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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 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantum Information for Fusion Energy Sciences (Final Technical Report)

The simulation of plasma dynamics is a critical area of Fusion Energy Sciences (FES) due to it’s usefulness in predicting, controlling, and confining plasmas in the context of potential fusion reactors. The simulation of plasmas is a computationally difficult problem in both classical and quantum physics, motivating investigation into the potential of quantum computers to simulate these systems. This project took several concrete steps towards this goal by developing tools for improving the control, characterization, and calibration of quantum gates on a superconducting quantum computer, developing error suppression and mitigation tools to reduce errors on the quantum computer, and utilizing these advancements to simulate reduced models of plasma dynamics on the quantum computer. In order to efficiently simulate plasma physics, an optimal control method which synthesizes, directly at the pulse level, any quantum gate on qubit and qutrit systems was developed. Using four superconducting transmon quantum processors at Rigetti and LLNL, it was demonstrated that any arbitrary quantum gate on qubits and qutrits could be implemented with high fidelity, leading to a significantly reduced length of a gate sequence. A problem of interest in FES is the nonlinear optical process of laser pulse compression within a plasma. Since quantum physics is linear, simulating nonlinear operations is not naturally feasible on a quantum computer, however it is possible to simulated a quantized version of the nonlinear process. A quantization approach to convert nonlinear wave-wave interaction problems to Hamiltonian simulation problems was developed and demonstrated using two qubits on a Rigetti device. In this experiment, a number of error suppression and mitigation techniques were investigated to determine how best to utilize the finite quantum resources. This study provides an example of how plasma problems may be solved on near-term, noisy quantum computing platforms and identified a promising set of techniques. Building on the insights of these experiments, the investigation turned to linear electron-plasma wave physics. A connection was identified between a local one-dimensional lattice spin model and linear wave phenomena, allowing a plasma physics problem to be efficiently mapped to the quantum computer. In this framework, reflection and transmission of plasma waves at a sharp boundary was studied, as well as the propagation of waves through an inhomogeneous plasma medium. In addition to the suite of error suppression and mitigation techniques developed, this experiment introduced the use of a digital-analog gate scheme designed to efficiently simulate the plasma Hamiltonian. With hardware available at the conclusion of the project, simulation at the scale of 9 qubits and 15 timesteps (60 entangling layers) was achieved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Probing Surface Hydration and Isotope Exchange Kinetics in Proton-Conducting Ceramics Using DRIFTS and EIS

This internship project investigates how water vapor partial pressure (pH2O) affects surface hydration and H/D isotope-exchange kinetics in BaZr0.4Ce0.4Y0.1Yb0.1O3?d (4411) proton-conducting ceramic electrolytes. Diffuse reflectance infrared Fourier-transform spectroscopy (DRIFTS) is used to monitor surface hydroxyl and deuteroxyl species under controlled humidified atmospheres during gas-switching experiments. These surface kinetic trends are to be correlated with bulk, grain-boundary, and total electrolyte resistance measured by electrochemical impedance spectroscopy (EIS) under matching conditions. The future goals of this study are to clarify the relationship between surface hydration dynamics and proton conduction behavior, improving interpretation of EIS data and guiding the optimization of ceramic electrolytes for energy applications.

08 - HYDROGEN↗
DOE OSTI2026

Harnessing Ocean Thermal Gradients Using Thermoelectric Based Submersibles for Ocean Power Applications

