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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Using MALDI-FTICR-MS Imaging to Track Low-Molecular-Weight Aromatic Derivatives of Fungal Decayed Wood

Low-molecular-weight (LMW) aromatics are crucial in meditating fungal processes for plant biomass decomposition. Some LMW compounds are employed as electron donors for oxidative degradation in brown rot (BR), an efficient wood-degrading strategy in fungi that selectively degrades carbohydrates but leaves modified lignins. Previous understandings of LMW aromatics were primarily based on “bulk extraction”, an approach that cannot fully reflect their real-time functions during BR. Here, we applied an optimized molecular imaging method that combines matrix-assisted laser desorption ionization (MALDI) with Fourier-transform ion cyclotron resonance mass spectrometry (FTICR-MS) to directly measure the temporal profiles of BR aromatics as Rhodonia placenta decayed a wood wafer. We found that some phenolics were pre-existing in wood, while some (e.g., catechin-methyl ether and dihydroxy-dimethoxyflavan) were generated immediately after fungal activity. These pinpointed aromatics might be recruited to drive early BR oxidative mechanisms by generating Fenton reagents, Fe2+ and H2O2. As BR progressed, ligninolytic products were accumulated and then modified into various aromatic derivatives, confirming that R. placenta depolymerizes lignin. Together, this work confirms aromatic patterns that have been implicated in BR fungi, and it demonstrates the use of MALDI-FTICR-MS imaging as a new approach to monitor the temporal changes of LMW aromatics during wood degradation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Genomic Diversity and Phenotypic Variation in Fungal Decomposers Involved in Bioremediation of Persistent Organic Pollutants

Fungi work as decomposers to break down organic carbon, deposit recalcitrant carbon, and transform other elements such as nitrogen. The decomposition of biomass is a key function of wood-decaying basidiomycetes and ascomycetes, which have the potential for the bioremediation of hazardous chemicals present in the environment. Due to their adaptation to different environments, fungal strains have a diverse set of phenotypic traits. This study evaluated 320 basidiomycetes isolates across 74 species for their rate and efficiency of degrading organic dye. We found that dye-decolorization capacity varies among and within species. Among the top rapid dye-decolorizing fungi isolates, we further performed genome-wide gene family analysis and investigated the genomic mechanism for their most capable dye-degradation capacity. Class II peroxidase and DyP-type peroxidase were enriched in the fast-decomposer genomes. Gene families including lignin decomposition genes, reduction-oxidation genes, hydrophobin, and secreted peptidases were expanded in the fast-decomposer species. This work provides new insights into persistent organic pollutant removal by fungal isolates at both phenotypic and genotypic levels.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Annual carbon sequestration and loss rates under altered hydrology and fire regimes in southeastern USA pocosin peatlands

Peatlands drained for agriculture or forestry are susceptible to the rapid release of greenhouse gases (GHGs) through enhanced microbial decomposition and increased frequency of deep peat fires. We present evidence that rewetting drained subtropical wooded peatlands (STWPs) along the southeastern USA coast, primarily pocosin bogs, could prevent significant carbon (C) losses. To quantify GHG emissions and storage from drained and rewetted pocosin we used eddy covariance techniques, the first such estimates that have been applied to this major bog type, on a private drained (PD) site supplemented by static chamber measurements at PD and Pocosin Lakes National Wildlife Refuge. Net ecosystem exchange measurements showed that the loss was 21.2 Mg CO2 ha –1 year –1 (1 Mg = 10 6 g) in the drained pocosin. Under a rewetted scenario, where the annual mean water table depth (WTD) decreased from 60 to 30 cm, the C loss was projected to fall to 2 Mg CO 2 ha –1 year –1 , a 94% reduction. If the WTD was 20 cm, the peatlands became a net carbon sink (–3.3 Mg CO2 ha –1 year –1 ). Hence, net C reductions could reach 24.5 Mg CO 2 ha –1 year –1 , and when scaled up to the 4000 ha PD site nearly 100,000 Mg CO 2 year –1 of creditable C could be amassed. We conservatively estimate among the 0.75 million ha of southeastern STWPs, between 450 and 770 km 2 could be rewet, reducing annual GHG emissions by 0.96–1.6 Tg (1 Tg = 10 12 g) of CO 2 , through suppressed microbial decomposition and 1.7–2.8 Tg via fire prevention, respectively. Despite covering <0.01% of US land area, rewetting drained pocosin can potentially provide 2.4% of the annual CO 2 nationwide reduction target of 0.18 Pg (1 Pg = 10 15 g). Finally, suggesting pocosin restoration can contribute disproportionately to the US goal of achieving net-zero emission by 2050.

