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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
DOE OSTI2026

Galaxy Size and Rotation Curve Diversity in ΛCDM with Baryons

The observed rotation curves of dwarf galaxies exhibit significant diversity at fixed halo mass, challenging galaxy formation within the cold dark matter (CDM) model. Previous cosmological galaxy formation simulations with baryonic physics fail to reproduce the full diversity of rotation curves, suggesting that there is a flaw in baryonic feedback models, observational bias, or that an alternative to CDM must be invoked. In this work, we use the Marvelous Massive Dwarf zoom-in simulations, a suite of high-resolution dwarf simulations with M 200 ∼ 10 10 –10 11 M ⊙ and M * ∼ 10 7 –10 9 M ⊙ , designed to target the mass range where the galaxy rotation curve diversity is maximized, i.e., between and 100 km s −1 . We add to this a set of low-mass galaxies from the Marvel Dwarf Zoom Volumes to extend the galaxy mass range to lower values. Our fiducial star formation and feedback models produce simulated dwarfs with a broader range of rotation curve shapes, similar to observations. These simulations both create dark matter cores via baryonic feedback, reproducing the slower-rising rotation curves, while also allowing for compact galaxies and steeply rising rotation curves. Our simulated dwarfs also reproduce the observed size–M * relation, including scatter, producing both extended and compact dwarfs for the first time in simulated field dwarfs. However, the slowly rising and high baryon mass fraction, as well as the steeply rising and low baryon mass fraction, remain missing. We explore star formation and feedback models and conclude that previous simulations may have had feedback that was too strong to produce compact dwarfs.

Cruz, Akaxia [Flatiron Institute, New York, NY (Un↗
DOE OSTI2026

In situ electric field X-ray total scattering reveals composition-dependent electromechanical strain mechanisms in (1 − x )BiFe 2/8 Ti 3/8 Mg 3/8 O 3 – x PbTiO 3 ceramics

Ferroelectric materials find many applications in energy and aerospace industries. A major challenge for ferroelectric materials is maintaining their properties at elevated temperatures. The (1 − x )BiFe 2/8 Ti 3/8 Mg 3/8 O 3 – x PbTiO 3 (BFTM–xPT) ferroelectric solid solution is a promising candidate for high-temperature applications as it has a high piezoelectric response while also maintaining its ferroelectric phase until a high Curie temperature (T C ) of 650 °C. In this work, we investigate the piezoelectric mechanism in BFTM–xPT, a novel high-T C ferroelectric ceramic. To elucidate the origin of its enhanced piezoelectric performance, relative to other piezoceramics of similar T C , in situ electric field X-ray total scattering experiments were performed. Total scattering combines Bragg scattering (diffraction) and diffuse scattering (pair distribution function), providing insight on various length scales. With information spanning different length scales, extrinsic contributions (i.e., domain wall motion and interphase boundary motion) can be separated from intrinsic contributions (i.e., piezoelectric lattice strain). We show that, for compositions within the morphotropic phase boundary (MPB, x = 0.325), the piezoelectric response is dominated by intrinsic piezoelectric lattice strain, whereas outside the MPB (x = 0.375) the major component of the piezoelectric response is from extrinsic mechanisms including an electric-field-induced phase transition and tetragonal domain wall motion. This article reveals that the origin of piezoelectric response in BFTM–xPT is composition-dependent and shows that high-performance materials may also be located outside the MPB. These findings can help guide material design to optimize properties for specific applications.

Richtik, Brooke N. [University of Calgary, AB (Can↗
NASA NTRS1989

Computational Fluid Dynamics at the Lewis Research Center: An Overview

Lewis is a multidisciplinary Center with strong research and development programs in aeronautical and space propulsion, power, space communications, space experiments and materials. Computational fluid dynamics (CFD) is playing an important and growing role in most of these areas. Described here is how CFD is integrated into these programs and highlights elements of the CFD activities. Examples are presented of codes developed to predict flow fields in advanced propulsion systems and several of the code validation experiments are described. The CFD effort at Lewis ranges from basic research on new and improved algorithms through code development to the application of these codes to specific engineering problems. Because of the substantial improvement in CFD's predictive capability, its use at Lewis is on a steep growth path, spreading rapidly into new areas which had not traditionally taken advantage of the techniques of numerical simulation. Multidisciplinary codes and the future direction of CFD at Lewis are discussed.

