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

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Inertial Pointing and Positioning System

An inertial pointing and control system and method for pointing to a designated target with known coordinates from a platform to provide accurate position, steering, and command information. The system continuously receives GPS signals and corrects Inertial Navigation System (INS) dead reckoning or drift errors. An INS is mounted directly on a pointing instrument rather than in a remote location on the platform for-monitoring the terrestrial position and instrument attitude. and for pointing the instrument at designated celestial targets or ground based landmarks. As a result. the pointing instrument and die INS move independently in inertial space from the platform since the INS is decoupled from the platform. Another important characteristic of the present system is that selected INS measurements are combined with predefined coordinate transformation equations and control logic algorithms under computer control in order to generate inertial pointing commands to the pointing instrument. More specifically. the computer calculates the desired instrument angles (Phi, Theta. Psi). which are then compared to the Euler angles measured by the instrument- mounted INS. and forms the pointing command error angles as a result of the compared difference.

Yee, Robert↗
NASA NTRS2012

NASA Electronic Parts and Packaging (NEPP) Program

Recent Findings from Audits, New Technology Data Reviews a) Disabled Chip Burn-ins A recent audit for a QML device discovered that the chip was disabled during the static burn-in, thus it was not drawing any current. Recommendation: For new SMDs add a statement within the burn-in paragraphs stating that the parts shall be kept in their enabled state during the burn-in. b) Class Q 160-hr/125oC Burn-in This is being interpreted as a static burn-in (even for CMOS technology). Recommendation: Provide clarification in MIL-STD-883, Test Method 5004. c) At Frequency (Dynamic) Burn-ins Test equipment limitation is being cited for not doing burn-ins at the application frequency. Recommendation: The burn-in task group to discuss and provide guidance. When the SMD says that the part can be used at 200 MHz, then doing burn-in at 6 MHz (cited as burn-in equipment limitation frequency) is not going to be meaningful! d) Two Static Burn-ins Some manufacturers are doing electrical testing between the two static burn-ins, whereas others do electricals after completing both static burn-ins. Recommendation: Provide clarification in MIL-STD-883, Test Method 5004. e) Thermal Imaging For a device with hot spots, the thermal resistance, junction-to-case, would be much higher than the guidelines given in MIL-STD-1835. One of the suppliers used thermal imaging to find hot spots on the die. Recommendation: Assign a task group to evaluate the effectiveness of thermal imaging at the product development stage.

Class Y↗
NASA NTRS2018

Optimization of Second Fault Detection Thresholds to Maximize Mission POS

In order to support manned spaceflight safety requirements, the Space Launch System (SLS) has defined program-level requirements for key systems to ensure successful operation under single fault conditions. To accommodate this with regards to Navigation, the SLS utilizes an internally redundant Inertial Navigation System (INS) with built-in capability to detect, isolate, and recover from first failure conditions and still maintain adherence to performance requirements. The unit utilizes multiple hardware- and software-level techniques to enable detection, isolation, and recovery from these events in terms of its built-in Fault Detection, Isolation, and Recovery (FDIR) algorithms. Successful operation is defined in terms of sufficient navigation accuracy at insertion while operating under worst case single sensor outages (gyroscope and accelerometer faults at launch). In addition to first fault detection and recovery, the SLS program has also levied requirements relating to the capability of the INS to detect a second fault, tracking any unacceptable uncertainty in knowledge of the vehicle's state. This detection functionality is required in order to feed abort analysis and ensure crew safety. Increases in navigation state error and sensor faults can drive the vehicle outside of its operational as-designed environments and outside of its performance envelope causing loss of mission, or worse, loss of crew. The criteria for operation under second faults allows for a larger set of achievable missions in terms of potential fault conditions, due to the INS operating at the edge of its capability. As this performance is defined and controlled at the vehicle level, it allows for the use of system level margins to increase probability of mission success on the operational edges of the design space. Due to the implications of the vehicle response to abort conditions (such as a potentially failed INS), it is important to consider a wide range of failure scenarios in terms of both magnitude and time. As such, the Navigation team is taking advantage of the INS's capability to schedule and change fault detection thresholds in flight. These values are optimized along a nominal trajectory in order to maximize probability of mission success, and reducing the probability of false positives (defined as when the INS would report a second fault condition resulting in loss of mission, but the vehicle would still meet insertion requirements within system-level margins). This paper will describe an optimization approach using Genetic Algorithms to tune the threshold parameters to maximize vehicle resilience to second fault events as a function of potential fault magnitude and time of fault over an ascent mission profile. The analysis approach, and performance assessment of the results will be presented to demonstrate the applicability of this process to second fault detection to maximize mission probability of success.

