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At least 1,027 records · Page 57

Enhanced Monte Carlo Simulations for Electron Energy Loss Mitigation in Real-Space Nanoimaging of Thick Biological Samples and Microchips

High-resolution imaging using Transmission Electron Microscopy (TEM) is essential for applications such as grain boundary analysis, microchip defect characterization, and biological imaging. However, TEM images are often compromised by electron energy spread and other factors. In TEM mode, where the objective and projector lenses are positioned downstream of the sample, electron–sample interactions cause energy loss, which adversely impacts image quality and resolution. This study introduces a simulation tool to estimate the electron energy loss spectrum (EELS) as a function of sample thickness, covering electron beam energies from 300 keV to 3 MeV. Leveraging recent advances in MeV-TEM/STEM technology, which includes a state-of-the-art electron source with 2-picometer emittance, an energy spread of 3 × 10 -5 , and optimized beam characteristics, we aim to minimize energy spread. By integrating EELS capabilities into the BNL Monte Carlo (MC) simulation code for thicker samples, we evaluate electron beam parameters to mitigate energy spread resulting from electron–sample interactions. Based on our simulations, we propose an experimental procedure for quantitively distinguishing between elastic and inelastic scattering. The findings will guide the selection of optimal beam settings, thereby enhancing resolution for nanoimaging of thick biological samples and microchips.

36 MATERIALS SCIENCE↗

MEASURING HIGH-PRECISION ASTROMETRY WITH THE INFRARED ARRAY CAMERA ON THE SPITZER SPACE TELESCOPE

The Infrared Array Camera (IRAC) on the Spitzer Space Telescope currently offers the greatest potential for high-precision astrometry of faint mid-IR sources across arcminute-scale fields, which would be especially valuable for measuring parallaxes of cold brown dwarfs in the solar neighborhood and proper motions of obscured members of nearby star-forming regions. To more fully realize IRAC's astrometric capabilities, we have sought to minimize the largest sources of uncertainty in astrometry with its 3.6 and 4.5 μm bands. By comparing different routines that estimate stellar positions, we have found that Point Response Function (PRF) fitting with the Spitzer Science Center's Astronomical Point Source Extractor produces both the smallest systematic errors from varying intra-pixel sensitivity and the greatest precision in measurements of positions. In addition, self-calibration has been used to derive new 7th and 8th order distortion corrections for the 3.6 and 4.5 μm arrays of IRAC, respectively. These corrections are suitable for data throughout the mission of Spitzer when a time-dependent scale factor is applied to the corrections. To illustrate the astrometric accuracy that can be achieved by combining PRF fitting with our new distortion corrections, we have applied them to archival data for a nearby star-forming region, arriving at total astrometric errors of ∼20 and 70 mas at signal to noise ratios of 100 and 10, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗

Time and Phase Resolved Optical Spectra of Potentially Hazardous Asteroid 2014 JO25

The asteroid 2014 JO25, considered to be potentially hazardous by the Minor Planet Center, was spectroscopically followed during its close-Earth encounter on 2017 April 19 and 20. The spectra of the asteroid were taken with the low-resolution spectrograph (LISA), mounted on the 1.2 m telescope at the Mount Abu Infrared Observatory, India. Coming from a region close to the Hungaria population of asteroids, this asteroid follows a comet-like orbit with a relatively high inclination and large eccentricity. Hence, we carried out optical spectroscopic observations of the asteroid to look for comet-like molecular emissions or outbursts. However, the asteroid showed a featureless spectrum, devoid of any comet-like features. The light curve of the asteroid was analyzed using V-band magnitudes derived from the spectra and the most likely solution for the rotation of the asteroid was obtained. The absolute magnitude H and the slope parameter G were determined for the asteroid in the V filter band using the IAU accepted standard two-parameter H–G model. A peculiar, rarely found result from these observations is its phase bluing trend. The relative B–V color index seems to decrease with increasing phase angle, which indicates a phase bluing trend. Such trends have seldom been reported in the literature. However, phase reddening in asteroids is very common. The asymmetry parameter g and the single-scattering albedo w were estimated for the asteroid by fitting the Hapke phase function to the observed data. The asteroid shows a relatively large value for the single-scattering albedo and a highly back-scattering surface.

