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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

A multiscale approach to analyze the effect of radial void fraction distributions on BWR neutronic lattice parameters

The goal of this study is to analyze the effect of radial void fraction distribution, considered at three degrees of fidelity, on lattice and 2-group homogenized cross sections. The novelty of this work lies in its use of experimentally-determined radial void fraction distributions which allows for fine-scale coolant density data with no predictive uncertainty and which could be prohibitively expensive to simulate over the range of operational parameters used in the experiments. The experimentally-determined radial void fraction distributions are also characterized using a statistical tool called a semi-variogram in order to determine the scale of continuity. Void fraction distributions are averaged at the lattice and subchannel level for comparison with the fine-scale model. Models averaged at the subchannel and lattice level show a difference in about 68% of the time. Also, by comparing 2-group homogenized cross-sections, the differences between the subchannel and homogeneous cases are measurable.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Flow pattern and void fraction characterization in nitrogen/water flows through a diamond-type triply periodic minimal surface lattice

Here, this study presents, to the authors knowledge, the first experimental investigation on the void fraction and flow patterns in two-phase flows through a diamond-type Triply Periodic Minimal Surface (TPMS) lattice. An additively manufactured TPMS structure was tested under upward co-current flow of a water/nitrogen mixture. Superficial velocities varied for a total of 42 test conditions (gas: 0.01–2.4 m/s; liquid: 0.01–2.4 m/s; mass flux: 20–2370 kg/m 2 ·s). High-speed video and X-ray imaging enabled time-averaged void fraction measurements and identified six distinct flow regimes which were used to develop a flow pattern map. Comparison of the void fraction data with correlations from literature demonstrated the Rouhani and Axelsson (1970) [49] correlation modified by Steiner (1993) [52] provided the best agreement, which was improved with empirically fit coefficients. This approach predicted the void fraction with errors < ±20% for 64% of the data, with a mean absolute percent deviation (MAPD) of 23%. The measured frictional pressure drop was compared to correlations from literature which captured the observed trends but did not provide good accuracy. The best agreement was found after optimizing the empirical coefficients of the Muller-Steinhagen & Heck (1986) [56] correlation; this approach captured 33% of the data within ±20% with a MAPD of 46% over the full range and captured 71% of the data within ±20% a MAPD of 13.3% at mass fluxes >1100 kg/m 2 -s. These results provide foundational insight into TPMS two-phase flow behavior and inform modeling and design of advanced heat exchange components incorporating TPMS geometries.

42 - ENGINEERING↗
DOE OSTI2021

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this study we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Evaluation of several relevant fractionation processes as possible explanation for radioxenon isotopic activity ratios in samples taken near underground nuclear explosions in shafts and tunnels

Gas samples taken from two historic underground nuclear tests done in 1989 at the Nevada National Security Site (NNSS), formerly the Nevada Test Site (NTS), were examined to determine how xenon isotopes fractionate because of early-time cavity processes, transport through the rock, or dispersal through tunnels. Xenon isotopes are currently being used to distinguish civilian sources of xenon in the atmosphere from sources associated with underground nuclear explosions (UNEs). The two nuclear tests included (1) BARNWELL, a test conducted in a vertical shaft approximately 600 m below ground surface at Pahute Mesa, and (2) DISKO ELM, a horizontal line-of-sight test done in P-tunnel approximately 261 m below the surface of Aqueduct Mesa. Numerical flow and transport models developed for the two sites had mixed success when attempting to match the observed xenon isotope ratios. At the BARNWELL site, the simulated xenon isotope ratios were consistent with measurements from the chimney and ground surface and appeared to have been affected primarily by fractionation during subsurface transport. At the DISKO ELM site, samples taken from two elevations in the chimney failed to show the degree of fractionation predicted by the models during transport and did not show evidence for significant fractionation due to early-time condensation of refractory xenon-precursor radionuclides into the melt glass. Gas samples taken from the adjacent tunnels in the days following the test showed mixed evidence for early-time separation of xenon isotopes from their iodine precursors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Elemental fractionation in aerosol laser-induced breakdown spectroscopy with nanosecond and femtosecond laser ablation