Anzalone, Evan↗
NASA NTRS2018

6DOF Testing of the SLS Inertial Navigation Unit

The Navigation System on the NASA Space Launch System (SLS) Block 1 vehicle performs initial alignment of the Inertial Navigation System (INS) navigation frame through gyrocompass alignment (GCA). In lieu of direct testing of GCA accuracy in support of requirement verification, the SLS Navigation Team proposed and conducted an engineering test to, among other things, validate the GCA performance and overall behavior of the SLS INS model through comparison with test data. This paper will detail dynamic hardware testing of the SLS INS, conducted by the SLS Navigation Team at Marshall Space Flight Center's 6DOF Table Facility, in support of GCA performance characterization and INS model validation. A 6-DOF motion platform was used to produce 6DOF pad twist and sway dynamics while a simulated SLS flight computer communicated with the INS. Tests conducted include an evaluation of GCA algorithm robustness to increasingly dynamic pad environments, an examination of GCA algorithm stability and accuracy over long durations, and a long-duration static test to gather enough data for Allan Variance analysis. Test setup, execution, and data analysis will be discussed, including analysis performed in support of SLS INS model validation.

Geohagan, Kevin W.↗
DOE OSTI2021

Theory-Guided Inelastic Neutron Scattering of Crystalline Alkaline Aluminate Salts Bearing Principal Motifs of Solution-State Species

Aluminate salts precipitated from caustic alkaline solutions exhibit a correlation between the anionic speciation and the identity of the alkali cation in the precipitate, with the aluminate ions occurring either in monomeric (Al(OH) 4 – ) or dimeric (Al 2 O(OH) 6 2– ) forms. The origin of this correlation is poorly understood as are the roles that oligomeric aluminate species play in determining the solution structure, prenucleation clusters, and precipitation pathways. Characterization of aluminate solution speciation with vibrational spectroscopy results in spectra that are difficult to interpret because the ions access a diverse and dynamic configurational space. To investigate the Al(OH) 4 – and Al 2 O(OH) 6 2– anions within a well-defined crystal lattice, inelastic neutron scattering (INS) and Raman spectroscopic data were collected and simulated by density functional theory for K 2 [Al 2 O(OH) 6 ], Rb 2 [Al 2 O(OH) 6 ], and Cs[Al(OH) 4 ]·2H 2 O. These structures capture archetypal solution aluminate species: the first two salts contain dimeric Al 2 O(OH) 6 2– anions, while the third contains the monomeric Al(OH) 4 – anion. Here, comparisons were made to the INS and Raman spectra of sodium aluminate solutions frozen in a glassy state. In contrast to solution systems, the crystal lattice of the salts results in well-defined vibrations and associated resolved bands in the INS spectra. The use of a theory-guided analysis of the INS of this solid alkaline aluminate series revealed that differences were related to the nature of the hydrogen-bonding network and showed that INS is a sensitive probe of the degree of completeness and strength of the bond network in hydrogen-bonded materials. Results suggest that the ionic size may explain cation-specific differences in crystallization pathways in alkaline aluminate salts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Simulation of Inelastic Neutron Scattering Spectra Directly from Molecular Dynamics Trajectories