58 GEOSCIENCES↗
DOE OSTI2022

Dissolved pyrogenic carbon leaching in soil: Effects of soil depth and pyrolysis temperature

We report Pyrogenic organic carbon (PyC) is found in soils as a heterogeneous mixture of thermally altered plant residues that range in their susceptibility to losses via mineralization, leaching, and erosion. Leaching of PyC as DOC (DPyC) within the soil profile is likely influenced by the chemical composition of solid PyC and the dominant soil processes and properties at a particular depth. Here we report the results of a 2-year laboratory decomposition and leaching study designed to investigate the interactive effects of pyrolysis temperature levels (no pyrolysis, 300 °C, and 450 °C) and soil depth (surface soil, 0–10 cm depth; subsurface soil, 50–70 cm depth) on losses of 13 C-labeled jack pine (Pinus banksiana) wood, wood pyrolyzed at 300 °C (PyC300) and wood pyrolyzed at 450 °C (PyC450) as dissolved organic carbon (DOC). Losses of wood and PyC in the 13 C- DOC pool were measured in leachates drained from soils once a month over the course of 1 year, and at one single leaching event after 2 years. We found that pyrolysis temperature levels interacted with time and soil depth to affect losses of wood and PyC as DOC throughout the 1-year incubation and leaching study, with greater DOC losses from wood in surface soil (0.73 ± 0.076% of added C) than in subsurface soil (0.40 ± 0.063% of added C) averaged across sampling time. Monthly DOC losses from PyC were not affected by soil depth. Cumulative data indicated a small contribution of wood (2.86 ± 0.07%), PyC300 (0.40 ± 0.04%), and PyC450 (0.16 ± 0.01%) to total DOC leached from soils. DOC losses from wood and PyC300 (as a proportion of added C) were greater in surface soil than in subsurface soil, whereas DOC losses from PyC450 were unaffected by differences between surface and subsurface soil. Losses of DOC were greater from PyC300 than from PyC450 in surface soil, with no significant differences in DOC losses between PyC300 and PyC450 in subsurface soil. One single leaching event at the end of the 2-year decomposition study resulted in higher DOC losses from wood in subsurface soil than in surface soil likely due to desorption, and no differences in DOC losses between PyC300 and PyC450 regardless of soil depth. Our results suggest strong interactions between the initial physicochemical composition of organic C inputs and soil properties (soil depth as a proxy) that control the mobility and transport of PyC and should be better represented in Earth system models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Defect redistribution along grain boundaries in SrTiO 3 by externally applied electric fields

During thermal annealing at 1425 °C nominal electric field strengths of 50 V/mm and 150 V/mm were applied along the grain boundary planes of a near 45° (100) twist grain boundary in SrTiO 3 . Electron microscopy characterization revealed interface expansions near the positive electrode around 0.8 nm for either field strength. While the interface width decreased to roughly 0.4 nm after annealing at 50 V/mm, the higher field strength caused decomposition of the boundary structure close to the negative electrode. Electron energy-loss and X-ray photoelectron spectroscopies demonstrated an increased degree of oxygen sublattice distortion at the negative electrode side, and enhanced concentrations of Ti 3+ and Ti 2+ compared to bulk for both single crystals and bicrystals annealed with an external electric field, respectively. Oxygen migration due to the applied electric field causes the observed alteration of grain boundary structures. At sufficiently high field strength the agglomeration of anion vacancies may lead to the decomposition of the grain boundary.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Intensified Soil Moisture Extremes Decrease Soil Organic Carbon Decomposition: A Mechanistic Modeling Analysis