The urgent need for energy solutions in marine environments has accelerated the development of innovative technologies capable of leveraging natural resources for power generation. This study introduces a buoyancy-driven submersible system designed to harness ocean thermal gradients using thermoelectric generators (TEGs) and phase change materials (PCMs). The technology aims to provide autonomous power to offshore aquaculture farms, unmanned underwater vehicles (UUVs), offshore platform illumination, and ocean sensors, significantly reducing dependence on fossil fuels. Ocean thermal gradients, especially prevalent in mid-latitude regions, exhibit temperature differences between surface and deep waters ranging from 7 degrees Celsius to 30 degrees Celsius depending on seasonal variations. The proposed submersible technology utilizes TEGs to convert thermal energy from these gradients into electrical power, generating between 0.2 and 0.5 watts, while PCMs are employed to store and regulate this energy, ensuring a stable and continuous power supply. The buoyancy-driven mechanism of the submersible enhances its capability to navigate through varying depths, optimizing its exposure to different thermal gradients and maximizing energy harvesting. The performance of this submersible system is analyzed through detailed thermodynamic assessments and computational fluid dynamics (CFD) modeling focused on heat transfer. These analyzes consider real-world ocean temperature profiles and seek to refine the interaction between TEGs and PCMs to optimize energy extraction. The evaluation encompasses several key performance metrics, including power output and energy efficiency. Results confirm the potential of this innovative technology to provide a continuous and reliable power source for marine applications. By demonstrating the feasibility of using ocean thermal gradients for energy generation, this study contributes to the broader efforts of innovation in energy technologies for harsh, remote marine environments. The implementation of such promises is significant advancements in the autonomy of marine operations. The ongoing research will further investigate scalability ensuring that the system can be effectively adapted to various marine settings and operational demands.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Multiphase computational fluid dynamics modeling of reacting flows in absorption columns for carbon capture

First-principles derived computational fluid dynamics (CFD) simulations have been proposed as a fundamental tool for investigating solvent-based CO 2 absorption in packed columns due to their ability to accurately represent the underlying nonlinear, multiscale dynamics. Numerous studies have previously utilized such CFD simulations to investigate hydrodynamics of columns with structured and random packings by assessing the key hydrodynamic metrics such as the interfacial and wetted areas. While mapping such metrics for different conditions is essential to the optimization of absorption columns, it is not sufficient, as the CO 2 capture rate depends also on the coupled, nonlinear dynamics from the underlying chemical reaction kinetics, thermodynamics, and heat-transfer rates. In this work, we present detailed CFD simulation results augmented by incorporating the effects of interfacial physical mass transfer of CO 2 , heat release from chemical reaction kinetics, and thermophysical property variations from resulting temperature gradients. We demonstrate the applicability of the proposed approach in numerically assessing the performance of packed columns by evaluating key hydrodynamic quantities, CO 2 absorption rates, and temperature rise in a reference column with packings that are structurally similar to the Sulzer Mellapak™ 250.Y packing, for different solvent inflow velocities and temperatures. Predictions from simulation results are found to be consistent with the trends in experimental observations from the literature, suggesting that the predictive capabilities of the simulation framework can be leveraged to guide the future development of absorber-column designs and optimized process flowsheets.

Absorption columns↗
DOE OSTI2024

3D small-gain formula allowing strong focusing and harmonic lasing for a ring-based x-ray free electron laser oscillator

We present a detailed derivation of a formula for the small-gain calculation for an x-ray free electron laser oscillator (XFELO) based on a medium-energy (3–4 GeV) storage ring. We found harmonic lasing and strong focusing are essential for this beam energy range. Taking the small-signal low-gain formula developed by Kim and his colleagues, we modified it in such a way that the gain can be calculated without the “no focusing approximation,” and a strong focusing can be applied, as well as harmonic lasing. In this formula, the gain is represented as a product of two factors with one of them depending only on the harmonic number, undulator period, and gap. Using this factor, we show that it is favorable to use harmonic lasing to achieve hard x-ray FEL working in the small-signal low-gain regime with the medium-energy electron beam. Our formula also allows FEL optimization by varying the vertical gradient of the undulator, the vertical dispersion, and the horizontal and vertical focusing, independently. As an example, we applied this formula to study the feasibility of an XFELO option for the National Synchrotron Light Source II (NSLS-II) upgrade. Since a quite high peak current is required for the FEL, collective effects of beam dynamics in medium-energy synchrotrons significantly affect the electron beam parameters. We carried out a multiparameter optimization taking collective effects into account. Note, even though our example is for a ring-based XFELO at 3 to 4 GeV, the formula and, in particular, the approach developed here may be applied to other types of FELs. Published by the American Physical Society 2024

36 MATERIALS SCIENCE↗
DOE OSTI2024

Model Quality and Measurement Density Impact on Volt/Volt Ampere Reactive Optimization Performance

