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At least 289 records · Page 16

Broadband X-ray ptychography using multi-wavelength algorithm

Ptychography is a rapidly developing scanning microscopy which is able to view the internal structures of samples at a high resolution beyond the illumination size. The achieved spatial resolution is theoretically dose-limited. A broadband source can provide much higher flux compared with a monochromatic source; however, it conflicts with the necessary coherence requirements of this coherent diffraction imaging technique. In this paper, a multi-wavelength reconstruction algorithm has been developed to deal with the broad bandwidth in ptychography. Compared with the latest development of mixed-state reconstruction approach, this multi-wavelength approach is more accurate in the physical model, and also considers the spot size variation as a function of energy due to the chromatic focusing optics. Therefore, this method has been proved in both simulation and experiment to significantly improve the reconstruction when the source bandwidth, illumination size and scan step size increase. It is worth mentioning that the accurate and detailed information of the energy spectrum for the incident beam is not required in advance for the proposed method. Further, we combine multi-wavelength and mixed-state approaches to jointly solve temporal and spatial partial coherence in ptychography so that it can handle various disadvantageous experimental effects. The significant relaxation in coherence requirements by our approaches allows the use of high-flux broadband X-ray sources for high-efficient and high-resolution ptychographic imaging.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Airborne LiDAR to Improve Canopy Fuels Mapping for Wildfire Modeling

Increasing conflict between wildfire and the built environment has increased the need for more up-to-date and finer resolution canopy fuels data to improve wildfire modeling and associated risk forecasts. The US Forest Service and US Department of the Interior’s LANDFIRE product, which provides 30-m resolution canopy fuels data for the entire US, is one of the most widely used sources of fuels data. However, the last complete mapping effort for LANDFIRE is based on 2016 conditions, and subsequent updates reflect disturbances 1-2 years behind the release year. Airborne systems equipped with Light Detection and Ranging (LiDAR) sensors can be deployed to actively sense canopy structure and estimate canopy fuels data (cover, height, base height, bulk density) at finer resolutions. Canopy base height (CBH) and canopy bulk density (CBD) are difficult to measure both in the field and in LiDAR point clouds. Still, they are important for accurately modeling crown fires, which are often intense and difficult to contain. Additionally, point cloud datasets are large, and calculations require efficient utilization of computational resources. To address these challenges, we are working on an approach that uses openly available National Ecological Observatory Network (NEON) airborne LiDAR data, with calculations processed in the R programming language and parallelized through the lidR package. CBH and CBD are often derived from tree height, diameter at breast height, and species-specific allometries using the Fire and Fuels Extension of the Forest Vegetation Simulator (FFE-FVS). We aim to test if airborne LiDAR can estimate CBH and CBD without the use of empirical equations. Reliable estimates of canopy fuels data directly from airborne LiDAR could streamline quick, fine-resolution updates for use in wildfire behavior models.

54 ENVIRONMENTAL SCIENCES↗

Sirius: Simulation and Evaluation of Tactical Conflict Management in an Urban Environment

This presentation provides an overview of the SIRIUS framework, updates to the ICAROUS core modules, and highlights the results of recent simulation and evaluation of tactical deconfliction in an urban environment. The SIRIUS simulation framework provides a fast time method for simulation a large number of aircraft in parallel. Updates to the ICAROUS core modules highlighted in the presentation include the evaluation of the encounter type geometry and changes to the resolution type selection based on the encounter type and following right of way (ROW) rules. The main objective of the simulation was to evaluate the use of strategic and tactical conflict management strategies using a set of simulated UAM scenarios.

Andrew Peters↗

Flow downstream of the heliospheric terminal shock. I - Irrotational flow

Recent reports of remote detection of the heliospheric terminal shock place it near 50 AU. These conflict with standard models which, when combined with current data on the local interstellar medium, place the shock beyod 100 AU. Resolution of this discrepancy has led to hypotheses that invoke cosmic ray pressure, momentum exchange with interstellar neutrals, and magnetic field effects between the shock and the contact discontinuity dividing the solar wind from interstellar plasma. These hypotheses depend not only on properties of the interstellar medium, but also on the downstream three-dimensional flow between the shock and the contact discontinuity, in the region called the 'heliosheath'. The downstream flow field in the absence of magnetic fields is examined here under the assumptions that the flow everywhere outside the shock can be approximated as irrotational and incompressible. It is found, in particular, that the distance between the terminal shock and the contact discontinuity is less than the heliocentric distance to the terminal shock, effectively eliminating magnetic field effects in the heliosheath as being dynamically important.