Inelastic neutron scattering (INS) is a widely used technique to study atomic and molecular vibrations. With the increasing complexity of materials and thus the INS spectra, being able to simulate the spectra from various atomistic models becomes an essential step and also a major bottleneck for INS data analysis. The conventional approach using density functional theory and lattice dynamics often falls short when the materials of interest are complex (e.g., defective, disordered, heterogeneous, amorphous, large-scale), for which molecular dynamics driven by an interatomic force field is a more common approach. In this paper, we demonstrate a method to directly convert molecular dynamics trajectories into simulated INS spectra, including not only fundamental but also higher order excitations. In this work, the results are compared with data collected on various representative samples from different neutron spectrometers. This development will open great opportunities by providing the key tool to perform in-depth analysis of INS data and to validate and optimize computer models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Association of AK4 Protein From Stem Cell–Derived Neurons With Cognitive Reserve

Background and Objectives: Identifying protein targets that provide cognitive reserve is a strategy to prevent and treat Alzheimer disease and Alzheimer disease related dementias (AD/ADRD). Previous studies using bulk human brain tissue reported 12 proteins associated with cognitive reserve. This study examined whether the same proteins from induced neurons (iNs) are associated with cognitive reserve of their human donors. Methods: Here, induced pluripotent stem cell (iPSC) lines were generated from cryopreserved peripheral blood mononuclear cells of older adults who were autopsied as part of the Religious Orders Study or Rush Memory and Aging Project. Neurons were induced from iPSCs using a standard neurogenin2 protocol. Tandem mass tag proteomics analyses were conducted on iNs day 21. Cognitive reserve of their human donors was measured as person-specific slopes of cognitive change not accounted for by common neuropathologies. Results: The 53 human donors died at a mean age of 91 years, all were non-Latino White, and 36 (67.9%) were female. Eighteen were diagnosed with Alzheimer dementia proximate to death, and 34 had pathologic AD diagnosis at autopsy. Approximately 60% of the donors had above-average cognitive reserve such that their cognition declined slower than an average person with comparable burdens of neuropathologies. Eight of the 12 candidate proteins were quantified in iNs proteomics analyses. Higher adenylate kinase 4 (AK4) expression in iNs was associated with lower cognitive reserve, consistent with the previous report for brain AK4 expression. Discussion: By replicating cortical protein associations with cognitive reserve in human iNs, these data provide a valuable molecular readout for studying complex clinical phenotypes such as cognitive reserve in a dish.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1972

Improved navigation by combining VOR/DME information with air or inertial data

The improvement was determined in navigational accuracy obtainable by combining VOR/DME information (from one or two stations) with air data (airspeed and heading) or with data from an inertial navigation system (INS) by means of a maximum-likelihood filter. It was found that the addition of air data to the information from one VOR/DME station reduces the RMS position error by a factor of about 2, whereas the addition of inertial data from a low-quality INS reduces the RMS position error by a factor of about 3. The use of information from two VOR/DME stations with air or inertial data yields large factors of improvement in RMS position accuracy over the use of a single VOR/DME station, roughly 15 to 20 for the air-data case and 25 to 35 for the inertial-data case. As far as position accuracy is concerned, at most one VOR station need be used. When continuously updating an INS with VOR/DME information, the use of a high-quality INS (0.01 deg/hr gyro drift) instead of a low-quality INS (1.0 deg/hr gyro drift) does not substantially improve position accuracy.

Bobick, J. C.↗
NASA NTRS2002

Integrated INS/GPS Navigation from a Popular Perspective

Inertial navigation, blended with other navigation aids, Global Positioning System (GPS) in particular, has gained significance due to enhanced navigation and inertial reference performance and dissimilarity for fault tolerance and anti-jamming. Relatively new concepts based upon using Differential GPS (DGPS) blended with Inertial (and visual) Navigation Sensors (INS) offer the possibility of low cost, autonomous aircraft landing. The FAA has decided to implement the system in a sophisticated form as a new standard navigation tool during this decade. There have been a number of new inertial sensor concepts in the recent past that emphasize increased accuracy of INS/GPS versus INS and reliability of navigation, as well as lower size and weight, and higher power, fault tolerance, and long life. The principles of GPS are not discussed; rather the attention is directed towards general concepts and comparative advantages. A short introduction to the problems faced in kinematics is presented. The intention is to relate the basic principles of kinematics to probably the most used navigation method in the future-INS/GPS. An example of the airborne INS is presented, with emphasis on how it works. The discussion of the error types and sources in navigation, and of the role of filters in optimal estimation of the errors then follows. The main question this paper is trying to answer is 'What are the benefits of the integration of INS and GPS and how is this, navigation concept of the future achieved in reality?' The main goal is to communicate the idea about what stands behind a modern navigation method.