The operation of the utility grid is being reshaped by the continuous addition of distributed energy resources and advanced metering infrastructure, which challenge existing grid control strategies. Some utilities deploy advanced distribution management systems (ADMS) to assist with the consolidation of various applications and to augment situational awareness in response to the new power delivery dynamics. An ADMS is an integrated software platform that provides utilities with a way to enhance their reliability, control, and optimization with advanced applications, such as volt/VAR optimization (VVO). A VVO application could serve as a vehicle to deliver cost savings by providing the utility with a method to reduce rates by controlling the voltage and decreasing the energy usage in their service territory. Some utilities are reluctant to integrate an ADMS, because it is a significant investment that requires approval from the public regulatory commission and/or their customers. This paper evaluates the impact on VVO performance when using a lower-quality network model supplemented with additional measurements, which could provide an implementation for cost savings. The results show that a better model quality would provide the highest energy savings; however, some level of telemetry is necessary in all scenarios to prevent voltage exceedances.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Machine Learning-Guided Optimization of SABRE Hyperpolarization for α-Ketoglutarate in Acetone–Water

Signal amplification by reversible exchange (SABRE) is a hyperpolarization method that polarizes target nuclei of metabolites quickly and efficiently. Recent SABRE advances, including Ace-SABRE, yield biocompatible, aqueous solutions of hyperpolarized markers for metabolic monitoring. Building on recent advancements, expanding the substrate scope of Ace-SABRE is desirable. However, SABRE polarization is sensitive to many different parameters; therefore, traditional optimization approaches are experimentally time-consuming. In this proof-of-concept application of machine learning (ML), Bayesian optimization (BO) is used for four important input parameters to model the complex SABRE dynamics while saving experimental time. The presented ML model also provides chemical insights that enable predictions of sample compositions for increased polarization levels. In this paper, we transition from an original average free polarization of p = ∼0.90% to a maximum observed free polarization of p = ∼6.6% for 1- 13 C alpha-ketoglutarate (AKG) with 13 C at natural abundance, utilizing both direct outputs as well as chemical insights revealed by the ML model.

Catalysts↗
DOE OSTI2026

Tandem bulk oxygen diffusion and surface reactions in reducible metal oxides control redox cycle dynamics

The interplay between bulk oxygen diffusion and surface reactions in reducible metal oxides is key in heterogeneous catalysts, but direct measurements of oxygen mobility, transient kinetics, and in situ spectroscopies have been lacking. Here, we reveal complex dynamic behavior of ceria-zirconia by H 2 using transient kinetics via mass spectrometry and in situ Raman and near-ambient pressure x-ray photoelectron spectroscopies. Molecular dynamics simulations with a machine learning potential delineate competitive oxygen diffusion mechanisms, with an optimal mobility at intermediate reductions. We expose a compensation between vacancy availability and lattice distortion at intermediate to high reductions and Frenkel defects at low reductions, underscoring a potential deficiency of 16 O/ 18 O exchange experiments in deducing oxygen mobility. Vacancies in proximity require electron localization on Ce atoms further away. The continuous replenishment of surface oxygen results in a varying reduction rate, with H 2 dissociation being the rate-limiting step. Multiscale transient simulations, consistent with experiments, indicate catalysts of potentially spatially varying oxidation states. The approach is broadly applicable to reducible oxide materials.

36 MATERIALS SCIENCE↗
DOE OSTI2026

A variational framework for residual-based adaptivity in neural PDE solvers and operator learning

Residual-based adaptive strategies are widely used in scientific machine learning yet remain largely heuristic. We introduce a variational framework that formalizes these methods through convex transformations of the residual, where different transformations correspond to distinct objective functionals. For instance, exponential weights target uniform error minimization, while linear weights recover quadratic error minimization. This perspective reveals adaptive weighting as a means of selecting sampling distributions that optimize a primal objective, directly linking discretization choices to error metrics. This principled approach yields three key benefits: it enables systematic design of adaptive schemes, reduces discretization error by lowering estimator variance, and enhances learning dynamics by improving gradient signal-to-noise ratio. Extending the framework to operator learning, we demonstrate substantial performance gains across diverse optimizers and architectures. Our results provide a theoretical perspective for residual-based adaptivity and establish a foundation for principled discretization and training.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Enhancing quantum clocks and sensors with randomization and decoherence

