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High energy X-ray characterization of the microstructure of PuGa alloy samples at macroscopic depths and non-ambient conditions

High energy (95 keV) X-rays were utilized to characterize the microstructure of eight PuGa alloy samples at room temperature and during cooling to ∼10 K. The samples had different Ga content (nominally 0-3.4 at.%), age, and history. A ninth sample, similarly characterized with neutron diffraction, was included to extend the Ga range to 7 at.%. The samples span the range from single phase α (monoclinic) to δ (face-centered cubic) PuGa, as well as a two-phase α′/δ sample. The crystallographic textures, phase fractions, lattice parameters and dislocation densities of each sample were evaluated through distinct analysis techniques. The textures of the samples were modest. In each case, the dislocation densities were relatively high, comparable to cold worked metals and metals exposed to similar radiation dose. At room temperature, the lattice parameters determined in the predominantly single-phase samples were larger than expected based on the nominal Ga concentration. The observed lattice thermal expansions of the single-phase δ samples to 10 K are self-consistent across the samples and consistent with previous measurements reported in the literature. Significantly larger thermal lattice strain is observed in the δ phase of the two-phase material due to mechanical constraint from the α′ phase, which has a three times larger thermal expansion and is much harder than the δ phase. In conclusion, the results demonstrate the unique value of high-energy X-rays for relatively routine microstructural characterization of Pu alloy samples.

36 MATERIALS SCIENCE↗

Bayesian Monte Carlo Evaluation Framework for Cross Sections Nuclear Data and Integral Benchmark Experiments

The new Bayesian Monte Carlo (MC) evaluation framework described in this abstract has been conceived as an attempt to improve nuclear data evaluations of differential crosssection data by removing the following two approximations conventionally employed for nuclear data evaluations: all probability density functions (PDFs) of all data and model parameters, both prior and posterior, are assumed to be normal (i.e., Gaussian) PDFs, and all uncertainties and covariances are propagated using a linear approximation. With these approximations removed, the Bayesian MC (BMC) framework could be used to account for nonlinear effects and would enable improved evaluations of differential cross sections and IBE data that are presently performed based on the assumptions itemized above. The BMC would also improve upon the uniform sampling of IBE parameters from within ranges defined by their evaluated uncertainties.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Early Results from AIRS/AMSU/HSB

AIRS was launched on EOS Aqua on May 5, 2002, together with AMSU A and HSB, to form a next generation polar orbiting infiared and microwave atmospheric sounding system. The primary products of AIRS/AMSU/HSB are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of lK, and layer precipitable water with an rms error of 20%, in cases with up to 80% effective cloud cover. Pre-launch simulation studies indicated that these results should be achievable. Minor modifications have been made to the pre-launch retrieval algorithm as described in this paper. Sample fields of parameters retrieved from AIRS/AMSU/HSB data are presented and validated as a function of retrieved fractional cloud cover. As in simulation, the degradation of retrieval accuracy with increasing cloud cover is small. Select fields are also compared to those contained in the ECMWF analysis, done without the benefit of AIRS data, to demonstrate information that AIRS can add to that already contained in the ECMWF analysis.

Susskind, Joel↗

Current results from AlRS/AMSU/HSB

AIRS was launched on EOS Aqua on May 4,2002, together with AMSU A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU/HSB are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of 1K, and layer precipitable water with an rms error of 20%, in cases with up to 80% effective cloud cover. Pre-launch simulation studies indicated that these results should be achievable. Minor modifications have been made to the pre-launch retrieval algorithm as alluded to in this paper. Sample fields of parameters retrieved from AIRS/AMSU/HSB data are presented and temperature profiles are validated as a function of retrieved fractional cloud cover. As in simulation, the degradation of retrieval accuracy with increasing cloud cover is small. Select fields are also compared to those contained in the ECMWF analysis, done without the benefit of AIRS data, to demonstrate information that AIRS can add to that already contained in the ECMWF analysis. Assimilation of AIRS temperature soundings in up to 80% cloud cover for the month of January 2003 into the GSFC FVSSI data assimilation system resulted in improved 5 day forecasts globally, both with regard to anomaly correction coefficients and the prediction of location and intensity of cyclones.

