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Simplified Aid for Extra-Vehicular Activity Rescue (SAFER) Battery Assessment

In 2013, the Boeing Company model 787-8 Dreamliner commercial aircraft experienced three catastrophic lithium (Li) battery failures. The cause of each failure resulted in a single-cell thermal runaway (TR) condition, which propagated to adjacent battery cells. Two of the failures involved rechargeable lithium-ion (Li-Ion) batteries, and the third event involved a nonrechargeable lithium-manganese dioxide (Li-MnO2) battery. In response to these Li battery failures, the NASA Engineering and Safety Center (NESC) approved a technical assessment of the International Space Station Simplified Aid for Extra-Vehicular Activity Rescue (SAFER) Li non-rechargeable battery. This assessment was conducted to evaluate the SAFER Li nonrechargeable battery safety design features against Boeing 787 Dreamliner Li battery failure lessons learned. Specifically, this investigation focused on assessing the severity of a SAFER battery TR hazard conditions.

Iannello, Christopher J.

Reliability Models and Demonstration of a Fault-Tolerant Motor Concept for Vertical Takeoff and Landing Vehicles

This report documents the completion of the Revolutionary Vertical Lift Technology Project Annual Performance Indicator 24-3.2.4.1: “Apply and document reliability prediction for high reliability motor concept.” Two modeling tools were completed for calculation of reliability of fault-tolerant (FT) motors, and key FT operations of a modular FT motor were demonstrated experimentally. The two models are complementary tools for the stakeholder and user community. Both models employ Markov chain theory. The first model is a time-homogeneous Markov chain model, and the second is a time-inhomogeneous Markov-Weibull model. This report’s main sections are as follows: 1.0 Introduction, 2.0 Theory, 3.0 Motor Reliability Models, 4.0 Validation of FT Operation by Hardware Demonstration, and 5.0 Concluding Remarks. Novel contributions to the field include development of a modular FT motor concept for electrified vertical takeoff and landing (eVTOL) application, solution methods to solve the reliability calculations, development of figures of merit, and the introduction of “linked chains” to formulate a building-block approach for time-inhomogeneous Markov-Weibull modeling of motor reliability. Example case studies have been completed, and results are provided and discussed herein. A four-module FT motor concept was developed to a preliminary-design level of detail. This eVTOL FT motor concept was designed for galvanic, magnetic, and thermal isolation of stator winding faults. The reliability of the concept motor was calculated using a time-inhomogeneous Markov chain model. Employing average failure rate as a metric, 570 times greater reliability was achieved as compared to a baseline motor without fault tolerance. A demonstrator motor was built and tested. The testing demonstrated the key features of FT operation and validated the essential premises of the FT motor concepts presented herein. The experiments included successful demonstration of the feasibility of the following four key FT features: (1) terminal open-circuit operation, (2) thermal isolation after fault, (3) terminal short-circuit operation, and (4) internal short-circuit operation. These works indicate that FT modular motor drives offer promise for addressing the daunting reliability gap that electric aircraft propulsor drives are facing relative to the best conventional motor drive technology that is available today.

Electric Motor

First multi-institutional systematic comparison of the neutron ambient dose equivalent produced by proton therapy systems

