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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
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↗
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↗
DOE OSTI2021

Improved Li + Transport in Polyacetal Electrolytes: Conductivity and Current Fraction in a Series of Polymers

Polymer electrolytes mitigate safety concerns surrounding flammable liquid electrolytes in lithium-ion batteries. Poly(ethylene oxide) (PEO) electrolytes demonstrate viable conductivity values (~1 × 10 -3 S/cm) at elevated temperatures (>70 °C) but a relatively low Li + current fraction (≤0.2) because strong Li + coordination inhibits cation mobility. We have developed a series of polyacetal electrolytes by systematically varying methylene oxide (MO) and ethylene oxide (EO) units in the polymer backbone. These materials maintain high oxygen-to-carbon ratios like PEO but offer improved ion transport, revealing trends of decreasing conductivity and increasing current fraction with respect to polymer composition. In particular, the increasing current fraction measured via the Bruce-Vincent method suggests that MO units improve Li+ mobility relative to anion mobility. Here, we calculate an overall efficacy (product of conductivity and current fraction) for each polymer/salt composition and identify two polymers - P(EO-MO) and P(EO-2MO) - that outperform PEO at high and low salt concentrations, respectively.

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

Oxidative Catalytic Fractionation of Lignocellulosic Biomass under Non-alkaline Conditions

Biomass pretreatment methods are commonly used to isolate carbohydrates from biomass, but they often lead to modification, degradation, and/or low yields of lignin. Catalytic fractionation approaches provide a possible solution to these challenges by separating the polymeric sugar and lignin fractions in the presence of a catalyst that promotes cleavage of the lignin into aromatic monomers. In this work, we demonstrate an oxidative fractionation method conducted in the presence of a heterogeneous non-precious-metal Co-N-C catalyst and O 2 in acetone as the solvent. The process affords a 15 wt% yield of phenolic products bearing aldehydes (vanillin, syringaldehyde) and carboxylic acids (p-hydroxybenzoic acid, vanillic acid, syringic acid), complementing the alkylated phenols obtained from existing reductive catalytic fractionation methods. The oxygenated aromatics derived from this process have appealing features for use in polymer synthesis and/or biological funneling to value-added products, and the non-alkaline conditions associated with this process support preservation of the cellulose, which remains insoluble at reaction conditions and is recovered as a solid.

09 BIOMASS FUELS↗
DOE OSTI2022

Fractional correlated insulating states at one-third filled magic angle twisted bilayer graphene

Abstract The observation of superconductivity and correlated insulating states in twisted bilayer graphene has motivated much theoretical progress at integer fillings. However, little attention has been given to fractional fillings. Here we show that the three-peak structure of Wannier orbitals, dictated by the symmetry and topology of flat bands, facilitates the emergence of a state we name a “fractional correlated insulator” at commensurate fractional filling of ν = n ± 1/3. Specifically for the filling of 1/3 electrons per moiré unit cell, we show that short-range interactions lead to an extensive entropy due to the “breathing” degree of freedom of an irregular honeycomb lattice that emerges through defect lines. The leading further-range interaction lifts this degeneracy and selects a ferromagnetic nematic state that breaks AB/BA sublattice symmetry. The proposed fractional correlated insulating state might underlie the suppression of superconductivity at ν = 2 − 1/3 filling observed in ref. 1 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Generalized vs. fractional: a comparative analysis of Maxwell models applied to entangled polymer solutions

Fractional viscoelastic models provide an excellent description of rheological data for polymer systems with power-law behaviour. However, the physical interpretation of their model parameters, which carry fractional units of time, often remains elusive. We show that for poly(ethylene oxide) (PEO) solutions, the fractional Maxwell model (FMM) requires much fewer model parameters than the classical generalized Maxwell model for a good description of the data and that it can be applied consistently to solutions with varying degrees of viscoelasticity. Despite their fractional units, the parameters exhibit scaling laws similar to classical parameters as a function of polymer concentration.