Susskind, Joel↗

Atmospheric Soundings from AIRS/AMSU/HSB

AIRS was launched on EOS Aqua on May 4, 2002, together with AMSU A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU/HSB are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of lK, and 1 km tropospheric layer precipitable water with an rms error of 20%, in cases with up to 80% effective cloud cover. Pre-launch simulation studies indicated that these results should be achievable. Minor modifications have been made to the pre-launch retrieval algorithm as alluded to in this paper. Sample fields of parameters retrieved from AIRS/AMSU/HSB data are presented and temperature profiles are validated as a function of retrieved effective fractional cloud cover. As in simulation, the degradation of retrieval accuracy with increasing cloud cover is small. Select fields are also compared to those contained in the ECMWF analysis, done without the benefit of AIRS data, to demonstrate information that AIRS can add to that already contained in the ECMWF analysis. Assimilation of AIRS temperature soundings in up to 80% cloud cover for the month of January 2003 into the GSFC FVSSI data assimilation system resulted in improved 5 day forecasts globally, both with regard to anomaly correlation coefficients and the prediction of location and intensity of cyclones.

Susskind, Joel↗

H i -rich but low star formation galaxies in MaNGA: physical properties and comparison to control samples

ABSTRACT Gas-rich galaxies are typically star forming. We make use of H i-MaNGA, a programme of H i follow-up for the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey of the Sloan Digital Sky Surveys, to construct a sample of unusual neutral hydrogen (H i, 21 cm)-rich galaxies that have low star formation rates (SFRs), using infrared colour from the Wide-field Infrared Survey Explorer as a proxy for specific SFR. Out of a set of 1575 MaNGA galaxies with H i-MaNGA detections, we find that 83 (5 per cent) meet our selection criteria to be H i rich with low SFR. We construct two stellar mass-matched control samples: H i-rich galaxies with typical SFR (high SF control) and H i-poor galaxies with low SFR (low H i control). We investigate the properties of each of these samples, comparing physical parameters such as ionization state maps, stellar and ionized gas velocity and dispersion, environment measures, metallicity, and morphology to search for the reasons why these unusual H i-rich galaxies are not forming stars. We find evidence for recent external accretion of gas in some galaxies (via high counter-rotating fractions), along with some evidence for active galactic nucleus (AGN) feedback (from a high central low-ionization emission-line region and/or red geyser fraction), and bar quenching (via an enhanced strong bar fraction). Some galaxies in the sample are consistent with simply having their H i in a high angular momentum, large-radius, low-density disc. We conclude that no single physical process can explain all H i-rich, low-SFR galaxies.