Objective. Isochronous cyclotrons, synchrocyclotrons, and synchrotrons are used to accelerate protons for proton therapy. An accurate measurement of neutron doses generated by these accelerators and associated delivery systems and its clinical relevance requires systematic protocols and proper neutron dosimetry for a meaningful assessment. We present the first comprehensive comparison of neutron ambient dose equivalent (H*(10)) produced by clinically operational proton therapy systems. Approach. Treatment plans with 10 cm modulation-depth and ranges of 10 cm (R10M10) and 25 cm (R25M10) were created to cover a 10 × 10 × 10 cm 3 water target. The pencil beam scanning proton therapy machines studied were: two gantry-mounted synchrocyclotrons (Hyperscan, Mevion, half-gantry), two isochronous cyclotrons (ProBeam, Varian, full-gantry), one isochronous cyclotron (Proteus, IBA, full-gantry), and two synchrotrons (PROBEAT, Hitachi, full- and half-gantry). Proton beams were delivered to 30 × 30 × 40 cm 3 plastic water phantoms. WENDI-II and LUPIN-BF3-NP neutron rem-meters were positioned at three angles (0°, 45°, 90°) relative to the beam direction to measure the neutron H*(10) at distances between 50–300 cm from the isocenter. Main results. H*(10) showed dependence on beam energy, machine type, and measurement location. The highest reading was for the gantry-mounted synchrocyclotron, whereas other systems produced approximately comparable neutron doses. In all cases, the H*(10) reduced with distance from the isocenter. The H*(10) drop at 2 m distance compared to that at 0.5 m was a factor of ∼5 for the gantry-mounted synchrocyclotron whereas in other systems the decrease was a factor of 10. The WENDI-II device suffered from dead-time-associated under-estimation of the dose by a factor of ∼2–3 under the synchrocyclotron beam due to its high dose-per-pulse. However, WENDI-II and LUPIN-BF3-NP results were within reasonable agreement in isochronous cyclotron and synchrotron beams, indicating that both devices are suitable for those systems. Significance. Neutron H*(10) is dependent on various parameters including beam energy, measurement location, as well as machine design. Caution must be exercised in choosing the appropriate neutron-dose-measurement device to be used for low-duty-factor, particularly in high-instantaneous-rate proton delivery systems. By delivering the same volumetric proton dose across different machines, this work provides a benchmark for inter-system comparisons and serves as a foundation for future studies.

LUPIN

Erosion of high-Z refractory coatings for helicon plasma source window

Proto-MPEX (Materials Plasma Exposure eXperiment), a linear plasma device (LPD), using a high power radio frequency (RF) (⩾100 kW, 13.56 MHz) helicon plasma source, has suffered RF sheath-induced window erosion. The sputtered impurities from the window surface transport toward the downstream target affecting plasma-material interaction studies. The rectified sheath voltage formed was high enough to cause window erosion by light ions due to its low-Z components (e.g. Si 3 N 4 and AlN). Hence, we are proposing impurity mitigation strategies, which involve the application of a Faraday screen to lower the rectified sheath voltage and the application of high-Z refractory coatings on the existing window plasma-facing surface. In this work, we report the erosion of two different coatings, i.e., tantalum oxide (Ta 2 O 5 ) and hafnium oxide (HfO 2 ) on a silicon nitride (Si 3 N 4 ) window material under conditions of low-energy deuterium (D) ion impact, well below the Ta 2 O 5 sputtering energy threshold (i.e. 250 eV). The test samples were RF-biased and exposed to a high D-ion fluence (∼10 26 m −2 ) in Plasma Interaction with Surface Component Experimental Station (PISCES-A) LPD. The experimentally measured sputtering yields of the high-Z refractory coatings below the sputtering energy threshold of Ta 2 O 5 indicate an increased erosion due to the plasma impurities, especially due to oxygen. Improving the vacuum level could reduce the oxygen impurities and increase the lifespan of the coated helicon window for plasma operation. Post-surface analysis indicates no preferential erosion of oxygen or enrichment of the high-Z surface component. This is likely due to an effective energy transfer from the impurity ion for sputtering of the high-Z component in the coating. With the reduced rectified sheath voltage at the window surface and improved vacuum conditions, the proposed high-Z refractory coatings offer a promising solution for reducing window erosion in future MPEX plasma operations at ORNL.

RF bias

Simulating the Lunar Thermal Environment for the Surface-Deployed LEMS Artemis III TVAC Test

The Lunar Environment Monitoring Station (LEMS) is an autonomous, survive-the lunar-night seismic suite to be deployed on the Lunar surface by the Artemis III crew and designed to operate continuously for two years. It will see the extremes of the Lunar south pole thermal environment where surface temperatures range from -200°C to +20°C and where nighttime duration is at least 354 hours. Given power and mass constraints, the thermal system is limited to 2.5 Watts of heat during the lunar night. Presented is the system thermal vacuum test plan and configuration to validate the thermal control system performance in a flight-like environment. The test will measure the nighttime heat leaks for the bus and 18 seismometers to ensure lunar night survival and operability.

