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At least 145 records · Page 8

Linear gyrokinetic stability of a high β non-inductive spherical tokamak

Spherical tokamaks (STs) have been shown to possess properties desirable for a fusion power plant such as achieving high plasma β and having increased vertical stability. To understand the confinement properties that might be expected in the conceptual design for a high β ST fusion reactor, a 1 GW ST plasma equilibrium was analyzed using local linear gyrokinetics to determine the type of micro-instabilities that arise. Kinetic ballooning modes and micro-tearing modes are found to be the dominant instabilities. The parametric dependence of these linear modes was determined and, from the insights gained, the equilibrium was tuned to find a regime marginally stable to all micro-instabilities at θ 0 = 0.0. This work identifies the most important micro-instabilities expected to generate turbulent transport in high β STs. The impact of such modes must be faithfully captured in first-principles-based reduced models of anomalous transport that are needed for predictive simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

ARC physics basis–magnetohydrodynamics

ARC is designed to produce 400 ⁢MW of net electricity and prove the commercial feasibility of a fusion power plant. In order to achieve this goal ARC has to operate with optimal core performance in a stationary scenario that minimises wear on the first wall and divertor. This requires avoiding or mitigating magnetohydrodynamic (MHD) instabilities which have the potential to not only degrade the plasma core but also lead to deleterious transient heat loads on plasma facing components. Therefore, this work aims at characterising the MHD stability of the high performance ARC scenario and inform the design of error field correction coils. Firstly, simulations of vertical displacement events show that an in-vessel coil is not needed and instead the poloidal shaping coils can be used to control vertical stability. These simulations also inform the demands on the corresponding coil power supplies. Stability analysis of the ideal kink mode with or without a conducting wall and kinetic effects suggests that the ARC baseline scenario operates deeply in the stable region. Using RDCON, tearing modes at the 𝑚/𝑛 =2/1 and 3/2 surfaces (with poloidal mode number 𝑚, and toroidal mode number 𝑛) are shown to be linearly stable, and including thermal transport effects in the rational surfaces lead to further stabilisation. However, other transient plasma instabilities can seed neoclassical tearing modes (NTMs). The marginally stable width of NTMs in ARC strongly depends on the internal inductance and can fall below 0.1% of the normalised poloidal flux. Furthermore, an empirical cross-machine model of the 𝑛 =1 error field leading to a disruption predicts a critical error field larger than SPARC but smaller than ITER. Three-dimensional coils can be designed with the Generalised Purturbed Equilbium Code based on a simple model that calculates the maximum correctable error field that is limited by the neoclassical toroidal viscosity torque. Broad scans of different coil geometries identify a set of 2 rows of off-midplane coils to be a suitable solution. It is also determined that such a set of three-dimensional coils is capable of correcting 𝑛 =2 error fields to some degree and creating strong enough 𝑛 =2 or 𝑛 =3 edge resonant perturbation fields for the suppression of edge-localised modes at reasonable coil currents. The final design of the first ARC will be further informed by results from SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Self-driving thin film laboratory: autonomous epitaxial atomic-layer synthesis via real-time computer vision analysis of electron diffraction

Emerging materials science platforms with the ability to make autonomous decisions on the fly are fundamentally changing the outlook and protocols for materials optimization and discovery. Because AI-driven self-navigating schemes can effectively reduce the total number of iterations needed to arrive at the "answer" (i.e. the best stochiometric composition for a desired physical property, optimum materials processing parameters, etc.) by significant margins, they have the potential to revolutionize materials and chemical manufacturing processes at large in research laboratory settings as well as in industrial plants. Here, we demonstrate a successful implementation of real-time closed-loop autonomous navigation of a multi-dimensional materials synthesis parameter space for fabricating phase-pure epitaxial films of a metastable phase of a functional oxide in a combinatorial pulsed laser deposition chamber. Sequential epitaxial growth iterations in search of the optimized recipe to stabilize the desired crystal phase were performed using frame-by-frame quantitative computer vision analysis of reflection high-energy electron diffraction (RHEED) images of the unit-cell level film being deposited. The autonomous scheme regularly resulted in > 30-fold reduction in the number of required experiments compared to a comprehensive mapping of the parameter space. The real-time workflow developed here can be readily extended to a variety of thin film synthesis platforms opening the door for self-driving atomic-level materials design as well as autonomous optimization of semiconductor manufacturing.