Astronomy & Astrophysics↗

Sensitivity and Uncertainty Quantification of Transition Scenario Simulations

This report documents the first collective attempt at developing and applying capabilities to quantify uncertainties, assess parametric sensitivities, and optimize multiple parameters and metrics in fuel cycle simulations generated by the SA&I Campaign. To do this, external codes that were designed to perform sensitivity analysis and uncertainty quantification (SA&UQ) needed to be coupled to the SA&I Campaign’s nuclear fuel cycle simulators (NFCS). In FY20, two approaches were pursued: 1) coupling Cyclus to an ORNL-internal code called MOT (Metaheuristic Optimization Tool) and 2) coupling DYMOND to the opensource SA&UQ tool kit Dakota. The primary objective of having these NFCS/SA&UQ coupled capabilities is to better inform DOE-NE and other stakeholders on the results generated from the NFCS. For a given set of fuel cycle strategies, policies, and technology assumptions that make up a fuel cycle scenario, these NFCS have traditionally been used by the SA&I Campaign to provide quantitative answers in terms of year-by-year mass flows, infrastructure requirements, costs, etc. With these newly developed coupled capabilities, the SA&I Campaign can now efficiently simulate hundreds or thousands of these scenarios, sample large ranges of parameters and assumptions, and use the unique features of the SA&UQ tools to process the data. This enables providing answers with known and propagated uncertainties, determining the sensitivity of important metrics to different parameters and assumptions, quantifying how much fuel cycle and technology parameters impact each other, and producing optimized fuel cycle strategies for single and multiple variables. To demonstrate these new capabilities, the Cyclus/MOT was used to model several scenarios ranging from simple fleet retirements to transitions to advanced reactors. Specifically, for a transition scenario from LWRs to SFRs and advanced LWRs, uncertainty quantification, sensitivity analysis, and optimization studies were applied to cases involving single and multiple parameter (input) and single and multiple metric (output) variations. In addition, a similar transition scenario was modeled to demonstrate how to optimize the reprocessing capacity parameter to minimize two performance metrics while taking into account uncertainties from two other parameters. Lastly, a depletion module based on SCALE/ORIGEN was added in Cyclus to simulate the third scenario that was designed to quantify the impact of the modeling assumption that all LWR used nuclear fuel have the same burnup. The newly developed DYMOND/Dakota capability was also applied to a transition scenario from the existing fleet to small modular reactors and fast reactors. This particular scenario involves not only explicit isotopic depletion via ORIGEN-2, but also includes multirecycling and utilizing the criticality search feature to determine the fresh fuel composition of recycled fuel, a feature unique to the DYMOND NFCS. A large database of simulations were run with 4 main parameters that were sampled: start date of reprocessing, reprocessing capacity, energy demand growth rate, and advanced reactor share of the fleet. The 4 main metrics were uranium consumption, enrichment requirements, waste generation, and levelized cost of electricity using data from the Cost Basis Report. The demonstrated SA&UQ results include those that inform on how to choose parameters to avoid “failed” scenarios, Sobol’ indices that inform on the importance of various parameters individually and synergistically, and Analysis of Variance (ANOVA) studies that decompose parameter ranges into groups and informs on whether variations are statistically significant.

Feng, B.↗

Accuracy of Geophysical Parameters Derived from AIRS/AMSU as a Function of Fractional Cloud Cover

AIRS was launched on EOS Aqua on May 4,2002, together with AMSU A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of 1K, and layer precipitable water with an rms error of 20%, in cases with up to 80% effective cloud cover. The basic theory used to analyze AIRS/AMSU/HSB data in the presence of clouds, called the at-launch algorithm, was described previously. Pre-launch simulation studies using this algorithm indicated that these results should be achievable. Some modifications have been made to the at-launch retrieval algorithm as described in this paper. Sample fields of parameters retrieved from AIRS/AMSU/HSB data are presented and validated as a function of retrieved fractional cloud cover. As in simulation, the degradation of retrieval accuracy with increasing cloud cover is small. HSB failed in February 2005, and consequently HSB channel radiances are not used in the results shown in this paper. The AIRS/AMSU retrieval algorithm described in this paper, called Version 4, become operational at the Goddard DAAC in April 2005 and is being used to analyze near-real time AIRS/AMSU data. Historical AIRS/AMSU data, going backwards from March 2005 through September 2002, is also being analyzed by the DAAC using the Version 4 algorithm.

Susskind, Joel↗

Accuracy of Geophysical Parameters Derived from AIRS/AMSU as a Function of Fractional Cloud Cover

AIRS was launched on EOS Aqua on May 4,2002, together with AMSU A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an rms error of lK, and layer precipitable water with an rms error of 20 percent, in cases with up to 80 percent effective cloud cover. The basic theory used to analyze Atmospheric InfraRed Sounder/Advanced Microwave Sounding Unit/Humidity Sounder Brazil (AIRS/AMSU/HSB) data in the presence of clouds, called the at-launch algorithm, was described previously. Pre-launch simulation studies using this algorithm indicated that these results should be achievable. Some modifications have been made to the at-launch retrieval algorithm as described in this paper. Sample fields of parameters retrieved from AIRS/AMSU/HSB data are presented and validated as a function of retrieved fractional cloud cover. As in simulation, the degradation of retrieval accuracy with increasing cloud cover is small and the RMS accuracy of lower tropospheric temperature retrieved with 80 percent cloud cover is about 0.5 K poorer than for clear cases. HSB failed in February 2003, and consequently HSB channel radiances are not used in the results shown in this paper. The AIRS/AMSU retrieval algorithm described in this paper, called Version 4, become operational at the Goddard DAAC (Distributed Active Archive Center) in April 2003 and is being used to analyze near-real time AIRS/AMSU data. Historical AIRS/AMSU data, going backwards from March 2005 through September 2002, is also being analyzed by the DAAC using the Version 4 algorithm.