For the purpose of realizing atmospheric radiation plume tracking, laser-induced breakdown spectroscopy (LIBS) was performed to characterize Cs atomic emissions from airborne nanoparticles in a binary particle matrix using nanosecond and femtosecond laser ablation. As a surrogate to multi-element nuclear fallout particulates, both Cs and Na solutions were mixed with Cu at a 1:1.45 M concentration ratio and aerosolized to study elemental fractionation in atomic emissions, revealing Na I resonance emissions are enhanced whereas Cs I resonance emissions are reduced with Cu present despite sharing similar electronic and chemical properties. Femtosecond laser ablation reduced elemental fractionation effects by more than 50% while retaining the same temporal fractionation trends for Cs and Na. The origin of elemental fractionation in aerosol LIBS was further investigated using Al and Ti aerosols which revealed that the particle matrix induces changes to the local plasma temperature, population of atomic states, and subsequent molecular association and emission.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Distribution of Bound and Free Water in Anatomical Fractions of Pine Residues and Corn Stover as a Function of Biological Degradation

Biomass quality is influenced by water’s abundance, distribution, and status in relation to other chemical species within the polymer matrix. Water interacts with polymers that make up the cell walls, and these interactions govern the physical and chemical changes that occur during the storage and preprocessing of biomass feedstocks. Time-domain nuclear magnetic resonance (TD-NMR) was employed to explore variations in the physical constraints of water within the lignocellulosic microstructure in distinct anatomical fractions of biomass and as a function of biological degradation. The Carr–Purcell–Meiboom–Gill sequence, when combined with knowledge of the chemical composition and physical structure of pine residues and corn stover anatomical fractions, gives an accurate measurement of the bound and free water. In this work, the impacts of storage and biological degradation were investigated to elucidate changes in the status and distribution of water within distinct plant tissues. We also investigate how degradation during storage affects water interactions in different pine residues (e.g., bark, branch, and needle) and corn stover (e.g., cob, leaf, and stalk) anatomical fractions using transverse relaxation times (T2). As demonstrated herein, TD-NMR provides quantitative data on lignocellulosic biomass–water interactions within anatomical fractions, which can further aid in the investigation of preprocessing effects on feedstock quality. Our findings suggest that biological heating enhances biomass–water interactions at the cellular and macromolecular scale. In addition, analysis of three-dimensional scanning electron microscopy reconstructions indicates that surface roughness wavelengths align with microscale roughness, suggesting that pine forestry residue and corn stover particles have primarily hydrophobic exterior surfaces. Furthermore, this study offers multiscale insights into understanding the microstructure, wettability, and chemical environment that dictate diffusion, enzyme access, and recalcitrance of lignocellulosic biomass.

09 BIOMASS FUELS↗
DOE OSTI2025

Generalized fractional approach to solving partial differential equations with arbitrary dispersion relations

The dynamics of physical systems are typically modeled by partial differential equations (PDEs). Because of the complexity in physical systems, PDE models rely on approximations or limiting cases. To model the full complexity of physical systems, it is necessary to use multiscale approaches where appropriate models are used at each level. Alternatively, complexity can be directly tackled by fractional integrodifferential equations that must be derived for each system. Here, we argue that complexity can be restored in PDEs by describing them from a fractional calculus perspective. Rather than deriving a fractional integrodifferential equation, we reinterpret the dispersion relation of the system by use of the Riesz definition, which contains the required information relating the energy and momentum space of the system and thus fully describes their dynamics. The approach is demonstrated by two examples: the Landau–Lifshitz equation in a 1D ferromagnetic chain and a modified KdV equation supporting surface gravity waves or Euler dispersion. The presented approach is applicable to fluids, soft matter, and solid-state matter and can be readily generalized to higher dimensions and more complex systems. While numerical calculations are needed to determine the fractional operator, the approach is analytical and can be utilized to determine analytical solutions and investigate nonlinear problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Assessing the accuracy of time-fraction and ductility exhaustion approaches for creep-fatigue damage prediction through feature-test validation