36 MATERIALS SCIENCE↗

A systematic literature review on residential demand response with a focus on opportunities for low-income communities

Demand Response improves efficiency and grid stability, reducing peak load and total system costs. It can potentially contribute to other societal aspects, including mitigating climate change and improving air quality, health, stress levels, and comfort. This paper reviewed the literature on residential demand response programs in the United States, through the lens of the five energy justice principles, identifying and categorizing a set of 165 papers from 1960 to 2024. As a result, we observe significant progress in distributive justice, however, mostly focused on increasing participation rather than attending specific needs of historically marginalized communities. Concordantly, recognition and procedural justice dimensions are lagging, while cosmopolitan justice studies are scarce, underscoring a need to improve the measurement of impacts resulting from the implementation of demand response programs. Future research opportunities include the consolidation of standardized definitions and metrics, to better understand burdens and needs of diverse residential users. In terms of policy, collection and transparent access to standardized data is required as a condition to the design of flexible, customizable, transparent, and easy to navigate demand response programs. As a result, a better understanding of and engagement with customers has the potential to increase adoption rates, persistence in the program, and overall impacts for the system, households, and society.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

ASEAN Technical Exchange Workshop for System Operators, Regulators, and Policymakers

This presentation provides an in-depth exploration of power system planning, cross-border electricity trading, and battery energy storage systems (BESS), offering actionable insights for system operators, regulators, and policymakers. The first section delves into power system planning and analysis, focusing on capacity expansion models and resource adequacy studies, including their role in optimizing system efficiency, managing emissions, and addressing system reliability risks. Key considerations, such as integration of transmission into generation planning and the forecasting versus optimization of customer distributed energy resources (DER) technologies, are explored. The session highlights critical trade-offs in spatial granularity and model runtimes, as well as the feasibility of aligning distribution investments with capacity expansion efforts. The second section examines cross-border electricity trading, with an emphasis on resource adequacy concepts such as reliability targets, loss of load expectation (LOLE), and planning reserve margins (PRM). Case studies on reserve market design and coordination across US regions provide insights into improving reserve deliverability and managing interregional power balance and congestion. This section also addresses market-to-market congestion management, including advanced strategies for high-voltage direct current (HVDC) optimization and ancillary service delivery. Finally, the presentation covers the rapid evolution of Battery Energy Storage Systems (BESS), highlighting their operational growth, regulatory frameworks, and use cases in grid flexibility, energy storage, and reliability. The discussion focuses on the benefits of BESS for system stability, resilience, and integration of renewable energy, offering insights into its role as a vital component in the transition toward a more sustainable and flexible grid. Key performance parameters, such as throughput, round-trip efficiency, and state of charge, are also examined.

25 ENERGY STORAGE↗

A comparison study on trading behavior and profit distribution in local energy transaction games

With the increasing integration of distributed energy resources, localized peer-to-peer energy transactions are receiving more attention since they could absorb more distributed renewables locally and stabilize the power grid. To better study the trading behavior and provide guidance for a viable local market design, different game-theoretical frameworks including cooperative and non-cooperative games are established and compared here. For the cooperative grand coalition, the maximum social welfare is guaranteed, the Shapley value and bargaining based approaches are implemented for further profit redistribution. It is shown that the asymmetrical bargaining power can be critical in the final payment clearing and it is equivalent to the Shapley value allocation if prosumers bargain based on their marginal contributions. Non-cooperative trading is formulated by using a Stackelberg bilevel model in which the upper level has the privilege in internal price setting. However, system optimum is not obtained due to competition, and the selfish leader could take away 89% of the collective benefit by price-gap based arbitraging. Aiming for a long-lasting trading market, a virtual benevolent leader and a uniform price structure in which purchase price equals selling price are tested. Experimental results indicate that maximum social welfare and a fairer profit allocation can be achieved with a uniform price structure, regardless of the selfish or benevolent attitude.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A robust statistical analysis of the role of hydropower on the system electricity price and price volatility