Robert M Stubbs↗
DOE OSTI2026

The Maximal Entanglement Limit in Statistical and High-energy Physics

These lectures advocate the idea that quantum entanglement provides a unifying foundation for both statistical physics and high-energy interactions. I argue that, at sufficiently long times or high energies, most quantum systems approach a Maximal Entanglement Limit (MEL) in which phases of quantum states become unobservable, reduced density matrices acquire a thermal form, and probabilistic descriptions emerge without invoking ergodicity or classical randomness. Within this framework, the emergence of probabilistic parton model, thermalization in the break-up of confining strings and in high-energy collisions, and the universal small-x behavior of structure functions arise as direct consequences of entanglement and geometry of high-dimensional Hilbert space.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Magnetically Arrested Circumbinary Accretion Flows

Abstract Binary systems with comparable masses and a surrounding accretion disk can accrete gas through spiral accretion streams penetrating the central cavity formed by tidal interactions. Using three-dimensional Newtonian magnetohydrodynamics simulations, we investigate the possibility of a magnetically arrested accretion flow through the cavity. Rather than solely continuously feeding the binary through spiral accretion streams, the accretion is regulated by the strong magnetic field inside the cavity. Transport of mass and angular momentum onto the binary then proceeds largely periodically in magnetic flux eruption episodes. The ejected flux tubes carry angular momentum outward and away from the binary, inject hot plasma into the disk, and can launch flares. This likely intermittent scenario could have potential implications for the emission signatures of supermassive black hole binaries and shed light onto the role magnetic fields play in the binary’s orbital evolution.

Astronomy & Astrophysics↗
DOE OSTI2025

Improving Ionic Conformality Across Polymer Electrolyte|Electrode Interfaces

Maintaining uniform ionic transport at electrode|electrolyte interfaces, i.e., ionic conformality, remains challenging in polymer electrolyte (PE)-based solid-state batteries. Morphological conformality does not necessarily imply ionic conformality. In PEs, which typically consist of a mechanically supporting component and distinct ionically conductive components, the rearrangement or depletion of mobile ion-conductive domains at interfaces can disrupt ionic transport pathways. Such localized ionic depletion contributes to interfacial instability and capacity degradation in high-voltage lithium-metal batteries. Herein, an electrolyte design approach aimed at minimizing interfacial heterogeneities is demonstrated through compositional adjustments, characterized by spatially resolved structural and chemical X-ray techniques and NMR diffusometry to elucidate ion transport dynamics. This approach improves ionic conformality at electrode interfaces, enhancing cycling stability in Li||LiNi 0.8 Co 0.1 Mn 0.1 O 2 (NMC811) coin and pouch cells cycled at high voltages. These results contribute to understanding interfacial behaviors in multiphase PEs and inform strategies for improving stability across solid-state battery interfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2026

The Development of Kinetic and Radiation Hydrodynamics Modeling of Thermonuclear Burn Propagation in Isochoric p - 11 B Through the Support of the INFUSE Program

The report summarizes DOE INFUSE-supported work between HB11 Energy and the University of Rochester’s TriForce Institute to improve computational modeling of advanced fusion fuels, especially proton–boron-11 (p- 11 B). The project extended the TriForce particle-in-cell/Monte Carlo collision code to include physics needed for dense, high-temperature p- 11 B burn studies, including p- 11 B fusion reactions, three-alpha-particle reaction products, relativistic Coulomb collisions, large-angle nuclear scattering, bremsstrahlung radiation, inverse bremsstrahlung absorption, and photon transport. The upgraded models were verified against focused physics tests and against known deuterium–tritium burn behavior. The study then used one-dimensional spherical simulations to estimate the conditions required for thermonuclear burn propagation in isochoric p- 11 B fuel. The calculations found that burn propagation is possible in the model, but only under very extreme hot-spot conditions, such as about 7000 g/cm 3 at 500 keV or 9000 g/cm 3 at 300 keV for a 20-micron hot spot. These conditions are much more demanding than current demonstrated inertial confinement fusion hot spots. The report concludes that the INFUSE collaboration successfully advanced kinetic and radiation modeling capabilities for p- 11 B fusion and provided useful estimates of ignition requirements. However, the simulated fuel gains remain below what would be needed for practical inertial fusion energy, and further work is needed to reconcile differences among kinetic, radiation-hydrodynamic, and analytic models and to identify more achievable target designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2026