79 ASTRONOMY AND ASTROPHYSICS↗

Eta Fragmentation Functions Revisited

We revisit the extraction of parton-to-eta meson fragmentation functions at next-to-leading order accuracy in QCD in the light of the recent hadroproduction measurements in proton-proton collisions obtained by the PHENIX, LHCb, and ALICE collaborations. In addition to an increased precision, the data explore complementary rapidity ranges and center-of-mass system energies. The analysis exploits the theoretical scale dependence to ease tensions among the data sets at different energies that are potentially caused by QCD corrections beyond the next-to-leading order. The resulting set of fragmentation functions yields a consistent description of all available data. Estimates of uncertainties are obtained with the Monte Carlo replica method.

FOS: Physical sciences↗

Towards an improved understanding of the influence of subpixel vegetation structure on pixel-level spectra: a simulation approach

The planned NASA Hyperspectral Infrared Imager (HyspIRI) mission, equipped with an imaging spectrometer that has the capability of monitoring ecosystems globally, will provide an unprecedented opportunity to address scientific challenges related to ecosystem function and change. However, uncertainty remains around the impact of subpixel vegetation structure, in combination with the point spread function, on pixel-level imaging spectroscopy data. We estimated structural parameters, e.g., leaf area index (LAI), canopy cover, and tree location, from HyspIRI spectral data, with the goal of assessing how subpixel variation in these parameters impact pixel-level imaging spectroscopy data. The fine-scale variability of real vegetation structure makes this a challenging endeavor. Therefore, we utilized a simulation-based approach to counter the time-consuming and often destructive sampling needs of vegetation structural analysis and to simultaneously generate synthetic HyspIRI data pre-launch. Three virtual scenes were constructed, corresponding to the actual vegetation structure in the National Ecological Observatory Network’s (NEON) Pacific Southwest Domain (Fresno, CA). These included an oak savanna, a dense coniferous forest, and a conifer-manzanita-mixed forest. Simulated spectroscopy data for these scenes were then generated using the Digital Imaging and Remote Sensing Image Generation (DIRSIG) model. Simulations first were used to verify the physical model, virtual scene geometrical information, and simulation parameters. This was followed by simulations of HyspIRI data, where within-pixel structural variability was introduced, e.g., by iteratively changing per-pixel canopy cover and tree placement, tree clustering, leaf area index (LAI), etc., between simulation runs for the virtual scenes. Finally, narrow-band vegetation indices (VIs) were extracted from the data in an attempt to describe the variability of the subpixel structural parameters; this was done in order to assess VI robustness to changes in structural “levels”, as well as placement of trees/canopies within the instrument’s instantaneous field-of-view (IFOV). Our ultimate goal is not only to better understand how such subpixel variability influence imaging spectroscopy outputs, but also to better estimate vegetation structural parameters using spectra. We constructed regression models for LAI (R2 = 0.92) and canopy cover (R2 = 0.97) with narrow-band VIs via this simulation approach. Our models ultimately are intended to improve the HyspIRI mission’s ability to monitor global vegetation structure.

Van Aardt, Jan↗

Uncertainty and Sensitivity Analysis of TREAT Transient Test #15

The U.S. Department of Energy (DOE) is preparing for the resumption of transient testing using the Transient Reactor Test Facility (TREAT) located at the Idaho National Laboratory (INL). In order to support the analysis of TREAT operation and experiment planning, the MAMMOTH reactor physics team has recently begun development of uncertainty and sensitivity analysis for the TREAT core simulated via MAMMOTH. MAMMOTH is a high-fidelity three-dimensional transient multi-physics code developed at INL under the DOE-NE Advanced Modeling and Simulation program (NEAMS) [1]. This research is part of the development presenting some initial uncertainty and sensitivity analysis of TREAT Transient Test #15 [2]. In this summary, we employ the Sobol sampling strategy implemented in RAVEN [3] to efficiently perform the sensitivity and uncertainty analysis. The idea is using Sobol functional decomposition with generalized polynomial chaos (gPC) expansions to estimate the responses of interest [4]. The gPC coefficients are then computed via the spectral projection method with sparse grid approach. In addition, this strategy includes evaluation of the second or higher order sensitivity indices, allowing the study of interactions between several input variables. The principal focus of this analysis is to quantify the uncertainties in the total power and maximum fuel temperatures with respect to uncertainties in the initial transient conditions, such as rated power, fuel temperature, graphite fuel density and control rod boron concentration. In addition, both the first order and second order time-dependent sensitivity indices are computed and analyzed. The results show that the interactions between initial control rod boron concentration and the rated power will contribute at most 1% to the total uncertainty of the power peak.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Apparatus and method for optimizing quantifiable behavior in configurable devices and systems