Susskind, Joel↗

Atmospheric Soundings from AIRS/AMSU/HSB

AIRS was launched on EOS Aqua on May 5, 2002, together with AMSU A and HSB, to form a next generation polar orbiting infrared and microwave atmospheric sounding system. The primary products of AIRS/AMSU/HSB are twice daily global fields of atmospheric temperature-humidity profiles, ozone profiles, sea/land surface skin temperature, and cloud related parameters including OLR. The sounding goals of AIRS are to produce 1 km tropospheric layer mean temperatures with an RMS error of 1K, and 1 km layer precipitable water with an rms error of 1K, and 1 km layer precipitable water with an rms error of 20 percent, in cases with up to 80 percent cloud cover. The AIRS data products are significant for studying climate variability and change, as well as for use in initialization of General Circulation Models with the objective of improving analysis fields and subsequent forecast skill. Data assimilation experiments to evaluate the impact of AIRS retrievals on analysis and forecast skill are being conducted. Sample fields of parameters retrieved from AIRS/AMSU/HSB data will be presented and validated as a function of retrieved fractional cloud cover. Select fields will also be compared to those contained in the ECMWF analysis, done without the benefit of AIRS data, on both an instantaneous and monthly mean basis, to demonstrate information that AIRS can add to that already contained in the ECMWF analysis.

Susskind, Joel↗

Predicting failure parameters of semiconductor devices subjected to stress conditions

A method for predicting failure parameters of semiconductor devices can include receiving a set of data that includes (i) characteristics of a sample semiconductor device, and (ii) parameters characterizing a stress condition. The method further includes extracting a plurality of feature values from the set of data and inputting the plurality of feature values into a trained model executing on the one or more processors, wherein the trained model is configured according to an artificial intelligence (AI) algorithm based on a previous plurality of feature values, and wherein the trained model is operable to output a failure prediction based on the plurality of feature values. Further, the method includes generating, via the trained model, a predicted failure parameter of the sample semiconductor device due to the stress condition.

Ahmed, Moinuddin↗

Intrinsic Dimensionality as a Metric for the Impact of Mission Design Parameters

High-resolution space-based spectral imaging of the Earth's surface delivers critical information for monitoring changes in the Earth system as well as resource management and utilization. Orbiting spectrometers are built according to multiple design parameters, including ground sampling distance (GSD), spectral resolution, temporal resolution, and signal-to-noise ratio. Different applications drive divergent instrument designs, so optimization for wide-reaching missions is complex. The Surface Biology and Geology component of NASA's Earth System Observatory addresses science questions and meets applications needs across diverse fields, including terrestrial and aquatic ecosystems, natural disasters, and the cryosphere. The algorithms required to generate the geophysical variables from the observed spectral imagery each have their own inherent dependencies and sensitivities, and weighting these objectively is challenging. Here, we introduce intrinsic dimensionality (ID), a measure of information content, as an applications-agnostic, data-driven metric to quantify performance sensitivity to various design parameters. ID is computed through the analysis of the eigenvalues of the image covariance matrix, and can be thought of as the number of significant principal components. This metric is extremely powerful for quantifying the information content in high-dimensional data, such as spectrally resolved radiances and their changes over space and time. We find that the ID decreases for coarser GSD, decreased spectral resolution and range, less frequent acquisitions, and lower signal-to-noise levels. This decrease in information content has implications for all derived products. ID is simple to compute, providing a single quantitative standard to evaluate combinations of design parameters, irrespective of higher-level algorithms, products, applications, or disciplines.