Timing the Flames: Geostationary Satellite Detection of Diurnally Shifting Stubble Burning in Northwestern India

Post-monsoon open-field stubble burning in northwestern (NW) India—a key agricultural region known as the “breadbasket”—is a longstanding practice used to clear fields. Satellite observations spanning over two decades have revealed significant upward trends in crop production, vegetative greenness, and the frequency of post-harvest fires, with this last contributing to hazardous air quality during the peak burning season (mid-October to mid-November). Since 2022, thermal anomaly data from Aqua-MODIS and SNPP-VIIRS sensors have shown a sharp decline in reported fire events—an observation that contrasts starkly with the concurrent rise in regional aerosol loading detected from space. This apparent discrepancy became particularly pronounced in 2024–2025, prompting a closer examination using high-temporal-resolution imagery from the Advanced Meteorological Imager (AMI) on the geostationary satellite GEO-KOMPSAT-2A. These observations revealed a clear spike in fire-related signals occurring around and after 4:00 p.m. local time, i.e., outside the typical noon to 2:00 p.m. detection window of the MODIS and VIIRS. A fire detection algorithm exploiting the fire-sensitive shortwave-infrared 3.8 μm signal and its contrast to 11.2 μm infrared observations is designed to adopt AMI observations and applied to its multi-year observations (2019–2025). The resulting fire dataset unambiguously shows a gradual shift in stubble burning activity toward the late afternoon hours beginning in 2022 which is underreported by polar-orbiting satellites. The orbital drift of NASA’s MODIS sensor on the Aqua platform allows detection of some of the gradually shifting fires during afternoon hours, but the MODIS still misses a large number of fires occurring around and after 4 p.m. The AMI’s relatively coarse spatial resolution (~4 km), a consequence of its slant viewing geometry over NW India, imposes inherent limitations on quantifying the full extent of fire occurrences. The operational air quality forecasting models currently assimilate satellite fire detections predominantly captured during early afternoon overpasses of the MODIS and VIIRS. The temporal shift in fire activity complicates such forecast, leading to a substantial underestimation of emissions. Intense stubble burning and the resulting air pollution highlight the need for effective crop residue management practices for mitigating the frequency of open biomass burning and thereby reducing episodic degradation of air quality and its associated public health and economic impacts.

post-monsoon stubble burning; northwestern India;↗
DOE OSTI2025

Review on Preprocessing Strategies, Deactivation, Thermal Safety, and Future Perspectives in Lithium-Ion Battery Recycling

The rapid growth in the use of lithium-ion batteries (LIBs) in electric vehicles, consumer electronics, and renewable energy storage has made effective end-of-life management essential. Recycling LIBs is critical not only for resource recovery and environmental protection but also for ensuring safety and economic viability. This review focuses on the preprocessing technologies that precede typical recovery processes, including disassembly, sorting, discharging, electrolyte removal, dismantling, thermal treatment, separation, and flotation. These steps play a foundational role in determining the efficiency, safety, and environmental impact of LIB recycling. LIBs pose substantial fire and explosion risks due to residual charge, flammable electrolytes, and reactive materials. The conditions and successive progression of the exothermic reactions which lead to thermal runaway has been discussed. It also explores secure deactivation techniques such as external circuit discharge, saline immersion, and thermomechanical methods, alongside fire prevention strategies including the use of flame retardants, elimination of oxidants, and reduction of heat generation and accumulation. Challenges and future directions are outlined, highlighting the need for standardized designs, automation, and safer, more sustainable recycling infrastructure. Furthermore, this review is distinguished by its focused analysis of preprocessing and deactivation steps, with particular attention to the thermal safety engineering aspects of LIB recycling.