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

Integrating catalytic fractionation and microbial funneling to produce 2-pyrone-4,6-dicarboxylic acid and ethanol

Replacing biorefinery designs that use stepwise fractionation, depolymerization, and conversion processes with designed tandem process steps can greatly reduce a biorefinery's operating costs and environmental impact. Reductive Catalytic Fractionation (RCF) is a highly efficient lignin-first approach that combines biomass fractionation and lignin depolymerization to generate a hydrogenolysis oil and pulp. The oil is composed of a complex mixture of phenolic monomers, dimers, and oligomers. Intergrating this chemical deconstruction process with microbial funneling of phenolics can simplify the product mixture and make high-value products. We applied RCF to poplar biomass in a biomass-to-bioproduct processing chain in which the phenolics were funneled to 2-pyrone-4,6-dicarboxylic acid (PDC) by an engineered strain of Novosphingobium aromaticivorans DSM12444. The pulp was enzymatically digested and the glucose and xylose was funneled to ethanol by an engineered strain of Saccharomyces cerevisiae GLBRCY945. By combining biomass fractionation and lignin depolymerization we removed a costly processing step that directly translated into a 29% reduction in the minimum selling price of PDC. This work combines experimentation with process modeling of an integrated biorefinery design to show how utilizing tandem process steps can significantly reduce operating expenses and environmental impact of upgrading lignocellulosic biomass to a portfolio of high value products.

Sener, Canan [Great Lakes Bioenergy Research Cente↗
DOE OSTI2020

Shear-induced lift force on spheres in a viscous linear shear flow at finite volume fractions

Several studies have shown a significant increase in drag on a distribution of solid spherical particles within a fluid with increasing particle volume fraction. As a result, many empirical drag laws accounting for the dependence on the Reynolds number and volume fraction can be found in the literature. This study investigates the possibility of a similar effect of the particle volume fraction on the mean hydrodynamic lift force on randomly distributed spherical particles in a linear shear flow. Particle-resolved direct numerical simulations are performed to evaluate the mean lift force, and the results are compared with the case of an isolated particle in a linear shear flow for the same Reynolds number and shear rate. The mean lift force acting on the particles appears to remain nearly the same as that on an isolated particle. However, due to the influence of neighboring particles, there is a substantial force variation in transverse directions on each individual particle, whose magnitude is comparable to the mean drag force. The distribution of drag force in a linear shear flow is shown to be nearly the same as in a uniform flow at the same volume fraction and Reynolds number. A simple stochastic model based on a Gaussian distribution is presented for the lift force variation, and its performance is compared to the prediction of the deterministic pairwise interaction extended point-particle model.

42 ENGINEERING↗
DOE OSTI2023

Carbon isotope fractionation by an ancestral rubisco suggests that biological proxies for CO 2 through geologic time should be reevaluated

The history of Earth’s carbon cycle reflects trends in atmospheric composition convolved with the evolution of photosynthesis. Fortunately, key parts of the carbon cycle have been recorded in the carbon isotope ratios of sedimentary rocks. The dominant model used to interpret this record as a proxy for ancient atmospheric CO 2 is based on carbon isotope fractionations of modern photoautotrophs, and longstanding questions remain about how their evolution might have impacted the record. Therefore, we measured both biomass (ε p ) and enzymatic (ε Rubisco ) carbon isotope fractionations of a cyanobacterial strain ( Synechococcus elongatus PCC 7942) solely expressing a putative ancestral Form 1B rubisco dating to ≫1 Ga. This strain, nicknamed ANC, grows in ambient pCO 2 and displays larger ε p values than WT, despite having a much smaller ε Rubisco (17.23 ± 0.61‰ vs. 25.18 ± 0.31‰, respectively). Surprisingly, ANC ε p exceeded ANC ε Rubisco in all conditions tested, contradicting prevailing models of cyanobacterial carbon isotope fractionation. Such models can be rectified by introducing additional isotopic fractionation associated with powered inorganic carbon uptake mechanisms present in Cyanobacteria, but this amendment hinders the ability to accurately estimate historical pCO 2 from geological data. Understanding the evolution of rubisco and the CO 2 concentrating mechanism is therefore critical for interpreting the carbon isotope record, and fluctuations in the record may reflect the evolving efficiency of carbon fixing metabolisms in addition to changes in atmospheric CO 2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