Suess, Steven T.↗

Nanometer Resolution Structure‐Emission Correlation of Individual Quantum Emitters via Enhanced Cathodoluminescence in Twisted Hexagonal Boron Nitride

Understanding the atomic structure of quantum emitters, often originating from point defects or impuritie, is essential for designing and optimizing materials for quantum technologies such as quantum computing, communication, and sensing. Despite the availability of atomic-resolution scanning transmission electron microscopy and nanoscale cathodoluminescence microscopy, experimentally determining the atomic structure of individual emitters is challenging due to the conflicting needs for thick samples to generate strong cathodoluminescence signals and thin samples for structural analysis. To overcome this challenge, significantly enhanced cathodoluminescence at twisted interfaces is leveraged to achieve sub-nanometer localization precision for the first time in mapping individual quantum emitters in carbon-implanted hexagonal boron nitride. This unprecedent spatial sensitivity, together with correlative electron energy loss spectroscopy quantitative scanning transmission electron microscopy imaging, and first principles density functional theory calculations, enables the identification of the atomic structure of the 440 nm blue emitter in hexagonal boron nitride as a substituted vertical carbon dimer. Building on the atomic structure insights, nanoscale spatially precise creation of blue emitters is demonstrated by electron beam irradiation of carbon-coated hexagonal boron nitride. This advancement in correlating atomic structures with optical properties lays the foundation for a deeper understanding and precise engineering of quantum emitters, significantly advancing the development of cutting-edge quantum information technologies.

2D material↗

Estimation of pollen productivity and dispersal: How pollen assemblages in small lakes represent vegetation

Abstract Quantitative understanding of vegetation dynamics over timespans beyond a century remains limited. In this regard, the pollen‐based reconstruction of past vegetation enables unique research opportunities by quantifying changes in plant community compositions during hundreds to thousands of years. Critically, the methodological basis for most reconstruction approaches rests upon estimates of pollen productivity and dispersal. Previous studies, however, have reached contrasting conclusions concerning these estimates, which may be perceived to challenge the applicability and reliability of pollen‐based reconstruction. Here we show that conflicting estimates of pollen production and dispersal are, at least in part, artifacts of fixed assumptions of pollen dispersal and insufficient spatial resolution of vegetation data surrounding the pollen‐collecting lake. We implemented a Bayesian statistical model that related pollen assemblages in surface sediments of 33 small lakes (<2 ha) in the northeastern United States, with surrounding vegetation ranging from 10 1 to >10 5 m from the lake margin. Our analysis revealed three key insights. First, pollen productivity is largely conserved within taxa and across forest types. Second, when local (within a 1‐km radius) vegetation abundances are not considered, pollen‐source areas may be overestimated for some common taxa (Cupressaceae, Pinus , Quercus , and Tsuga ). Third, pollen dispersal mechanisms may differ between local and regional scales; this is missed by pollen‐dispersal models used in previous studies. These findings highlight the complex interactions between vegetation heterogeneity on the landscape and pollen dispersal. We suggest that, when estimating pollen productivity and dispersal, both detailed local and extended regional vegetation must be taken into account. Also, both deductive (mechanistic models) and inductive (statistical models) approaches are needed to better understand the emergent properties of pollen dispersal in heterogeneous landscapes.