Battery deactivation↗
NASA NTRSDate not supplied

A Machine Learning Framework for Error Compensation in Radiative Transfer Calculations

Radiative heat transfer influences the amount of heat flux transferred to the surface of the hypersonic vehicle, which is essential to evaluate the performance of thermal protection systems. The radiative heat flux is found to be computationally prohibitive while accounting for the variation in spatial, angular, and spectral domains. A new methodology has been recently developed to alleviate the cost of computation in the spectral domain by constructing flow-agnostic reduced-order models (ROMs). The developed spectral ROM databases provide grouping strategies that account for non-equilibrium absorption and emission as well as interaction between disparate species due to spectral overlap in associated radiative processes. However, the developed ROMs need to be optimized for a specific combination of interacting gas species and would need to re-calibrated in case individual species are added/omitted. In this work, we use various machine learning (ML) techniques to approximate the radiative intensities determined by a ROM optimized for a specific gas mixture. The ML model relies on the ROM databases developed for a single species which ignores any spectral overlap. Thus, radiation evaluation starts with a simple summation of radiative intensities predicted using these non-calibrated ROMs for the contributing species. The ML framework then provides a correction to account for the interplay in the frequency, i.e., emission of photons by one species and absorption by another, and yields mixture-specific radiation fields. Once trained on the individual ROM databases, the ML framework offers instantaneous corrections that serves as a time/cost effective alternative to the optimization of ROMs for a specific gas mixture. The ML framework is trained on both the high fidelity and ROM evaluated line of sight (LOS) data from Orion, Stardust, and FIRE II cases to obtain a general purpose correction model for earth re-entry scenarios when radiation contributions from both atomic nitrogen and atomic oxygen are considered. A geometric length scale parameter is used in the training process to account for errors introduced in the ROM databases as a consequence of high optical thickness. The efficacy of the ML framework is underscored through extensive analysis of train and test errors with respect to all the re-entry scenarios. The applicability of such an ML framework was further corroborated by embedding it in a state-of-the-art US3D - NERO system for determining the radiative heat flux transferred to the hypersonic vehicle surface.

Radiation↗
NASA NTRSDate not supplied

Phosphate Textural Diversity in CI Chondrites and C-Type Asteroids

Introduction: Apatite, Ca 5 (PO 4 ) 3 (CL/F/OH-), is a ubiquitous phosphate found throughout the solar system, including the most primitive solids, CI-chondrites [1,2] and related samples of carbonaceous asteroids Ryugu [3] and Bennu [4], returned by JAXA’s Hayabusa2 and NASA’s OSIRIS-REx missions, respectively. Apatite in these primitive solids is found as individual grains or mineral clusters and has been inferred to form from the hydrothermal sequence during cooling of their respective parent body or bodies. To better understand the formation history and reworking of these early phosphates we have undertaken a highly coordinated study of phosphate microstructures, geochemistry and U/Pb geochronology from a suite of CI meteorites and carbonaceous asteroid samples. These data have identified novel phosphate microstructures and complex relationships across a suite of apatite grains from the early solar system, indicating multiple episodes of growth and modification on the CI parent body(ies). Methods: Samples of CI chondrites, Alais, Ivuna, Orgueil, Oued Chebeika 002, Yamato (Y) 82162, Y980115, Y980134, and two chips of Hayabusa2 Ryugu particles (A0262 and C0263) have been acquired for analysis. The bulk texture of the samples were first scanned by X-ray Computed Tomography (XCT) using the Nikon XT H 320 within the XFACT facility at NASA JSC or the Xradia 620 Versa at the UTCT facility. Based on the identification of petrofabrics or features of interest from the XCT data, samples were chipped, oriented, potted in epoxy and thick sections were prepared. After anhydrously polishing the samples with silicon carbide and dry diamond powder down to 1 µm, the samples were ion polished using a Hitachi ArBlade. Energy dispersive Xray spectrometry (EDS) maps were collected to ID phosphates of interest using a JEOL 7900F SEM. The internal microstructures of identified phosphates were then mapped by electron backscatter diffraction (EBSD) using the JEOL 7900F. Based on the EDS and EBSD data, domains of interest were targeted for quantitative chemical analyses using a JEOL 8530 EPMA. Subsequently, in situ U-Pb and 207 Pb/ 206 Pb ages will be collected using a Cameca ims1290 secondary ion mass spectrometer at UCLA across a range of microstructures. Results: Apatite grains are ubiquitous throughout the CI chondrites and carbonaceous asteroid materials, found as individual grains, disseminated clusters or grain aggregates. Apatite grains are associated with serpentine, magnet-ite, and/or carbonate. Of particular interest, we have identified individual and aggregate polycrystalline grains ex-hibiting an internal ‘honeycomb’ texture (Fig. 1). Some of these grains appear overprinted by subsequent alteration while others remain unaltered. Apatite halogen sites are dominated by the missing component, assumed to be OH, and F, comparable to published values from Bennu, Ryugu and CM-chondrites [3-5]. However, the Yamato CI-like meteorites show a broader range of Cl values, and one grain from Alais is dominated by CL. Summary: Apatite growth features indicate a protracted and complex growth history, consistent with precipitation from an evolving fluid system. The ‘honeycomb’ texture identified in some CI meteorites is, to the best of our knowledge, the first report of such a microstructure in meteoritic phosphate. The microtextures and zoning will guide subsequent age analyses, to better constrain the formation and reworking of phosphate in CI(-like) materials. Acknowledgments: We thank the National Institute of Polar Research, Japan for samples of Y82162, 980115 and 980134 meteorites, ASU’s Buseck Center for Meteorite Studies for samples of Ivuna and Alais meteorites, and JAXA curation for chips of Ryugu material. This work was funded by NASA ROSES LARS grant 24-LARS24-0014. References: [1] Morlok et al., 2016, GCA 70:5371-5394. [2] Alfin g et al., 2019, Geochemistry 79:125532. [3] Nakamura et al. (2022) Science 379:1-15. [4] Seifert et al. (2026) MAPS 61:504-521. [5] Piralla et al. (2021) MAPS 56:809-828.

