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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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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Thermodynamic modeling of countercurrent chemical looping reverse water gas shift process for redox material screening

The reverse water gas shift (RWGS) reaction is a key pathway for CO 2 utilization, particularly within Power-to-X process chains aimed at sustainable fuel and chemical production. Countercurrent chemical looping (CL-RWGS) using non-stoichiometric oxides can overcome equilibrium limitations of conventional RWGS reactors, enabling significantly higher CO 2 conversions. However, modeling the limiting performance of such systems is challenging due to their multiphase nature and coupled spatial and temporal variation in chemical composition. In this work, we present a discretized batch equilibrium model that simulates CL-RWGS reactors as a series of localized equilibrium exchanges between gas and solid elements. The model is numerically stable, computationally efficient, and free of kinetic source terms, making it well-suited for parametric studies and system-level integration. It is validated against established convection–diffusion models and shown to predict reasonable upper bounds on experimental results. Application of the model to a range of oxygen carrier materials identifies cerium–zirconium solid solutions, particularly Ce 0.80 Zr 0.20 O 2 , as a promising class offering superior oxygen storage characteristics compared to state-of-the-art La 0.6 Sr 0.4 FeO 3 . This framework provides a robust platform for materials screening, reactor sizing, and performance optimization in chemical looping systems. The model implementation is available as open-source software to support further research and development.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Computing the QRPA level density with the finite amplitude method

Here, we describe a new algorithm to calculate the vibrational nuclear level density of an atomic nucleus. Fictitious perturbation operators that probe the response of the system are generated by drawing their matrix elements from some probability distribution function. We use the Finite Amplitude Method to explicitly compute the response for each such sample. With the help of the Kernel Polynomial Method, we build an estimator of the vibrational level density and provide the upper bound of the relative error in the limit of infinitely many random samples. The new algorithm can give accurate estimates of the vibrational level density. Since it is based on drawing multiple samples of perturbation operators, its computational implementation is naturally parallel and scales like the number of available processing units.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Time-Varying Output Delay Compensation-A Model-Free Approach and its Application on Cooperative On-Ramp Merging

This paper presents a model-free approach to compensate for time-varying output delay in networked control systems. The proposed architecture combines a model-free observer and the Smith predictor. The model-free observer estimates the current state while handling modeling errors and uncertainties of the system. The Smith predictor moves the effect of time delay outside the control closed-loop using the estimated delayed output and the actual output of the plant. The proposed method is applied to a cooperative on-ramp merging problem. First, an ultra-local model predictive control is implemented to provide a computationally efficient online speed planner agnostic to the vehicle dynamics. After that, a model-free observer is designed to estimate the current state. Finally, the proposed architecture is tested against a time-varying output delay with an upper bound of 200 milliseconds. The results demonstrate the effectiveness of the proposed method with improved tracking of intervehicle distance.

Waleed khan, Muhammad [The University of Texas at ↗
DOE OSTI2026

Basin-scale analysis of Mokelumne River Formation for multi-well CO 2 injection

Large-scale carbon sequestration will likely require multiple projects injecting CO 2 into the same subsurface formation, raising concerns about safe operation and efficient use of storage capacity. This study evaluates the long-term response of the Mokelumne River Formation in California’s Sacramento Basin to multi-megaton CO 2 injection using three geologic models of the formation and the open-source simulator GEOS. The analysis focuses on three aspects of reservoir performance: (1) average pressure increase and dissolved CO 2 mass after 30 years for varying well counts and injection rates, (2) pressure interference in a multi-well configuration, and (3) dynamic storage capacity with identification of overpressure-prone regions. The results show that average formation pressure increases linearly with injected mass, while CO 2 dissolution exhibits mixed scaling: approximately linear with the number of wells but sublinear with injection rate, indicating that distributing injection across more wells enhances dissolution more effectively than increasing per-well rates. Pressure-interference effects are significant, with lower-permeability conditions delaying their onset but amplifying their magnitude at later times. Dynamic capacity, defined by the first occurrence of pressure exceeding the local overburden-based limit anywhere in the formation, varies across geologic models and assumed overburden pressure gradients. A lower fidelity geologic model predicts nearly twice the storage capacity of the two higher fidelity models, which consistently estimate approximately 1 Gt under the upper-bound overburden pressure gradient considered for the Sacramento Basin. In all model scenarios, overpressure develops away from injection wells, particularly in higher-elevation regions, highlighting the importance of basin-scale modelling for identifying risks beyond the immediate well vicinity.