54 ENVIRONMENTAL SCIENCES↗

Seasonal Variability in Local Carbon Dioxide Biomass Burning Sources Over Central and Eastern US Using Airborne In Situ Enhancement Ratios

We present observations of local enhancements in carbon dioxide (CO 2 ) from local emissions sources over three eastern US regions during four deployments of the Atmospheric Carbon Transport-America (ACT-America) campaign between summer 2016 and spring 2018. Local CO 2 emissions were characterized by carbon monoxide (CO) to CO 2 enhancement ratios (i.e., ΔCO/ΔCO 2 ) in air mass mixing observed during aircraft transects within the planetary boundary layer. By analyzing regional-scale variability of CO 2 enhancements as a function of ΔCO/ΔCO 2 enhancement ratios, observed relative contributions to CO 2 emissions were separated into fossil fuel and biomass burning (BB) regimes across regions and seasons. CO 2 emission contributions attributed to biomass burning (ΔCO/ΔCO 2 > 4%) were negligible during summer and fall in all regions but climbed to ∼9%–11% of observed combustion contributions in the South during winter and spring. Relative CO 2 fire emission trends matched observed winter and spring BB contributions, but conflictingly predicted similar levels of BB during the fall. Satellite fire data from MODIS and VIIRS suggested the use of higher spatial resolution fire data that might improve modeled BB emissions but were not able to explain the bulk of the discrepancy.

54 ENVIRONMENTAL SCIENCES↗

The precision of today's satellite laser ranging systems

Recent improvements in the accuracy of modern satellite laser ranging (SLR) systems are strengthened by the new capability of many instruments to track an increasing number of geodetic satellite targets without significant scheduling conflict. This will allow the refinement of some geophysical parameters, such as solid Earth tidal effects and GM, and the improved temporal resolution of others, such as Earth orientation and station position. Better time resolution for the locations of fixed observatories will allow us to monitor more subtle motions at the stations, and transportable systems will be able to provide indicators of long term trends with shorter occupations. If we are to take advantage of these improvements, care must be taken to preserve the essential accuracy of an increasing volume of range observations at each stage of the data reduction process.

Dunn, Peter J.↗

Assessing the Impact of Laurentide Ice-sheet Topography on Glacial Climate

Simulations of past climates require altered boundary conditions to account for known shifts in the Earth system. For the Last Glacial Maximum (LGM) and subsequent deglaciation, the existence of large Northern Hemisphere ice sheets caused profound changes in surface topography and albedo. While ice-sheet extent is fairly well known, numerous conflicting reconstructions of ice-sheet topography suggest that precision in this boundary condition is lacking. Here we use a high-resolution and oxygen-isotopeenabled fully coupled global circulation model (GCM) (GISS ModelE2-R), along with two different reconstructions of the Laurentide Ice Sheet (LIS) that provide maximum and minimum estimates of LIS elevation, to assess the range of climate variability in response to uncertainty in this boundary condition.We present this comparison at two equilibrium time slices: the LGM, when differences in ice-sheet topography are maximized, and 14 ka, when differences in maximum ice-sheet height are smaller but still exist. Overall, we find significant differences in the climate response to LIS topography, with the larger LIS resulting in enhanced Atlantic Meridional Overturning Circulation and warmer surface air temperatures, particularly over northeastern Asia and the North Pacific. These up- and downstream effects are associated with differences in the development of planetary waves in the upper atmosphere, with the larger LIS resulting in a weaker trough over northeastern Asia that leads to the warmer temperatures and decreased albedo from snow and sea-ice cover. Differences between the 14 ka simulations are similar in spatial extent but smaller in magnitude, suggesting that climate is responding primarily to the larger difference in maximum LIS elevation in the LGM simulations. These results suggest that such uncertainty in ice-sheet boundary conditions alone may significantly impact the results of paleoclimate simulations and their ability to successfully simulate past climates, with implications for estimating climate sensitivity to greenhouse gas forcing utilizing past climate states.

glaciology↗

Design studies of large aperture, high-resolution Earth science microwave radiometers compatible with small launch vehicles

High-spatial-resolution microwave radiometer sensing from space with reasonable swath widths and revisit times favors large aperture systems. However, with traditional precision antenna design, the size and weight requirements for such systems are in conflict with the need to emphasize small launch vehicles. This paper describes tradeoffs between the science requirements, basic operational parameters, and expected sensor performance for selected satellite radiometer concepts utilizing novel lightweight compactly packaged real apertures. Antenna, feed, and radiometer subsystem design and calibration are presented. Preliminary results show that novel lightweight real aperture coupled with state-of-the-art radiometer designs are compatible with small launch systems, and hold promise for high-resolution earth science measurements of sea ice, precipitation, soil moisture, sea surface temperature, and ocean wind speeds.