Earth system models have predicted that there will be more frequent and severe precipitation and drought events in terrestrial ecosystems. Microbially mediated decomposition of soil organic carbon (SOC) tends to increase as soils wet and decrease as soils dry. However, the long-term SOC change under intensified moisture extremes remains poorly known as it depends on the frequency and intensity of soil drying and wetting. In this study, we explored long-term SOC dynamics under scenarios of alternating drying-wetting cycles using the Microbial-ENzyme Decomposition model, a mechanistic microbial model. The model was parameterized with 11 years of observations from a temperate deciduous broadleaf forest site, showing satisfactory model performance in both model calibration (R 2 = 0.67) and validation (R 2 = 0.69) against heterotrophic respiration. We then used the model to simulate the long-term SOC dynamics under five scenarios of alternating drying-wetting cycles with different frequencies and severities over a period of 100 years. Results showed that the changes in active microbial biomass C and the corresponding turnover rates of SOC pools were more sensitive to soil drying than soil wetting. As a result, the cumulative soil carbon emission from microbial respiration decreased by 433.7 g C m -2 after the 100-year simulation in the highest frequency and intensity moisture scenario, but was not significantly affected by the lowest frequency and intensity scenario. This study emphasizes the nonlinear response of SOC decomposition to soil moisture changes, which causes decreased decomposition by microbes under drying that is, not compensated by increased decomposition under wetting conditions.

58 GEOSCIENCES↗
DOE OSTI2021

MOFLUX Intensified Soil Moisture Extremes Decrease Soil Organic Carbon Decomposition: Modeling Archive

This Modeling Archive is in support the publication “Intensified Soil Moisture Extremes Decrease Soil Organic Carbon Decomposition: A Mechanistic Modeling Analysis” (Liang et al., 2021). Here we provide model code, inputs, outputs and evaluation datasets for the Microbial ENzyme Decomposition (MEND) model for the Missouri Ozarks AmeriFlux eddy covariance measurement site (MOFLUX) near Ashland, Missouri USA. The MEND model was developed with explicit representation of microbial and enzyme pools to mechanistically simulate the role of microbial organisms and extracellular enzymes in soil organic carbon (SOC) decomposition. Long-term SOC dynamics under intensified moisture extremes are studied using the MEND model that is parameterized with 11 years of measurements from the MOFLUX forest. The model explicitly represents microbial dormancy and resuscitation, different types of SOC-degrading enzymes, and how they vary with changes in soil moisture (Wang et al. 2015, 2019). A combination of two levels of frequency and severity of soil moisture, as well as a control with normal interannual variability, are used to simulate a range of moisture scenarios over 100 years. The code of Microbial-ENzyme Decomposition (MEND) as well as the input and output data are included in the archive. A user’s manual (MEND_Readme.pdf) is included with instructions for compiling and running the model to simulate soil organic carbon decomposition under various moisture scenarios. This dataset contains the modelling archive contained within a compressed (*.zip) file, a file-level metadata file in comma separate (*.csv) format, and two instructional files in PDF (*.pdf) format.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Scale dependence in functional equivalence and difference in the soil microbiome

Climatic history can shape the functioning of soil microbial communities and thus rates of ecosystem processes such as organic matter decomposition. For example, broad spatial scale differences in climatic history, such as contrasting precipitation regimes, have been shown to generate unique microbial functional responses to contemporary moisture conditions. Yet it is an open question as to whether local differences in soil microclimate similarly influence the functional potential of decomposer communities. Here, we use a multi-scale approach within and among two temperate forest field sites to investigate this question. Soils from fifty-four microsites, that vary in their soil moisture climate-regimes, were used as inocula for a common leaf litter (Quercus rubra L.) in a controlled, laboratory microcosm study. Microcosms were placed under dry, mesic and wet lab-moisture conditions and the rate of carbon (C) mineralization of the litter was measured over 202 days. Our results reveal differences in decomposition rates under controlled conditions that highlight broad-scale functional differences between the soil communities at each site. Specifically, we found that C mineralization differed by as much as two-fold for soil communities when compared between the sites. Our results also show that functional differences of soil communities are observable within one site but not the other. In the site where local-scale functional legacies were apparent, the historical soil moisture microclimate-regimes generated as much as an 89% change in C mineralization rates of the leaf litter under the same contemporary, lab-imposed moisture conditions. Here, a similar pattern was not observable in the other site; instead, laboratory moisture conditions explained almost all variation in C mineralization. Notably, for the site with pronounced local-scale functional legacies, there was much greater within-site variation in field-soil microsite moisture than at the site which did not exhibit functional legacies, suggesting that the extent of local-scale variation in microclimate may act as control on whether local-scale functional legacies are observed. Regardless of whether this mechanism does explain our findings, our observations do confirm those from prior studies where regional-scale moisture-regime differences shape microbial function, and extend this prior work by providing evidence that pronounced local-scale differences in soil moisture microclimate-regimes are associated with microbial functional legacies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Investigation of Biomass Fouling on Screw Feeder in Preconversion of Pyrolysis

