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Improved methods for Feynman path integral calculations and their application to calculate converged vibrational–rotational partition functions, free energies, enthalpies, entropies, and heat capacities for methane
We present an improved version of our “path-by-path” enhanced same path extrapolation scheme for Feynman path integral (FPI) calculations that permits rapid convergence with discretization errors ranging from O(P{sup −6}) to O(P{sup −12}), where P is the number of path discretization points. We also present two extensions of our importance sampling and stratified sampling schemes for calculating vibrational–rotational partition functions by the FPI method. The first is the use of importance functions for dihedral angles between sets of generalized Jacobi coordinate vectors. The second is an extension of our stratification scheme to allow some strata to be defined based only on coordinate information while other strata are defined based on both the geometry and the energy of the centroid of the Feynman path. These enhanced methods are applied to calculate converged partition functions by FPI methods, and these results are compared to ones obtained earlier by vibrational configuration interaction (VCI) calculations, both calculations being for the Jordan–Gilbert potential energy surface. The earlier VCI calculations are found to agree well (within ∼1.5%) with the new benchmarks. The FPI partition functions presented here are estimated to be converged to within a 2σ statistical uncertainty of between 0.04% and 0.07% for the given potential energy surface for temperatures in the range 300–3000 K and are the most accurately converged partition functions for a given potential energy surface for any molecule with five or more atoms. We also tabulate free energies, enthalpies, entropies, and heat capacities.
Root traits as drivers of plant and ecosystem functioning: current understanding, pitfalls and future research needs
The effects of plants on the biosphere, atmosphere and geosphere are key determinants of terrestrial ecosystem functioning. However, despite substantial progress made regarding plant belowground components, we are still only beginning to explore the complex relationships between root traits and functions. Drawing on the literature in plant physiology, ecophysiology, ecology, agronomy and soil science, we reviewed 24 aspects of plant and ecosystem functioning and their relationships with a number of root system traits, including aspects of architecture, physiology, morphology, anatomy, chemistry, biomechanics and biotic interactions. Based on this assessment, we critically evaluated the current strengths and gaps in our knowledge, and identify future research challenges in the field of root ecology. Most importantly, we found that belowground traits with the broadest importance in plant and ecosystem functioning are not those most commonly measured. Also, the estimation of trait relative importance for functioning requires us to consider a more comprehensive range of functionally relevant traits from a diverse range of species, across environments and over time series. Finally, we also advocate that establishing causal hierarchical links among root traits will provide a hypothesis-based framework to identify the most parsimonious sets of traits with the strongest links on functions, and to link genotypes to plant and ecosystem functioning.
Measuring the Conditional Luminosity and Stellar Mass Functions of Galaxies by Combining the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys Data Release 9, Survey Validation 3, and Year 1 Data
In this investigation, we leverage the combination of the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys Data Release 9, Survey Validation 3, and Year 1 data sets to estimate the conditional luminosity functions and conditional stellar mass functions (CLFs and CSMFs) of galaxies across various halo mass bins and redshift ranges. To support our analysis, we utilize a realistic DESI mock galaxy redshift survey (MGRS) generated from a high-resolution Jiutian simulation. An extended halo-based group finder is applied to both MGRS catalogs and DESI observation. By comparing the r- and z-band luminosity functions (LFs) and stellar mass functions (SMFs) derived using both photometric and spectroscopic data, we quantified the impact of photometric redshift (photo-z) errors on the galaxy LFs and SMFs, especially in the low-redshift bin at the low-luminosity/mass end. By conducting prior evaluations of the group finder using MGRS, we successfully obtain a set of CLF and CSMF measurements from observational data. We find that at low redshift, the faint-end slopes of CLFs and CSMFs below ~10 9 h –2 L ⊙ (or h –2 M ⊙ ) evince a compelling concordance with the subhalo mass functions. After correcting the cosmic variance effect of our local Universe following Chen et al., the faint-end slopes of the LFs/SMFs turn out to also be in good agreement with the slope of the halo mass function.