Omerbashich, Mensur↗
NASA NTRS2017

Systems and Methods for Determining Inertial Navigation System Faults

An inertial navigation system (INS) includes a primary inertial navigation system (INS) unit configured to receive accelerometer measurements from an accelerometer and angular velocity measurements from a gyroscope. The primary INS unit is further configured to receive global navigation satellite system (GNSS) signals from a GNSS sensor and to determine a first set of kinematic state vectors based on the accelerometer measurements, the angular velocity measurements, and the GNSS signals. The INS further includes a secondary INS unit configured to receive the accelerometer measurements and the angular velocity measurements and to determine a second set of kinematic state vectors of the vehicle based on the accelerometer measurements and the angular velocity measurements. A health management system is configured to compare the first set of kinematic state vectors and the second set of kinematic state vectors to determine faults associated with the accelerometer or the gyroscope based on the comparison.

Bharadwaj, Raj Mohan↗
DOE OSTI2022

Computational investigation of hydrogen-induced phonon changes in carbon fiber

Optical vibrational spectroscopy has shown promise as a noninvasive means of monitoring the mechanical properties of carbon fiber (CF), which is increasingly used for industrial and consumer purposes. However, interpretation of optical vibrational spectra for solid materials is inferential, particularly when defects are present. Because inelastic neutron scattering (INS) spectroscopy is not subject to selection rules, the full vibrational spectra can be measured. And, identifying correlations between INS features and tensile properties can assist in the interpretation of spectra from more commonly used optical vibrational spectroscopic techniques, such as Raman and infrared (IR) spectroscopy. Recent INS experiments on high-performance commercial carbon fibers showed features near 900 and 1100 cm –1 in addition to a broad feature near 3000 cm –1 that increased in intensity with decreasing tensile strength. These features were assigned to hydrogen defects. Here, we use density functional theory to simulate the INS spectra of several hydrogen defect geometries in graphite as a model for carbon fiber structure units, confirming the experimental assignment of these peaks to hydrogen modes and providing insights into the structure and lattice dynamics of the defects.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Lattice dynamics of high-pressure hydrides studied by inelastic neutron scattering

Due to the small mass and anomalously large neutron scattering cross-section of proton (about 80 barns compared to a few barns for other nuclei), inelastic neutron scattering is considered as one of the most effective tools in studying optical vibrations of hydrogen atoms in metal hydrides. The current review is focused on the binary hydrides of 3d- and 4d-metals of groups VI–VIII, which were produced at high hydrogen pressures of several gigapascals in relatively large quantities of hundreds of mg, quenched to low temperature and studied by INS ex situ at ambient pressure with high statistical accuracy. One of the unusual effects revealed by INS is a strong increase in the strength of the metal-hydrogen interactions with decreasing atomic number of the d-metal accompanied by an increase in the Me-H distance. Based on the available experimental results, the spectra g(E) of the phonon density of states and temperature dependencies CV(T) of the heat capacity at constant volume at T up to 1000 K have been derived in this paper and presented both in the figures and in digital form. This provides the reference data for the theoretical investigations of the crystal structures and compositions of new practically important hydrides giving the opportunity to validate calculation methods by comparing the calculated g(E) and CV(T) with the accurate experimental dependencies for the binary hydrides. Recent INS studies showed [R.A. Klein et al., J. Alloy. Compd. 894 (2022) 162381] that the fingerprints of anomalously short H-H separations of 1.6 Å violating the “2 Å rule” can be easily and unambiguously identified in the complex INS spectra of quaternary hydrides (La,Ce)NiInH 1+x . This makes neutron spectroscopy an attractive means for obtaining valuable data in the search for novel hydrides with a record high hydrogen capacity.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Inelastic Neutron Scattering from Thin Film Biaxially Oriented Polyethylene Terephthalate