Basin-scale↗
DOE OSTI2026

Re-evaluating probable maximum precipitation estimates: sensitivity to transposition domains and storm rotation using modern datasets

This study examines the sensitivity of Probable Maximum Precipitation (PMP) estimates to key methodological decisions embedded in the legacy approach adopted in the U.S. National Weather Service Hydrometeorological Reports No. 51 and No. 52. Although widely used for infrastructure design and risk regulation, fundamental aspects of PMP estimation—such as storm sample size, transposition domain, maximization procedures, and storm rotation—remain poorly constrained and lack formal guidance. Using the Red Rock watershed in Iowa as a case study, and leveraging the 2002–2023 NOAA Analysis of Record for Calibration (AORC) precipitation dataset, we systematically evaluate how each methodological choice, individually and in combination, influences PMP estimates. Our findings demonstrate that PMP is not a fixed physical upper bound but rather a modeling construct shaped heavily by user-defined assumptions. Notably, PMP values derived from modern gridded rainfall datasets can be substantially higher than the legacy estimate used in the original spillway design for Red Rock Dam. Decisions regarding storm sample size, domain extent, climatological window, and particularly storm rotation all contributed to higher PMP estimates. Storm rotation alone—a loosely constrained element in the current PMP practice—can amplify PMP by more than 25%. These results reveal the lack of standardized bounds in current PMP workflows and the need for systematic sensitivity and uncertainty analysis. As PMP estimation shifts toward probabilistic approaches, incorporating physically meaningful storm attributes will be key to developing more transparent, defensible methods for dam safety and climate-resilient infrastructure.

Probable maximum precipitation↗
DOE OSTI2025

Efficient screening of rare large pit anomalies on polished surfaces using a minimalist sampling scheme

Lawrence Livermore National Laboratory (LLNL) has made significant strides in generating clean energy through its inertial confinement fusion (ICF) experiments. These experiments rely on high-density carbon (HDC) coated shells to encapsulate the fusion fuel. The success of these experiments is heavily dependent on the surface quality of these shells, as even minor imperfections, such as deep pits, can negatively impact fusion yield. Ensuring the required smoothness involves an extensive surface-finishing process that spans approximately 20 stages, making it both time-intensive and resource-demanding. A critical challenge in this process is the need for high-resolution scans to detect rare deep pits, which can be costly and impractical if performed on every shell. This highlights the necessity of developing more efficient scanning methods to optimize time and cost without compromising accuracy. To address these challenges, we introduce a novel approach that employs the multivariate Dvoretzky–Kiefer–Wolfowitz (DKW) inequality to provide a probabilistic upper bound on the error in estimating pit distribution characteristics via a Kernel Density Estimator (KDE). This error bound enables efficient and reliable estimation of pit distribution characteristics at a specified statistical confidence level using a minimal number of surface scans. The integrated DKW-KDE approach was validated through surface-finishing experiments across two batches of HDC-coated shells, demonstrating consistent and robust performance across multiple stages of the surface-finishing experiments. The validation studies suggest that the integrated DKW-KDE approach achieves comparable accuracy in estimating the risk of deleterious large pits with six scans, thus conserving time and resources. Further evaluations show that performance remains consistent across batches and over multiple polishing stages. In conclusion, based on these findings, one can leverage the minimal-scan insights to strategically improve the bottleneck inspection process, thus enhancing the productivity and quality of shell polishing and similar challenging manufacturing processes.