Estimating Material Properties Under Extreme Conditions by Using Bayesian Model Calibration with Functional Outputs
Summary Dynamic material properties experiments provide access to the most extreme temperatures and pressures attainable in a laboratory setting; the data from these experiments are often used to improve our understanding of material models at these extreme conditions. We apply Bayesian model calibration to dynamic material property applications where the experimental output is a function: velocity over time. This framework can accommodate more uncertainties and facilitate analysis of new types of experiments relative to techniques traditionally used to analyse dynamic material experiments. However, implementation of Bayesian model calibration requires more sophisticated statistical techniques, because of the functional nature of the output as well as parameter and model discrepancy identifiability. We propose a novel Bayesian model calibration process to simplify and improve the estimation of the material property calibration parameters. Specifically, we propose scaling the likelihood function by an effective sample size rather than modelling the auto-correlation function to accommodate the functional output. Additionally, we propose sensitivity analyses by using the notion of 'modularization' to assess the effect of experiment-specific nuisance input parameters on estimates of the physical parameters. The Bayesian model calibration framework proposed is applied to dynamic compression of tantalum to extreme pressures, and we conclude that the procedure results in simple, fast and valid inferences on the material properties for tantalum.
Data-driven acoustic measurement of moisture content in flowing biomass
Measuring the moisture content in flowing biomass is critical to processes such as liquid biofuel conversion, such as biogasoline, biodiesel, bio jet kerosene, etc. However, biomass tends to flow in aggregates, which results in significant inhomogeneities in the amount of biomass flowing in front of a sensor at a given time, and there can be significant overlap in the material properties of dry vs wet biomass, leading to poor signal-to-noise ratio. We present a technique for identifying biomass moisture content using a series of acoustic pitch-catch measurements to quantify the sound speed and acoustic amplitude through the biomass, in conjunction with classical machine learning techniques, including Naive Bayes, Random Forest, and K-Nearest Neighbors classification. We amplify the differences between the acoustic measurements in different moisture levels by collecting a series of pulse-echo measurements, which we sort in order of ascending sound speed. We test the accuracy of the technique on experimentally-prepared batches of corn stover biomass with specified moisture levels and measure the average error in the estimated moisture level as a function of the number of pitch-catch measurements used. We observe average estimation errors as low as 6.7% by increasing the number of measurements and optimizing the hyperparameters. This work presents a novel method determining moisture content in flowing biomass with inhomogeneous flow. Additionally, this technique has application in optimizing biomass conversion processes, as well as other fields including, paper production, natural fiber processing, and mineral extraction.
The effect of high-level waste glass composition on spinel liquidus temperature
Spinel crystals precipitate in high-level waste glasses containing Fe, Cr, Ni , Mn, Zn, and Ru. The liquidus temperature (TL) of spinel as the primary crystallization phase is a function of glass composition and the spinel solubility (c0) is a function of both glass composition and temperature (T). Previously reported models of TL as a function of composition are based on TL measured directly, which requires laborious experimental procedures. Viewing the curve of c0 versus T as the liquidus line allows a significant broadening of the composition region for model fitting. This paper estimates TL as a function of composition based on c0 data obtained with the X-ray diffraction technique.
Assessing the Performance of Exchange‐Correlation Density Functionals in Describing the Iron‐Catalyzed Ammonia Synthesis System
Density functional theory (DFT) has been widely employed for elucidating mechanistic aspects of heterogeneous catalysis. However, the accuracy of DFT calculations relies heavily on selecting an exchange-correlation (XC) functional that correctly describes the electronic structure of materials involved in the reactions. This study assesses the accuracy of several XC density functionals for modeling the iron-catalyzed ammonia synthesis system. In the assessment of functional accuracy, experimental references are compared to DFT-calculated values for the formation energy of gas-phase ammonia and nitrogen, bulk Fe/Fe-nitride (γ′-Fe 4 N) lattice constants and cohesive/formation energies, and nitrogen and ammonia binding energies on Fe(100), Fe(111), Fe(110), and γ′-Fe 4 N(111). It is observed that the experimental value for each of these descriptors is accurately modeled by at least one functional. RPBE alone provides reliable estimates for both the lattice constant and cohesive energy of Fe and γ′-Fe 4 N. Temperature-programmed desorption experiments led to estimates for N and NH 3 adsorption across several Fe-based facets that are best captured by RPBE. These results highlight the importance of choosing an appropriate XC functional that accurately describes experimental systems and offer insights into effectively modeling the interactions between nitrogen and ammonia on Fe-based surfaces.