Biomass is a source of renewable energy and can undergo thermochemical processes to be converted into gaseous and liquid fuels. Thermal decomposition-induced biomass fouling on the screw feeder is a major challenge in preconversion of pyrolysis, leading to plugging of the feed line. Here, this work intends to gain fundamental understanding of the biomass fouling phenomena across the heat gradient on the screw feeder via a combination of materials characterization and thermal simulation. An actual screw feeder that failed because of biomass fouling was examined to reveal the deposit’s morphology, composition, and mechanical properties. Thermal simulations were developed for both the screw feeder and the wood particles being transported using a combined analytical and numerical approach. The simulated temperature profiles correlated well with the deposit observations, based on which potential mitigations were proposed from both the operation and screw design perspectives and supported by preliminary experimental validation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Microbial community shifts correspond with suppression of decomposition 25 years after liming of acidic forest soils

Microbial community structure and function regularly covary with soil pH, yet effects of these interactions on soil carbon are rarely tested experimentally within natural ecosystems. We investigated the enduring (25 year) impacts of liming on microbial community structure and decomposition at an acidic northern hardwood forest, where experimental liming increased pH one unit and surprisingly doubled the organic carbon stocks of the forest floor. Here we show that this increase in carbon storage corresponded with restructuring of the bacterial and fungal communities that drive decomposition. In the Oe horizon, liming reduced the activities of five extracellular enzymes that mediate decomposition, while the Oa horizon showed an especially large (64%) reduction in the activity of a sixth, peroxidase, which is an oxidative enzyme central to lignocellulose degradation. Decreased enzyme activities corresponded with loss of microbial taxa important for lignocellulose decay, including large reductions in the dominant ectomycorrhizal genera Russula and Cenococcum, saprotrophic and wood decaying fungi, and Actinobacteria (Thermomonosporaceae). These results demonstrate the importance of pH as a dominant regulator of microbial community structure and illustrate how changes to this structure can produce large, otherwise unexpected increases in carbon storage in forest soils.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Gene regulatory networks controlling carbohydrate selective deconstruction pathways in fungi

The work performed at Clark University (PI, David Hibbett) was a subcomponent of the research lead by Jonathan Schilling at University of Minnesota (award number DE-SC0019427). The overall goal of this project was to address how fungi metabolize lignocellulose. Specifically, we targeted a carbohydrate-selective group of fungi known as 'brown rot' fungi that are well-aligned to be harness for bioconversion to biofuels and other products. These organisms orchestrate a two-step mechanism that initiates decomposition using oxidative radical-based chemistry and follows with enzymatic attack. We have helped characterize that this mechanism occurs in this sequence, but currently lack the fundamental regulatory information needed to harness these fungi for application. Thus, the major goal of this project was to use systems biology to create an integrated model of brown rot wood decay that couples fungal gene regulation with the metabolite feedbacks used to coordinate a two-step oxidative-hydrolytic mechanism. The research at Clark University focused on phylogenomic analyses of data produced by other project partners. Hence, the Clark component of the research was staged to initiate somewhat after that in other partner laboratories. The major Clark-based accomplishment was to advise on selection of fungal species for analyses of brown rot decay chemistry, and to interpret results in a phylogenetic context. The Clark University group also performed complementary analyses of gene families encoding plant cell wall-degrading enzymes in the the basidiomycete genus Lentinula, as well as analyses of substrate-specific gene expression and RNA editing in brown rot fungi.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Nanostructured ligament and fiber Al–doped Li 7 La 3 Zr 2 O 12 scaffolds to mediate cathode-electrolyte interface chemistry

