real time in the field. The Clinical Investigation Facility (CIF) at Travis Air Force Base is currently conducting research with the goal to develop improved field-able technologies and procedures for the emergency response to life threatening injuries soldiers may receive in theater. This work includes experimental large animal systems and comprehensive collection of clinical specimens and physiological data. NASA and LLNL are partnering with Travis to test and further develop the Tricorder technology for high priority military applications, initially focused on lung injury models and traumatic brain injury.

Loftus, David J.↗

Trace Element and Isotopic Evidence for Bennu's Primitive Provenance

The delivery of material from asteroid (101955) Bennu by NASA’s OSIRIS-REx mission provides the opportunity to investigate some of the most pristine material from the early Solar System [1]. Our team at Lawrence LivermoreNational Laboratory (LLNL) utilized the equivalent of 5.0 mg from Bennu sampleOREX-803015-100 to quantify the major and trace element contents and investigate major element isotopics (Ca, Ti, Cr, Fe, and Ni). Our 5.0 mg aliquot ofOREX-803015-100 was a subsample of dissolved homogenized material representing 20.66 mg [2]. A separate 5.0 mg aliquot was sent to ETH Zürich and is discussed in a companion abstract [3]. Before any chemical separation on our 5.0 mg aliquot, the equivalent of 0.5 mg was removed and analyzed for elemental abundances at LLNL using a ThermoScientific Element XR. Our data agree exceptionally well with those reported by[2], showing that Bennu is primitive and compositionally similar to CI chondrites, Ryugu [4], and the solar photosphere [5]. The remaining ~4.5 mg underwent purification procedures to chemically isolate and purify Ca, Ti, Cr, Fe, and Ni from one another and the sample matrix. Their isotopic compositions were measured on either the Triton TIMS (Ca) at JohnsonSpace Center in Houston, Neoma MC-ICPMS (Ti, Cr) at LLNL, or the Neptune MC-ICPMS (Fe, Ni) at LLNL. Results from the Ca, Ti, Cr, Fe, and Ni isotopic compositions suggest that Bennu is closely related to CI chondrites—consistent with conclusions from elemental composition [2] and oxygen isotopics [6]reported for Bennu. The major element isotope compositions that we will present demonstrate that Bennu likely formed in a similar region of the SolarSystem as CI chondrites and potentially at a similar time of Solar System evolution.

Greg Brennecka↗

X ray imaging microscope for cancer research

The NASA technology employed during the Stanford MSFC LLNL Rocket X Ray Spectroheliograph flight established that doubly reflecting, normal incidence multilayer optics can be designed, fabricated, and used for high resolution x ray imaging of the Sun. Technology developed as part of the MSFC X Ray Microscope program, showed that high quality, high resolution multilayer x ray imaging microscopes are feasible. Using technology developed at Stanford University and at the DOE Lawrence Livermore National Laboratory (LLNL), Troy W. Barbee, Jr. has fabricated multilayer coatings with near theoretical reflectivities and perfect bandpass matching for a new rocket borne solar observatory, the Multi-Spectral Solar Telescope Array (MSSTA). Advanced Flow Polishing has provided multilayer mirror substrates with sub-angstrom (rms) smoothnesss for the astronomical x ray telescopes and x ray microscopes. The combination of these important technological advancements has paved the way for the development of a Water Window Imaging X Ray Microscope for cancer research.

Hoover, Richard B.↗

Future aircraft and potential effects on stratospheric ozone and climate

Initial studies with LLNL models of global atmospheric chemical, radiative, and transport processes have indicated that substantial decreases in stratospheric ozone concentrations could result from emissions of NO(x) from aircraft flying in the stratosphere, depending on fleet size and magnitude of the engine emissions. These studies used homogeneous chemical reaction rates (e.g., gas-phase chemistry). Recent evidence indicates that reactions on particles in the stratosphere may be important. Heterogeneous chemical reactions convert NO(x) (NO and NO2) molecules to HNO3. This decreases the odd oxygen loss from the NO(x) catalytic cycle and increases the odd oxygen loss from the Cl(x) catalytic cycle. By including these heterogeneous reactions in the LLNL model, the relative partitioning of odd oxygen loss between these two families changes, with the result that emissions of NO(x) from proposed aircraft fleets flying in the stratosphere now increase ozone. Having these heterogeneous processes present also increases ozone concentration in the troposphere relative to gas-phase only chemistry calculations for emissions of NO(x) from subsonic aircraft.