Characterization of energy response for photon-counting detectors using x-ray fluorescence
Purpose: To investigate the feasibility of characterizing a Si strip photon-counting detector using x-ray fluorescence. Methods: X-ray fluorescence was generated by using a pencil beam from a tungsten anode x-ray tube with 2 mm Al filtration. Spectra were acquired at 90° from the primary beam direction with an energy-resolved photon-counting detector based on an edge illuminated Si strip detector. The distances from the source to target and the target to detector were approximately 19 and 11 cm, respectively. Four different materials, containing silver (Ag), iodine (I), barium (Ba), and gadolinium (Gd), were placed in small plastic containers with a diameter of approximately 0.7 cm for x-ray fluorescence measurements. Linear regression analysis was performed to derive the gain and offset values for the correlation between the measured fluorescence peak center and the known fluorescence energies. The energy resolutions and charge-sharing fractions were also obtained from analytical fittings of the recorded fluorescence spectra. An analytical model, which employed four parameters that can be determined from the fluorescence calibration, was used to estimate the detector response function. Results: Strong fluorescence signals of all four target materials were recorded with the investigated geometry for the Si strip detector. The average gain and offset of all pixels for detector energy calibration were determined to be 6.95 mV/keV and −66.33 mV, respectively. The detector’s energy resolution remained at approximately 2.7 keV for low energies, and increased slightly at 45 keV. The average charge-sharing fraction was estimated to be 36% within the investigated energy range of 20–45 keV. The simulated detector output based on the proposed response function agreed well with the experimental measurement. Conclusions: The performance of a spectral imaging system using energy-resolved photon-counting detectors is very dependent on the energy calibration of the detector. The proposed x-ray fluorescence technique offers an accurate and efficient way to calibrate the energy response of a photon-counting detector.
A neural-network based estimator to search for primordial non-Gaussianity in Planck CMB maps
We present an upgraded combined estimator, based on Minkowski Functionals and Neural Networks, with excellent performance in detecting primordial non-Gaussianity in simulated maps that also contain a weighted mixture of Galactic contaminations, besides real pixel's noise from Planck cosmic microwave background radiation data. We rigorously test the efficiency of our estimator considering several plausible scenarios for residual non-Gaussianities in the foreground-cleaned Planck maps, with the intuition to optimize the training procedure of the Neural Network to discriminate between contaminations with primordial and secondary non-Gaussian signatures. We look for constraints of primordial local non-Gaussianity at large angular scales in the foreground-cleaned Planck maps. For the SMICA map we found f{sub NL} = 33 ± 23, at 1σ confidence level, in excellent agreement with the WMAP-9yr and Planck results. In addition, for the other three Planck maps we obtain similar constraints with values in the interval f{sub NL} element of [33, 41], concomitant with the fact that these maps manifest distinct features in reported analyses, like having different pixel's noise intensities.
THE SUBARU HIGH-z QUASAR SURVEY: DISCOVERY OF FAINT z ∼ 6 QUASARS
We present the discovery of one or two extremely faint z ∼ 6 quasars in 6.5 deg{sup 2} utilizing a unique capability of the wide-field imaging of the Subaru/Suprime-Cam. The quasar selection was made in (i'-z{sub B} ) and (z{sub B} -z{sub R} ) colors, where z{sub B} and z{sub R} are bandpasses with central wavelengths of 8842 Å and 9841 Å, respectively. The color selection can effectively isolate quasars at z ∼ 6 from M/L/T dwarfs without the J-band photometry down to z{sub R} < 24.0, which is 3.5 mag deeper than the Sloan Digital Sky Survey (SDSS). We have selected 17 promising quasar candidates. The follow-up spectroscopy for seven targets identified one apparent quasar at z = 6.156 with M {sub 1450} = –23.10. We also identified one possible quasar at z = 6.041 with a faint continuum of M {sub 1450} = –22.58 and a narrow Lyα emission with HWHM =427 km s{sup –1}, which cannot be distinguished from Lyman α emitters. We derive the quasar luminosity function at z ∼ 6 by combining our faint quasar sample with the bright quasar samples by SDSS and CFHQS. Including our data points invokes a higher number density in the faintest bin of the quasar luminosity function than the previous estimate employed. This suggests a steeper faint-end slope than lower z, though it is yet uncertain based on a small number of spectroscopically identified faint quasars, and several quasar candidates still remain to be diagnosed. The steepening of the quasar luminosity function at the faint end does increase the expected emission rate of the ionizing photon; however, it only changes by a factor of approximately two to six. This was found to still be insufficient for the required photon budget of reionization at z ∼ 6.