Schroeder, Lyle C.↗

Demand Capacity Balancing at Vertiports for Initial Strategic Conflict Management of Urban Air Mobility Operations

Urban Air Mobility (UAM) is a new transportation concept that enables highly automated, cooperative, passenger or cargo-carrying air transportation services in and around urban areas. To achieve the high level of operational density and complexity desired by the UAM community, an airspace system that allows UAM operators to readily access and operate safely and efficiently in the airspace is needed. This airspace system will require air traffic management designed to reduce the risk of conflicts and loss of separation between UAM flights. In general, strategic conflict management is considered as the first layer of conflict management for safe flight operations to condition the traffic to reduce the need for airborne separation provision, the second layer of conflict management. Demand Capacity Balancing (DCB) is one of the concept components to achieve strategic conflict management. DCB strategically evaluates traffic demand and resource capacities to allow UAM operators to determine when, where and how they operate, while mitigating conflicting needs for airspace and vertiport capacity. DCB can be applied whenever UAM demand exceeds the capacity in airspace or at vertiports. As the UAM ecosystem evolves with advanced technologies and matured operational procedures, more complicated conflict management will likely be needed. In the current UAM ‘Concept of Operation (ConOps) 1.0’ operational stage defined by FAA, however, it will be meaningful to explore the demand capacity balancing at vertiports only, as an initial strategic conflict management approach for UAM operations because vertiport capacity seems to be a bottleneck of UAM traffic. For this research, we developed a demand-capacity imbalance detection and resolution service for UAM. This DCB service identifies the demand from operators and compares the demand to a given capacity at the shared resources (i.e., vertiports) over the upcoming time horizon which is divided into time bins having a constant interval. When a new flight plan is submitted, the algorithm embedded in the DCB service checks the available time bins based on the desired departure time and estimated arrival time at origin and destination vertiports, respectively. If the time bins for the originally desired times are already occupied by other flights (i.e., demand is at or above capacity), the algorithm finds the next available time bins for takeoff and landing and shifts the conflicting departure time to the earliest time that satisfies the capacity constraints at both origin and destination vertiports. The details of the algorithm will be described in the final manuscript. Figure 1 shows that the proposed DCB algorithm works well for a sample traffic scenario. In this example, a total of 144 flights, split between two operators, are planned over 2 hours, traveling 10 routes between five vertiports. In the heatmaps, the horizontal axis shows 12 time bins where each bin represents a 12-minute interval, and the vertical axis shows five vertiports. The number in each cell shows the number of operations, counting both departures and arrivals, at a specific vertiport in each time bin. For the given capacity of 2 operations/vertiport/bin, Figure 1 shows that the original demand sometimes exceeds the capacity, but the modified demand is reduced to the given capacity after resolving demand-capacity imbalances. When UAM flights are operated, it is expected that many practical issues would arise in the federated system architecture with multiple operators. UAM operators may experience a time synchronization issue due to communication delay between operator and vehicle. UAM vehicles would fly at different flight speeds, depending on vehicle models. Actual departure and arrival times can have large variations, compared to the schedule. The lead time from flight plan submission to desired departure time can vary by service type (e.g., regular shuttle service vs. on-demand service). Using the proposed DCB algorithm, we also investigated how the actual flight schedule and DCB performance are affected by these uncertainties such as unsynchronized times between operators, flight speed differences, lead time differences, and departure time errors. The final manuscript will include the background of this research work, the description of the DCB algorithm and its use cases with traffic scenarios. It will also provide the analytical results about the impact of various uncertainties that can occur in actual UAM operations on the DCB at vertiports, in terms of demand distribution changes, number of simultaneous operations, and delay propagation.