This letter shows how incoherent dynamics can lead to metrological advantages in quantum sensing. The results rely on the fact that incoherent dynamics lead to an additive contribution to the quantum Fisher information about time. Such an additive contribution can reduce the error of optimal estimation protocols, as implied by the quantum Cramér–Rao bound. I characterize regimes in which the estimation of a time interval or a frequency is enhanced by decoherence, thereby identifying cases in which incoherent dynamics serve as a metrological resource. The decoherence processes that yield enhanced precision of quantum sensors can be engineered by randomized Hamiltonian dynamics. I illustrate the results with protocols that display improved sensing of time intervals or global fields by qubit and photonic sensors. Enhanced precision of time intervals is achieved with Hamiltonians that include randomized global parameters. Enhanced precision in field estimation is obtained by randomized sensing times.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Additive Manufacturing with Cellulose-Based Composites: Materials, Modeling, and Applications

Recent advances in large-scale additive manufacturing (AM) with polymer-based composites have enabled efficient production of high-performance materials. Cellulose nanomaterials (CNMs) have emerged as bio-based feedstocks due to their exceptional strength and sustainability. However, challenges such as hornification and poor dispersion in polymer matrices still limit large-scale CNM–polymer composite manufacturing, requiring novel strategies. Here, this review outlines an approach starting with atomic-level simulations to link molecular composition to key parameters like bulk density, viscosity, and modulus. These simulations provide data for finite element analysis (FEA), which informs large-scale experiments and reduces the need for extensive trials. The strategy explores how atomic interactions impact the morphology, adhesion, and mechanical properties of CNM-based composites in AM processes. The review also discusses current developments in AM, along with predictions of mechanical and thermal properties for structural applications, packaging, flexible electronics, and hydrogel scaffolds. By integrating experimental findings with molecular dynamics (MD) simulations and finite element modeling (FEM), valuable insights for material design, process optimization, and performance enhancement in CNM-based AM are provided to address ongoing challenges.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Multi-objective automatic discovery of optimized metamaterials for varying velocity impact protection

Mechanical metamaterials have demonstrated exceptional impact performance while remaining lightweight. Impact resistance has traditionally been investigated using quasi-static simulations, often with the assumption that performance will translate to high-velocity impact scenarios. However, critical crash protection parameters—such as peak stress and absorbed energy—are highly sensitive to impact velocity, leading to inconsistent performance under dynamic loading. To address this, we introduce a strain-rate-aware, active deep learning framework that enables multi-objective optimization of impact protection metrics across a wide range of impact velocities. Our framework captures the strain-rate sensitivity of architected lattices by learning to control spatial gradation in cellular metamaterials, resulting in over 200 % enhancement in impact protection relative to state-of-the-art designs such as Voronoi and re-entrant lattices. We demonstrate its practical utility by designing next-generation lattice structures for automotive bumper systems that satisfy multiple, velocity-specific safety criteria—capabilities beyond those of conventional designs. More than just a predictive tool, this framework marks the first step towards enabling adaptable impact-resistant structures across dynamic regimes.

Deep learning↗
DOE OSTI2025

Dynamic Metal–Support Interaction Dictates Cu Nanoparticle Sintering on Al 2 O 3 Surfaces