Monte Carlo simulation methodology for characterizing the energy response function and resolving power of a digital Flat Panel Detector (FPD) assembly
The use of high-resolution, digital flat panel detectors (FPDs) makes quantitative assessments of radiographic and 3D tomographic representations feasible. However, the energy response function and spatial resolving power of the detector must be known. Here, we present a methodology for characterizing an FPD assembly using Monte Carlo simulations. The detector assembly modeled here was fielded in the 3-Ring Flash X-ray Imaging System designed and built at Lawrence Livermore National Laboratory (LLNL), which employs fifteen Carestream ® HPX-DR3543 FPDs enclosed in protective housings. Detailed Monte Carlo (MCNP6) simulations of an as-fielded detector assembly were performed to estimate its energy response function in terms of analog-to-digital unit (ADU) “counts” per pixel per incident x-ray as a function of energy up to ∼ 500 keV and its theoretical (idealized) resolving power. The practical resolving power of the FPD assembly in a realistic scenario was then estimated by simulating radiographic images of a variant of the United Kingdom (U.K.) “Kaleidoscope” resolution target.
Direct path integral estimators for isotope fractionation ratios
Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical, and atmospheric phenomena. Accurate evaluation of isotope ratios in atomistic simulations is challenging, because one needs to perform a thermodynamic integration with respect to the isotope mass, along with time-consuming path integral calculations. By re-formulating the problem as a particle exchange in the ring polymer partition function, we derive new estimators giving direct access to the differential partitioning of isotopes, which can simplify the calculations by avoiding thermodynamic integration. We demonstrate the efficiency of these estimators by applying them to investigate the isotope fractionation ratios in the gas-phase Zundel cation, and in a few simple hydrocarbons.
SU-G-206-11: The Effect of Table Height On CTDIvol and SSDE in CT Scanning: A Phantom Study
Purpose: Localizer projection radiographs acquired prior to CT scans are used to estimate patient size, affecting the function of Automatic Tube Current Modulation (ATCM) and calculation of the Size Specific Dose Estimate (SSDE). Due to geometric effects, the projected patient size varies with scanner table height and with the orientation of the localizer (AP versus PA). Consequently, variations in scanner table height may affect both CTDIvol and the calculated size-corrected dose index (SSDE). This study sought to characterize these effects. Methods: An anthropomorphic phantom was imaged using an AP localizer, followed by a diagnostic scan using ATCM and our institution’s routine abdomen protocol. This was repeated at various scanner table heights, recording the scanner-reported CTDIvol for each diagnostic scan. The width of the phantom was measured from the localizer and diagnostic images using in-house software. The measured phantom width and scanner-reported CTDIvol were used to calculate SSDE. This was repeated using PA localizers followed by diagnostic scans. Results: 1) The localizer-based phantom width varied by up to 54% of the nominal phantom width between minimum and maximum table heights. 2) Changing the table height caused a variation in scanner-reported CTDIvol of a factor greater than 4.6 when using a PA localizer and almost 2 when using an AP localizer. 3) SSDE, calculated from measured phantom size and scanner-reported CTDIvol, varied by a factor of more than 2.8 when using a PA localizer and almost 1.5 when using an AP localizer. Conclusion: Our study demonstrates that off-center patient positioning affects the efficacy of ATCM, more severely when localizers are acquired in the PA rather than AP projection. Further, patient positioning errors can cause a large variation in the calculated SSDE. This hinders interpretation of SSDE for individual patients and aggregate SSDE data when evaluating CT protocols and clinical practices.
A density functional theory based approach for predicting melting points of ionic liquids
Accurate prediction of melting points of ILs is important both from the fundamental point of view and from the practical perspective for screening ILs with low melting points and broadening their utilization in a wider temperature range. In this work, we present an ab initio approach to calculating melting points of ILs with known crystal structures and illustrate its application for a series of 11 ILs containing imidazolium/pyrrolidinium cations and halide/polyatomic fluoro-containing anions. The melting point is determined as a temperature at which the Gibbs free energy of fusion is zero. The Gibbs free energy of fusion can be expressed through the use of the Born-Fajans-Haber cycle via the lattice free energy of forming a solid IL from gaseous phase ions and the sum of the solvation free energies of ions comprising IL. Dispersion-corrected density functional theory (DFT) involving (semi)local (PBE-D3) and hybrid exchange-correlation (HSE06-D3) functionals is applied to estimate the lattice enthalpy, entropy, and free energy. The ions solvation free energies are calculated with the SMD-generic-IL solvation model at the M06-2X/6-31+G(d) level of theory under standard conditions. The melting points of ILs computed with the HSE06-D3 functional are in good agreement with the experimental data, with a mean absolute error of 30.5 K and a mean relative error of 8.5%. The model is capable of accurately reproducing the trends in melting points upon variation of alkyl substituents in organic cations and replacement one anion by another. The results verify that the lattice energies of ILs containing polyatomic fluoro-containing anions can be approximated reasonably well using the volume-based thermodynamic approach. However, there is no correlation of the computed lattice energies with molecular volume for ILs containing halide anions. Moreover, entropies of solid ILs follow two different linear relationships with molecular volume for halides and polyatomic fluoro-containing anions. As a result, continuous progress in predicting crystal structures of organic salts with halide anions will be a key factor for successful prediction of melting points with no prior knowledge of the crystal structure.