Abstract Hydroelectric power (hydropower) is unique in that it can function as both a conventional source of electricity and as backup storage (pumped hydroelectric storage and large reservoir storage) for providing energy in times of high demand on the grid (S. Rehman, L M Al-Hadhrami, and M M Alam), (2015 Renewable and Sustainable Energy Reviews , 44 , 586–98). This study examines the impact of hydropower on system electricity price and price volatility in the region served by the New England Independent System Operator (ISONE) from 2014-2020 (ISONE, ISO New England Web Services API v1.1 .” https://webservices.iso-ne.com/docs/v1.1/ , 2021. Accessed: 2021-01-10). We perform a robust holistic analysis of the mean and quantile effects, as well as the marginal contributing effects of hydropower in the presence of solar and wind resources. First, the price data is adjusted for deterministic temporal trends, correcting for seasonal, weekend, and diurnal effects that may obscure actual representative trends in the data. Using multiple linear regression and quantile regression, we observe that hydropower contributes to a reduction in the system electricity price and price volatility. While hydropower has a weak impact on decreasing price and volatility at the mean, it has greater impact at extreme quantiles (>70th percentile). At these higher percentiles, we find that hydropower provides a stabilizing effect on price volatility in the presence of volatile resources such as wind. We conclude with a discussion of the observed relationship between hydropower and system electricity price and volatility.

13 HYDRO ENERGY↗

Geometry-complete diffusion for 3D molecule generation and optimization

Abstract Generative deep learning methods have recently been proposed for generating 3D molecules using equivariant graph neural networks (GNNs) within a denoising diffusion framework. However, such methods are unable to learn important geometric properties of 3D molecules, as they adopt molecule-agnostic and non-geometric GNNs as their 3D graph denoising networks, which notably hinders their ability to generate valid large 3D molecules. In this work, we address these gaps by introducing the Geometry-Complete Diffusion Model (GCDM) for 3D molecule generation, which outperforms existing 3D molecular diffusion models by significant margins across conditional and unconditional settings for the QM9 dataset and the larger GEOM-Drugs dataset, respectively. Importantly, we demonstrate that GCDM’s generative denoising process enables the model to generate a significant proportion of valid and energetically-stable large molecules at the scale of GEOM-Drugs, whereas previous methods fail to do so with the features they learn. Additionally, we show that extensions of GCDM can not only effectively design 3D molecules for specific protein pockets but can be repurposed to consistently optimize the geometry and chemical composition of existing 3D molecules for molecular stability and property specificity, demonstrating new versatility of molecular diffusion models. Code and data are freely available on GitHub .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluation of flow-induced plate deflection for University of Missouri research reactor low-enriched uranium fuel element

The University of Missouri Research Reactor (MURR), located on the campus of the University of Missouri in Columbia, Missouri, is one of the six United States (U.S.) High Performance Research Reactors (USHPRR), including one critical facility, that are actively collaborating with the U.S. Department of Energy (DOE) National Nuclear Security Administration (NNSA) Office of Material Management and Minimization (M3) Reactor Conversion Program to convert from highly enriched uranium (HEU, ≥20 wt% U-235) fuel to low-enriched uranium (LEU, <20 wt% U-235) fuel. A new type of very high-density LEU fuel based on a monolithic alloy of uranium and 10 wt% molybdenum (U-10Mo) is expected to allow conversion of some USHPRR, including MURR. In the design of its fuel elements, MURR is using thin parallel curved fuel plates separated by coolant channels. In this work, fluid-structure interaction (FSI) analysis of the MURR LEU fuel element is performed at the element level (as compared to the plate level analysis), which models all components of the LEU fuel element, including fuel plates and the supporting structures. Therefore, the effect of supporting structures on the flow distribution within the element and the fuel plate deflection are evaluated. In addition to the element nominal flow rate and dimensions, the tolerances in the geometry of the coolant channel and plate thickness, the effect of a comb on plate deflection, and the uncertainty of the flow rate per element are evaluated. For the LEU fuel plates, which are thinner than the current HEU plates, the predicted plate deflection is found to be small compared to the fabrication and assembly tolerances. Thus, the FSI-induced deflections are not expected to noticeably reduce the coolant flow rate or predicted safety margins in the limiting channels for the MURR LEU fuel element. In addition to the simulation work, a hydraulic performance test of the MURR LEU fuel element is currently being planned to support conversion to the use of LEU fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A CHIL Validation of Machine Learning-Assisted Methods for Real-Time Controls of Solar PV for Grid Services

