Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “analytical model”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,027 records · Page 57

Extending Component Lifetime And Improving Inverter Reliability (ECLAIIR)

Inverter reliability remains one of the most persistent challenges limiting the performance, availability, and economic viability of utility‑scale photovoltaic (PV) plants. Industry data consistently show that inverters account for the highest share of corrective maintenance events and unplanned outages across PV fleets. These failures result in energy losses, increased O&M costs, and reduced confidence in long‑term solar asset performance. Motivated by these challenges, this project—Extending Component Lifetime and Improving Inverter Reliability (ECLAIIR)—was undertaken to systematically investigate inverter degradation and failure mechanisms, develop predictive maintenance capabilities, and establish data‑driven pathways to improve service life and reduce the Levelized Cost of Energy (LCOE) for large‑scale PV systems. The primary goal of the project was to identify pre‑failure signatures in string inverters using both lab‑based accelerated lifetime testing and field‑based data and to develop predictive maintenance algorithms that can anticipate inverter faults before they occur. Through collaboration with inverter testing laboratory, solar PV plant owner, and failure‑analysis experts, the project advanced the technical understanding of inverter reliability. By instrumenting inverters with thermistors, humidity sensors, power‑quality meters, and acoustic sensors, the research established how multiple sensing modalities can reliably detect deviations from normal behavior hours to days before failure. These findings substantially enhance scientific understanding of inverter failure kinetics and provide the PV industry with the most comprehensive cross‑OEM characterization of early‑stage failure indicators reported to date. Technically, the project demonstrated the effectiveness of predictive maintenance by developing and validating the PreDICT (Predictive Diagnostics of PV Inverters Using Condition Monitoring and Trend Analysis) framework—a multi‑layer diagnostic architecture combining peer‑to‑peer analytics, historical trend modeling, and advanced machine‑learning techniques such as the Sequential Conditional Variational Autoencoder (SCVAE). This predictive model achieved more than 90% accuracy in detecting pre‑failure conditions and provided up to four days of lead time before inverter failure in field scenarios. Economically, the project’s LCOE analysis showed that predictive maintenance can reduce lifetime energy losses and minimize corrective maintenance interventions. Modeling indicated that, depending on inverter failure rates and replacement timelines, predictive maintenance can significantly reduce LCOE impacts associated with inverter downtime: from as high as 19.4% under conventional maintenance strategies to 0.1%–10.17% when predictive analytics are adopted. These results confirm that predictive maintenance is both technically feasible and economically advantageous for utilities and plant operators. The project’s findings also have broad public benefit. By improving inverter reliability and reducing downtime, predictive maintenance directly increases electricity generation from existing PV assets. Enhanced reliability lowers operational costs for utilities, which can translate over time into lower energy costs for consumers. Furthermore, the project’s technical publications, conference presentations, and industry workshops ensure that knowledge gained is shared broadly across the solar industry, supporting workforce development and enabling utilities of all sizes to adopt modern asset‑health monitoring practices. The retrofitting case study and service‑life prediction framework further support informed decision‑making for aging PV fleets, helping operators extend system life and reduce electronic waste. In summary, the ECLAIIR project significantly advanced the state of knowledge on inverter degradation, demonstrated the technical and economic value of predictive maintenance, and delivered actionable tools and insights that support more reliable, cost‑effective, and sustainable PV plant operation. The outcomes of this project will continue to inform utility practices, guide inverter design improvements, and strengthen the long‑term performance of solar assets nationwide.