Inertial confinement fusion↗
DOE OSTI2025

Microporous pentiptycene-based polybenzimidazole membranes for high temperature H 2 /CO 2 separation

Separating H 2 from syngas at elevated temperatures (100–250 °C) have attracted significant attention in recent years as a means to reduce energy consumption and capital costs in precombustion carbon capture processes, such as those following steam reforming of natural gas or coal gasification. Polybenzimidazole (PBI), particularly m-PBI, has been reported as a leading membrane material for high-temperature H 2 /CO 2 separation. However, m-PBI exhibits extremely low H 2 permeability, even at high temperatures, which limits its productivity in H 2 /CO 2 separation applications. Here, to address this limitation, this work introduces a new pentiptycene-based polybenzimidazole (PPBI) featuring significantly enhanced H 2 permeability and attractive high-temperature H 2 /CO 2 separation performance, which stems from the unique configurational free volume elements introduced by pentiptycene moieties. Further tuning of the free volume architecture of PPBI films is achieved via acid doping with phosphoric acid (PA) or trans-aconitic acid (TaA), which introduces crosslinking among PPBI chains. Under mixed-gas environment (50/50 mol% H 2 /CO 2 ) at 180 °C, the acid-doped PPBI films exhibit a ∼230 % increase in H 2 /CO 2 selectivity compared to pristine PPBI film while maintaining high H 2 permeability that is nearly 500 % of m-PBI. These properties approach the predicted upper bound for membrane operating at 180 °C, highlighting its great potential for high-temperature H 2 /CO 2 separation.

Liu, Mengdi [University of Notre Dame, IN (United ↗
DOE OSTI2025

Investigation of competitive sorption and plasticization of hyperaged CANAL ladder polymers for acid gas purification

Identifying membrane materials that have exceptional separation performance and stability to complex CO 2 -containing mixtures is a pressing topic in separation science. In this work, the membrane separation performance for a recently discovered class of contorted polymers synthesized via catalytic arene-norbornene annulation (CANAL) polymerization is presented. These CANAL polymers achieve high CO 2 /CH 4 selectivity of 68 after physical aging (up to ∼1 year), which significantly augments the size-sieving capabilities of the membranes. Binary CO 2 /CH 4 and ternary H 2 S/CO 2 /CH 4 testing result in a 41 % and 50 % enhancement in selectivities, respectively, for hyperaged (∼1 year) contorted CANAL polymers, highlighting their size-sieving capabilities. The remarkably high CO 2 /CH 4 mixed-gas and combined acid gas (CAG, (CO 2 +H 2 S)/CH 4 ) selectivities of 88 and 95, respectively, for CANAL-Me-S 5 F in particular surpass both the 2018 CO 2 /CH 4 mixed-gas and CAG upper bounds. Performance stability was also investigated for high concentrations of CO 2 , revealing a reduction in CO 2 /CH 4 mixed-gas selectivity without compromising CO 2 permeability, suggesting strong sorption of CO 2 but minimal plasticization effects for short testing periods. In addition, time-dependent plasticization shows negligible effects on CO 2 /CH 4 mixed-gas selectivity despite an increase in CO 2 permeability when exposed to high concentrations of plasticizing CO 2 over an extended period of 170 h. This study provides valuable insights into hyperaged CANAL polymers and their performance in practical industrial processes.

03 NATURAL GAS↗
DOE OSTI2026

BISON analyses of TRISO fuel performance, its dependence on time-at-temperature, and possible implications for fuel design and qualification

The Advanced Gas Reactor Fuel Development and Qualification (AGR) program has established a substantial technical foundation to support private entry into the U.S. high-temperature gas-cooled reactor market. However, emerging tristructural isotropic (TRISO)-fueled reactor applications include small modular reactors and microreactors with longer fuel residence times, which may expose fuels to higher time-at-temperature (TAT) values than were explored by the AGR program. Increased TAT could affect diffusive and thermomechanical behaviors such as Pd penetration, fission gas release, creep, and fission product transport. In this work, we applied multiscale best-estimate BISON fuel performance modeling to assess these effects within a representative design space based on the AGR-5/6/7 experiment and analyzed trends in predicted particle and compact fuel performance metrics with possible implications for near-term fuel design and qualification. BISON unambiguously predicted that TRISO fuel performance is sensitive to TAT. Increasing TAT was not predicted to increase the magnitude of failure-inducing tangential stresses in particle coating layers. Predictions obtained using a mechanistic model for Pd penetration indicated that penetration depth does not depend strongly on TAT. While these observations suggest that AGR testing provides a conservative upper bound for the steady-state operation of TRISO particles at lower powers and higher residence times, BISON also predicted that the release of poorly retained Ag would increase with TAT. Because these analyses applied models to extrapolate beyond the available experimental data, the authors recommend performing targeted experiments to confirm these predictions. Nevertheless, these predictions may provide reactor developers with enough confidence to make near-term design decisions associated with the potential fuel performance trade-offs of increasing TAT.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

