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Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. Here, we demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.

97 MATHEMATICS AND COMPUTING↗

Synthesizing 3D Surfaces from Parameterized Strip Charts

We believe 3D information visualization has the power to unlock new levels of productivity in the monitoring and control of complex processes. Our goal is to provide visual methods to allow for rapid human insight into systems consisting of thousands to millions of parameters. We explore this hypothesis in two complex domains: NASA program management and NASA International Space Station (ISS) spacecraft computer operations. We seek to extend a common form of visualization called the strip chart from 2D to 3D. A strip chart can display the time series progression of a parameter and allows for trends and events to be identified. Strip charts can be overlayed when multiple parameters need to visualized in order to correlate their events. When many parameters are involved, the direct overlaying of strip charts can become confusing and may not fully utilize the graphing area to convey the relationships between the parameters. We provide a solution to this problem by generating 3D surfaces from parameterized strip charts. The 3D surface utilizes significantly more screen area to illustrate the differences in the parameters and the overlayed strip charts, and it can rapidly be scanned by humans to gain insight. The selection of the third dimension must be a parallel or parameterized homogenous resource in the target domain, defined using a finite, ordered, enumerated type, and not a heterogeneous type. We demonstrate our concepts with examples from the NASA program management domain (assessing the state of many plans) and the computers of the ISS (assessing the state of many computers). We identify 2D strip charts in each domain and show how to construct the corresponding 3D surfaces. The user can navigate the surface, zooming in on regions of interest, setting a mark and drilling down to source documents from which the data points have been derived. We close by discussing design issues, related work, and implementation challenges.

Robinson, Peter I.↗

GeneLab for High Schools: Data Mining for the Next Generation

Modern biological sciences have become increasingly based on molecular biology and high-throughput molecular techniques, such as genomics, transcriptomics, and proteomics. NASA Scientists and the NASA Space Biology Program have aimed to examine the fundamental building blocks of life (RNA, DNA and protein) in order to understand the response of living organisms to space and aid in fundamental research discoveries on Earth. In an effort to enable NASA funded science to be available to everyone, NASA has collected the data from omics studies and curated them in a data system called GeneLab. Whilst most college-level interns, academics and other scientists have had some interaction with omics data sets and analysis tools, high school students often have not. Therefore, the Space Biology Program is implementing a new Summer Program for high-school students that aims to inspire the next generation of scientists to learn about and get involved in space research using GeneLabs Data System. The program consists of three main components core learning modules, focused on developing students knowledge on the Space Biology Program and Space Biology research, Genelab and the data system, and previous research conducted on model organisms in space; networking and team work, enabling students to interact with guest lecturers from local universities and their fellow peers, and also enabling them to visit local universities and genomics centers around the Bay area; and finally an independent learning project, whereby students will be required to form small groups, analyze a dataset on the Genelab platform, generate a hypothesis and develop a research plan to test their hypothesis. This program will not only help inspire high-school students to become involved in space-based research but will also help them develop key critical thinking and bioinformatics skills required for most college degrees and furthermore, will enable them to establish networks with their peers and connections with university Professors that may help them achieve their educational goals.

genelab↗

HF radar signatures of the cusp and low-latitude boundary layer

Continuous ground-based observations of ionospheric and magnetospheric regions are critical to the Geospace Environmental Modeling (GEM) program. It is therefore important to establish clear intercalibrations between different ground-based instruments and satellites in order to clearly place the ground-based observations in context with the corresponding in situ satellite measurements. HF-radars operating at high latitudes are capable of observing very large spatial regions of the ionosphere on a nearly continuous basis. In this paper we report on an intercalibration study made using the Polar Anglo-American Conjugate Radar Experiment radars located at Goose Bay, Labrador, and Halley Station, Antarctica, and the Defense Meteorological Satellite Program (DMSP) satellites. The DMSP satellite data are used to provide clear identifications of the ionospheric cusp and the low-latitude boundary layer (LLBL). The radar data for eight cusp events and eight LLBL events have been examined in order to determine a radar signature of these ionospheric regions. This intercalibraion indicates that the cusp is always characterized by wide, complex Doppler power spectra, whereas the LLBL is usually found to have spectra dominated by a single component. The distribution of spectral widths in the cusp is of a generally Gaussian form with a peak at about 220 m/s. The distribution of spectral widths in the LLBL is more like an exponential distribution, with the peak of the distribution occurring at about 50 m/s. There are a few cases in the LLBL where the Doppler power spectra are strikingly similar to those observed in the cusp.