An apparatus and method are provided to perform constrained optimization of a constrained property of an apparatus, which is complex due to having several components, and these components are configurable in real-time. The optimization is achieved by detecting values of the constrained property and a plurality of other properties of the apparatus when the apparatus is configured in a first subset of the plurality of configurations. A model is learned using the detected values of the constrained property. The model represents the constrained property and can also represent other properties as a function of the configurations. The model can also include estimated uncertainties of the constrained property in the model. Then, using the d model and the estimated uncertainties, the optimal configuration can be selected to minimize an error value (e.g., the difference between a desired value and an observed value of the at least one constrained property).

Hoffmann, Henry↗

Uncertainty and Sensitivity Analysis of TREAT Transient Test no. 15

The U.S. Department of Energy (DOE) is preparing for the resumption of transient testing using the Transient Reactor Test Facility (TREAT) located at the Idaho National Laboratory (INL). In order to support the analysis of TREAT operation and experiment planning, the MAMMOTH reactor physics team has recently begun development of uncertainty and sensitivity analysis for the TREAT core simulated via MAMMOTH. MAMMOTH is a high-fidelity three-dimensional transient multi-physics code developed at INL under the DOE-NE Advanced Modeling and Simulation program (NEAMS). This research is part of the development presenting some initial uncertainty and sensitivity analysis of TREAT Transient Test no. 15. In this summary, we employ the Sobol sampling strategy implemented in RAVEN to efficiently perform the sensitivity and uncertainty analysis. The idea is using Sobol functional decomposition with generalized polynomial chaos (gPC) expansions to estimate the responses of interest. The gPC coefficients are then computed via the sparse grid spectral projection method. In addition, this strategy includes evaluation of the second or higher order sensitivity indices, allowing the study of interactions between several input variables. The principal focus of this analysis is to quantify the uncertainties in the total power and maximum fuel temperatures with respect to uncertainties in the initial transient conditions, such as rated power, fuel temperature, graphite fuel density and control rod boron concentration. In addition, both the first order and second order time-dependent sensitivity indices are computed and analyzed. The results show that the interactions between initial control rod boron concentration and the rated power will contribute at most 1% to the total uncertainty of the power peak.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Searching for Neutrino Tridents in the NOvA Near Detector

This dissertation presents a search for neutrino trident production in the NOvA near detector through the coherent ``dimuon" channel: $\nu_\mu +\hspace{1pt}\text{X} \rightarrow \nu_\mu + \mu^- + \mu^+ +\hspace{1pt}\text{X}$. Trident production is a rare, purely electroweak process with sensitivity to physics beyond the Standard Model. The theoretical background, motivation for studying the process, and previous experimental measurements are reviewed. The analysis uses data collected by the NOvA near detector (ND) from Fermilab's Neutrinos at the Main Injector (NuMI) beam between November 2014 and February 2024, corresponding to an exposure of $25.5\times 10^{20}$ protons on target. The ND is a segmented tracking calorimeter located 800~m from the beam target, receiving neutrinos with a mean energy of 2~GeV. A multi-pass background reduction strategy is implemented, including the development of a novel dimuon-specific tracking technique. Trident candidates are identified using a boost ed decision tree classifier trained on simulated signal and background events. Limited background Monte Carlo statistics necessitate the use of functional fits to sideband data, which are extrapolated to estimate backgrounds in the signal region. The unblinded data contain 9 trident-like events, with an estimated background of 5.66 $\pm$ 5.15 events. This yields a best fit estimate of 3.34 tridents compared to the Standard Model prediction of 4.66. A profiled Feldman-Cousins method is used to determine a 90\% confidence interval of [0,9.1] on the number of signal events, corresponding to an upper limit of 1.95$\times$ the Standard Model prediction. This result represents the lowest energy search for trident events to date, and the first experimental contribution to the process in 27 years.

