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At least 325 records · Page 18

The Imaging X-Ray Polarimetry Explorer (IXPE): Technical Overview II

The Imaging X-ray Polarimetry Explorer (IXPE) will add polarization to the properties (time, energy, and position) observed in x-ray astronomy. A NASA Astrophysics Small Explorer (SMEX) in partnership with the Italian Space Agency (ASI), IXPE will measure the 2–8-keV polarization of a few dozen sources during the first 2 years following its 2021 launch. The IXPE Observatory includes three identical x-ray telescopes, each comprising a 4-m-focal-length (grazingincidence) mirror module assembly (MMA) and a polarization-sensitive (imaging) detector unit (DU), separated by a deployable optical bench. The Observatory’s Spacecraft provides typical subsystems (mechanical, structural, thermal, power, electrical, telecommunications, etc.), an attitude determination and control subsystem for 3-axis stabilized pointing, and a command and data handling subsystem communicating with the science instrument and the Spacecraft subsystems.

X-ray astronomy↗

Probabilistic Groundwater Modeling of the RDX Plume at Los Alamos National Laboratory to Support Risk Assessment - 20359

A plume of the contaminant hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) with concentrations greater than the New Mexico tap water drinking standard (9.66 ppb) is present in the regional aquifer near the southwestern boundary of Los Alamos National Laboratory (LANL). A risk assessment is performed for exposure to regional aquifer groundwater, with long-term predictions of RDX concentrations provided by a calibrated, probabilistic, numerical fate and transport model. The structure of the model is hierarchical, with the RDX Regional Aquifer (RA) groundwater model acting as the primary tool for analysis of downgradient RDX concentrations. The RA model is deeply informed by the conceptual site model (CSM) and is calibrated using site RDX concentration data and hydraulic head measurements, along with other analyses. The model is calibrated using data through December 2019. Where data are scarce other lines of evidence are used to inform inputs, including the multiphase RDX Vadose Zone (VZ) model and Pipe and Disk analytical screening tool. Model inputs are described with informative prior distributions using a robust approach to development that incorporates all available lines of evidence for every parameter used as an input to the RA model. Calibration is performed using a classical nonlinear optimization routine, which is then used to initialize a Bayesian calibration. The Bayesian calibration constrains the uncertainty in the classical calibration, ultimately providing posterior distributions for all model parameters. The challenges of the calibration include high-dimensional parameter space, including spatially heterogeneous hydraulic conductivities, comparatively sparse data, and low RDX concentrations. Posterior parameter distributions developed in the calibration process are then used for stochastic predictive model runs into the future. The result of the forward runs is spatially and temporally explicit estimates of head and concentration with uncertainty at all points in space and time. The probabilistic modeling approach presented here includes innovative computational and statistical methods that leverage high-performance computing (HPC) resources. It makes use of prior modeling work performed at the chromium plume site in the central LANL area, with extensive updates. The risk assessment will ultimately be used to support decision-making at the site, using multiple appropriately weighted sources of information, as well as uncertainty, sensitivity, and value-of-information analyses. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Improved Angular Uncertainty Estimation for Compton Imagers

Compton imaging is a method for localizing a photon source using Compton scatter events as measured by a position sensitive photon detector. Using the measured interaction positions and energy depositions for a Compton event, a cone can be back projected which represents all possible origin locations for that source photon. Given enough Compton events, the source can be localized via identifying the regions where many of these cones intersect. An illustration of this effect is given in the figure below. The region intersected by the three cones in this case is a likely origin point for the photon source.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Probing anisotropies of the Stochastic Gravitational Wave Background with LISA