Intrinsic dimensionality↗

Comprehensive Analysis of Model Parameter Uncertainty Influence on Evaluation of HVAC Operation to Mitigate Indoor Virus: A Case Study for an Office Building in a Cold and Dry Climate

Simulation-based studies of HVAC operation to mitigate indoor virus have been conducted to understand tradeoffs between indoor air quality (IAQ) and energy consumption. However, the influence of model parameter uncertainty in these studies has not been systematically quantified, which is critical when providing guidance to building operators. To address this gap, we identify 20 model parameters for a typical medium office building system in a cold and dry climate that can influence IAQ and energy consumption for indoor virus scenarios. Next, the distributions of the parameter values are estimated from literature and a set of simulation samples for three representative days is generated that simultaneously sample all of the parameters from their distributions. Two HVAC virus mitigation strategies are studied: increased filtration using MERV 13 filters and increased ventilation, via supply of 100% outdoor air into buildings. The model parameter uncertainty leads to significant variability in the results, particularly for the IAQ because of the highly uncertain virus generation rate. Use of 100% outdoor air can be beneficial for some uncertain scenarios on the hot day, but shows less IAQ improvement and/or significant energy increases on the other days. The virus removal efficiency and pressure drop of the HVAC filter, fan efficiency, and internal heat gain are the most important parameters to determining the tradeoffs of the two strategies. Our results demonstrate how this model parameter uncertainty analysis methodology can provide practical guidance to building operators.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

An error criterion for determining sampling rates in closed-loop control systems

The determination of an error criterion which will give a sampling rate for adequate performance of linear, time-invariant closed-loop, discrete-data control systems was studied. The proper modelling of the closed-loop control system for characterization of the error behavior, and the determination of an absolute error definition for performance of the two commonly used holding devices are discussed. The definition of an adequate relative error criterion as a function of the sampling rate and the parameters characterizing the system is established along with the determination of sampling rates. The validity of the expressions for the sampling interval was confirmed by computer simulations. Their application solves the problem of making a first choice in the selection of sampling rates.

Brecher, S. M.↗

RAPID UNSEPARATED RARE EARTH ELEMENT ANALYSES BY ISOTOPE DILUTION MULTICOLLECTOR INDUCTIVELY COUPLED MASS SPECTROMETRY (ID-MC-ICP-MS)

We present a method for analyzing rare earth elements (REEs) by isotope dilution without separation of individual elements. Utilizing a Nu Plasma 2 multicollector inductively coupled plasma mass spectrometer (MC-ICP-MS) equipped with an Aridus II desolvation nebulizer, sample introduction tuning parameters (torch position, gas flows) were investigated and used to minimize oxide formation (e.g., NdO/Nd <0.05%) and remove the need to analyze the REEs as separated “cuts.” Ratios for spike/sample isotopes in mixed synthetic standards containing varying amounts of Ce, Nd, Sm, Eu, Gd, Dy, Er, and Yb were measured accurately within 1% of IUPAC values. La and Lu in the standards were more than 2% off from expected values due to more demanding interference corrections. A USGS BCR-2 rock standard was also processed with flux fusion, iron coprecipitation and a single column pass bulk separation followed by analysis. The concentrations for Ce, Nd, Sm, Eu, Dy, Er, and Yb fell within 2% of consensus values. A United States Geological Survey (USGS) BIR-1A rock standard was also processed in triplicate by hydrofluoric and nitric acid digestion, yielding rare earth concentrations within 3% of consensus values with 0.3% relative standard deviation (n=3). This demonstrates the ability to produce high quality REE patterns of comparable quality to traditional methods involving labor and time intensive REE separation, with sample preparation and analytical times that are comparable to analyses against isotope dilution by single-collector ICP-MS.