Bowles, Reed Scott [Indiana U.]↗

Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations

We present accurate many-body results of the electronic densities in several solid materials, including Si, NaCl, and Cu. These results are obtained using the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a plane-wave basis with norm-conserving, multiple-projector pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation, whose adaption and implementation in the plane-wave basis AFQMC framework are discussed in the present paper. This development allows us to compute correlation functions, electronic densities, and interatomic forces, paving the way for geometry optimizations and calculations of thermodynamic properties in solids. Finite supercell size effects are considerably more subtle in the many-body framework than in independent-electron calculations. We analyze the convergence of the electronic density, and obtain best estimates for the thermodynamic limit. The densities from several typical density functionals are benchmarked against our near-exact results. The electronic densities we obtained can also be used to help construct improved density functionals.

36 MATERIALS SCIENCE↗

IMPACT OF η{sub Earth} ON THE CAPABILITIES OF AFFORDABLE SPACE MISSIONS TO DETECT BIOSIGNATURES ON EXTRASOLAR PLANETS

We present an analytic model to estimate the capabilities of space missions dedicated to the search for biosignatures in the atmosphere of rocky planets located in the habitable zone of nearby stars. Relations between performance and mission parameters, such as mirror diameter, distance to targets, and radius of planets, are obtained. Two types of instruments are considered: coronagraphs observing in the visible, and nulling interferometers in the thermal infrared. Missions considered are: single-pupil coronagraphs with a 2.4 m primary mirror, and formation-flying interferometers with 4 × 0.75 m collecting mirrors. The numbers of accessible planets are calculated as a function of η{sub Earth}. When Kepler gives its final estimation for η{sub Earth}, the model will permit a precise assessment of the potential of each instrument. Based on current estimations, η{sub Earth} = 10% around FGK stars and 50% around M stars, the coronagraph could study in spectroscopy only ∼1.5 relevant planets, and the interferometer ∼14.0. These numbers are obtained under the major hypothesis that the exozodiacal light around the target stars is low enough for each instrument. In both cases, a prior detection of planets is assumed and a target list established. For the long-term future, building both types of spectroscopic instruments, and using them on the same targets, will be the optimal solution because they provide complementary information. But as a first affordable space mission, the interferometer looks the more promising in terms of biosignature harvest.

79 ASTRONOMY AND ASTROPHYSICS↗

Parameter estimation for incidence angle modifier models for photovoltaic modules

We present methods to estimate parameters for models for the incidence angle modifier for simulating irradiance on a photovoltaic array. The incidence angle modifier quantifies the fraction of direct irradiance that is reflected away at the array’s face, as a function of the direct irradiance’s angle of incidence. Parameters can be estimated from data and the fitting method can be used to convert between models. We show that the model conversion procedure results in models that produce similar annual insolation on a fixed plane.

14 SOLAR ENERGY↗

On the correlation between plastic strain and misorientation in polycrystalline body-centered-cubic microstructures with an emphasis on the grain size, loading history, and crystallographic orientation

In this work, the correlation between plastic strain and crystallographic misorientation, grain size, grain orientation, distance from grain boundary, and loading history were investigated experimentally and numerically for body-centered-cubic (BCC) polycrystalline microstructures based on a misorientation deviation (MD) approach. Nine monotonic tensile experiments were performed on two BCC titanium alloys inside a scanning electron microscope (SEM). The influence of reference orientation was explored both at the grain scale and at the mesoscale using electron backscattered diffraction (EBSD). The correlation between global plastic strain and the MD was quantified. The tendency for orientation change was quantified as a function of plastic strain and grain orientation for three crystallographic orientations (i.e., [100], [110], and [111]) with respect to tensile direction. The subpopulation of small grains exhibited a lower level of misorientation dispersion compared with larger grains, and this discrepancy became more pronounced at higher strains. An empirical equation was proposed to estimate the level of misorientation dispersion for individual grains as a function of grain size and global plastic strain level. Two interrupted in-situ SEM experiments were performed, and this resulted in a significantly increased misorientation compared with uninterrupted tests performed to similar plastic strain levels.