Kinnison, Douglas E.↗

Simulated meteorite impacts and volcanic explosions: Ejecta analyses and planetary implications

Past cratering studies have focused primarily on crater morphology. However, important questions remain about the nature of crater deposits. Phenomena that need to be studied include the distribution of shock effects in crater deposits and crater walls; the origin of mono- and polymict breccia; differences between local and distal ejecta; deformation induced by explosive volcanism; and the production of unshocked, high-speed ejecta that could form the lunar and martian meteorites found on the Earth. To study these phenomena, one must characterize ejecta and crater wall materials from impacts produced under controlled conditions. New efforts at LLNL simulate impacts and volcanism and study resultant deformation. All experiments use the two-stage light-gas gun facility at LLNL to accelerate projectiles to velocities of 0.2 to 4.3 km/s, including shock pressures of 0.9 to 50 GPa. We use granite targets and novel experimental geometries to unravel cratering processes in crystalline rocks. We have thus far conducted three types of simulations: soft recovery of ejecta, 'frozen crater' experiments, and an 'artificial volcano. Our ejecta recovery experiments produced a useful separation of impactites. Material originally below the projectile remained trapped there, embedded in the soft metal of the flyer plate. In contrast, material directly adjacent to the projectile was jetted away from the impact, producing an ejecta cone that was trapped in the foam recovery fixture. We find that a significant component of crater ejecta shows no signs of strong shock; this material comes from the near-surface 'interference zone' surrounding the impact site. This phenomenon explains the existence of unshocked meteorites on the Earth of lunar and martian origin. Impact of a large bolide on neighboring planets will produce high-speed, weakly shocked ejecta, which may be trapped by the Earth's gravitational field. 'Frozen crater' experiments show that the interference zone is highly localized; indeed, disaggregation does not extend beyond approx. 1.5 crater radii. A cone-shaped region extending downward from the impact site is completely disaggregated, including powdered rock that escaped into the projectile tube. Petrographic analysis of crater ejecta and wall material will be presented. Finally, study of ejecta from 0.9- and 1.3-GPa simulations of volcanic explosions reveal a complete lack of shock metamorphism. The ejecta shows no evidence of PDF's, amorphization, high-pressure phases, or mosaicism. Instead, all deformation was brittle, with fractures irregular (not planar) and most intergranular. The extent of fracturing was remarkable, with the entire sample reduced to fragments of gravel size and smaller.

Gratz, A. J.↗

Storage needs in future supercomputer environments

The Lawrence Livermore National Laboratory (LLNL) is a Department of Energy contractor, managed by the University of California since 1952. Major projects at the Laboratory include the Strategic Defense Initiative, nuclear weapon design, magnetic and laser fusion, laser isotope separation, and weather modeling. The Laboratory employs about 8,000 people. There are two major computer centers: The Livermore Computer Center and the National Energy Research Supercomputer Center. As we increase the computing capacity of LLNL systems and develop new applications, the need for archival capacity will increase. Rather than quantify that increase, I will discuss the hardware and software architectures that we will need to support advanced applications.