Shen, Steve D.↗

A Multiyear Gridded Data Ensemble of Surface Biogenic Carbon Fluxes for North America: Evaluation and Analysis of Results

Accurate and fine-scale estimates of biogenic carbon fluxes are critical for measuring and monitoring the biosphere's responses and feedback to the climate system. Currently available data products from flux towers and model-intercomparison projects struggle to adequately represent spatiotemporal dynamics of surface biogenic carbon fluxes, and to quantify their uncertainties, which also are crucial to atmospheric inversion systems. To address these gaps, we introduce a new perturbed-parameter model ensemble with the CASA model to estimate surface biogenic carbon fluxes at monthly and 3-hourly scales for North America at ~500-m and 5-km resolutions. We first use the Extended Fourier Amplitude Sensitivity Testing to choose the three most sensitive parameters to be perturbed, maximum light use efficiency (E max ), optimal temperature of photosynthesis (T opt ), and temperature response of respiration (Q 10 ). The initial range for each parameter is broadly sampled for the L1 ensemble, but then we pruned E max with site-level primary productivity to derive an L2 ensemble with narrower uncertainty ranges. Ensembles are strongly correlated with site-level results at both monthly and 3-hourly scales, and the spread across L1/L2 ensemble members encompasses the range of AmeriFlux observations. Monthly variability in the L2 ensemble mean is 85% of the observed variability. The L2 ensemble outperforms diverse data products with the highest Taylor skill scores at diurnal to annual scales. Finally, the ensemble's seasonality agrees well with other models for most biome types and in high and middle latitudes, but inconsistencies are found in subtropical and tropical ecoregions and for annual totals over North America.

54 ENVIRONMENTAL SCIENCES↗

Characterization of Properties of Laser Powder Bed Fusion 3D-Printed Inconel 718 for Centrifugal Turbomachinery Applications

Here, this paper presents the results of a comprehensive effort to characterize the properties of Inconel 718 produced by a form of laser powder bed fusion (LPBF) additive manufacturing (AM) or 3D-printing, subsequently subjected to hot isostatic pressing (HIP) and heat treatment according to standards F3055-14a and AMS 5663, respectively. Material property data, while broadly available for traditional Inconel 718 presentations (e.g. forgings or castings), is currently lacking for the 3D-printed material. It is expected that while limited in size, the experimental data sets presented provide sufficient information to glean the capability of LPBF Inconel 718. These include: 1) Chemical composition, electron backscatter diffraction (EBSD), and x-ray energy dispersive spectroscopy (XEDS) characterization of 3D-printed material structure; 2) Tensile properties — 0.2% yield stress, ultimate stress, modulus of elasticity, and elongation to failure — based on 108 samples, as functions of temperature and sample print orientation; 3) Creep rupture data including the Larson-Miller parameter, based on 21 samples; and 4) High cycle fatigue data based on 21 samples as a function of temperature. Results are compared to available standards and/or data for forged, cast, and other AM Inconel 718. A key observation of this study, based on the EBSD results, is that while the material appears to approach full recrystallization following heat treatment, there is a detectable fraction of the material that does not fully recrystallize, resulting in a material with mechanical properties (e.g. yield stress, creep rupture) measurably lower than those of forgings, but higher than those of castings.

30 DIRECT ENERGY CONVERSION↗

Leading-color two-loop amplitudes for four partons and a $\textit{W}$ boson in QCD

We present the leading-color two-loop QCD corrections for the scattering of four partons and a W boson, including its leptonic decay. The amplitudes are assembled from the planar two-loop helicity amplitudes for four partons and a vector boson decaying to a lepton pair, which are also used to determine the planar two-loop amplitudes for four partons and a $Z/γ^\ast$ boson with a leptonic decay. The analytic expressions are obtained by setting up a dedicated Ansatz and constraining the free parameters from numerical samples obtained within the framework of numerical unitarity. The large linear systems that must be solved to determine the analytic expressions are constructed to be in Vandermonde form. Such systems can be very efficiently solved, bypassing the bottleneck of Gaussian elimination. Our results are expressed in a basis of one-mass pentagon functions, which opens the possibility of their efficient numerical evaluation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