Baker, K. B.↗

Status on NGST Mirror Technology

The NGST primary mirror is anticipated to be a segmented deployable optic with segment size being in the range of 1 - 3 m depending on the details of the architecture. The secondary mirror will likely be a monolith similar in size to one of the primary mirror segments. Over the past 4 years the NGST program has initiated and implemented an aggressive lightweight cryogenic mirror technology program. The program was designed to challenge and excite the optical community in reaching a new standard in production of lightweight optics. The goal was to develop optics at less than 15 kg/sq m, operational at approx. 40 K and meeting the overall NGST observatory requirement for diffraction limited performance at 2 microns. In order to meet the NGST needs, technology efforts were initiated to investigate and develop mirrors in a variety of materials, which held promise for the program. The basic technology approaches have initially targeted the production of large mirrors in the 1.2 - 2.0 m diameter range (or side-to-side distance in the case of hexagonal optics). Although this size may not be the final size of an NGST primary mirror segment, it was felt that a 1.2 - 2.0 m optic would be of sufficient size to understand the mirror material and fabrication processes which drive the cost and schedule of mirror production. The ultimate goals of the technology program are both to demonstrate mirrors meeting, the NGST performance requirements, and to establish cost and schedule credibility for producing and implementing the mirrors for the NGST flight system. Establishing cost and schedule credibility is essential to NGST which is a cost capped mission, with past program experience demonstrating that the optics will be a large portion of the total cost of the program. The first two years of the program were dedicated to understanding; the various applicable materials, funding those materials to various levels of maturity and implementing the first large mirror procurement, the NGST Mirror System Demonstrator (NMSD), in order to establish a benchmark for the state-of-the-art in lightweight optics and to establish credibility that the goals of NGST could be achieved. The past two years of the program has seen major steps in the development of several mirror materials, which not only might have NGST applicability but could also support other programs for other customers. Additionally, a second large mirror procurement, the Advanced Mirror System Demonstrator (AMSD), has been implemented providing a focal point to complete the mirror technology development and lead ultimately to the production of mirrors that will fly on NEXUS (the NGST flight experiment- discussed below) and NGST. This talk will focus on the mirror technology developed over the past 4 years on the NGST program.

Jacobson, David↗

3D Simulation: Microgravity Environments and Applications

Most, if not all, 3-D and Virtual Reality (VR) software programs are designed for one-G gravity applications. Space environments simulations require gravity effects of one one-thousandth to one one-million of that of the Earth's surface (10(exp -3) - 10(exp -6) G), thus one must be able to generate simulations that replicate those microgravity effects upon simulated astronauts. Unfortunately, the software programs utilized by the National Aeronautical and Space Administration does not have the ability to readily neutralize the one-G gravity effect. This pre-programmed situation causes the engineer or analysis difficulty during micro-gravity simulations. Therefore, microgravity simulations require special techniques or additional code in order to apply the power of 3D graphic simulation to space related applications. This paper discusses the problem and possible solutions to allow microgravity 3-D/VR simulations to be completed successfully without program code modifications.