14 SOLAR ENERGY↗

Analytic continuation of noisy data using Adams Bashforth residual neural network

We propose a data-driven learning framework for the analytic continuation problem in numerical quantum many-body physics. Designing an accurate and efficient framework for the analytic continuation of imaginary time using computational data is a grand challenge that has hindered meaningful links with experimental data. The standard Maximum Entropy (MaxEnt)-based method is limited by the quality of the computational data and the availability of prior information. Also, the MaxEnt is not able to solve the inversion problem under high level of noise in the data. Here we introduce a novel learning model for the analytic continuation problem using a Adams-Bashforth residual neural network (AB-ResNet). Additionally, the advantage of this deep learning network is that it is model independent and, therefore, does not require prior information concerning the quantity of interest given by the spectral function. More importantly, the ResNet-based model achieves higher accuracy than MaxEnt for data with higher level of noise. Finally, numerical examples show that the developed AB-ResNet is able to recover the spectral function with accuracy comparable to MaxEnt where the noise level is relatively small.

97 MATHEMATICS AND COMPUTING↗

Field Data Analysis and Modeling of Drillstring Vibrations to Identify Inefficiency in Deep Geothermal Drilling

One challenge that hinders efficient drilling and causes downhole tool failures is severe drillstring vibrations. The objective of this paper is to identify the root cause of drillstring vibrations in deep geothermal wells and investigate their effect on drilling performance using data analytics and vibration modeling. A near-bit sub was utilized to collect vibration data, where the burst data was used to obtain the drillstring torsional natural frequency. The data showed that the highest lateral acceleration and stick-slip severities (SSS) occur at the higher mechanical specific energy (MSE) range, while the low vibration levels were encountered in the optimum range of the MSE curve. The elevated SSS levels consistently occur at the low to mid-range of applied RPM and the highest sonic velocity. Additionally, the lateral acceleration levels are higher at the low to mid-range of the applied RPM. The effect of drillstring vibration on drilling performance was recognized by the presented MSE analysis.

15 GEOTHERMAL ENERGY↗

Analytical population dynamics underlying harmful algal blooms triggered by prey avoidance

A modified version of the NPZD ecosystem model is used to analytically examine the effects of predation avoidance, a possible mechanism for triggering harmful algal blooms (HAB). To resolve HAB development caused by predation avoidance, an additional phytoplankton functional group is considered, one that has slower nutrient uptake and better predation avoidance characteristics than the non-harmful phytoplankton group used in traditional NPZD models. Because the two phytoplankton groups (one non-harmful and one HAB) compete for only one resource within the same system, steady state (equilibrium) conditions cannot occur without the presence of zooplankton; only the non-harmful phytoplankton group, which defeats the HAB group in the resource competition, can survive in the equilibrium. The presence of sufficient zooplankton effectively acts to replenish the nutrient pool by consuming the non-harmful phytoplankton. When this occurs, two equilibrium states are found: one with both phytoplankton groups coexisting, and one that only includes the HAB group. Further, the condition required for equilibrium is that the total nitrogen within the system should be larger than a threshold determined by model coefficients. The threshold and feasibility of the equilibrium are sensitive to the relative HAB predation avoidance coefficient. If the coefficient is larger than the ratio of net growth rates between the HAB and non-harmful phytoplankton group, the threshold becomes infinite, and an equilibrium is not feasible. The time scale for the system to reach an equilibrium state that includes a HAB group is determined asymptotically. The dependence of a threshold condition as a controlling factor may explain the regime shift of dominant species causing HABs. The ecosystem model is fully implemented into the Regional Ocean Modeling System and applied to an idealized coastal embayment (with depths and geometry taken from San Francisco Bay) to show numerically the dominance of prey avoidance dynamics in a natural shallow water environment that includes advection and diffusion. The analytical results improve strategies for HAB modeling and provide guidance for setting model coefficients necessary to resolve a HAB event.