Thermal

Simulating the Lunar Thermal Environment for the Surface-Deployed LEMS Artemis III TVAC Test

The Lunar Environment Monitoring Station (LEMS) is an autonomous, survive-the lunar-night seismic suite to be deployed on the Lunar surface by the Artemis III crew and designed to operate continuously for two years. It will see the extremes of the Lunar south pole thermal environment where surface temperatures range from -200°C to +20°C and where nighttime duration is at least 354 hours. Given power and mass constraints, the thermal system is limited to 2.5 Watts of heat during the lunar night. Presented is the system thermal vacuum test plan and configuration to validate the thermal control system performance in a flight-like environment. The test will measure the nighttime heat leaks for the bus and 18 seismometers to ensure lunar night survival and operability.

Thermal

Simulating the Lunar Thermal Environment for the Surface-Deployed LEMS Artemis III TVAC Test

The Lunar Environment Monitoring Station (LEMS) is an autonomous, survive-the lunar-night seismic suite to be deployed on the Lunar surface by the Artemis III crew and designed to operate continuously for two years. It will see the extremes of the Lunar south pole thermal environment where surface temperatures range from -200°C to +20°C and where nighttime duration is at least 354 hours. Given power and mass constraints, the thermal system is limited to 2.5 Watts of heat during the lunar night. Presented is the system thermal vacuum test plan and configuration to validate the thermal control system performance in a flight-like environment. The test will measure the nighttime heat leaks for the bus and 18 seismometers to ensure lunar night survival and operability.

TVAC

SAM Code Enhancements for Fission Product Tracking of Noble Gases and Metals in MSRs

This report documents fiscal year 2026 enhancements to the System Analysis Module (SAM) for modeling fission product transport in liquid-fueled molten salt reactors (MSRs). The work advances three principal areas: noble gas transport, noble metal deposition, and user interface improvements. The noble gas transport capability integrates drift-flux gas transport, Henry’s law two-film interphase mass transfer with pressure-based nucleation suppression, Knudsen-regime pore diffusion into porous graphite with a conjugate salt-graphite interface constraint, built-in material properties, five Sherwood-number mass transfer correlations including three derived from high-fidelity NekRS simulations, and xenon-135 reactivity feedback through SAM’s point-kinetics model. This work also presents a comprehensive verification test suite, including new analytically verified cases for pressure-dependent onset of interphase gas transfer in a stagnant vertical pipe, a postulated FLiBe-graphite Xe extraction permeator, a gravity riser with a fission-product source, and a descending pipe with gas redissolution driven by hydrostatic pressure. A machine learning framework for bubble rise velocity prediction in molten salt systems is developed and benchmarked on molten-salt and diverse aqueous bubble datasets. The best-performing fine-tuned transfer-learning networks achieve an 82% reduction in RMSE relative to the Clift correlation, and is implemented directly in SAM. The noble metal transport capability is developed, including a liquid-wall deposition model and a gas-surface flotation mechanism that transfers insoluble particles entrained by sparging gas to wetted structures. Verification tests and demonstration cases cover the surface deposition, flotation efflux, and flotation shedding. Finally, a new [SpeciesTransport] input structure replaces positional global vectors with selfcontained, order-independent, named species blocks, simplifies the specification of multiphase species and decay chains, and remains fully compatible with existing SAM input files. Together, these developments improve the physical fidelity, verification basis, and usability of SAM for system-level analyses of fissionproduct behavior in MSRs.

Mui, Travis (ORCID:0000000303736470)

Landmark Publications in Analytical Atomic Spectrometry: Fundamentals and Instrumentation Development

The almost-two-centuries history of spectrochemical analysis has generated a body of literature so vast that it has become nearly intractable for experts, much less for those wishing to enter the field. Authoritative, focused reviews help to address this problem but become so granular that the overall directions of the field are lost. This broader perspective can be provided partially by general overviews but then the thinking, experimental details, theoretical underpinnings, and instrumental innovations of the original work must be sacrificed. In the present compilation, this dilemma is overcome by assembling the most impactful publications in the area of analytical atomic spectrometry. Each entry was proposed by at least one current expert in the field and supported by a narrative that justifies its inclusion. The entries were then assembled into a coherent sequence and returned to contributors for a round-robin review. A total of 48 scientists participated in this endeavor, contributing a combined list of 1055 individual articles spanning 17 sub-disciplines of spectrochemical analysis into what the current community views as “key” publications. Of these cited articles, 60 received nominations from four or more scientists, establishing them as the most indispensable reading materials. The outcome of this collaborative effort is intended to serve as a valuable resource not only for current practitioners in atomic spectroscopy but also for present and future students who represent coming generations of analytical atomic spectroscopists.