Recent research has highlighted the potential for solar to act as a zero-marginal-cost and zero-emission flexibility resource on the bulk power system when operated with advanced control systems. To increase the performance of these systems, leading technologies, including machine learning (ML) and hierarchical inverter set point allocation, have been proposed; however, these technologies lack comprehensive validation under real-world application scenarios. This paper addresses this gap by designing and developing a controller-hardware-in-the-loop framework to evaluate the performance of different flexible solar technologies in responding to automatic generation control signals in a closed-loop fashion. Simulation results indicate the superior performance of an ML-based approach compared to the conventional reference-control grouping-based approach, showcasing its potential to support grid stability and operational efficiency.

closed-loop validation↗

A CHIL Validation of Machine Learning-Assisted Methods for Real-Time Controls of Solar PV for Grid Services

Recent research has highlighted the potential for solar to act as a zero-marginal-cost and zero-emission flexibility resource on the bulk power system when operated with advanced control systems. To increase the performance of these systems, leading technologies, including machine learning (ML) and hierarchical inverter set point allocation, have been proposed; however, these technologies lack comprehensive validation under real-world application scenarios. This paper addresses this gap by designing and developing a controller-hardware-in-the-loop framework to evaluate the performance of different flexible solar technologies in responding to automatic generation control signals in a closed-loop fashion. Simulation results indicate the superior performance of an ML-based approach compared to the conventional reference-control grouping-based approach, showcasing its potential to support grid stability and operational efficiency.

14 SOLAR ENERGY↗

A CHIL Validation of Machine Learning-Assisted Methods for Real-Time Controls of Solar PV for Grid Services: Preprint

Recent research has highlighted the potential for solar to act as a zero-marginal-cost and zero-emission flexibility resource on the bulk power system when operated with advanced control systems. To increase the performance of these systems, leading technologies, including machine learning (ML) and hierarchical inverter set point allocation, have been proposed; however, these technologies lack comprehensive validation under real-world application scenarios. This paper addresses this gap by designing and developing a controller-hardware-in-the-loop framework to evaluate the performance of different flexible solar technologies in responding to automatic generation control signals in a closed-loop fashion. Simulation results indicate the superior performance of an ML-based approach compared to the conventional reference-control grouping-based approach, showcasing its potential to support grid stability and operational efficiency.

closed-loop validation↗

Salt Diapir‐Driven Recycling of Gas Hydrate

Abstract By harnessing both hypothetical, synthetic basin and gas hydrate (GH) system models and real‐world models of well‐studied salt diapir‐associated GH sites at Green Canyon (Gulf of Mexico) and Blake Ridge (U.S. Atlantic coast), we propose and demonstrate salt movement (and in particular, diapirism) to be a new mechanism for the recycling of marine GH. At Green Canyon, for example, we show that by considering this newly proposed diapir‐driven recycling mechanism in conjunction with previously proposed lithological control on sandy‐reservoir‐hosted hydrate at the base of the GH stability zone (BGHSZ; ∼bottom‐simulating reflector, BSR), modeled GH saturations match drilling data. Overall, salt diapir movement‐induced GH recycling provides a temperature‐driven mechanism by which GH saturations at the BGHSZ may reach >90 vol. % and by which GH volumes near and free gas volumes beneath the BGHSZ may be increased significantly through time. Interestingly, comparison of salt diapir‐driven recycling and sediment burial‐driven recycling scenarios suggests notably higher rates of recycling via diapir‐driven versus burial‐driven processes. Our results suggest that GH and associated free gas accumulations above salt diapir crests represent particularly attractive targets for unconventional and conventional hydrocarbon resource exploration and for scientific and academic drilling expeditions aimed at exploiting GH systems. Salt basins containing GH systems—including passive margin basins of the Gulf of Mexico, southeastern Brazil, and southwestern Africa—are therefore compelling localities for studying salt‐driven GH recycling and for salt diapir‐associated natural gas exploration.