54 ENVIRONMENTAL SCIENCES↗

General Multifidelity Surrogate Models: Framework and Active-Learning Strategies for Efficient Rare Event Simulation

Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process more feasible, but merging information from multiple low-fidelity and high-fidelity models poses several challenges. Here, this paper presents a robust multi-fidelity surrogate modeling strategy in which the multi-fidelity surrogate is assembled using an active learning strategy using an on-the-fly model adequacy assessment set within a subset simulation framework for efficient reliability analysis. The multi-fidelity surrogate is assembled by first applying a Gaussian process correction to each low-fidelity model and assigning a model probability based on the model's local predictive accuracy and cost. Three strategies are proposed to fuse these individual surrogates into an overall surrogate model based on model averaging and deterministic/stochastic model selection. The strategies also dictate which model evaluations are necessary. No assumptions are made about the relationships between low-fidelity models, while the high-fidelity model is assumed to be the most accurate and most computationally expensive model. Through two analytical and two numerical case studies, including a case study evaluating the failure probability of Tristructural isotropic-coated (TRISO) nuclear fuels, the algorithm is shown to be highly accurate while drastically reducing the number of high-fidelity model calls (and hence computational cost).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Analytical benchmark solution for 1-D neutron transport coupled with thermal conduction and material expansion

In this work we present fully analytical solutions for a class of finite, homogeneous, 1-D slab benchmark problems with nonlinear temperature feedback effects. The proposed class of benchmarks include multiplicative 1-D neutron transport (limited to quasistatic S{sub 2} with μ = ±1) coupled with thermal conduction, convection, Doppler broadening, and expansion effects along the length of the slab. This class of benchmark models, along with the corresponding analytical solutions, are valuable for validating multiphysics analysis frameworks that support coupled neutronics/thermal/structural calculations. Analytical solutions for the benchmarks are obtained by introducing an ansatz that the equilibrium flux and temperature distributions in the slab have the same shape. Specific values for the total microscopic cross section, σ{sub t,0}, and conductive heat transfer coefficient, h, that satisfy the assumed ansatz are then determined. A discussion of the procedure for generating benchmark models and analytical solutions is provided, along with numerical results for an example set of model parameters and thoughts on practical applications of the benchmarks for multiphysics code validation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Magic-angle twisted symmetric trilayer graphene as a topological heavy-fermion problem

Recently, Song and Bernevig [Phys. Rev. Lett. 129, 047601 (2022)] reformulated magic-angle twisted bilayer graphene as a topological heavy fermion problem, and used this reformulation to provide a deeper understanding for the correlated phases at integer fillings. Here, in this work, we generalize this heavy-fermion paradigm to magic-angle twisted symmetric trilayer graphene, and propose a low-energy f–c–d model that reformulates magic-angle twisted symmetric trilayer graphene as heavy localized f modes coupled to itinerant topological semimetalic c modes and itinerant Dirac d modes. Our f–c–d model well reproduces the single-particle band structure of magic-angle twisted symmetric trilayer graphene at low energies for displacement field $\mathcal{E}$ ϵ [0,300]⁢ meV. By performing Hartree-Fock calculations with the f–c–d model for v = 0,–1,–2 electrons per Moiré unit cell, we reproduce all the correlated ground states obtained from the previous numerical Hartree-Fock calculations with the Bistritzer-MacDonald-type model, and we find additional new correlated ground states at high displacement field. Based on the numerical results, we propose a simple rule for the ground states at high displacement fields by using the f–c–d model, and provide analytical derivation for the rule at charge neutrality. We also provide analytical symmetry arguments for the (nearly) degenerate energies of the high-$\mathcal{E}$ ground states at all the integer fillings of interest, and make experimental predictions of which charge-neutral states are stabilized in magnetic fields. Our f–c–d model provides a new perspective for understanding the correlated phenomena in magic-angle twisted symmetric trilayer graphene, suggesting that the heavy fermion paradigm of Song and Bernevig [Phys. Rev. Lett. 129, 047601 (2022)] should be the generic underpinning of correlated physics in multilayer moire graphene structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A process to verify numerical models for seismic fluid-structure interaction in advanced reactor vessels