A mesoscopic link-transmission-model able to track individual vehicles

Macroscopic traffic flow is a common choice for large-scale traffic simulations. These models do not provide individual-specific metrics as outputs. However, this treatment is necessary in agent-based-models, as in, for example, assigning routes based on personal characteristics. Here, in this paper, we propose an extension of the link-transmission-model, an efficient and yet accurate discretization of the Lighthill-Whitham-Richards (LWR) model, which allow vehicles to be tracked individually while keeping the main features of the underlying model. The extension comprises modifying the link and node models to ensure that the flow between links is always at discrete levels. Therefore, every unit of flow is associated with one individual vehicle moving from its current to its next link. An upper bound of the discretization error is provided. We show that the proposed model resembles its continuous counterpart on lane drop, merge, and diverge cases. In addition, we apply the model into three different networks to validate its applicability in large networks. Finally, we also confirm the parameter transferability between continuous and discrete models and that both can well reproduce field data.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Creation of Self-Semi-Interpenetrating Network Structures in PIM-1 Membranes for Enhanced Physical Aging Resistance

A series of self-semi-interpenetrating network (ssIPN) thin films based on PIM-1 structure were developed by end-cross-linking telechelic PIM-1 oligomers end-capped with curable carboxylic acid groups to form model networks, which are penetrated by linear high-molecular-weight PIM-1 chains. ssIPN films with systematically varied network content ranging from 10 to 30 wt % were comprehensively examined on their microstructure and gas permeation properties. Fresh PIM-1 ssIPN films exhibited gas separation performances close to those of as-cast linear PIM-1, where the films closely followed the upper bound trade-off line, gaining as much selectivity as they lose gas permeability as the network content increases. This indicates that gas permeability is largely preserved despite cross-linking. Wide-angle X-ray scattering supported this observation, with peaks shifting toward lower d-spacing as oligomer content increased, suggesting tighter chain packing with higher cross-linkable oligomer loading. In physical aging studies over two months, all ssIPN films outperform linear PIM-1 for H 2 /CH 4 and O 2 /N 2 separations. Notably, the PIM-1 ssIPN with 10 wt % network content showed the best physical aging resistance, with negligible permeability loss even after one month. Finally, these findings highlight a promising macromolecular strategy for enhancing the physical aging resistance of microporous polymer membranes for gas separation.

PIM-1↗
DOE OSTI2025

Atomically Fine-Tuning Organic–Inorganic Carbon Molecular Sieve Membranes for Hydrogen Production

Polymeric membranes with great processability are attractive for the H 2 /CO 2 separation required for hydrogen production from renewable biomass with carbon capture for utilization and sequestration. However, it remains elusive to engineer polymer architectures to obtain desired sub-3.3 Å ultramicropores to efficiently sieve H 2 from CO 2 . Herein, we demonstrate a scalable way of carbonizing polybenzimidazole (PBI) at low temperatures, followed by vapor phase infiltration (VPI) to atomically narrow ultramicropores throughout the films, forming hybrid organic–inorganic carbon molecular sieves (CMSs). One VPI cycle (100 s) for the PBI carbonized at 500 °C remarkably increases H 2 /CO 2 selectivity from 9.6 to 83 at 100 °C, surpassing Robeson’s upper bound. The CMS demonstrates a stable H 2 /CO 2 separation performance when challenged with simulated syngas streams and can be fabricated into thin-film composite membranes, outperforming state-of-the-art membranes. Finally, the scalable approach can be ubiquitous to molecularly fine-tune ultramicropores of leading polymeric membranes to further improve their size-sieving ability and thus separation efficiency.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Time-Resolved Probing of the Iodobenzene C-Band Using XUV-Induced Electron Transfer Dynamics