Determining creep-fatigue damage formation is critical for elevated temperature components integrity. This study evaluates creep-fatigue assessments with emphasis on differences between creep damage models. Evaluated are the time-fraction model and the classical and stress-modified ductility exhaustion creep damage models. This work extends the domain of stress-modified ductility exhaustion models by introducing and validating such formalism to Ni-based alloys. The fidelity of the assessments was benchmarked against uniaxial creep-fatigue and multiaxial feature tests of Alloy 617. For uniaxial specimens, best estimate predictions rank ductility exhaustion as the most accurate and precise and time-fraction as markedly conservative. For feature tests, ductility exhaustion predictions are within < 4.0 times difference, whereas time-fraction underpredicts life by factors of 7–14. The observations suggest ductility exhaustion models as alternative to time-fraction models in design codes for situations requiring characterization of the design margin. Further work in employing such models to assess other relevant phenomena (e.g., stress relaxation cracking) is discussed.

creep-fatigue↗
DOE OSTI2021

Towards a Unified theory of Fractional and Nonlocal Vector Calculus

Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green’s identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green’s identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. Here, the proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Relationships between summertime surface albedo and melt pond fraction in the central Arctic Ocean: The aggregate scale of albedo obtained on the MOSAiC floe

As part of the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC), the HELiX uncrewed aircraft system (UAS) was deployed over the sea ice in the central Arctic Ocean during summer 2020. Albedo measurements were obtained with stabilized pyranometers, and melt pond fraction was calculated from orthomosaic imagery from a surface-imaging multispectral camera. This study analyzed HELiX flight data to provide insights on the temporal and spatial evolution of albedo and melt pond fraction of the MOSAiC floe during the melt season as it drifted south through Fram Strait. The surface albedo distributions showed peak values changing from high albedo (0.55–0.6) to lower values (0.3) as the season advanced. Inspired by methods developed for satellite data, an algorithm was established to retrieve melt pond fraction from the orthomosaic images. We demonstrate that the near-surface observations of melt pond fraction were highly dependent on sample area, offering insight into the influence of subgrid scale features and spatial heterogeneity in satellite observations. Vertical observations conducted with the HELiX were used to quantify the influence of melt pond scales on observed surface albedo as a function of sensor footprint. These scaling results were used to link surface-based measurements collected during MOSAiC to broader-scale satellite data to investigate the influence of surface features on observed albedo. Albedo values blend underlying features within the sensor footprint, as determined by the melt pond size and concentration. This study framed the downscaling (upscaling) problem related to the airborne (surface) observations of surface albedo across a variety of spatial scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A Unified Theory of Fractional Nonlocal and Weighted Nonlocal Vector Calculus

Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or anomalous behavior. This has driven a desire for a vector calculus that includes nonlocal and fractional gradient, divergence and Laplacian type operators, as well as tools such as Green's identities, to model subsurface transport, turbulence, and conservation laws. In the literature, several independent definitions and theories of nonlocal and fractional vector calculus have been put forward. Some have been studied rigorously and in depth, while others have been introduced ad-hoc for specific applications. The goal of this work is to provide foundations for a unified vector calculus by (1) consolidating fractional vector calculus as a special case of nonlocal vector calculus, (2) relating unweighted and weighted Laplacian operators by introducing an equivalence kernel, and (3) proving a form of Green's identity to unify the corresponding variational frameworks for the resulting nonlocal volume-constrained problems. The proposed framework goes beyond the analysis of nonlocal equations by supporting new model discovery, establishing theory and interpretation for a broad class of operators, and providing useful analogues of standard tools from the classical vector calculus.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An optimization-based approach to parameter learning for fractional type nonlocal models

Nonlocal operators of fractional type are a popular modeling choice for applications that do not adhere to classical diffusive behavior; however, one major challenge in nonlocal simulations is the selection of model parameters. In this work we propose an optimization-based approach to parameter identification for fractional models with an optional truncation radius. We formulate the inference problem as an optimal control problem where the objective is to minimize the discrepancy between observed data and an approximate solution of the model, and the control variables are the fractional order and the truncation length. For the numerical solution of the minimization problem we propose a gradient-based approach, where we enhance the numerical performance by an approximation of the bilinear form of the state equation and its derivative with respect to the fractional order. Several numerical tests in one and two dimensions illustrate the theoretical results and show the robustness and applicability of our method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Fractionation of carbon isotopes by phytoplankton and estimates of ancient CO2 levels