Seismic design and qualification of a liquid-filled advanced nuclear reactor will have to account for fluid-structure interaction (FSI). Interaction between the tank, internal components, and contained liquid will rely on analysis of numerical models that must be verified and validated. Here this study demonstrates a verification process for models of a base-supported cylindrical tank by comparing numerical predictions and analytical solutions. The numerical models are consistent with the assumptions made to derive analytical solutions, namely, either a rigid or a linear elastic tank, ideal fluid, and small-amplitude, unidirectional, horizontal inputs. One software platform is used to illustrate the process. Seismic FSI analysis is performed using the Arbitrary Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD) solvers in LS-DYNA. Reported responses are those used for design, including hydrodynamic pressures on the tank wall, shear forces and moments at the tank base, and wave heights of the contained liquid. The accuracy of the numerical results is discussed. The numerical models are verified for calculating the pressures on the tank wall and reactions at its base. Accurate simulation of wave action is challenging for both solvers. Recommendations for modeling, code development, and steps for verification are provided. Although focused on reactor vessels and one software platform, the verification process described herein is broadly applicable to liquid-filled vessels and other finite element codes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Generalizing the Gurson model using symbolic regression and transfer learning to relax inherent assumptions

Abstract To generate material models with fewer limiting assumptions while maintaining closed-form, interpretable solutions, we propose using genetic programming based symbolic regression (GPSR), a machine learning (ML) approach that describes data using free-form symbolic expressions. To maximize interpretability, we start from an analytical, derived material model, the Gurson model for porous ductile metals, and systematically relax inherent assumptions made in its derivation to understand each assumption’s contribution to the GPSR model forms. We incorporate transfer learning methods into the GPSR training process to increase GPSR efficiency and generate models that abide by known mechanics of the system. The results show that regularizing the GPSR fitness function is critical for generating physically valid models and illustrate how GPSR allows a high level of interpretability compared with other ML approaches. The method of systematic assumption relaxation allows the generation of models that address limiting assumptions found in the Gurson model, and the symbolic forms allow conjecture of decreased material strength due to void interaction and non-symmetric void shapes.

36 MATERIALS SCIENCE↗

Precise Modeling of a Complex Solenoidal Magnetic Field Using a Combination of Analytic Functions and a PINN

We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.

Kampa, Cole [Caltech] (ORCID:0000000192972920)↗

Radiation Effects Model for Ultra-Thin Silicon Solar Cells

This work is focused on investigation of radiation effects in Ultra-Thin Silicon solar cells with a particular emphasis on electron irradiation. The study is motivated by the application of these solar cells, developed by Solestial, Inc., for powering space missions, including those led by NASA, the Department Of Defence (DOD), and commercial satellite missions. Our research encompasses both experimental and theoretical approaches, addressing unique challenges posed by ultra-thin solar cell technology that deviates from the traditional models. From the experimental point of view, the test structures were irradiated with 1 MeV electrons up to the fluence of 1E+15 e/cm$^{2}$. Radiation effects due to accumulated electron dose were noticed as a drop in open-circuit voltage (Voc). An analytical expression for modeling the Voc characteristic of the UT-Si cell after exposure to electron irradiation was formulated and subsequently compared with experimental data. The theoretical foundation of the proposed approach builds upon the Non-Ionising Energy Loss (NIEL) concept, a fundamental parameter in addressing radiation damage modelling and survivability predictions.

Fedoseyev, Alex↗

Sapsan: Framework for Supernovae Turbulence Modeling with Machine Learning

Sapsan is a framework designed to make Machine Learning (ML) more accessible in the study of turbulence, with a focus on astrophysical applications. Sapsan includes modules to load, filter, subsample, batch, and split the data from hydrodynamic (HD) simulations for training and validation. Next, the framework includes built-in conventional and physically-motivated estimators that have been used for turbulence modeling. This ties into Sapsan’s custom estimator module, aimed at designing a custom ML model layer-by-layer, which is the core benefit of using the framework. To share your custom model, every new project created via Sapsan comes with pre-filled, ready-for-release Docker files. Furthermore, training and evaluation modules come with Sapsan as well. The latter, among other features, includes the construction of power spectra and comparison to established analytical turbulence closure models, such as a gradient model. Thus, Sapsan attempts to minimize the hard work required for data preparation and analysis, leaving one to focus on the ML model design itself.