Time-resolved extreme ultraviolet spectroscopy was used to investigate photodissociation within the iodobenzene C-band. The carbon–iodine bond of iodobenzene was photolyzed at 200 nm, and the ensuing dynamics were probed at 10.3 nm (120 eV) over a 4 ps range. Two product channels were observed and subsequently isolated by using a global fitting method. Their onset times and energetics were assigned to distinct electron transfer dynamics initiated following site-selective ionization of the iodine photoproducts, enabling the electronic states of the phenyl fragments to be identified using a classical over-the-barrier model for electron transfer. In combination with previous theoretical work, this allowed the corresponding neutral photochemistry to be assigned to (1) dissociation via the 7B2, 8A2, and 8B1 states to give ground-state phenyl, Ph(X), and spin–orbit excited iodine and (2) dissociation through the 7A1 and 8B2 states to give excited-state phenyl, Ph(A), and ground-state iodine. The branching ratio was determined to be 87 ± 4% Ph(X) and 13 ± 4% Ph(A). Similarly, the corresponding amount of energy deposited into the internal phenyl modes in these channels was determined to be 44 ± 10 and 65 ± 21%, respectively, and upper bounds to the channel rise times were found to be 114 ± 6 and 310 ± 60 fs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Optimal Pathways from Alternative Carbon Feedstocks to Organic Commodity Chemicals

The use of biogenic and waste feedstocks is a promising strategy to improve the chemical sector's supply chain resiliency and carbon intensity. To help inform research efforts that transform these feedstocks into industrial chemicals, we used a systematic analysis framework to consistently evaluate the economics and environmental impacts of >200 alternative production pathways for 51 organic commodity chemicals in the United States under an optimistic future scenario that reflects the potential upper bounds of process scalability, energy availability, and carbon uptake. Lower-impact and lower-cost alternative pathways were identified for all but three chemicals, with 75% using thermochemical routes and half leveraging existing manufacturing infrastructure. Scenario analysis shows that the ranking of these pathways for half of the assessed chemicals is particularly sensitive to carbon uptake assumptions and criteria prioritization (i.e., cost only, environmental impact only, or both), with changes in electricity grid mix, hydrogen source, and underlying mass and energy flow data proving less influential. Implementing alternative pathways for just 11 chemicals could support a transition to net-zero greenhouse gas emissions from chemical production by 2050, with 11% lower cost than business as usual, similar water requirements, quadrupled electricity demand, and the use of most available woody biomass. These findings provide an exploratory guide toward a future chemical industry that harnesses alternative feedstocks.

09 BIOMASS FUELS↗
DOE OSTI2026

Direction-specific enhanced diffusion of CO 2 in chiral hexagonal boron nitride nanotubes

To meet performance requirements, the next generation of gas separation membranes will need both high gas permeability and selectivity, attainable if we could coax adsorbates to minimize random Brownian motion and produce direction-specific diffusion along a desired axis. In this atomistic modeling study, we detail how direction-specific diffusion of CO 2 can be achieved in chiral hexagonal boron nitride nanotubes (hBNNTs) by means of a non-Knudsen diffusion mechanism. Our findings detail how this mechanism of diffusion is driven by interactions with the tube walls and enables the CO 2 molecules to diffuse along the nanotube’s z-axis with minimized collisions and directional changes. hBNNTs with chiral indices exhibit CO 2 diffusion rates faster than non-chiral tubes of comparable and larger diameters. Of the hBNNTs studied, a (7,3) tube appears to be ideally sized (3.7 Å radius) exhibiting CO 2 diffusion that is 3.4 times faster than diatomic N 2 . Applying this mechanism of diffusion to hypothetical sheet membranes prepared with aligned chiral (7,3) hBNNTs results in membranes with a calculated CO 2 /N 2 permselectivity of 170 and a CO 2 permeability limit of nearly 1.35 ×10 7 Barrer, readily surpassing the Robeson upper bound for CO 2 /N 2 separations.