In this study, scaffold structures of electrospun aluminum–substituted lithium lanthanum zirconate Li 7 La 3 Zr 2 O 12 (Al-LLZO) were synthesized and used as an additive in a LiNi 0.6 Mn 0.2 Co 0.2 O 2 composite cathode. The scaffolds were crystalized in the cubic phase after calcination at 700 °C. The Al-LLZO scaffold morphology was dependent on the precursor formulation (aqueous and dimethylformamide. The aqueous precursors resulted in scaffolds of densely coalesced ligaments, whereas the dimethylformamide precursors resulted in high–aspect ratio nanofiber scaffolds. The long-term cycling stability and rate performance of the cells were found to depend on the Al-LLZO scaffold morphology. The uniformly dispersed Al-LLZO fibers resulted in a more stable cathode electrolyte interface formation through the reduced decomposition of the LiPF 6 salt during cycling, resulting in a better high-rate and long-term cycling performance.

25 ENERGY STORAGE↗
DOE OSTI2022

First-Principles Elucidation of Initial Dehydrogenation Pathways in Mg(BH 4 ) 2

Complex borohydrides such as Mg(BH 4 ) 2 offer one of highest capacities to chemically store hydrogen for onboard applications; however, it suffers greatly from kinetic constraints that prevent realization of full capacity and reversibility. Understanding these kinetic limitations solely from experiments is extremely challenging due to the unusual complexity of various competing elemental reaction steps involved during the de/rehydrogenation reaction. This work aims to map out the energetics associated with initial dehydrogenation of Mg(BH 4 ) 2 from first-principles simulations and to identify the preferred reaction pathways. Our calculations suggest the rate-limiting step during BH 4 – –B 3 H 8 – conversion is the formation of the B 2 H 7 – intermediate. We further emphasize and clarify that the B 3 H 8 – and H – intermediates, formed during initial Mg(BH 4 ) 2 decomposition, appear as molecular species that are embedded in the Mg–BH 4 –Mg matrix as evidenced in the nuclear magnetic resonance measurements and not as bulk MgH 2 and Mg(B 3 H 8 ) 2 as previously assumed in theoretical predictions of the thermodynamics.

08 HYDROGEN↗
DOE OSTI2020

Bio-treatment of poplar via amino acid for interface control in biocomposites

Advanced biocomposites reinforced by abundant biomass-derived fillers can add a revenue stream to enhance the economic viability of biofuel production chains and the energy efficiency of the composite industry. However, the low stiffness of biopolymers limits their use in structural applications. Poplar fibers (mesh size: <180 μm, Populus spp.), an abundant waste from the wood industry, were used as bio-filler to fabricate high-performance biocomposites based on polylactic acid (PLA), in which the poplar fibers were modified by an amino acid (l-lysine). As a benefit of the amino acid treatment, the tensile Young's moduli of the lysine/poplar/PLA composites increased by up to 68% with the addition of a small amount of lysine, compared with neat PLA. At the same time, the tensile strength, failure strain, and Young's modulus of the poplar/PLA composites all increased after adding only 0.1 wt % of lysine. It has been observed that the lysine content has a significant effect on the decomposition temperature, complex viscosity, storage modulus, crystallization temperature, and crystallinity of composites. The fracture surfaces of the composites with an optimum lysine content had fewer voids and were more compact compared with composites without any lysine. The pores on the surfaces of poplar fibers became more available for the penetration of PLA molecules as a result of lysine addition. Finally, this study presents a facile method for reinforcing biocomposites with extremely low-cost and environmentally friendly biofillers.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Quantum beats in two-color photoionization to the spin-orbit split continuum of Ar