36 MATERIALS SCIENCE↗

Prevalence of Self-Reported Bothersome Tinnitus in U.S. Army Soldiers From January 1, 2015, Through September 30, 2019

Purpose: Tinnitus is a symptom of auditory dysfunction or injury and can be a precursor to permanent hearing loss. Tinnitus can interfere with communication, sleep, concentration, and mood; when this occurs, it is referred to as bothersome tinnitus. Annual hearing surveillance in the U.S. Army includes screening for bothersome tinnitus. Estimating the prevalence of self-reported bothersome tinnitus can facilitate prioritization of prevention and education efforts. The objective of this study was to examine Army hearing conservation data to estimate the prevalence of self-reported bothersome tinnitus as a function of age, hearing, sex, service component, and pay grade. Method: The study employed a cross-sectional, retrospective design. Records from 1,485,059 U.S. Army Soldiers retrieved from the Defense Occupational and Environmental Health Readiness System–Hearing Conservation were analyzed. Descriptive statistics and multinomial logistic regression analysis were used to estimate the prevalence of bothersome tinnitus and its associations with Soldiers' demographic characteristics. Results: The estimated prevalence of self-reported bothersome tinnitus was 17.1% between January 1, 2015, and September 30, 2019; 13.6% of the Soldiers reported “bothered a little” and 3.5% reported “bothered a lot.” Proportionally, the prevalence of self-reported bothersome tinnitus was higher for males, older Soldiers, and Reserve Component Soldiers. For every 1-year increase in age, the odds of self-reporting “bothered a little” tinnitus relative to “bothered not at all tinnitus” would be expected to increase by 2.2% (2.1%, 2.3%), and the odds of self-reporting “bothered a lot” tinnitus relative to “bothered not at all” tinnitus would be expected to increase by 3.6% (3.5%, 3.7%). Conclusions: The self-reported prevalence of bothersome tinnitus in the U.S. Army (17.1%) is substantially higher than that of the general population, where prevalence of bothersome tinnitus is estimated at 6.6%. Examination of bothersome tinnitus among Soldiers is an important step toward optimizing prevention, education, and intervention efforts.

Audiology & Speech-Language Pathology↗

Linking Community‐Climate Disequilibrium to Ecosystem Function

Turnover in species composition often lags behind the pace of climate change, resulting in mismatches between climate and communities. However, the impact of these community‐climate disequilibria on ecosystem functions is rarely considered, and current methods for measuring disequilibria assume that species ranges were, until recently, in equilibrium with climate. Here, in this work, we develop a simple theoretical model to address both of these problems by linking community‐climate disequilibrium with ecosystem functioning. We show how disequilibrium can impair functioning in the near‐term even when climate change is expected to enhance functioning in the long‐term. Responses are most likely to change over time in communities where turnover is slow, the impact of disequilibrium counteracts the direct effects of climate on ecosystem function, and pre‐existing disequilibrium is large. These findings emphasise the importance of precise and unbiased estimates of community‐climate disequilibria for improving ecological forecasts. By fitting our model to time series of both climate and ecosystem function from a metacommunity simulation, we show the potential for community‐climate disequilibrium to be inferred without direct knowledge about species' distributions or climatic tolerances. We end by outlining a research agenda to apply dynamic disequilibrium concepts and test novel hypotheses across diverse ecosystems.