Nanoparticle sintering remains a critical challenge in heterogeneous catalysis. In this work, we present a unified deep potential (DP) model based on the Perdew–Burke–Ernzerhof approximation of density functional theory for Cu nanoparticles on three Al 2 O 3 surfaces (γ-Al 2 O 3 (100), γ-Al 2 O 3 (110), and α-Al 2 O 3 (0001)). Using DP-accelerated simulations, we reveal that the nanoparticle size-mobility relationship strongly depends on the supporting surface. The diffusion of nanoparticles on the two γ-Al 2 O 3 surfaces is almost independent of the size of the nanoparticle, while the diffusion on α-Al 2 O 3 (0001) decreases rapidly with increasing size. Interestingly, nanoparticles with fewer than 55 atoms diffuse several times faster on α-Al 2 O 3 (0001) than on γ-Al 2 O 3 (100) at 800 K while expected to be more sluggish based on their larger binding energy at 0 K. The diffusion on α-Al 2 O 3 (0001) is facilitated by dynamic metal–support interaction (MSI), where Al atoms move out of the surface plane to optimize contact with the nanoparticle and relax back to the plane as the nanoparticle moves away. In contrast, the MSI on γ-Al 2 O 3 (100) and on γ-Al 2 O 3 (110) is dominated by more stable and directional Cu–O bonds, consistent with the limited diffusion observed on these surfaces. Our extended MD simulations provide insight into the sintering processes, showing that the dispersity of the nanoparticles strongly influences the coalescence driven by nanoparticle diffusion. We observed that the coalescence of Cu 13 nanoparticles on α-Al 2 O 3 (0001) can occur in a short time (10 ns) at 800 K even with an initial internanoparticle distance increased to 3 nm, while the coalescence on the two γ-Al 2 O 3 surfaces are inhibited significantly by increasing the initial internanoparticle distance. These findings demonstrate that the dynamics of the supporting surface is crucial to understanding the sintering mechanism and offer guidance for designing sinter-resistant catalysts by engineering the support morphology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Dynamical Ion Correlations in Polymer and Membrane Electrolytes: Recent Advances and Open Questions

Ion transport in polymer and membrane electrolytes is often described using uncorrelated models like the Nernst–Einstein (NE) approximation, which link conductivity, transference number, and salt diffusivity to individual ion mobilities. However, growing evidence shows that dynamical ion correlations─arising from ion pairing, polymer-mediated coupling, confinement, and electrostatic interactions─can substantially alter macroscopic transport properties. The Onsager transport formalism offers a rigorous framework to quantify these effects via cross-correlated ionic displacements. This Perspective highlights how such correlations manifest across dry and hydrated systems, including salt-doped polymers, block copolymers, hydrogels, and ion-exchange membranes. Here, we examine key physical origins, the influence of salt chemistry and polymer structure, and open questions in measuring and controlling correlated motion. Embracing correlation-aware design enables new pathways to optimize conductivity, transference number, and selectivity─shifting the focus from individual ion mobility to engineered collective dynamics for next-generation electrolytes in energy storage and separations.

Charge transport↗
DOE OSTI2024

Optimizing the Heisenberg Vortex Tube for Hydrogen Cooling (Final Technical Report)

Hydrogen utilization at Plug Power sites ranges between 70-93% with the remainder vented and lost to the atmosphere. The goal of this project was to improve hydrogen utilization at Plug Power fulfillment centers via the patented Heisenberg vortex tube (HVT). The HVT combines conventional counterflow vortex tubes with para-orthohydrogen conversion catalyst to allow the cooling of hydrogen flows with no moving parts or external energy inputs. In year 1 of this project the HVT was evaluated to improve hydrogen utilization via the following concepts: 1) increasing liquid hydrogen pump volumetric efficiency by 20% through vapor separation and subcooling of the liquid, 2) reducing liquid hydrogen storage tank boil-off losses by 20% through thermal vapor shielding (TVS), and 3) increase isentropic efficiency of supercritical hydrogen expansion at 40-50 K, from 31% to over 40%. The TVS concept was selected as the most favorable application for further development. While the conceptual analysis was underway, the cryocatalysis hydrogen experiment facility (CHEF) was retrofitted with a new cryocooler, higher pressure condenser tanks, and in-situ fiber-optic Raman probes for ortho-parahydrogen composition analysis at the inlets and outlets of the HVT. To our knowledge this is the first in-situ implementation of cryogenic Raman probes for ortho-parahydrogen analysis. Subsequent testing of catalyzed and non-catalyzed HVT identified a low flow rate, high-conversion efficacy regime well suited for TVS development. Computational fluid dynamics (CFD), Reduced order modeling (ROM), and quantum Monte Carlo atomistic simulations were applied to optimize the design of the HVT implemented for TVS. The simulations and analysis identified a ruthenium-based catalyst as the most optimal for high conversion with little pressure losses and was matched to experimental measurements. These results indicated the design could achieve the 20% boil-off reduction target. An HVT field-trial was designed and constructed by Plug Power and implemented at a customer site. However, budget limitations reduced the amount of catalyst that could be applied to the HVT. With the reduced amount of catalyst, CFD analysis estimated about 3% reduction in boil-off. A similar amount of boil-off reduction was observed during preliminary measurements during tank commissioning. However, the results have a large margin for error and were operated at relatively low tank temperatures when the HVT has the lowest potential for improvement. This project demonstrated the use of para-orthohydrogen catalysis for reducing liquid hydrogen tank boil-off losses. The field trial system is anticipated to provide long-term experimental measurements on tank operational performance that will allow Plug Power to instrument additional tanks in the future. Recommendations for future work include the development of higher activity, lower cost para-orthohydrogen conversion catalyst for use in the HVT. Tank process optimizations could maximize the efficacy of the HVT and further improve hydrogen utilization.