We report a study of the quantum beats in two-color photoionization of argon. An attosecond extreme ultraviolet pulse train prepares an electronic wave packet of definite odd parity, with total angular momentum J = 1, targeting the states between 14.0 and 14.5 eV from the ground state. Two-photon ionization of this wave packet with a tunable infrared probe pulse makes the constituent states interfere in both continuum channels, corresponding to the core angular momenta j c = 1/2 and 3/2, respectively. We analyze photoelectron spectrograms as a function of the time delay of the probe pulse and identify oscillations due to several pairs of states through Fourier decomposition. We observe phase differences between the corresponding beat signals in the two spin-orbit split continua. Comparison of theoretical simulations with the experimental measurements allows us to interpret the amplitudes and phases of ionization signals. Furthermore, we express the observed phase differences in terms of the off-diagonal elements of the short-range scattering matrix and the dipole matrix elements to the continuum eigenchannels.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Data from Raczka et al., Interactions between microbial diversity and substrate chemistry determine the fate of carbon in soil, from Elizabeth Woods in Morgantown, West Virginia, USA

File types include: Soil respiration as 13C cumulative respiration from soil incubation experiment, qSIP (quantitative stable isotope probing) data that is "18S apes wide" which is the fungal atom percent excess or how much the fungi took up of the labeled litter and "16S apes wide" which is the bacterial atom percent excess or how much the bacteria took up of the labeled litter, metabolomic data from the incubated soil samples called "Metab Soil Unique Filtered", which is the metabolomic data that had an initial filter from the raw data, and lipidomic data from the incubated soil samples called "All lipids soil". These files were used according to methods in Raczka et al. 2021 Scientific Reports. Headers show soil type (Oak, Poplar) and litter type (also called substrate here, which is labeled as no litter (control), poplar, and oak). This research was done to understand interactions between ecosystem-level processes and microbial diversity that impacts the composition of decomposition products that can form stable soil organic matter.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Formation of Fully Stoichiometric, Oxidation-State Pure Neptunium and Plutonium Dioxides from Molecular Precursors

Amidate-based ligands (N-(tert-butyl)isobutyramide, ITA) bind κ 2 to form homoleptic, 8-coordinate complexes with tetravalent 237 Np (Np(ITA) 4 , 1-Np) and 242 Pu (Pu(ITA) 4 , 1-Pu). These compounds complete an isostructural series from Th, U–Pu and allow for the direct comparison between many of the early actinides with stable tetravalent oxidation states by nuclear magnetic resonance (NMR) spectroscopy and single crystal X-ray diffraction (SCXRD). The molecular precursors are subjected to controlled thermolysis under mild conditions with the exclusion of exogenous air and moisture, facilitating the removal of the volatile organic ligands and ligand byproducts. The preformed metal–oxygen bond in the precursor, as well as the metal oxidation state, are maintained through the decomposition, forming fully stoichiometric, oxidation-state pure NpO 2 and PuO 2 . Powder X-ray diffraction (PXRD), scanning transmission electron microscopy (STEM), and energy dispersive X-ray spectroscopy (EDS) elemental mapping supported the evaluation of these high-purity materials. This chemistry is applicable to a wide range of metals, including actinides, with accessible tetravalent oxidation states, and provides a consistent route to analytical standards of importance to the field of nuclear nonproliferation, forensics, and fundamental studies.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2024

The development of Gibbs's dyadic and implications for the gradient of a vector field

In this paper, we review the history of the dyadic as developed by Gibbs. This mathematical construct appeared in the second part of Gibbs's pamphlet on vector analysis (published in 1884), and it represented the first known development of a Cartesian theory of tensors. Gibbs made extensive use of the dyadic to express his theory of linear vector functions, that is, functions that acted on vectors and mapped them to new vectors. The dyadic proved to be a capable vehicle in Gibbs's hands, and his theory for dyadics (which we would now call second-order Cartesian tensors) was relatively advanced. The theory detailed notions such as the decomposition of vectors and conditions under which a tensor would have an inverse. While Gibbs's theory for linear operators expressed by dyadics was robust, it did not seem to garner the attention that the more conventional vector analysis (published in the first half of his pamphlet in 1881) did. Perhaps in part because of the general unfamiliarity with the dyadic, two distinct and conflicting definitions of the gradient of a vector field have arisen in the literature. The details of these differences in notation, possible reasons for the difference, and a potential resolution are proposed.

97 MATHEMATICS AND COMPUTING↗