Coleman, Sam↗

Mirror fusion propulsion system - A performance comparison with alternate propulsion systems for the manned Mars mission

The performance characteristics of several propulsion technologies applied to piloted Mars missions are compared. The characteristics that are compared are Initial Mass in Low Earth Orbit (IMLEO), mission flexibility, and flight times. The propulsion systems being compared are both demonstrated and envisioned: Chemical (or Cryogenic), Nuclear Thermal Rocket (NTR) solid core, NTR gas core, Nuclear Electric Propulsion (NEP), and a mirror fusion space propulsion system. The proposed magnetic mirror fusion reactor, known as the Mirror Fusion Propulsion System (MFPS), is described. The description is an overview of a design study that was conducted to convert a mirror reactor experiment at Lawrence Livermore National Lab (LLNL) into a viable space propulsion system. Design principles geared towards minimizing mass and maximizing power available for thrust are identified and applied to the LLNL reactor design, resulting in the MFPS. The MFPS' design evolution, reactor and fuel choices, and system configuration are described. Results of the performance comparison shows that the MFPS minimizes flight time to 60 to 90 days for flights to Mars while allowing continuous return-home capability while at Mars. Total MFPS IMLEO including propellant and payloads is kept to about 1,000 metric tons.

Deveny, M.↗

Mirror fusion propulsion system: A performance comparison with alternate propulsion systems for the manned Mars Mission

The performance characteristics of several propulsion technologies applied to piloted Mars missions are compared. The characteristics that are compared are Initial Mass in Low Earth Orbit (IMLEO), mission flexibility, and flight times. The propulsion systems being compared are both demonstrated and envisioned: Chemical (or Cryogenic), Nuclear Thermal Rocket (NTR) solid core, NTR gas core, Nuclear Electric Propulsion (NEP), and a mirror fusion space propulsion system. The proposed magnetic mirror fusion reactor, known as the Mirror Fusion Propulsion System (MFPS), is described. The description is an overview of a design study that was conducted to convert a mirror reactor experiment at Lawrence Livermore National Lab (LLNL) into a viable space propulsion system. Design principles geared towards minimizing mass and maximizing power available for thrust are identified and applied to the LLNL reactor design, resulting in the MFPS. The MFPS' design evolution, reactor and fuel choices, and system configuration are described. Results of the performance comparison shows that the MFPS minimizes flight time to 60 to 90 days for flights to Mars while allowing continuous return-home capability while at Mars. Total MFPS IMLEO including propellant and payloads is kept to about 1,000 metric tons.

Schulze, Norman R.↗

Invasion of the Giant X-Ray Bubbles

More bizarre news from the bizarre world of neutron stars: They got dozens of giant X-ray bubbles taller than the Empire State Building forming and popping every second. Yet finding evidence of this bubble blowing was no childish endeavor. It took a team of Berkeley scientists just about all they could muster: three days' worth of observational data and 1,200 hours of number-crunching on the slickest of supercomputers at the Lawrence Livermore National Laboratory (LLNL). Mind you, these are the same powerful computers used to model nuclear reactions and calculate Bill Gates' salary. Neutron stars are already known as the bad boys of the cosmic neighborhood. They are the core remains of exploded stars, with a mass greater than our sun condensed into a sphere no bigger than Manhattan, A teaspoon of its densely-packed surface matter, the analogy goes, would weigh three billion tons back on earth. Its 10 trillion gauss magnetic field could wipe your credit card clean at a distance half-way to the moon. Its intense gravity lures gas from nearby stars, spinning the neutron star to speeds of up to a thousand times a second. But giant X-ray bubbles dancing on the surface? That even freaked out the discoverers. "Early on, I tended to disbelieve what the calculations were telling me," said Richard Klein, who splits his time between Berkeley and LLNL. "The bubbles 'appeared' and I wasn't convinced they were real."