08 HYDROGEN↗
DOE OSTI2025

Experimental test of model predictive control in a variable air volume system

Model predictive control (MPC) has been widely studied as a promising approach for improving energy efficiency and operational flexibility in buildings, yet its real-world performance for commercial variable air volume (VAV) systems remains insufficiently characterized. In particular, the impacts of model mismatch on control robustness, real-time computational burden, and device-level operation are rarely evaluated using long-term field data. Here, this study presents a comprehensive experimental evaluation of MPC applied to a full-scale VAV system in Oak Ridge National Laboratory’s Flexible Research Platform-2 building with constant cooling/heating temperature setpoints and no occupancy. The study offers three key advantages over existing work: (1) it uses a representative building in a full-scale experimental test, capturing realistic system dynamics and complexity; (2) it evaluates a relatively sophisticated MPC formulation using two different optimization solvers (Gurobi and PSO), fully accounting for computational complexity and methodological diversity; and (3) it systematically assesses potential negative impacts on various building devices, benchmark against a well-established baseline, ASHRAE Guideline 36 (G36). To isolate zone- and air-handling-unit–level supervisory control effects, the supply fan was operated with a fixed static pressure setpoint under all strategies, and the trim-and-response static pressure reset in G36 was not enabled. Results show that MPC maintained thermal comfort while improving energy efficiency. Abrupt solar radiation variations degraded performance. Computation times ranged from ∼1 s (Gurobi) to ∼ 70 s (PSO). Compared with G36, MPC achieves 33% energy savings and reduces median reheat coil output by approximately a factor of 5–10 for a representative cooling day under matched weather conditions. However, it increases the maximum discomfort deviation from 0.5 to 1°C and results in a 32% increase in staging frequency. In addition, PSO-based MPC introduced damper oscillations, also affecting actuator longevity.

ASHRAE guideline 36↗
DOE OSTI2025

The effects of photosynthetic rate on respiration in light, starch/sucrose partitioning, and other metabolic fluxes within photosynthesis

In the future, plants may encounter increased light and elevated CO 2 levels. How consequent alterations in photosynthetic rates will impact fluxes in photosynthetic carbon metabolism remains uncertain. Respiration in light ( R L ) is pivotal in plant carbon balance and a key parameter in photosynthesis models. Understanding the dynamics of photosynthetic metabolism and R L under varying environmental conditions is essential for optimizing plant growth and agricultural productivity. However, measuring R L under high light and high CO 2 (HLHC) conditions poses challenges using traditional gas exchange methods. In this study, we employed isotopically nonstationary metabolic flux analysis (INST-MFA) to estimate RL and investigate photosynthetic carbon flux, unveiling nuanced adjustments in Camelina sativa under HLHC. Despite numerous flux alterations in HLHC, RL remained stable. HLHC affects several factors influencing RL, such as starch and sucrose partitioning, v o /v c ratio, triose phosphate partitioning, and hexose kinase activity. Analysis of A/C i curve operational points reveals that HLHC’s major changes primarily stem from CO 2 suppressing photorespiration. Integration of these fluxes into a simplified model predicts changes in CBC labeling under HLHC. This study extends our prior discovery that incomplete CBC labeling is due to unlabeled carbon reimported during R L , offering insights into manipulating labeling through adjustments in photosynthetic rates.

Elevated CO2↗