CI chondrites↗
DOE OSTI2025

Machine Learning for Predicting Multipactor Susceptibility in Planar RF Structures

Multipactor discharge is a persistent challenge in high-power microwave (HPM) and accelerator systems, where secondary electron avalanches can cause heating, vacuum degradation, and failure. This work presents the first supervised machine learning (ML) framework for multipactor prediction, trained on high-fidelity 3D Particle-in-Cell (PIC) simulation data in planar geometries. The model maps operational, geometric, and material-dependent secondary electron yield (SEY) parameters to the time-averaged electron growth rate, enabling rapid reconstruction of susceptibility charts. Among the models evaluated, tree-based ensemble methods such as Random Forest and Extra Trees demonstrate superior generalization to unseen materials compared to neural networks such as multilayer perceptron (MLP). Performance metrics, including Intersection over Union (IoU), Structural Similarity Index Measure (SSIM), and Pearson correlation, show close agreement with simulation benchmarks. Principal Component Analysis attributes generalization limits to material feature-space disjointedness.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Two-mode bosonic quoctit for high energy physics

In this work, we study a two-mode bosonic encoding of a quoctit inside a non-Abelian group-structured constellation of coherent states. This work is motivated by the importance of non-Abelian symmetry in particle physics and the desire to have transversal non-Abelian logical gates. We use the previously developed 2 T constellation of states used to encode a so-called 2 T qutrit. The fidelity of the 2 T quoctit is benchmarked against other bosonic qudits for different noise models and find it compare favorably when power constraints are considered. This paves the way for the construction of higher-dimensional qudits (e.g., a quicosotetrit with 2 T group structure) in bosonic systems with practical applications in quantum simulations of particle physics.

Kürkçüoglu, Doga Murat [Fermilab] (ORCID:000000031↗
DOE OSTI2026

Superconductivity in Ruddlesden–Popper nickelates: a review of recent progress, focusing on thin films

The discovery of superconductivity with Tc ∼ 80 K in the nickelate Ruddlesden-Popper bilayer La3Ni2O7 at high pressure has opened a new platform for unconventional superconductivity, followed by the subsequent observation of superconductivity in trilayer La4Ni3O10, also at high pressure. Remarkably, ambient-pressure superconductivity was also observed recently in La3Ni2O7 ultra-thin films when grown on substrates that provide compressive strain. This discovery significantly extends the type of experimental techniques that can be used in nickelates, previously limited due to the high-pressure constraint. Discussing the similarities and differences among these nickel oxides will provide new insights into understanding the mechanism of high-Tc superconductivity in correlated electron systems. In this paper, we review the experimental and theoretical progress on Ruddlesden–Popper nickelates, with emphasis on thin films, and discuss future perspectives and research directions.