Hunter, Steve L.↗

Real-Time Optimization Workflow Status Update

Economically optimal and safe operation of integrated energy systems (IES) requires optimization at many different time scales. A real-time optimization (RTO) workflow will attempt to maximize revenue and minimize operational costs on a time scale of minutes to hours. Such a workflow requires the use of a digital twin (DT), which is a virtual representation of a physical system. The DT is updated using real-time data from the physical system, and serves as a model in an optimization framework. The optimization results are then sent back to the physical system to complete the loop. This report details the progress made in developing building blocks for a DT/RTO framework. The Risk Analysis Virtual Environment (RAVEN) platform within the Framework for Optimization of Resources and Economics (FORCE) tool suite can perform many of the tasks required for building a DT and performing RTO. The first item of this report details RAVEN enhancements that enable RAVEN workflows to be run in various environments. Data communication between the physical system and its DT is essential for successful RTO. This includes preprocessing real-time data, loading data into a data warehouse, and querying the stored data. The second section of this report describes the progress made in implementing an adapter in Python in order for Deep Lynx to handle the data communication. Typical dispatch optimization frameworks are built on linear programming (LP). The prototype RTO workflow developed in this report uses an LP problem as a part of a receding-horizon- or economic model predictive control (EMPC) based optimization. The third section of this report details the framework of an RTO workflow in which the system consists of a simple electrical storage device. A DT can be built from a reduced-order model (ROM). Integrating a ROM into a typical LP optimization framework has been challenging because most optimization packages require the user to write algebraic expressions for the system model. The final section of this report shows how an externally built RAVEN ROM can be integrated in an RTO framework by using the Python package Pyomo. This demonstrates the RTO workflow capability from a software-only perspective and is an important step in demonstrating the capability to implement an RTO workflow for a physical system.

97 MATHEMATICS AND COMPUTING↗

Kinetic and mechanistic analysis of dinucleotide and oligonucleotide formation from the 5'-phosphorimidazolide of adenosine on Na(+)-montmorillonite

The rate constants for the condensation reaction of the 5'-phosphorimidazolide of adenosine (ImpA) to form dinucleotides and oligonucleotides have been measured in the presence of Na(+)-volclay (a Na(+)-montmorillonite) in pH 8 aqueous solution at 25 degrees C. The rates of the reaction of ImpA with an excess of adenosine 5'-monophosphoramidate (NH2pA), P1,P2-diadenosine 5',5'-pyrophosphate (A5'ppA), or adenosine 5'-monophosphate (5'-AMP or pA) in the presence of the montmorillonite to form NH2pA3'pA, A5'ppA3'pA, and pA3'pA, respectively, were measured. Only 3',5'-linked products were observed. The magnitude of the rate constants decrease in the order NH2pA3'pA > A5'-ppA3'pA > pA3'pA. The binding of ImpA to montmorillonite was measured, and the adsorption isotherm was determined. The binding of ImpA to montmorillonite and the formation of higher oligonucleotides is not observed in the absence of salts. Mg2+ enhances binding and oligonucleotide formation more than Ca2+ and Na+. The rate constants for the oligonucleotide formation were determined from the reaction products formed from 10 to 40 mM ImpA in the presence of Na(+)-montmorillonite using the computer program SIMFIT. The magnitudes of the rate constants for the formation of oligonucleotides increased in the order 2-mer < 3-mer < 4-mer ... 7-mer. The rate constants for dinucleotide and trinucleotide formation are more than 1000 times larger than those measured in the absence of montmorillonite. The rate constants for the formation of dinucleotide, trinucleotide, and tetranucleotide are 41,2.6, and 3.7 times larger than those for the formation of oligo(G)s with a poly(C) template. The hydrolysis of ImpA was accelerated 35 times in the presence of the montmorillonite. The catalytic ability of montmorillonite to form dinucleotides and oligonucleotides is quantitatively evaluated and possible pathways for oligo(A) formation are proposed.

NASA Discipline Exobiology↗

Shuttle Risk Progression: Use of the Shuttle Probabilistic Risk Assessment (PRA) to Show Reliability Growth

It is important to the Space Shuttle Program (SSP), as well as future manned spaceflight programs, to understand the early mission risk and progression of risk as the program gains insights into the integrated vehicle through flight. The risk progression is important to the SSP as part of the documentation of lessons learned. The risk progression is important to future programs to understand reliability growth and the first flight risk. This analysis uses the knowledge gained from 30 years of operational flights and the current Shuttle PRA to calculate the risk of Loss of Crew and Vehicle (LOCV) at significant milestones beginning with the first flight. Key flights were evaluated based upon historical events and significant re-designs. The results indicated that the Shuttle risk tends to follow a step function as opposed to following a traditional reliability growth pattern where risk exponentially improves with each flight. In addition, it shows that risk can increase due to trading safety margin for increased performance or due to external events. Due to the risk drivers not being addressed, the risk did not improve appreciably during the first 25 flights. It was only after significant events occurred such as Challenger and Columbia, where the risk drivers were apparent, that risk was significantly improved. In addition, this paper will show that the SSP has reduced the risk of LOCV by almost an order of magnitude. It is easy to look back afte r 30 years and point to risks that are now obvious, however; the key is to use this knowledge to benefit other programs which are in their infancy stages. One lesson learned from the SSP is understanding risk drivers are essential in order to considerably reduce risk. This will enable the new program to focus time and resources on identifying and reducing the significant risks. A comprehensive PRA, similar to that of the Shuttle PRA, is an effective tool quantifying risk drivers if support from all of the stakeholders is given.