58 GEOSCIENCES↗

A coupled thermo-hydro-mechanical model for simulating leakoff-dominated hydraulic fracturing with application to geologic carbon storage

A potential risk of injecting CO2 into storage reservoirs with marginal permeability (≲ 10 mD (1 mD = 10 –15 m 2 )) is that commercial injection rates could induce fracturing of the reservoir and/or the caprock. Such fracturing is essentially fluid-driven fracturing in the leakoff-dominated regime. Recent studies suggested that fracturing, if contained within the lower portion of the caprock complex, could substantially improve the injectivity without compromising the overall seal integrity. Modeling this phenomenon entails complex coupled interactions among the fluids, the fracture, the reservoir, and the caprock. Here, we develop a simple method to capture all these interplays in high fidelity by sequentially coupling a hydraulic fracturing module with a coupled thermal-hydrological-mechanical (THM) model for nonisothermal multiphase flow. The model was made numerically tractable by taking advantage of self-stabilizing features of leakoff-dominated fracturing. The model is validated against the PKN solution in the leakoff-dominated regime. Moreover, we employ the model to study thermo-poromechanical responses of a fluid-driven fracture in a field-scale carbon storage reservoir that is loosely based on the In Salah project's Krechba reservoir. The model reveals complex yet intriguing behaviors of the reservoir-caprock-fluid system with fracturing induced by cold CO 2 injection. We also study the effects of the in situ stress contrast between the reservoir and caprock and thermal contraction on the vertical containment of the fracture. The proposed model proves effective in simulating practical problems on length and time scales relevant to geological carbon storage.

58 GEOSCIENCES↗

Data-based filtered dissipation rate modelling for multi-modal turbulent combustion: evaluating a priori model generalizability

Manifold-based models offer a computationally efficient alternative to directly transporting the thermochemical state in computational simulations of turbulent reacting flows, projecting the high-dimensional thermochemical state-space onto a low-dimensional manifold. Recent efforts have yielded a manifold-based model applicable to multi-modal combustion, enabling reconstruction of the thermochemical state from solutions to two-dimensional manifold equations in mixture fraction and generalized progress variable that are parameterised by three scalar dissipation rates. In coarse-grained simulations such as Large Eddy Simulation (LES), closure of the multi-modal manifold equations and subfilter variances/covariance requires closure of three filtered scalar dissipation rates. Here, the present work adopts a data-based approach, providing closure for the three filtered scalar dissipation rates via deep neural networks (DNNs). High-fidelity datasets corresponding to an autoigniting n-dodecane jet flame and a bluff body swirl-stabilized confined lifted spray flame of two aviation fuels (Jet-A and C1) with different ignition propensities are leveraged to generate training data that spans a diverse range of thermodynamic conditions and combustion modes, including low- and high-temperature ignition regimes in addition to premixed and nonpremixed behaviour. A final DNN model is trained to enforce inherent physical constraints by learning nonlinear functional transformations of the three filtered scalar dissipation rates. The generalizability of this constrained DNN model is demonstrated a priori via conditional statistics evaluated on the lifted spray flame with C1–a configuration that had not been included in the training data. Excellent DNN agreement with conditional DNS statistics is observed, and integrated gradients are computed to identify the most sensitive input variables. The similarity of the marginal PDFs of the most informative input variables and outputs across configurations are quantified via the Wasserstein metric, demonstrating that data-based models may successfully generalize to unseen parametric conditions so long as the most informative input variables share similar distributions across training and testing datasets.

Data-based modelling↗

Assessing Global Ocean Circulation Sensitivity to Changes in Antarctic Ice Discharge