Wanjek, Christopher↗

A Model of Reduced Kinetics for Alkane Oxidation Using Constituents and Species for N-Heptane

The reduction of elementary or skeletal oxidation kinetics to a subgroup of tractable reactions for inclusion in turbulent combustion codes has been the subject of numerous studies. The skeletal mechanism is obtained from the elementary mechanism by removing from it reactions that are considered negligible for the intent of the specific study considered. As of now, there are many chemical reduction methodologies. A methodology for deriving a reduced kinetic mechanism for alkane oxidation is described and applied to n-heptane. The model is based on partitioning the species of the skeletal kinetic mechanism into lights, defined as those having a carbon number smaller than 3, and heavies, which are the complement of the species ensemble. For modeling purposes, the heavy species are mathematically decomposed into constituents, which are similar but not identical to groups in the group additivity theory. From analysis of the LLNL (Lawrence Livermore National Laboratory) skeletal mechanism in conjunction with CHEMKIN II, it is shown that a similarity variable can be formed such that the appropriately non-dimensionalized global constituent molar density exhibits a self-similar behavior over a very wide range of equivalence ratios, initial pressures and initial temperatures that is of interest for predicting n-heptane oxidation. Furthermore, the oxygen and water molar densities are shown to display a quasi-linear behavior with respect to the similarity variable. The light species ensemble is partitioned into quasi-steady and unsteady species. The reduced model is based on concepts consistent with those of Large Eddy Simulation (LES) in which functional forms are used to replace the small scales eliminated through filtering of the governing equations; in LES, these small scales are unimportant as far as the overwhelming part of dynamic energy is concerned. Here, the scales thought unimportant for recovering the thermodynamic energy are removed. The concept is tested by using tabular information from the LLNL skeletal mechanism in conjunction with CHEMKIN II utilized as surrogate ideal functions replacing the necessary functional forms. The test reveals that the similarity concept is indeed justified and that the combustion temperature is well predicted, but that the ignition time is over-predicted, a fact traced to neglecting a detailed description of the processes leading to the heavies chemical decomposition. To palliate this deficiency, functional modeling is incorporated into this conceptual reduction in addition to the modeling the evolution of the global constituent molar density, the enthalpy evolution of the heavies, the contribution to the reaction rate of the unsteady lights from other light species and from the heavies, the molar density evolution of oxygen and water, and the mole fractions of the quasisteady light species. The model is compact in that there are only nine species-related progress variables. Results are presented showing the performance of the model for predicting the temperature and species evolution. The model reproduces the ignition time over a wide range of equivalence ratios, initial pressure, and initial temperature.

Harstad, Kenneth G.↗

Composite Overwrapped Pressure Vessels (COPV): Flight Rationale for the Space Shuttle Program

Each Orbiter Vehicle (Space Shuttle Program) contains up to 24 Kevlar49/Epoxy Composite Overwrapped Pressure Vessels (COPV) for storage of pressurized gases. In the wake of the Columbia accident and the ensuing Return To Flight (RTF) activities, Orbiter engineers reexamined COPV flight certification. The original COPV design calculations were updated to include recently declassified Kevlar COPV test data from Lawrence Livermore National Laboratory (LLNL) and to incorporate changes in how the Space Shuttle was operated as opposed to orinigially envisioned. 2005 estimates for the probability of a catastrophic failure over the life of the program (from STS-1 through STS-107) were one-in-five. To address this unacceptable risk, the Orbiter Project Office (OPO) initiated a comprehensive investigation to understand and mitigate this risk. First, the team considered and eventually deemed unfeasible procuring and replacing all existing flight COPVs. OPO replaced the two vessels with the highest risk with existing flight spare units. Second, OPO instituted operational improvements in ground procedures to signficiantly reduce risk, without adversely affecting Shuttle capability. Third, OPO developed a comprehensive model to quantify the likelihood of occurrance. A fully-instrumented burst test (recording a lower burst pressure than expected) on a flight-certified vessel provided critical understanding of the behavior of Orbiter COPVs. A more accurate model was based on a newly-compiled comprehensive database of Kevlar data from LLNL and elsewhere. Considering hardware changes, operational improvements and reliability model refinements, the mean reliability was determined to be 0.998 for the remainder of the Shuttle Program (from 2007, for STS- 118 thru STS-135). Since limited hardware resources precluded full model validation through multiple tests, additional model confidence was sought through the first-ever Accelerated Stress Rupture Test (ASRT) of a flown flight article. A Bayesian statistical approach was developed to interpret possible test results. Since the lifetime observed in the ASRT exceeded initial estimates by one to two orders of magnitude, the Space Shuttle Program deemed there was significant conservatism in the model and accepted continued operation with existing flight hardware. Given the variability in tank-to-tank original prooftest response, a non-destructive evaluation (NDE) technique utilizing Raman Spectroscopy was developed to directly measure COPV residual stress state. Preliminary results showed that patterns of low fiber elastic strains over the outside vessel surface, together with measured permanent volume growth during proof, could be directly correlated to increased fiber stress ratios on the inside fibers adjacent to the liner, and thus reduced reliability.