Here, we investigate the sensitivity of the Laser Interferometer Space Antenna (LISA) to the anisotropies of the Stochastic Gravitational Wave Background (SGWB). We first discuss the main astrophysical and cosmological sources of SGWB which are characterized by anisotropies in the GW energy density, and we build a Signal-to-Noise estimator to quantify the sensitivity of LISA to different multipoles. We then perform a Fisher matrix analysis of the prospects of detectability of anisotropic features with LISA for individual multipoles, focusing on a SGWB with a power-law frequency profile. We compute the noise angular spectrum taking into account the specific scan strategy of the LISA detector. We analyze the case of the kinematic dipole and quadrupole generated by Doppler boosting an isotropic SGWB. We find that β Ω GW ~ 2 × 10 -11 is required to observe a dipolar signal with LISA. The detector response to the quadrupole has a factor ~ 10 3 β relative to that of the dipole. The characterization of the anisotropies, both from a theoretical perspective and from a map-making point of view, allows us to extract information that can be used to understand the origin of the SGWB, and to discriminate among distinct superimposed SGWB sources.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmic Axion Background detection using resonant cavity arrays

The axion is a well-motivated and generic extension of the Standard Model. If produced in the early universe, axions may still be relativistic today, forming a Cosmic Axion Background (CaB) potentially detectable in direct detection experiments. Although CaB is expected to be broadband, which makes it challenging to be detected, a high-quality-factor microwave cavity acts as a narrowband filter with response peaked at its resonant frequency. We propose a new strategy using multi-cavity arrays to distinguish signal from background noise by exploiting spatial correlations of the axion-induced electric field which are set by the cavity quality factor. We compute the two-point correlation function for electric fields in spatially separated cavities sourced by an isotropic CaB. Analyzing various cavity geometries, we find that stacked, wide-base cavity arrays offer coherent enhancement of the axion signal. We apply our formalism to prospective upgrades of the ADMX experiment, including configurations with four and eighteen coupled cavities. Although these arrays do not achieve a coherent enhancement, optimizing the geometry could potentially yield an $\mathcal{O}(1)$ improvement in the sensitivity to the CaB.

Axions and ALPs↗

Images in the rocket ultraviolet - Photometry of M101

It is pointed out that ultraviolet imagery of spiral galaxies is a sensitive probe of the large-scale morphology of the star-forming regions and the associated interstellar dust. A rocket-borne Ritchey-Chretien telescope was employed to obtain three ultraviolet images of the Sc 1 galaxy M101 (NGC 5457). The present investigation is concerned with the procedures for reduction and absolute calibration of the obtained images and an analysis in terms of discrete sources. Attention is also given to the radial variation and the azimuthal variation of disk and arms. It is found that the emission from M101 in the UV bandpass is dominated by extreme Population I, in the form of discrete OB/H II complexes.

Hill, J. K.↗

Silicon chemistry in interstellar clouds

Interstellar SiO was discovered shortly after CO but it has been detected mainly in high density and high temperature regions associated with outflow sources. A new model of interstellar silicon chemistry that explains the lack of SiO detections in cold clouds is presented which contains an exponential temperature dependence for the SiO abundance. A key aspect of the model is the sensitivity of SiO production by neutral silicon reactions to density and temperature, which arises from the dependence of the rate coefficients on the population of the excited fine structure levels of the silicon atom. This effect was originally pointed out in the context of neutral reactions of carbon and oxygen by Graff, who noted that the leading term in neutral atom-molecule interactions involves the quadrupole moment of the atom. Similar to the case of carbon, the requirement that Si has a quadrupole moment requires population of the J = 1 level, which lies 111K above the J = 0 ground state and has a critical density n(cr) equal to or greater than 10(6)/cu cm. The SiO abundance then has a temperature dependence proportional to exp(-111/T) and a quadratic density dependence for n less than n(cr). As part of the explanation of the lack of SiO detections at low temperatures and densities, this model also emphasizes the small efficiencies of the production routes and the correspondingly long times needed to reach equilibrium. Measurements of the abundance of SiO, in conjunction with theory, can provide information on the physical properties of interstellar clouds such as the abundances of oxygen bearing molecules and the depletion of interstellar silicon.