Urban Air Mobility↗

Nature of S-States in the Oxygen-Evolving Complex Resolved by High-Energy Resolution Fluorescence Detected X-ray Absorption Spectroscopy

Photosystem II, the water splitting enzyme of photosynthesis, utilizes the energy of sunlight to drive the four-electron oxidation of water to dioxygen at the oxygen-evolving complex (OEC). The OEC harbors a Mn 4 CaO 5 cluster that cycles through five oxidation states S i (i = 0–4). The S 3 state is the last metastable state before the O 2 evolution. Its electronic structure and nature of the S 2 → S 3 transition are key topics of persisting controversy. Most spectroscopic studies suggest that the S 3 state consists of four Mn(IV) ions, compared to the Mn(III)Mn(IV) 3 of the S 2 state. However, recent crystallographic data have received conflicting interpretations, suggesting either metal- or ligand-based oxidation, the latter leading to an oxyl radical or a peroxo moiety in the S 3 state. Herein, we utilize high-energy resolution fluorescence detected (HERFD) X-ray absorption spectroscopy to obtain a highly resolved description of the Mn K pre-edge region for all S-states, paying special attention to use chemically unperturbed S 3 state samples. In combination with quantum chemical calculations, we achieve assignment of specific spectroscopic features to geometric and electronic structures for all S-states. These data are used to confidently discriminate between the various suggestions concerning the electronic structure and the nature of oxidation events in all observable catalytic intermediates of the OEC. Our results do not support the presence of either peroxo or oxyl in the active configuration of the S 3 state. This establishes Mn-centered storage of oxidative equivalents in all observable catalytic transitions and constrains the onset of the O–O bond formation until after the final light-driven oxidation event.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Observation of [VCu1–Ini2+VCu1–] Defect Triplets in Cu-Deficient CuInS2

Copper indium disulfide (CuInS2) is a semiconductor with a direct energy band gap of 1.53 eV, an optimal value for highly efficient thin-film solar cells. But it has reached only ~ 11 % power conversion efficiency, far less than the theoretically achievable value of ~ 30 %. The cause of this low performance is not understood. A single crystal grown from 1 mol% Cu-deficient melt was studied, using atomic resolution high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) and electron dispersive spectroscopy (EDS). While the bulk crystal is exactly stoichiometric CuInS2, it contains nanometer-thick, structurally coherent, Cu-deficient interphases that form along rotational twin boundaries in the {112} plane. Transition zones from bulk crystal to interphase are observed, where In is seen to move from its normal site InIn in the chalcopyrite structure to a tetrahedral interstitial site Ini, while Cu remains in its normal CuCu position. Two InIn rows of the bulk crystal merge into one row of Ini, causing excess Ini in the interphase. The concentrations of CuCu and Ini reflect a ratio of Cu vacancies, VCu, to excess Ini of ~ 2. Their relative lattice positions, and the high electrical resistivity of the crystal, suggests that VCu and excess Ini ‘precipitate’ as self-compensating, electrically neutral, [VCu1- Ini2+ VCu1-] defect triplets. This is the first atomic-level observation of the ordered defect that has been invoked as the basic structural modifier in chalcopyrite compound homologs. The interphases introduce an optical gap of 1.47 eV. Electron trapping in band tail states, evident from a photoconductivity exponent of 0.54, is the likely cause of an unusually low electron mobility of 0.1 cm2V-1s-1. The overall result is that making CuInS2 slightly copper-poor inserts nanometer-thick layers of the interphase into the bulk crystal. This study shows that apparently conflicting results of the effect of Cu deficiency on CuInS2 thin-film solar cells may be resolved by analyzing structure and composition at nanometer spatial resolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A Family of Well-Clear Boundary Models for the Integration of UAS in the NAS

The FAA-sponsored Sense and Avoid Workshop for Unmanned Aircraft Systems (UAS) defines the concept of sense and avoid for remote pilots as "the capability of a UAS to remain well clear from and avoid collisions with other airborne traffic." Hence, a rigorous definition of well clear is fundamental to any separation assurance concept for the integration of UAS into civil airspace. This paper presents a family of well-clear boundary models based on the TCAS II Resolution Advisory logic. For these models, algorithms that predict well-clear violations along aircraft current trajectories are provided. These algorithms are analogous to conflict detection algorithms but instead of predicting loss of separation, they predict whether well-clear violations will occur during a given lookahead time interval. Analytical techniques are used to study the properties and relationships satisfied by the models.