Recent interest in emerging processes for polymer manufacturing and bio-based chemistries for direct chemical recycling/upcycling has motivated new research focused on a deeper understanding of atomic-scale polymer properties and how they influence macroscopic phenomena. Uncovering the fundamental properties of polymers that give rise to macroscopic behavior could enable new pathways for improved recyclability or utilization of alternative “greener” polymer analogues. In this study, the neutron vibrational spectrum was measured for a film of biaxially oriented polyethylene terephthalate (BoPET) using inelastic neutron scattering (INS), to investigate the relationship between the structure and dynamics of a widely used polymer. Compared to conventional spectroscopic techniques, the use of INS is advantageous for polymeric materials due to the absence of selection rules (i.e., all transitions are allowed), broad-band energy range, and considerable sensitivity to hydrogen modes. In order to distinguish the vibrational modes caused by trans and gauche rotational isomerism, the normal modes of vibration were calculated from a density functional theory-optimized structure of crystalline PET (cPET), representative of the all-trans state, and compared with INS from “highly crystalline” PET powder. Although in- and out-of-plane wagging of hydrogens on the ring structure exhibit significant contribution to both BoPET and cPET spectra, the wagging, rocking, and twisting modes of hydrogen on the ethylene glycol group are, in most cases, conformation-specific. These results were further rationalized by investigating the role of hyperconjugation in stabilizing both conformations using the natural bond order method. Here, through comparison of experimental and calculated INS results, this work provides the fundamental basis for discovering the role of structure and dynamics in shaping the macroscopic properties of PET and polymer analogues.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Inelastic Neutron Scattering Study of Magnetic Exchange Pathways in MnS

We report an investigation of the magnetic structure and magnetic exchange pathways in MnS via neutron scattering methods, aided by density functional theory (DFT) modeling. The material has been confirmed to undergo antiferromagnetic (AFM) ordering at 152 K, with the magnetic structure representing AFM stacking of ferromagnetic (FM) (111) planes of Mn magnetic moments. Correspondingly, the magnetic structure is described by a propagation vector k = (1/2, 1/2, 1/2), with the volume of the magnetic unit cell being 8 times larger than the volume of the nuclear unit cell. Analysis of inelastic neutron scattering (INS) data collected on a powder sample of MnS revealed that the next-nearest-neighbor magnetic exchange constant (J 2 ) exceeds the nearest-neighbor exchange constant (J 1 ) by more than 3 times, while in the case of MnO, which exhibits the same nuclear and magnetic structures as MnS, the J 2 /J 1 ratio was reported to be below 1.5. Although for MnO the signs of both J 1 and J 2 indicated AFM exchange interactions, machine-learning INS data analysis in combination with DFT calculations suggests that the INS data collected on MnS are best described with J 1 < 0 and J 2 > 0, corresponding to FM and AFM exchange couplings, respectively. To achieve a satisfactory fit to the experimentally observed data, the Hamiltonian used to model the INS spectra also included the next-next-nearest-neighbor magnetic exchange constant (J 3 ). The best-fit model has been obtained with the values of the exchange constants J 1 = -0.27 meV, J 2 = 1.05 meV, and J 3 = -0.19 meV.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Computing inelastic neutron scattering spectra from molecular dynamics trajectories

Abstract Inelastic neutron scattering (INS) provides a weighted density of phonon modes. Currently, INS spectra can only be interpreted for perfectly crystalline materials because of high computational cost for electronic simulations. INS has the potential to provide detailed morphological information if sufficiently large volumes and appropriate structural variety are simulated. Here, we propose a method that allows direct comparison between INS data with molecular dynamics simulations, a simulation method that is frequently used to simulate semicrystalline/amorphous materials. We illustrate the technique by analyzing spectra of a well-studied conjugated polymer, poly(3-hexylthiophene-2,5-diyl) (P3HT) and conclude that our technique provides improved volume and structural variety, but that the classical force field requires improvement before the morphology can be accurately interpreted.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Libration of hydroxyl groups in layered aluminum (oxy)hydroxides and other material analogs: insights from inelastic neutron scattering and theory