The principal goal of this research is to assess how projected increases in meltwater discharge and iceberg calving from the Antarctic Ice Sheet will impact climate in the next 250 years. In short, the sensitivity of the global ocean circulation and climate, and in particular the Atlantic Meridional Overturning Circulation (AMOC), to large increases in iceberg calving and meltwater discharges to the Southern Ocean are poorly understood. The requirement to investigate this topic is heightened by growing evidence that the West Antarctic Ice Sheet (WAIS) is vulnerable to rapid retreat and collapse through marine-ice-sheet-instability (MISI) on multidecadal-to-centennial timescales. Future model simulations of the AIS show the potential for rapid ice sheet retreat in the next 50 – 300 years, with such a collapse associated with the discharge of enormous volumes of ice and meltwater to the Southern Ocean. This project uses a combination of an ice sheet/shelf model and a fully coupled (ocean-atmosphere-seaice) model (CESM 1.2) to explore the sensitive of global climate to future changes in runoff from the Antarctic continent under future greenhouse gas emissions scenarios IPCC RCP4.5 and 8.5. Overall, accounting for Antarctic meltwater reduces the projected global mean anthropogenic greenhouse warming by up to 2 deg C. during peak WAIS collapse and by ~1 deg. for most of the simulation. In addition, the increased meltwater contribution raises sub-surface ocean temperatures at the Antarctic ice sheet margin by more than 1ºC, such that the ice shelf basal melt rates increase beyond those currently projected. In contrast, the model predicts a strong cooling of both the surface air and ocean temperatures over the Southern Ocean that results in a massive expansion and thickening of the perennial sea-ice. The slow-down in anthropogenic warming also results in the onset of ice-free conditions in the Arctic being delayed in the model by several decades, and the projected slowdown in the AMOC to reduce.

58 GEOSCIENCES↗

Mechanistic study of pH effect on organic solvent nanofiltration using carboxylated covalent organic framework as a modeling and experimental platform

Covalent organic framework (COF) membranes for organic solvent nanofiltration (OSN) have attracted growing interest due to their high stability, well-defined pore size, and controllable pore functionality. In aqueous nanofiltration processes, solution pH has a significant effect on membrane permeability, selectivity, and fouling. However, our understanding of pH effects on OSN processes is still limited. In this work, we present experimental and reactive force field molecular dynamics (ReaxFF MD) simulation results on the effect of pH on OSN using a well-characterized carboxylated COF (C-COF) membrane. Filtration experimental and modeling results both demonstrate that pH changes can affect solvent permeance and solute rejection dramatically. Specifically, methanol permeance decreases with the increase of NaOH and HCl concentration, respectively. When Alcian Blue dye was used as the solute in methanol, the selectivity increased from 23% to 98% when changing the feed pH from 2.2 to 10.1, respectively. While ReaxFF MD results show that C-COF solvated pore size is only marginally affected by the pH of solution, methanol diffusion is affected by the size of methanol-solvated Na + and Cl - ions, which increase with increasing Na + and Cl - concentrations. Solution pH change also affected solute solvation layer thicknesses and C-COF pore charges, contributing to the significant AB dye selectivity increase with pH increase. To summarize, we have shown that dramatic changes in C-COF selectivity are not anomalous in OSN, but are instead controllable by varying feed solution pH to modify solvated solute radii and surface charge.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Bioenergy Cropping Reduces the Spatiotemporal Scaling of Soil Bacterial Biodiversity

Widespread bioenergy cropping can transform landscapes, strongly affecting biodiversity. However, the impact of bioenergy cropping on the spatiotemporal scaling of soil biodiversity remains virtually unknown, despite its profound implications for the functioning of the ecological community. Here, we investigated how bioenergy cropping influenced the spatiotemporal scaling of soil bacterial biodiversity in marginal soils (sandy loam and clay loam soils) in Oklahoma, USA. We detected strong, significant species-time-area relationships (STARs) and phylogenetic-time-area relationships (PTARs) in bacterial communities and their lineages, suggesting that STARs and PTARs exist in microbial ecology within the studied system. Also, spatiotemporal scaling rates (the slopes of STAR and PTAR models) varied substantially among bacterial lineages and were positively correlated with their 16S rRNA gene copy numbers, a genomic trait indicative of microbial growth potentials. Strikingly, bioenergy cropping significantly reduced spatiotemporal scaling rates by 6.8%-14.1%, with a more pronounced reduction observed in sandy loam soils, where those rates were significantly lower than in clay loam soils. The heterogeneity of soil phosphorus and carbon resulted in variations in bacterial spatiotemporal scaling rates. Collectively, our findings suggest that bioenergy cropping may alleviate rapid shifts in soil biodiversity across space and time, thereby stabilizing soil biodiversity and supporting its role as part of sustainable land management and climate mitigation strategies.

bacterial diversity↗