Kezirian, Michael T.↗

Multi-Organization Multi-Discipline Effort Developing a Mitigation Concept for Planetary Defense

There have been significant recent efforts in addressing mitigation approaches to neutralize Potentially Hazardous Asteroids (PHA). One such research effort was performed in 2015 by an integrated, inter-disciplinary team of asteroid scientists, energy deposition modeling scientists, payload engineers, orbital dynamist engineers, spacecraft discipline engineers, and systems architecture engineer from NASAs Goddard Space Flight Center (GSFC) and the Department of Energy (DoE) National Nuclear Security Administration (NNSA) laboratories (Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratories (LLNL) and Sandia National Laboratories). The study team collaborated with GSFCs Integrated Design Centers Mission Design Lab (MDL) which engaged a team of GSFC flight hardware discipline engineers to work with GSFC, LANL, and LLNL NEA-related subject matter experts during a one-week intensive concept formulation study in an integrated concurrent engineering environment. This team has analyzed the first of several distinct study cases for a multi-year NASA research grant. This Case 1 study references the Near-Earth Asteroid (NEA) named Bennu as the notional target due to the availability of a very detailed Design Reference Asteroid (DRA) model for its orbit and physical characteristics (courtesy of the Spectral Interpretation, Resource Identification, Security-Regolith Explorer (OSIRIS-REx) mission team). The research involved the formulation and optimization of spacecraft trajectories to intercept Bennu, overall mission and architecture concepts, and high-fidelity modeling of both kinetic impact (spacecraft collision to change a NEAs momentum and orbit) and nuclear detonation effects on Bennu, for purposes of deflecting Bennu.

Planetary Defense↗

Studies of Short Time Response Options for Potentially Hazardous Objects: Current and Forthcoming Results

NASA's Goddard Space Flight Center (GSFC) and the National Nuclear Security Administration (NNSA), Department of Energy (DOE) National Laboratories, Lawrence Livermore National Laboratory (LLNL), Los Alamos National Laboratory(LANL), and Sandia National Laboratory (SNL) are collaborating on Planetary Defense Research. The research program is organized around three case studies: 1. Deflection of the Potentially Hazardous Asteroid (PHA) 101955 Bennu (1999 RQ36)[OSIRIS-REx mission target], 2. Deflection of the secondary member of the PHA 65803 Didymos (1996 GT) [DART mission target], 3. Deflection of a scaled-down version of the comet 67PChuryumov-Gerasimenko [Rosetta mission target]. NASAGSFC is providing astrodynamics and spacecraft mission design expertise, while NNSA, DOE, LLNL, LANL and SNL are providing expertise in modeling the effects of kinetic impactor spacecraft and nuclear explosive devices on the target objects.

Mission Design↗

Requirements for migration of NSSD code systems from LTSS to NLTSS

The purpose of this document is to address the requirements necessary for a successful conversion of the Nuclear Design (ND) application code systems to the NLTSS environment. The ND application code system community can be characterized as large-scale scientific computation carried out on supercomputers. NLTSS is a distributed operating system being developed at LLNL to replace the LTSS system currently in use. The implications of change are examined including a description of the computational environment and users in ND. The discussion then turns to requirements, first in a general way, followed by specific requirements, including a proposal for managing the transition.

Pratt, M.↗