Munoz, Cesar A.↗

Los Alamos National Laboratory Ombuds Office Biennial Report FY2017-2018

Visitors contact the Ombuds Office to obtain coaching, explore options, develop strategies, learn about LANL resources, understand formal processes and policies, or request a facilitated discussion/mediation. The number of visitors who contacted the office in FY17 and FY18 was 540 and 555, respectively - the highest annual numbers since FY08. The Ombuds Office supports professional workplace communication and conflict management skills through individual consultations, presentations, the resource library, and special events. Courses are regularly scheduled and available to the LANL workforce. Annually, an average of ~1950 participants attended Ombuds courses, workshops, and talks in FY17-18. The total number of individuals who attended presentations in FY17-18, both internal and external to LANL, was 4005. Staff continue to present annually at the International Ombudsman Association Conferences and New Mexico Alternative Dispute Resolution Symposiums. In this reporting period, the Laboratory Ombudsman was recruited to present communication and negotiation skills courses for several universities and prestigious national science and engineering organizations. The mission of the Ombuds Office is to enhance communication and mitigate conflict. Staff provide expertise, feedback and resources to employees, leaders and organizations in order to strengthen conflict and communication capabilities. A related function of the office is to identify and report trends, without breaching confidentiality or anonymity. Trends and concerns may be raised around policies and procedures - including potential future issues – or concerning unhealthy patterns within an organization. The underpinnings of Organizational Ombuds work at LANL are provided by the International Ombudsman Association (IOA) Standards of Practice, (IOA Standards of Practice, 2009; Code of Ethics, 2007). The four IOA tenets are neutrality/impartiality, independence, confidentiality and informality.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Declining tropical cyclone frequency under global warming

Assessing the role of anthropogenic warming from temporally inhomogeneous historical data in the presence of large natural variability is difficult and has caused conflicting conclusions on detection and attribution of tropical cyclone (TC) trends. Here, using a reconstructed long-term proxy of annual TC numbers together with high-resolution climate model experiments, we show robust declining trends in the annual number of TCs at global and regional scales during the twentieth century. The Twentieth Century Reanalysis (20CR) dataset is used for reconstruction because, compared with other reanalyses, it assimilates only sea-level pressure fields rather than utilize all available observations in the troposphere, making it less sensitive to temporal inhomogeneities in the observations. It can also capture TC signatures from the pre-satellite era reasonably well. The declining trends found are consistent with the twentieth century weakening of the Hadley and Walker circulations, which make conditions for TC formation less favourable.

54 ENVIRONMENTAL SCIENCES↗

Grid generation about complex three-dimensional aircraft configurations

The problem of obtaining three dimensional grids with sufficient resolution to resolve all the flow or other physical features of interest is addressed. The generation of a computational grid involves a series of compromises to resolve several conflicting requirements. On one hand, one would like the grid to be fine enough and not too skewed to reduce the numerical errors and to adequately resolve the pertinent physical features of the flow field about the aircraft. On the other hand, the capabilities of present or even future supercomputers are finite and the number of mesh points must be limited to a reasonable number: one which is usually much less than desired for numerical accuracy. One technique to overcome this limitation is the 'zonal' grid approach. In this method, the overall field is subdivided into smaller zones or blocks in each of which an independent grid is generated with enough grid density to resolve the flow features in that zone. The zonal boundaries or interfaces require special boundary conditions such that the conservation properties of the governing equations are observed. Much work was done in 3-D zonal approaches with nonconservative zonal interfaces. A 3-D zonal conservative interfacing method that is efficient and easy to implement was developed during the past year. During the course of the work, it became apparent that it would be much more feasible to do the conservative interfacing with cell-centered finite volume codes instead of the originally planned finite difference codes. Accordingly, the CNS code was converted to finite volume form. This new version of the code is named CNSFV. The original multi-zonal interfacing capability of the CNS code was enhanced by generalizing the procedure to allow for completely arbitrarily shaped zones with no mesh continuity between the zones. While this zoning capability works well for most flow situations, it is, however, still nonconservative. The conservative interface algorithm was also implemented but was not completely validated.

Klopfer, Goetz H.↗

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↗