A Bayesian approach for parameter estimation and prediction using a computationally intensive model
Bayesian methods have been successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model eta(theta), where theta denotes the uncertain, best input setting. Hence the statistical model is of the form y = eta(theta) + c, where epsilon accounts for measurement, and possibly other, error sources. When nonlinearity is present in eta(center dot), the resulting posterior distribution for the unknown parameters in the Bayesian formulation is typically complex and nonstandard, requiring computationally demanding computational approaches such as Markov chain Monte Carlo (MCMC) to produce multivariate draws from the posterior. Although generally applicable, MCMC requires thousands (or even millions) of evaluations of the physics model eta(center dot). This requirement is problematic if the model takes hours or days to evaluate. To overcome this computational bottleneck, we present an approach adapted from Bayesian model calibration. This approach combines output from an ensemble of computational model runs with physical measurements, within a statistical formulation, to carry out inference. A key component of this approach is a statistical response surface, or emulator, estimated from the ensemble of model runs. We demonstrate this approach with a case study in estimating parameters for a density functional theory model, using experimental mass/binding energy measurements from a collection of atomic nuclei. We also demonstrate how this approach produces uncertainties in predictions for recent mass measurements obtained at Argonne National Laboratory.
Determining initial enrichment, burnup, and cooling time of pressurized-water reactor spent fuel assemblies by analyzing passive gamma spectra measured at the Clab interim-fuel storage facility in Sweden
The purpose of the Next Generation Safeguards Initiative (NGSI)–Spent Fuel (SF) project is to strengthen the technical toolkit of safeguards inspectors and/or other interested parties. The NGSI–SF team is working to achieve the following technical goals more easily and efficiently than in the past using nondestructive assay measurements of spent fuel assemblies: (1) verify the initial enrichment, burnup, and cooling time of facility declaration; (2) detect the diversion or replacement of pins; (3) estimate the plutonium mass [which is also a function of the variables in (1)]; (4) estimate the decay heat; and (5) determine the reactivity of spent fuel assemblies. Since August 2013, a set of measurement campaigns has been conducted at the Central Interim Storage Facility for Spent Nuclear Fuel (Clab), in collaboration with Swedish Nuclear Fuel and Waste Management Company (SKB). One purpose of the measurement campaigns was to acquire passive gamma spectra with high-purity germanium and lanthanum bromide scintillation detectors from Pressurized Water Reactor and Boiling Water Reactor spent fuel assemblies. The absolute 137 Cs count rate and the 154 Eu/ 137 Cs, 134 Cs/ 137 Cs, 106 Ru/ 137 Cs, and 144 Ce/ 137 Cs isotopic ratios were extracted; these values were used to construct corresponding model functions (which describe each measured quantity’s behavior over various combinations of burnup, cooling time, and initial enrichment) and then were used to determine those same quantities in each measured spent fuel assembly. Furthermore, the results obtained in comparison with the operator declared values, as well as the methodology developed, are discussed in detail in the paper.
Accurately estimating and minimizing costs for the cellulosic biomass supply chain with statistical process control and the Taguchi Loss Function
This research focuses on the statistical evaluation of the feedstock attributes of the biomass supply chain and the estimation of attribute costs as a function of the feedstock variability. Challenges of using cellulosic feedstocks include the variability of feedstock quality (e.g., ash content and moisture content), which impacts the final cost of the manufactured product. Statistical Process Control (SPC), Taguchi Loss Function, and components of variance techniques were illustrated for quantifying cumulative variance in the biomass supply chain. Costs in the presence of cumulative variance were estimated for switchgrass (Panicum virgatum L.) and loblolly pine residues (Pinus taeda L.). Findings of the study indicated that additional costs from ash content variability in switchgrass increased the net cost by $\$19.15$ per dry tonne. Additional costs from densification due to particle size variation increased net cost by $\$11.59$ per dry tonne. Moisture content variation increased costs by $\$14.86$ per dry tonne. This would represent a 50 to 100% increase in costs due to variation based on a $\$60$ to $\$70$ per dry tonne manufactured product cost. This study illustrates that total costs may be considerably underestimated if the influence of variance for key factors in the supply chain and associated costs are not estimated.