Langer, William D.↗

Rapid Airplane Parametric Input Design (RAPID)

RAPID is a methodology and software system to define a class of airplane configurations and directly evaluate surface grids, volume grids, and grid sensitivity on and about the configurations. A distinguishing characteristic which separates RAPID from other airplane surface modellers is that the output grids and grid sensitivity are directly applicable in CFD analysis. A small set of design parameters and grid control parameters govern the process which is incorporated into interactive software for 'real time' visual analysis and into batch software for the application of optimization technology. The computed surface grids and volume grids are suitable for a wide range of Computational Fluid Dynamics (CFD) simulation. The general airplane configuration has wing, fuselage, horizontal tail, and vertical tail components. The double-delta wing and tail components are manifested by solving a fourth order partial differential equation (PDE) subject to Dirichlet and Neumann boundary conditions. The design parameters are incorporated into the boundary conditions and therefore govern the shapes of the surfaces. The PDE solution yields a smooth transition between boundaries. Surface grids suitable for CFD calculation are created by establishing an H-type topology about the configuration and incorporating grid spacing functions in the PDE equation for the lifting components and the fuselage definition equations. User specified grid parameters govern the location and degree of grid concentration. A two-block volume grid about a configuration is calculated using the Control Point Form (CPF) technique. The interactive software, which runs on Silicon Graphics IRIS workstations, allows design parameters to be continuously varied and the resulting surface grid to be observed in real time. The batch software computes both the surface and volume grids and also computes the sensitivity of the output grid with respect to the input design parameters by applying the precompiler tool ADIFOR to the grid generation program. The output of ADIFOR is a new source code containing the old code plus expressions for derivatives of specified dependent variables (grid coordinates) with respect to specified independent variables (design parameters). The RAPID methodology and software provide a means of rapidly defining numerical prototypes, grids, and grid sensitivity of a class of airplane configurations. This technology and software is highly useful for CFD research for preliminary design and optimization processes.

Smith, Robert E.↗

Extra-Solar Planetary Imager (ESPI) for Space Based Jovian Planetary Detection

We report on out Extra-Solar Planetary Imager (ESPI) study for a recent Midex (NASA Medium Class Explorer Mission) proposal. Proposed for ESPI was a 1.5 x 1.5 square meter Jacquinot apodized square aperture telescope. The combination of apodization and a square aperture telescope significantly reduces the diffracted light from a bright central source over much of the telescope focal plane. As a result, observations of very faint astronomical objects next to bright sources with angular separations as small as 0.32 arcseconds become possible. This permits a sensitive search for exo-planets in reflected light. The system is capable of detecting a Jupiter-like planet in a relatively long-period orbit around as many as 160 to 175 stars with a signal-to-noise ratio greater than 5 in observations lasting maximally 100 hours per star. We discuss the effects of wavefront error, mirror speckle, pointing error and signal-to-noise issues, as well as the scalability of our ESPI study with respect to NASA's Terrestrial Planet Finder mission.

Lyon, Rick G.↗

High-Performance Reaction Wheel Optimization for Fine-Pointing Space Platforms: Minimizing Induced Vibration Effects on Jitter Performance plus Lessons Learned from Hubble Space Telescope for Current and Future Spacecraft Applications