climate change↗

Clustering of CODEX clusters

The clustering of galaxy clusters links the spatial nonuniformity of dark matter halos to the growth of the primordial spectrum of perturbations. The amplitude of the clustering signal is widely used to estimate the halo mass of astrophysical objects. The advent of cluster mass calibrations enables using clustering in cosmological studies. Aims. We analyze the autocorrelation function of a large contiguous sample of galaxy clusters, the Constrain Dark Energy with X-ray (CODEX) sample, in which we take particular care of cluster definition. These clusters were X-ray selected using the ROentgen SATellite All-Sky Survey and then identified as galaxy clusters using the code redMaPPer run on the photometry of the Sloan Digital Sky Survey. We develop methods for precisely accounting for the sample selection effects on the clustering and demonstrate their robustness using numerical simulations. Methods. Using the clean CODEX sample, which was obtained by applying a redshift-dependent richness selection, we computed the two-point autocorrelation function of galaxy clusters in the 0.1 < z < 0.3 and 0.3 < z < 0.5 redshift bins. We compared the bias in the measured correlation function with values obtained in numerical simulations using a similar cluster mass range. Results. By fitting a power law, we measured a correlation length r 0 = 18.7 ± 1.1 and slope γ = 1.98 ± 0.14 for the correlation function in the full redshift range. By fixing the other cosmological parameters to their nine-year Wilkinson Microwave Anisotropy Probe values, we reproduced the observed shape of the correlation function under the following cosmological conditions: Ω m0 = $0.22_{-0.03}^{+0.04}$ and S 8 = σ 8 (Ω m0 /0.3)0.5 = $0.85_{-0.08}^{+0.10}$ with estimated additional systematic errors of σ Ω m0 = 0.02 and σS 8 = 0.20. We illustrate the complementarity of clustering constraints by combining them with CODEX cosmological constraints based on the X-ray luminosity function, deriving Ωm = 0.25 ± 0.01 and σ 8 = $0.81_{-0.02}^{+0.01}$ with an estimated additional systematic error of σ Ω m0 = 0.07 and σ σ8 = 0.04. The mass calibration and statistical quality of the mass tracers are the dominant source of uncertainty.

79 ASTRONOMY AND ASTROPHYSICS↗

Advanced Methods for Modeling Water-Levels and Estimating Drawdowns with SeriesSEE, an Excel Add-In

Water-level modeling is used for multiple-well aquifer tests to reliably differentiate pumping responses from natural water-level changes in wells, or environmental fluctuations. Synthetic water levels are created during water-level modeling and represent the summation of multiple component fluctuations, including those caused by environmental forcing and pumping. Pumping signals are modeled by transforming step-wise pumping records into water-level changes by using superimposed Theis functions. Water-levels can be modeled robustly with this Theis-transform approach because environmental fluctuations and pumping signals are simulated simultaneously. Water-level modeling with Theis transforms has been implemented in the program SeriesSEE, which is a Microsoft® Excel add-in. Moving average, Theis, pneumatic-lag, and gamma functions transform time series of measured values into water-level model components in SeriesSEE. Earth tides and step transforms are additional computed water-level model components. Water-level models are calibrated by minimizing a sum-of-squares objective function where singular value decomposition and Tikhonov regularization stabilize results. Drawdown estimates from a water-level model are the summation of all Theis transforms minus residual differences between synthetic and measured water levels. The accuracy of drawdown estimates is limited primarily by noise in the data sets, not the Theis-transform approach. Drawdowns much smaller than environmental fluctuations have been detected across major fault structures, at distances of more than 1 mile from the pumping well, and with limited pre-pumping and recovery data at sites across the United States. In addition to water-level modeling, utilities exist in SeriesSEE for viewing, cleaning, manipulating, and analyzing time-series data.

58 GEOSCIENCES↗

First-Principles Calculation of Water p K a Using the Newly Developed SCAN Functional

Acid/base chemistry is an intriguing topic that still constitutes a challenge for computational chemistry. While estimating the acid dissociation constant (or pK a ) could shed light on many chemistry processes, especially in the fields of biochemistry and geochemistry, evaluating the relative stability between protonated and nonprotonated species is often very difficult. Indeed, a prerequisite for calculating the pK a of any molecule is an accurate description of the energetics of water dissociation. In this study, we applied constrained molecular dynamics simulations, a noncanonical sampling technique, to investigate the water deprotonation process by selecting the OH distance as the reaction coordinate. The calculation is based on density functional theory and the newly developed SCAN functional, which has shown excellent performance in describing water structure. This first benchmark of SCAN on a chemical reaction shows that this functional accurately models the energetics of proton transfer reactions in an aqueous environment. After taking Coulomb long-range corrections and nuclear quantum effects into account, the estimated water pK a is only 1.0 pK a unit different from the target experimental value. Our results show that the combination of SCAN and constrained MD successfully reproduces the chemistry of water and constitutes a good framework for calculating the free energy of chemical reactions of interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