Instruments & Instrumentation

Lunar Surface Crater Thermal Effects on Lander Radiator Performance

Lunar surface craters smaller than the spatial resolution of surface meshes used in typical Lunar surface thermal models (10 to 60 meters per pixel) may impact the accuracy of thermal model extrema predictions. The goal of this study is to investigate the thermal sensitivity of representative lander systems with realistic thermal surface orientations in bare and cratered terrain environments at relevant Artemis mission locations. This thermal analysis task investigates the impact of lunar surface craters on lander radiator performance by comparing heat rejection capability results between bare and cratered terrain environments. This study examines external body-mounted lander radiator thermal performance across varying lander heights (5.5m, 20m, 50m) and radiator orientations (horizontal, 45º tilted, and vertical) at two representative Artemis mission latitudes (-89.5ºS and -82.5ºS), spanning from the Shackleton Connecting Ridge to Mons Mouton Plateau.

Lunar Surface

Challenges in Continuous In-Field Critical Current Testing of High-Temperature Superconducting Tapes: Thermal and Mechanical Perspectives

High-temperature superconductors (HTS) are essential for ultra-high-field applications requiring exceptional current-carrying capacity under extreme conditions. However, systematic characterization of critical current in long-length conductors remains challenging due to complex thermal, electromag netic, and mechanical interactions during continuous testing. This study reports the development of a continuous in-field magnetization testing system for position-dependent critical current measurement in HTS tapes at 20 K under 7.5 T fields applied normal to the tape plane, enabling identification of performance-limiting regions that could compromise magnet stability. Here, the system addresses two fundamental challenges inherent to cryogenic reel to-reel testing. First, thermal management requires continuous cooling of a moving conductor to 20 K, achieved through liquid nitrogen precooling combined with a 100 W@20 K Gifford McMahon cryocooler. Second, screening currents in high fields generate Lorentz forces that induce twisting, bowing, and potential delamination. To mitigate these risks, we propose mechanical reinforcement and active current density suppression strategies. Numerical simulations using the stream function formulation reveal four primary failure modes: frictional heating at guide interfaces, unstable equilibria causing deformation, transverse current-induced stresses at guide transitions, and unsupported forces in vertical spans. Our mitigation strategies include PTFE coated guides to minimize friction, spring-loaded stabilization mechanisms to maintain tape alignment, controlled pre-heating using the liquid nitrogen thermal jacket to suppress critical current at stress points, and optimized guide positioning to minimize force accumulation. The experimental system is nearing completion, with testing planned to commence within two months. Preliminary validation at 65 K under 0.5 T demonstrates strong correlation between simulation-predicted mechanical instabilities and observed critical current variations during conductor tran sitions through the measurement region. These findings establish a robust foundation for quality assurance protocols essential to next-generation superconducting magnet applications.

Chen, Siwei [Princeton Plasma Physics Laboratory (

The Effect of Gravity on the Combustion Synthesis of Porous Ceramics and Metal Matrix Composites

Combustion synthesis (self propagating, high temperature synthesis-SHS) is a novel technique that is capable of producing many advanced materials. The ignition temperature (Tig) of such combustion synthesis reactions is often coincident with that of the lowest melting point reactant. The resultant liquid metal wets and spreads around the other solid reactant particles of higher melting points, thereby improving the reactant contact and kinetics, followed by formation of the required compounds. This ignition initiates a combustion propagating wave whose narrow reaction front rapidly travels through the reactants. Since this process is highly exothermic, the heat released by combustion often melts the reactant particles ahead of the combustion front and ignites the adjacent reactant layer, resulting in a self-sustaining reaction. Whenever a fluid phase (liquid or gas) is generated by the reaction system, gravity-driven phenomena can occur. Such phenomena include convective flows of fluid by conventional or unstable convection and settling of the higher density phases. A combustion process is often associated with various kinds of fluid flow. For instance, if the SHS reaction is carried out under inert or reactive gas atmospheres, or a volatile, e.g., B2O3, is deliberately introduced as a reactant, convective flows of the gas will occur due to a temperature gradient existing in the atmosphere when a combustion wave is initiated. The increased gas flow will produce a porous (or expanded) SHS product. Owing to the highly exothermic nature of many SHS reactions, liquid phase(s) can also form before, at, or after the combustion front. The huge temperature gradient at the combustion front can induce convective flows (conventional or unstable) of the liquid phase. Each of these types of convective fluid flow can change the combustion behavior of the synthesizing reaction, and, therefore, the resultant product microstructure. In addition, when two or more phases of different density are produced at or ahead of the propagating combustion front settling of the higher density phase will occur resulting in a non-uniform product microstructure and properties.