Zhang, Yang [ORNL] (ORCID:0000000336235883)↗
DOE OSTI2026

Advancing Building Performance: Field Results of Thin-Glass Triple-Pane Window Demonstrations

To meet California and the nation's ambitious energy targets, energy use in the building sector must drop dramatically. Windows continue to be the lowest thermally performing envelope system in the nation's buildings, resulting in poor overall envelope performance and potential impacts to human health and comfort. Current best practice new window performance is typically met by double-pane low-solar-gain glazing. Thin-glass triple-pane windows are a highly promising next step forward in performance and have been deployed in two California multi-family sites to quantify field performance and building energy savings. The technology assessed offers the performance benefits of traditional triple-pane but with little increase in weight or cost, enabling incremental costs competitive with alternative energy reduction solutions for the building envelope. This paper covers a detailed investigation into the demonstration project and measured performance benefits of the windows after a full year of data collection.

Hart, Robert↗
DOE OSTI2026

Mechanistic Understanding of Interphase-driven Aging in Silicon Anodes

Conventional solid electrolyte interphases (SEIs) strongly adhere to micro-silicon (µ-Si) and crack under volume changes, causing poor cycling performance. Nano-silicon improves cycling performance but remains costly with limited calendar life. Here potentiostatic ageing tests demonstrate that both calendar and cycle ageing are governed by SEI cracking and dissolution with different relative contributions. When the system is not dominated by SEI dissolution, the relative calendar life of Si anodes could correlates positively with their cycle life. LiF-rich SEI that enables long cycle life in µ-Si is therefore expected to enhance calendar life as well. Using this framework, we screened electrolytes, SEIs and electrodes and validated them with full-cell storage. LiF-rich SEI minimizes cracking and dissolution, enabling μ-Si to achieve excellent calendar life, whereas nano-silicon suffers from SEI dissolution and needs reduced electrolyte–electrode contact for better calendar life. This work clarifies calendar-ageing behaviour and accelerates electrolytes and SEI development for long-life Si anodes.

Johnson, Christopher S.↗
NASA NTRS2026

Evidence of an Extended Period of Aqueous Alteration on the Bennu Parent Body Revealed By I-Xe Analyses

NASA’s OSIRIS-REx mission delivered to Earth 121.6 g of regolith material from asteroid Bennu on 24th September 2023. We report multi-step laser pyrolysis xenon isotopic analysis to investigate the I-Xe system in individual particles separated from aggregate material (a mixture of small particles of undefined lithology). The high sensitivity of the RELAX mass spectrometer allows us to observe small excesses of individual isotopes and separate out different components, which may not be possible using a conventional noble gas mass spectrometer. The temperature resolution of RELAX is sufficient to seek an I-Xe isochron from step heating analysis of a sample mass <100 μg, which can contribute to our understanding of the nature and timing of aqueous alteration on Bennu’s parent body. We also aim to better estimate and understand the iodine concentration of CI chondrite-like material.

S A Crowther↗
DOE OSTI2025

Impact of Advances in Anion Exchange Membranes and Ionomers on Alkaline Fuel Cells

Abstract The operation of low‐temperature electrochemical energy conversion systems (fuel cells, electrolyzers) at high pH values is of perennial interest due to the possibility of moving away from expensive platinum group metal catalysts and reducing cost. Historically, the anion exchange membranes (AEMs) and ionomers have been hampered by performance (ionic conductivity, mechanical strength) and chemical stability issues. In this context, select developments over the past decade in alternate AEM chemistries, water management methods, and production of membrane electrode assemblies (MEAs) that have enabled a significant leap in performance of alkaline fuel cells are examined. These developments are linked to performance improvements in alkaline H 2 /O 2 fuel cells and also consider developments in alkaline fuel cells using nitrogen‐containing fuels (ammonia, hydrazine), carbon‐containing fuels (alcohols, glycols), and boron‐containing fuels (sodium borohydride, ammonia borane). Finally, current challenges and bottlenecks are identified, and potential solutions are proposed.

Chemistry↗