Hamlin, Teri L.↗

ROSAT observation program

In this annual progress report (November 1, 1993 to October 31, 1994), the geminga pulsar was observed by the ROSAT PSPC for 37,000 s in September 1993, in order to make a more detailed study than was previously possible of the pulse profile and two-component spectrum, and to do phase-resolved spectroscopy. This exposure was 2.5 times longer than the original discovery observation. In addition, a shorter 4,000 s exposure was made in October 1992, simultaneously with a GRO observation of Geminga, in order to verify the absolute phasing of the X-ray and gamma-ray peaks. We verified that the spectrum can be described as the sum of two black bodies, whose temperatures are 6 x 10(exp 5) K and 3 - 4 x 10(exp 6) K, with the latter covering 3 x 10(exp -5) the area of the former. The pulse profiles indicate that the intensity of the two emitting regions peak is approximately 90 deg out of phase in rotation, but that the temperatures are otherwise independent of phase. An improved estimate of the distance can be made from the cooler (larger) blackbody component, yielding d = 440 +/- 120 pc. Another program of this report was to obtain PSPC spectra of an important class of Seyfert galaxies which have narrow lines and stron permitted Fe II emission. Sometines called I Zw 1 objects, or narrow-line Seyfert 1s, they are crucial to our understanding of Seyfert classification and models of Seyfert unification. We observed four new objects and, in addition, obtained data on 17 more from the ROSAT archive. A third program combined PSPC and HRI observations of selected Seyfert galaxies which have unusual and variable spectra. The purpose was to disentangle diffuse X-ray emission from the nuclear source, in order to properly interpret the soft X-ray spectral shapes in terms of partial covering and/or warm-absorber models. The targets of the program are NGC 3516, NGC 3227, and NGC 7314. So far, we have only performed a dtailed analysis on NGC 3516. The fourth program of this report is the NGC 1672, the second brightest Seyfert galaxy and one or the original 'composite' Seyfert/starburst galaxies which have evidence for both Seyfert activity and H II regions in their optical spectra. It is one of the lowest luminosity Seyfert 2 galaxies that can be studied in detail.

Halpern, Jules P.↗

Research in mathematical theory of computation

Research progress in the following areas is reviewed: (1) new version of computer program LCF (logic for computable functions) including a facility to search for proofs automatically; (2) the description of the language PASCAL in terms of both LCF and in first order logic; (3) discussion of LISP semantics in LCF and attempt to prove the correctness of the London compilers in a formal way; (4) design of both special purpose and domain independent proving procedures specifically program correctness in mind; (5) design of languages for describing such proof procedures; and (6) the embedding of ideas in the first order checker.

Mccarthy, J.↗

Reliability and Maintainability Engineering - A Major Driver for Safety and Affordability