J J Moore

Optical properties of morphologically complex black carbon aerosols: Effects of coatings

Optical properties are computed for fractal-like aggregate black carbon (BC) aerosols coated with different substances. Two models are used for these aerosols: (i) the coated aggregate model (model I), where coating is added to the voids and surroundings of BC fractal-like aggregates; and (ii) the closed-cell aggregate model (model II), where coating is added concentrically to each monomer of BC fractal-like aggregates. Our results favor choosing the coated aggregate model (model I) to simulate scattering and absorption by coated BC aerosols because this model is morphologically more realistic, and because this model yields mass absorption cross section (MAC) and backscattering linear depolarization ratio (LDR) values that are consistent with field measurements. Moreover the corresponding computed degree of linear polarization (DoLP) and LDR values are very sensitive to changes in the coating volume fraction (fvol) and the coating refractive index (m). With the same absorbing BC core, the MAC value increases steadily with increasing fvol and m values. For example, using a density of 1.8 g/cm 3 and BC refractive index 1.95 + i0.79, the calculated MAC values for uncoated BC aggregates range from 6.2 to 6.8 m 2 /g at 0.55 µm. When coating material is applied to the BC aggregates, the calculated MAC values for model I particles increase to between 9.8 and 13.2 m 2 /g (depending on m) when fvol = 87.5%. The backscattering LDR values also tend to increase with the increasing m values for the shapes and sizes considered in our study. For model I particles, the backscattering LDR values span a wide range of 4.2–27.8% at a wavelength of 0.35 µm at fvol = 87.5% when m increases from 1.33 to 1.55. Our results are relevant to analyses of polarimetric and lidar observations of smoke particles, especially when these particles undergo hygroscopic growth.

Black carbon aerosols

A comparison of compact, presumably young with extended, evolved radio active galactic nuclei

Context.The triggering and evolution of active galactic nuclei (AGNs) and the interaction of the AGN with its host galaxy is an important topic in extragalactic astrophysics. Radio sources with peaked spectra (peaked spectrum sources, PSS) and compact symmetric objects (CSO) are powerful, compact, and presumably young AGNs and therefore particularly suitable to study aspects of the AGN-host connection. Aims.We use a statistical approach to investigate properties of a PSS-CSO sample that are related to host galaxies and could potentially shed light on the link between host galaxies and AGNs. The main goal is to compare the PSS-CSO sample with a matching comparison sample of extended sources (ECS) to see if the two have significant differences. Methods.We analysed composite spectra, diagnostic line diagrams, multi-band spectral energy distributions (MBSEDs), star formation (SF) indicators, morphologies, and cluster environments for a sample of 121 PSSs and CSOs for which spectra are available from the Sloan Digital Sky Survey (SDSS). The statistical results were compared with those of the ECS sample, where we generally considered the two subsamples of quasi-stellar objects (QSOs) and radio galaxies separately. The analysis is based on a large set of archival data in the spectral range from the ultraviolet to mid-infrared. Results.We find significant differences between the PSS-CSO and the ECS sample. In particular, we find that the ECS sample has a higher proportion of passive galaxies with a lower star formation activity. This applies to both sub-samples (QSOs or radio galaxies) as well as to the entire sample. The star formation rates of the PSS-CSO host galaxies with available data are typically in the range ∼0 to 5 ℳ ⊙ yr −1 , and the stellar masses are in the range 3 × 10 11 to 10 12 ℳ ⊙ . Secondly, in agreement with previous results, we find a remarkably high proportion of PSS-CSO host galaxies with merger signatures. The merger fraction of the PSS-CSO sample is 0.61 ± 0.07, which is significantly higher than that of the comparison sample (0.15 ± 0.06). We suggest that this difference can be explained by assuming that the majority of the PSSs and CSOs cannot evolve to extended radio sources and are therefore not represented in our comparison sample.