CO2↗
DOE OSTI2026

BCS-BEC crossover driven by small Fermi pockets of a high- T c cuprate superconductor

Fermi arcs observed in underdoped cuprates have sparked debate over whether they represent segments of a large Fermi surface or small Fermi pockets. This ambiguity has long hindered their classification as either the conventional Bardeen-Cooper-Schrieffer (BCS) regime or the strongly coupled Bose-Einstein condensation (BEC) crossover limit. Here, using angle-resolved photoemission spectroscopy and quantum oscillations, we demonstrate the coexistence of a small Fermi pocket and a large superconducting gap in the clean inner CuO 2 layers of the four-layer cuprate Ba 2 Ca 3 Cu 4 O 8 (F,O) 2 . This coexistence constitutes a hallmark of the BCS-BEC crossover and has remained elusive for decades. Despite the presence of antiferromagnetic (AF) order, the superconducting gap in the small pocket is remarkably large, yielding a gap-to-Fermi energy ratio (Δ pocket /ε F ~ 0.6) and a critical-to-Fermi temperature ratio (T c /T F ~ 0.13) that reach the theoretical upper bound for two-dimensional superconductivity. Unexpectedly, this BCS-BEC crossover emerges not as the carrier density decreases but as it increases, abruptly within a narrow doping range of less than 1%. These results provide a long-sought microscopic foundation for the d-wave pairing mechanism in doped AF-Mott insulators.

Jeong, Junhyeok [University of Tokyo, Kashiwa (Jap↗
DOE OSTI2025

Charting the chemical space of Zintl phases with graph neural networks and bonding insights

A large number of Zintl phases have been discovered by solid-state chemists driven by empirical knowledge, chemical intuition and in some cases, through serendipitous accidents. These discoveries have only scratched the surface, given the vast compositional and structural diversity that Zintl phases can accommodate. The large chemical space of Zintl phases, as well as intermetallic compounds in general, remain under-explored. Here, we use graph neural networks and the upper bound energy minimization approach to efficiently scan a large chemical space of >90 000 hypothetical Zintl phases and accurately discover 1810 new thermodynamically stable phases with 90% precision, as validated with first-principles calculations. We show that our approach is more than 2× more accurate in predicting DFT stability than M3GNet (40% precision) on the same dataset. Using a random forest model and SHAP analysis, we demonstrate the critical role of ionic bonding in the thermodynamic stability of Zintl phases. Our results not only expand the known chemical landscape of Zintl phases but also highlight the efficacy of machine learning frameworks combined with domain knowledge in uncovering chemically meaningful insights across complex intermetallics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

The SRG/eROSITA All-Sky Survey: Constraints on ultralight axion dark matter through galaxy cluster number counts

Ultralight axions are hypothetical scalar particles that influence the evolution of large-scale structures of the Universe. Depending on their mass, they can potentially be part of the dark matter component of the Universe as candidates commonly referred to as fuzzy dark matter. While strong constraints have been established for pure fuzzy dark matter models, the more general scenario where ultralight axions constitute only a fraction of the dark matter has been limited to only a few observational probes. In this work, we use the galaxy cluster number counts obtained from the first All-Sky Survey (eRASS1) of the SRG/eROSITA mission together with gravitational weak lensing data from the Dark Energy Survey, the Kilo-Degree Survey, and the Hyper Suprime-Cam to constrain the fraction of ultralight axions in the mass range 10 −32 eV to 10 −24 eV. We put upper bounds on the ultralight axion relic density Ω a in independent logarithmic axion mass bins by performing a full cosmological parameter inference. We find an exclusion region in the intermediate ultralight axion mass regime with the tightest bounds reported so far in the mass bins around m a = 10 −27 eV with Ω a < 0.0035 and m a = 10 −26 eV with Ω a < 0.0079; both are at a 95% confidence level. When combined with cosmic microwave background probes, these bounds are tightened to Ω a < 0.0030 in the m a = 10 −27 eV mass bin and Ω a < 0.0058 in the m a = 10 −26 eV mass bin, with both at a 95% confidence level. This is the first time that constraints on ultralight axions have been obtained using the growth of structure measured by galaxy cluster number counts. These results pave the way for large surveys, which can be utilized to obtain tight constraints on the mass and relic density of ultralight axions with better theoretical modeling of the abundance of halos.

cosmological parameters↗