79 ASTRONOMY AND ASTROPHYSICS↗

A parametric model for self-interacting dark matter halos

Abstract We propose a parametric model for studying self-interacting dark matter (SIDM) halos. The model uses an analytical density profile, calibrated using a controlled N-body SIDM simulation that covers the entire gravothermal evolution, including core-forming and -collapsing phases. By normalizing the calibrated density profile, we obtain a universal description for SIDM halos at any evolution phase. The model allows us to infer properties of SIDM halos based on their cold dark matter (CDM) counterparts. As a basic application, we only require two characteristic parameters of an isolated CDM halo atz = 0. We then extend the model to incorporate effects induced by halo mass changes, such as major mergers or tidal stripping, making it applicable to both isolated halos and subhalos. The parametric model is tested and validated using cosmological zoom-in SIDM simulations available in the literature.

Astronomy & Astrophysics↗

Coupled model for liquid lithium plasma facing components

Numerical analysis provides the design choice and operating window of liquid metal Plasma Facing Components (PFC) concepts. Coupled analysis of boundary plasma together with the surrounding boundary structures is required. Here, to achieve this goal, PPPL is developing a comprehensive multi-physics model for modeling of PFCs in fusion devices. The model includes the fluid-kinetic code SOLPS-ITER and the flow and heat transfer code CFX from ANSYS. SOLPS-ITER was augmented with a liquid metal boundary condition algorithm, allowing direct two-way coupling of the plasma analysis with the two-dimensional analytical slab flow model which includes heat convection in the liquid metal PFC. The target heat flux resulting from this coupled analysis is used as a boundary condition for detailed 3D Computational Fluid Dynamics (CFD) Magneto Hydro Dynamics (MHD) and heat transfer analysis. A new formulation of MHD equations is introduced in the numerical procedure ensuring current conservation of the discretized equations. Results of the 3D analysis are used for final validation of the coupled model. A PFC design where a porous wall is used to stabilize the liquid metal surface, while MHD drive is used to push the liquid metal flow inside the PFC, will be investigated in the regimes where vapor shielding is created for enhanced volumetric plasma heat dissipation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Toward Drilling the Perfect Geothermal Well: An International Research Coordination Network for Geothermal Drilling Optimization Supported by Deep Machine Learning and Cloud Based Data Aggregation

The EDGE project, supported by the U.S. Department of Energy Geothermal Technologies Office under award DE-EE0008793, established a data-driven framework for improving the efficiency, cost-effectiveness, and reliability of geothermal well drilling. The project focused on developing scalable data infrastructure, advanced machine learning and probabilistic models, and integrated analytics tools to support continuous drilling optimization. A central objective was to reduce geothermal drilling costs by up to seventy percent while minimizing the risk of well failure through predictive diagnostics and adaptive planning. Over the project period, a comprehensive data repository was designed and deployed, incorporating records from over one hundred geothermal wells across varied geological settings. This repository supported both structured and unstructured data and adhered to FAIR data principles, enabling provenance tracking, quality control, and standardized metadata. The project introduced automated ingestion pipelines and a cloud-hosted platform that facilitated access to raw, processed, and derived datasets. This infrastructure served as the foundation for model development and analysis. Machine learning workflows were developed to predict key drilling metrics including rate of penetration, non-productive time, and total drilling costs. Self-organizing maps and dimensionality reduction methods were used to uncover operational patterns and outliers, while supervised learning algorithms such as random forests and deep neural networks were applied to forecast performance outcomes. The models were validated on heterogeneous datasets from both U.S. and Icelandic fields, demonstrating variable but significant predictive accuracy. The results indicated that finer temporal resolution, inclusion of lithological data, and consistency in operational annotations could substantially improve model performance. The project also implemented process mining techniques to reconstruct state-transition models from drilling event logs. These models enabled the identification of deviations from optimal workflows and provided insights into recurring failure modes. Analysis of non-productive time highlighted the impact of equipment failures, geological challenges, and human factors, offering opportunities for targeted mitigation strategies. The EDGE Dashboard was developed as a web-based expert system integrating data visualization, model outputs, and user-driven queries. It provided an accessible interface for operators to explore historical data, evaluate predicted outcomes, and compare drilling scenarios. Initial feedback from project partners suggested that the dashboard could serve as a foundation for more advanced advisory and optimization tools. Overall, the EDGE project demonstrated the feasibility and value of applying modern data science techniques to geothermal drilling. It delivered a set of interoperable tools and models that can support more efficient, lower-risk well development. The findings point toward a viable path for transitioning from advisory analytics to semi-autonomous drilling systems, contingent on continued collaboration, expanded datasets, and field validation. The project results have immediate relevance for drilling operations, data management practices, and future geothermal R&D efforts aimed at achieving reliable, cost-competitive geothermal energy at scale.