Reports of the 13C content of marine particulate organic carbon are compiled and on the basis of GEOSECS data and temperatures, concentrations, and isotopic compositions of dissolved CO2 in the waters in which the related phytoplankton grew are estimated. In this way, the fractionation of carbon isotopes during photosynthetic fixation of CO2 is found to be significantly correlated with concentrations of dissolved CO2. Because ancient carbon isotopic fractionations have been determined from analyses of sedimentary porphyrins [Popp et al., 1989], the relationship between isotopic fractionation and concentrations of dissolved CO2 developed here can be employed to estimate concentrations of CO2 dissolved in ancient oceans and, in turn, partial pressures of CO2 in ancient atmospheres. The calculations take into account the temperature dependence of chemical and isotopic equilibria in the dissolved-inorganic-carbon system and of air-sea equilibria. Paleoenvironmental temperatures for each sample are estimated from reconstructions of paleogeography, latitudinal temperature gradients, and secular changes in low-latitude sea surface temperature. It is estimated that atmospheric partial pressures of CO2 were over 1000 micro atm 160 - 100 Ma ago, then declined to values near 300 micro atm during the next 100 Ma. Analysis of a high-resolution record of carbon isotopic fractionation at the Cenomanian-Turonian boundary suggests that the partial pressure of CO2 in the atmosphere was drawn down from values near 840 micro atm to values near 700 micro atm during the anoxic event.

NASA Discipline Exobiology↗
NASA NTRS2019

Can Organic Haze and O2 Plumes Explain Patterns of Sulfur Mass-Independent Fractionation During the Archean?

The existence of mass-independently fractionated sulfur in Archean rocks is almost universally accepted as evidence for low atmospheric O2 and O3 concentrations at that time. But the detailed patterns of the values and of the ratios / and / remain to be explained, and the mechanism for producing the mass-independent fractionation remains controversial. Here, we explore the hypothesis that the relatively low values seen during the Mid-Archean, 2.7-3.5 Ga, were caused by the presence of organic haze produced from photolysis of methane. This haze helped shield SO2 from photolysis, while at the same time providing surfaces on which unfractionated short-chain sulfur species could condense. The evolution of oxygenic photosynthesis, and the concomitant disappearance of organic haze towards the end of the Archean allowed more negatively fractionated S4 and S8 to form, thereby generating large positive fractionations in other sulfur species, including sulfate and H2S. Reduction of this sulfate to H2S by bacteria, followed by incorporation of H2S into pyrite, produced the large positive values observed in the Neoarchean rock record, 2.5-2.7 Ga.

Great Oxidation Event↗
DOE OSTI2022

An index to characterize gas‐solid and solid‐solid mixing from average volume fraction fields

Abstract A mixing index based on solid volume fraction fields is developed for gas‐solid flows. Conventional mixing indices are based on particle realizations of granular mixing and are applicable to experimental data or discrete element method simulations. However, these indices cannot be used as‐is for multifluid models, and an index for characterizing mixing in gas‐solid flows from continuous fields is needed. The performance of the new mixing index is tested in two applications. The first is a 3D simulation of the mixing of biomass and sand in a fluidized bed reactor, and the second is a 2D simulation of binary particle segregation in a fluidized bed. The simulations are performed using OpenFOAM®. The mixing index is used to quantify gas‐solid mixing using solid volume fractions and solid‐solid mixing using solid fractions. The formulation of conventional mixing indices is extended to be used with solid volume fractions fields, and methods for performance improvement are presented.