We analyzed the hydroxyl librational signatures of five structurally related aluminum (oxy)hydroxides, using inelastic neutron scattering (INS) and plane-wave lattice dynamics simulations. A clear trend across these aluminum-containing phases illustrates the relationship between hydrogen bonding, local atomic structure, and the spectral location and profile of the librational bands. The INS spectra have been compared to previous optical spectroscopy and computational studies, highlighting the complementary nature of the INS technique. Taking into account other structurally or chemically related material analogs, we have identified a correlation between a blueshift (to higher energy) of the upper librational band edge and the geometry of the hydrogen bond interactions, mirroring (with opposite correlation) the well-known redshift in the intramolecular O–H stretching energy with increasing hydrogen bond strength. For hydroxyl groups that do not participate in hydrogen bonding effectively, the bending librations occur at lower energies and hybridize with metal–oxygen lattice modes. Standard density functional theory approximations, including dispersion corrections, struggle to correctly predict vibrational frequencies of motions dominated by H but perform well for metal–oxygen modes, allowing us to make detailed mode assignments in several cases, including a demonstration of how layer-to-layer disorder in boehmite hydrogen bond orientations is reflected in the sharp but minor low energy peaks (at ∼70–80 meV) of the INS spectrum.

Wang, Hsiu-Wen [Oak Ridge National Laboratory (ORN↗
DOE OSTI2026

Machine learning inversion of interatomic force constants from single-crystal inelastic neutron scattering

Atomic vibrations govern many macroscopic properties of materials, but experiments to comprehensively probe them remain challenging. Inelastic neutron scattering (INS) is a powerful technique to map phonon dispersions in crystals, especially when leveraging modern time-of-flight (ToF) spectrometers with large detectors. However, efficiently and robustly extracting interatomic force constants (FCs) parameterizing phonon dynamics from experimental spectra remains a bottleneck due to the complexity and high dimensionality of ToF INS datasets. Here, we present a machine learning approach for the direct inversion of FCs from single-crystal INS measurements. The framework leverages synthetic training data generated using universal machine-learned force fields and an efficient physics-based forward model. We benchmark two neural architectures–one emphasizing structured latent representation learning and the other direct, supervised spectral regression–across simulated datasets for two materials under idealized and noisy conditions. The latent-representation model is subsequently applied to experimental single-crystal INS data on germanium. The model is shown to reproduce FCs derived from both first-principles simulations and from iterative optimization, and furthermore achieves reliable inference even from sparse, single-orientation measurements representing short data acquisitions. Analysis of the learned latent space reveals semantically continuous and physically interpretable encodings that support strong cross-domain generalization. By bridging theoretical and experimental domains, we establish a path toward rapid inversion of experimental spectra and data-driven interpretation of temperature-dependent lattice dynamics.

42 ENGINEERING↗
DOE OSTI2024

Implementation of a laser–neutron pump–probe capability for inelastic neutron scattering

Knowledge about nonequilibrium dynamics in spin systems is of great importance to both fundamental science and technological applications. Inelastic neutron scattering (INS) is an indispensable tool to study spin excitations in complex magnetic materials. However, conventional INS spectrometers currently only perform steady-state measurements and probe averaged properties over many collision events between spin excitations in thermodynamic equilibrium, while the exact picture of re-equilibration of these excitations remains unknown. In this paper, we report on the design and implementation of a time-resolved laser–neutron pump–probe capability at hybrid spectrometer (beamline 14-B) at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory. This capability allows us to excite out-of-equilibrium magnons with a nanosecond pulsed laser source and probe the resulting dynamics using INS. Here, we discussed technical aspects to implement such a capability in a neutron beamline, including choices of suitable neutron instrumentation and material systems, laser excitation scheme, experimental configurations, and relevant firmware and software development to allow for time-synchronized pump–probe measurements. We demonstrated that the laser-induced nonequilibrium structure factor is able to be resolved by INS in a quantum magnet. In conclusion, the method developed in this work will provide SNS with advanced capabilities for performing out-of-equilibrium measurements, opening up an entirely new research direction to study out-of-equilibrium phenomena using neutrons.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