Astronomy & Astrophysics

Evaluation of Anomaly Detection Capability for Ground-Based Pre-Launch Shuttle Operations

This chapter will provide a thorough end-to-end description of the process for evaluation of three different data-driven algorithms for anomaly detection to select the best candidate for deployment as part of a suite of IVHM (Integrated Vehicle Health Management) technologies. These algorithms were deemed to be sufficiently mature enough to be considered viable candidates for deployment in support of the maiden launch of Ares I-X, the successor to the Space Shuttle for NASA's Constellation program. Data-driven algorithms are just one of three different types being deployed [3],[5]. The other two types of algorithms being deployed include a "rule-based" expert system, and a "model-based" system. Within these two categories, the deployable candidates have already been selected based upon qualitative factors such as flight heritage. For the rile-based system, SHINE (Spacecraft High-speed Inference Engine) has been selected for deployment, which is a component of BEAM (Beacon-based Exception Analysis for Multimissions) [4], a patented technology developed at NASA's JPL (Jet Propulsion Laboratory) and serves to aid in the management and identification of operational modes. For the "model-based" system, a commercially available package developed by QSI (Qualtech Systems, Inc.), TEAMS (Testability Engineering and Maintenance System) [1] has been selected for deployment to aid in diagnosis. In the context of this particular deployment, distinctions among the use of the terms "data-driven," "rule-based," and "model-based," call found in [5]. Although there are three different categories of algorithms that have been selected for deployment, our main focus in this chapter will be on the evaluation of three candidates for data-driven anomaly detection. These algorithms will be evaluated upon their capability for robustly detecting incipient faults or failures in the ground-based phase of pre-launch space shuttle operations, rather than based oil heritage as performed in previous studies [5]. Robust detection will allow for the achievement of pre-specified minimum false alarm and/or missed detection rates in the selection of alert thresholds. All algorithms will also be optimized with respect to all of these same criteria. Our study relies upon the use of Shuttle data to act as was a proxy for and in preparation for application to Ares I-X data, which uses a very similar hardware platform for the subsystems that are being targeted (TVC - Thrust Vector Control subsystem for the SRB (Solid Rocket Booster)).

False Alarms

Analysis of Surface and Bulk Behavior in Ni-Pd Alloys

The most salient features of the surface structure and bulk behavior of Ni-Pd alloys have been studied using the BFS method for alloys. Large-scale atomistic simulations were performed to investigate surface segregation profiles as a function of temperature, crystal face, and composition. Pd enrichment of the first layer was observed in (111) and (100) surfaces, and enrichment of the top two layers occurred for (110) surfaces. In all cases, the segregation profile shows alternate planes enriched and depleted in Pd. In addition, the phase structure of bulk Ni-Pd alloys as a function of temperature and composition was studied. A weak ordering tendency was observed at low temperatures, which helps explain the compositional oscillations in the segregation profiles. Finally, based on atom-by-atom static energy calculations, a comprehensive explanation for the observed surface and bulk features will be presented in terms of competing chemical and strain energy effects.

Ordering

Phase 1 Engagement Summary: Rural Alabama

An Alabama community coalition received technical assistance through the U.S. Department of Energy's Communities Local Energy Action Program (LEAP) to expand awareness of alternative transportation fuels through stakeholder engagement efforts. Phase 1 of the project centered on outreach, relationship-building, and the identification of community priorities. Through two workshops held in October and December 2024, the coalition engaged over 120 stakeholders - including county commissioners, school district representatives, and public and private fleet operators. These sessions included presentations from technical experts and industry partners, as well as a vehicle showcase and structured discussions to assess stakeholder needs and concerns. This report summarizes these efforts and identifies three key priority areas for Phase 2 of the project.

29 ENERGY PLANNING, POLICY, AND ECONOMY

Expansion of Check-Cases for 6DOF Simulation

This is the Appendix containing a description of the solution for Case 1 in the assessment, “Expansion of Check-Cases for 6DOF Simulation”. For cases of spherical gravity, it is possible to provide a two-body solution without recourse to numerical integration and thus it is accurate to machine precision. Python code for a Keplerian Propagator (propagate.py) which produced a reference trajectory for Case 1 is provided in this appendix. There is also code for generating test cases which was used as an independent verification of the propagator. This is a high-level description of the algorithm employed. The documentation of each function includes implementation details, including equations for each task.

Modeling