09 BIOMASS FUELS↗
DOE OSTI2025

Measurements of the branching fractions of ${\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0}$, ${\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+}$, and ${\Xi }_{c}^{+}\to {\Xi }^{0}{K}+$ at Belle and Belle II

Using 983.0 fb −1 and 427.9 fb −1 data samples collected with the Belle and Belle II detectors at the KEKB and SuperKEKB asymmetric energy e + e − colliders, respectively, we present studies of the Cabibbo-favored ${\Xi }_{c}^{+}$ decays ${\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0}$ and ${\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+}$, and the singly Cabibbo-suppressed decay ${\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+}$. The ratios of branching fractions of ${\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0}$ and ${\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+}$ relative to that of ${\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}$ are measured for the first time, while the ratio $\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+})/\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+})$ is also determined and improved by an order of magnitude in precision. The measured branching fraction ratios are $\begin{array}{c}\frac{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0}\right)}{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=0.067\pm 0.007\pm 0.003,\\ \frac{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+}\right)}{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=0.251\pm 0.005\pm 0.010,\\ \frac{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+}\right)}{\mathcal{B}\left({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+}\right)}=0.017\pm 0.003\pm 0.001.\end{array}$ Additionally, the ratio $\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+})/\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+})$ is measured to be 0.068 ± 0.010 ± 0.004. Here, the first and second uncertainties are statistical and systematic, respectively. Multiplying the ratios by the branching fraction of the normalization mode, $\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+})=(2.9\pm 1.3)%$, we obtain the following absolute branching fractions $\begin{array}{c}\mathcal{B}({\Xi }_{c}^{+}\to {\Sigma }^{+}{K}_{S}^{0})=(0.194\pm 0.021\pm 0.009\pm 0.087)\text{%},\\ \mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{\pi }^{+})=(0.728\pm 0.014\pm 0.027\pm 0.326)\text{%},\\ \mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{0}{K}^{+})=(0.049\pm 0.007\pm 0.003\pm 0.022)\text{%},\end{array}$ where the third uncertainties are from $\mathcal{B}({\Xi }_{c}^{+}\to {\Xi }^{-}{\pi }^{+}{\pi }^{+})$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Solidification texture, variant selection, and phase fraction in a spot-melt electron-beam powder bed fusion processed Ti-6Al-4V

The effect of a spot melt strategy on the solidification texture, variant selection, phase fraction, and their variations along the build height was investigated in comparison to a conventional linear melt strategy. Ti-6Al-4V alloy samples were manufactured by an electron-beam powder bed fusion process using two different melt strategies and characterized using high-energy synchrotron x-ray diffraction. The linear and spot melt cases resulted in β<100> cube and fiber textures, respectively, with the cube/fiber axis nearly parallel to the build direction. The α phase exhibited Burgers orientation relationship (BOR) with the parent β phase for both melt strategies. Although all of the key texture components and the BOR between the α and β phases were consistently observed in both cases along the build height, there were several measurable differences between the two. At the top of the build height, the β<100> build texture intensity was stronger in the linear case. However, the texture intensity in the linear case decreased gradually from the top to near the substrate, whereas the spot melt case did not show this trend. Moreover, the BOR was examined along the build height and the results showed that there is a distinct variant selection in the spot melt case, unlike the linear case. Specifically, the planar variants sharing ($\bar101$) β || (0002) α with [$\bar2\bar2\bar2$]β and [$2\bar22$]β were the most prominent in the spot melt, but no preference was identified in the directional variants. The β phase fraction was slightly lower in the spot melt case compared to the linear case. In both the cases, the β phase fraction decreased moving towards the substrate but remained significantly higher than that of the powder feedstock. Overall, the novel spot melt strategy produced a more homogeneous microstructure in terms of both the phase fraction and texture across the build height.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Linking Manganese Fractions and Organic Carbon in Soils of Contrasting Land Use Systems

Manganese (Mn) is an essential micronutrient that influences carbon (C) cycling by binding or oxidizing soil organic matter. Mn fractions in soil and their plant availability depend largely on soil pH, which is commonly altered by agricultural practices. Fractions of Mn in soils range from readily available (e.g., bioavailable Mn, exchangeable Mn) to stabilized (e.g., Mn-oxide minerals, Mn contained in silicates). Furthermore, the distribution of soil Mn with depth was assessed in contrasting land use systems (organic agriculture, conventional agriculture, and unmanaged forest) using a sequential extraction method that targets Mn fractions ranging in bioavailability. Both agricultural sites had similar amounts of total Mn but had available Mn (1–7% of total Mn) lower than that of the unmanaged forested site (15% of total Mn). Manganese and organic C were generally positively correlated, but this relationship depended on soil depth, Mn fractions, and concentrations, while land management change had little influence.

Crops↗