The United States National Aeronautics and Space Administration (NASA) is in the midst of an effort to design and build a safe and affordable heavy lift vehicle to go to the moon and beyond. To achieve that, NASA is seeking more innovative and efficient approaches to reduce cost while maintaining an acceptable level of safety and mission success. One area that has the potential to contribute significantly to achieving NASA safety and affordability goals is Reliability and Maintainability (R&M) engineering. Inadequate reliability or failure of critical safety items may directly jeopardize the safety of the user(s) and result in a loss of life. Inadequate reliability of equipment may directly jeopardize mission success. Systems designed to be more reliable (fewer failures) and maintainable (fewer resources needed) can lower the total life cycle cost. The Department of Defense (DOD) and industry experience has shown that optimized and adequate levels of R&M are critical for achieving a high level of safety and mission success, and low sustainment cost. Also, lessons learned from the Space Shuttle program clearly demonstrated the importance of R&M engineering in designing and operating safe and affordable launch systems. The Challenger and Columbia accidents are examples of the severe impact of design unreliability and process induced failures on system safety and mission success. These accidents demonstrated the criticality of reliability engineering in understanding component failure mechanisms and integrated system failures across the system elements interfaces. Experience from the shuttle program also shows that insufficient Reliability, Maintainability, and Supportability (RMS) engineering analyses upfront in the design phase can significantly increase the sustainment cost and, thereby, the total life cycle cost. Emphasis on RMS during the design phase is critical for identifying the design features and characteristics needed for time efficient processing, improved operational availability, and optimized maintenance and logistic support infrastructure. This paper discusses the role of R&M in a program acquisition phase and the potential impact of R&M on safety, mission success, operational availability, and affordability. This includes discussion of the R&M elements that need to be addressed and the R&M analyses that need to be performed in order to support a safe and affordable system design. The paper also provides some lessons learned from the Space Shuttle program on the impact of R&M on safety and affordability.

Safie, Fayssal M.↗

Plant-specific Model and Data Analysis using Dynamic Security Modeling and Simulation

The requirements for U.S. nuclear power plants to maintain a large on-site physical security force contribute to their high operational costs. The cost of maintaining the current physical security posture is approximately 10% of the overall operation and maintenance budget for commercial nuclear power plants. The goal of the Light Water Reactor Sustainability (LWRS) program’s physical security pathway is to develop tools, methods, and technologies and provide the technical basis for an optimized physical security posture. The conservatisms built into current security postures may be analyzed and minimized in order to reduce security costs while still ensuring adequate security and operational safety. The research performed at Idaho National Laboratory within LWRS program’s physical security pathway has successfully developed a dynamic force-on-force modeling framework using various computer simulation tools and integrating them with the dynamic assessment Event Modeling Risk Assessment using Linked Diagrams (EMRALD) tool. This document provides an update on the progress in applying a dynamic computational framework that links results from a commercially available force-on-force simulation tool, a commercially available thermal-hydraulic tool, and EMRALD to an operating commercial nuclear power plant. This report is only a summary of the progress and does not contain specific modeling results as those contain sensitive security information. This process of including plant procedures and multiple analysis results is being called Modeling and Analysis for Safety Security using Dynamic EMRALD Framework or MASS-DEF. Previous reports described how a user could integrate their plant-specific force-on-force models with the dynamic simulation tool EMRALD, model operator actions, integrate with probabilistic risk assessment tools, such as CAFTA (Computer Aided Fault Tree Analysis System) or SAPHIRE (Systems Analysis Programs for Hands-on Integrated Reliability Evaluations), and with thermal-hydraulic tools, such as RELAP-5. Previous reports applied various combinations of available simulations codes with EMRALD using generic plant models to demonstrate how to perform the analysis. This report documents the results of applying the dynamic computational framework to an actual nuclear facility using their security scenarios and timelines. This report does not contain any plant's sensitive information and/or Safeguards Information. The purpose of this study was to verify that results achieved using generic models are similar to actual plant results and to refine our guidance on the use of the framework. This assessment enables further analysis, such as what-if scenarios and staff-reduction evaluation, thereby optimizing physical security at plants.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Fluids and Materials Science Studies Utilizing the Microgravity-vibration Isolation Mount (MIM)

Canada's Microgravity Sciences Program (MSP) is the smallest program of the ISS partners and so can participate in only a few, highly focused projects in order to make a scientific and technological impact. One focused project involves determining the effect of accelerations (g-jitter) on scientific measurements in a microgravity environment utilizing the Microgravity-vibration Isolation Mount (MIM). Many experiments share the common characteristic of having a fluid stage in their process. The quality of the experimental measurements have been expected to be affected by g-jitters which has lead the ISS program to include specifications to limit the level of acceleration allowed on a subset of experimental racks. From finite element analysis (FEM), the ISS structure will not be able to meet the acceleration specifications. Therefore, isolation systems are necessary. Fluid science results and materials science results show significant sensitivity to g-jitter. The work done to date should be viewed only as a first look at the issue of g-jitter sensitivity. The work should continue with high priority such that the international science community and the ISS program can address the requirement and settle on an agreed to overall approach as soon as possible.