15 GEOTHERMAL ENERGY↗

Molecular models for creep in oriented polyethylene fibers

Highly oriented and crystalline polyetheylene (PE) fibers have a large failure stress under rapid tensile loading but exhibit significant creep at much smaller stresses that limits applications. A possible mechanism is slip of chains due to stress-enhanced, thermally activated nucleation of dislocations at chain ends in crystalline regions. Molecular dynamics simulations are used to parameterize a Frenkel–Kontorova model that provides analytic expressions for the limiting stress and activation energy for dislocation nucleation as a function of stress. Results from four commonly used hydrocarbon potentials are compared to show that the qualitative behavior is robust and estimate quantitative uncertainties. In all cases, the results can be described by an Eyring model with values of the zero-stress activation energy Ea0≈1.5 eV and activation volume V* ≈ 45 Å3 that are consistent with the experimental results for increasingly crystalline materials. The limiting yield stress is ∼8 GPa. These results suggest that activated dislocation nucleation at chain ends is an important mechanism for creep in highly oriented PE fibers.

O’Connor, Thomas C. (ORCID:0000000293930295)↗

From pools to flow: The PROMISE framework for new insights on soil carbon cycling in a changing world

Soils represent the largest terrestrial reservoir of organic carbon, and the balance between soil organic carbon (SOC) formation and loss will drive powerful carbon-climate feedbacks over the coming century. To date, efforts to predict SOC dynamics have rested on pool-based models, which assume classes of SOC with internally homogenous physicochemical properties. However, emerging evidence suggests that soil carbon turnover is not dominantly controlled by the chemistry of carbon inputs, but rather by restrictions on microbial access to organic matter in the spatially heterogeneous soil environment. The dynamic processes that control the physicochemical protection of carbon translate poorly to pool-based SOC models; as a result, we are challenged to mechanistically predict how environmental change will impact movement of carbon between soils and the atmosphere. In this study, we propose a novel conceptual framework to explore controls on belowground carbon cycling: Probabilistic Representation of Organic Matter Interactions within the Soil Environment (PROMISE). In contrast to traditional model frameworks, PROMISE does not attempt to define carbon pools united by common thermodynamic or functional attributes. Rather, the PROMISE concept considers how SOC cycling rates are governed by the stochastic processes that influence the proximity between microbial decomposers and organic matter, with emphasis on their physical location in the soil matrix. We illustrate the applications of this framework with a new biogeochemical simulation model that traces the fate of individual carbon atoms as they interact with their environment, undergoing biochemical transformations and moving through the soil pore space. We also discuss how the PROMISE framework reshapes dialogue around issues related to SOC management in a changing world. We intend the PROMISE framework to spur the development of new hypotheses, analytical tools, and model structures across disciplines that will illuminate mechanistic controls on the flow of carbon between plant, soil, and atmospheric pools.

54 ENVIRONMENTAL SCIENCES↗