Herring, Rodney↗

Over-relaxation applied to the MacCormack finite-difference scheme

An over-relaxation procedure is applied to the MacCormack finite-difference scheme in order to reduce the computation time required to obtain a steady-state solution. The implementation of this acceleration procedure to an existing computer program using the regular MacCormack method is extremely simple and does not require additional storage. The over-relaxation procedure does not alter the steady-state solution, which is second-order accurate. The method is first applied to Burgers' equation. A stability condition and an expression for the increase in the rate of convergence are derived. The method is then applied to the calculation of the hypersonic viscous flow over a flat plate, using the complete Navier-Stokes equations, and the inviscid flow over a wedge. Reductions in computing time by factors of 3 and 1.5, respectively, are obtained by over-relaxation.

Desideri, J.-A.↗

NASA trend analysis procedures

This publication is primarily intended for use by NASA personnel engaged in managing or implementing trend analysis programs. 'Trend analysis' refers to the observation of current activity in the context of the past in order to infer the expected level of future activity. NASA trend analysis was divided into 5 categories: problem, performance, supportability, programmatic, and reliability. Problem trend analysis uncovers multiple occurrences of historical hardware or software problems or failures in order to focus future corrective action. Performance trend analysis observes changing levels of real-time or historical flight vehicle performance parameters such as temperatures, pressures, and flow rates as compared to specification or 'safe' limits. Supportability trend analysis assesses the adequacy of the spaceflight logistics system; example indicators are repair-turn-around time and parts stockage levels. Programmatic trend analysis uses quantitative indicators to evaluate the 'health' of NASA programs of all types. Finally, reliability trend analysis attempts to evaluate the growth of system reliability based on a decreasing rate of occurrence of hardware problems over time. Procedures for conducting all five types of trend analysis are provided in this publication, prepared through the joint efforts of the NASA Trend Analysis Working Group.

Source record↗

A Lab-Scale CELSS

It has been shown that prohibitive resupply costs for extended-duration manned space flight missions will demand that a high degree of recycling and in situ food production be implemented. A prime candidate for in situ food production is the growth of higher level plants. Research in the area of plant physiology is currently underway at many institutions. This research is aimed at the characterization and optimization of gas exchange, transpiration and food production of higher plants in order to support human life in space. However, there are a number of unresolved issues involved in making plant chambers an integral part of a closed life support system. For example, issues pertaining to the integration of tightly coupled, non-linear systems with small buffer volumes will need to be better understood in order to ensure successful long term operation of a Controlled Ecological Life Support System (CELSS). The Advanced Life Support Division at NASA Ames Research Center has embarked on a program to explore some of these issues and demonstrate the feasibility of the CELSS concept. The primary goal of the Laboratory Scale CELSS Project is to develop a fully-functioning integrated CELSS on a laboratory scale in order to provide insight, knowledge and experience applicable to the design of human-rated CELSS facilities. Phase I of this program involves the integration of a plant chamber with a solid waste processor. This paper will describe the requirements, design and some experimental results from Phase I of the Laboratory Scale CELSS Program.

Flynn, Mark E.↗

Spinteract: a program to refine magnetic interactions to diffuse scattering data

Magnetic diffuse scattering—the broad magnetic scattering features observed in neutron-diffraction data above a material's magnetic ordering temperature—provides a rich source of information about the material's magnetic Hamiltonian. However, this information has often remained under-utilised due to a lack of available computer software that can fit values of magnetic interaction parameters to such data. Here, an open-source computer program, Spinteract, is presented, which enables straightforward refinement of magnetic interaction parameters to powder and single-crystal magnetic diffuse scattering data. Here, the theory and implementation of this approach are summarised. Examples are presented of refinements to published experimental diffuse-scattering data sets for the canonical antiferromagnet MnO and the highly-frustrated classical spin liquid Gd 3 Ga 5 O 12 . Guidelines for data collection and refinement are outlined, and possible developments of the approach are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