The Hubble Space Telescope (HST) applies large-diameter optics (2.5-m primary mirror) for diffraction-limited resolution spanning an extended wavelength range (approx. 100-2500 nm). Its Pointing Control System (PCS) Reaction Wheel Assemblies (RWAs), in the Support Systems Module (SSM), acquired an unprecedented set of high-sensitivity Induced Vibration (IV) data for 5 flight-certified RWAs: dwelling at set rotation rates. Focused on 4 key ratios, force and moment harmonic values (in 3 local principal directions) are extracted in the RWA operating range (0-3000 RPM). The IV test data, obtained under ambient lab conditions, are investigated in detail, evaluated, compiled, and curve-fitted; variational trends, core causes, and unforeseen anomalies are addressed. In aggregate, these values constitute a statistically-valid basis to quantify ground test-to-test variations and facilitate extrapolations to on-orbit conditions. Accumulated knowledge of bearing-rotor vibrational sources, corresponding harmonic contributions, and salient elements of IV key variability factors are discussed. An evolved methodology is presented for absolute assessments and relative comparisons of macro-level IV signal magnitude due to micro-level construction-assembly geometric details/imperfections stemming from both electrical drive and primary bearing design parameters. Based upon studies of same-size/similar-design momentum wheels' IV changes, upper estimates due to transitions from ground tests to orbital conditions are derived. Recommended HST RWA choices are discussed relative to system optimization/tradeoffs of Line-Of-Sight (LOS) vector-pointing focal-plane error driven by higher IV transmissibilities through low-damped structural dynamics that stimulate optical elements. Unique analytical disturbance results for orbital HST accelerations are described applicable to microgravity efforts. Conclusions, lessons learned, historical context/insights, and perspectives on future applications are given; these previously unpublished data and findings represents a valuable resource for fine-pointing spacecraft or space-based platforms using RWAs, Control Moment Gyros (CMGs), Momentum Wheels, or other ball-bearing-based rotational units.

Hasha, Martin D.↗

Moiré commensurability and the quantum anomalous Hall effect in twisted bilayer graphene on hexagonal boron nitride

The quantum anomalous Hall (QAH) effect is sometimes observed in twisted bilayer graphene (tBG) when it is nearly aligned with an encapsulating hexagonal boron nitride (hBN) layer. We propose that the appearance or absence of the QAH effect in individual devices could be related to commensurability between the graphene/graphene and graphene/hBN moiré patterns. We identify a series of points in the (θ GG , θ GBN ) twist-angle space at which the two moiré patterns are commensurate, allowing moiré band theory to be applied, and we show that the band Chern numbers are in this case sensitive to a rigid in-plane hBN displacement. Given this property, we argue that the QAH effect is likely only when (i) the (θ GG , θ GBN ) twist-angle-pair is close enough to a commensurate point that the two moiré patterns yield a supermoiré pattern with a sufficiently long length scale, and (ii) the supermoiré has a percolating topologically nontrivial QAH phase. For twist angles far from commensurability, the hBN layer acts as a source of disorder that can destroy the QAH effect. Our proposal can explain a number of current experimental observations. Finally, further experimental studies that can test this proposal more directly are suggested.

36 MATERIALS SCIENCE↗

Black Holes and Neutron Stars in Nearby Galaxies: Insights from NuSTAR

Nearby galaxy surveys have long classified X-ray binaries (XRBs) by the mass category of their donor stars (high-mass and low-mass). The NuSTAR (Nuclear Spectroscopic Telescope Array) observatory, which provides imaging data at E greater than 10 keV (kiloelectronvolts), has enabled the classification of extragalactic XRBs by their compact object type: neutron star (NS) or black hole (BH). We analyzed NuSTAR/Chandra/XMM-Newton observations from a NuSTAR-selected sample of 12 galaxies within 5 Mpc (megaparsecs) having stellar masses (M (sub asterisk)) 10 (sup 7-11) solar masses and star formation rates (SFRs) approximately 0.01-15 solar masses per year. We detected 128 NuSTAR sources to a sensitivity of 10 (sup 38) ergs per second. Using NuSTAR color-intensity and color-color diagrams we classified 43 of these sources as candidate NSs and 47 as candidate BHs. We further subdivide BHs by accretion states (soft, intermediate, and hard) and NSs by weak (Z/Atoll) and strong (accreting pulsar) magnetic field. Using eight normal (Milky Way-type) galaxies in the sample, we confirm the relation between the SFR and galaxy X-ray point source luminosity in the 4-25 and 12-25 keV energy bands. We also constrained galaxy X-ray point source luminosity using the relation L (sub X) equals M (sub asterisk) plus Beta SFR, finding agreement with previous work. The X-ray luminosity function (XLF) of all sources in the 4-25 and 12-25 keV energy bands matches the alpha = 1.6 slope for high-mass XRBs. We find that NS XLFs suggest a decline beginning at the Eddington limit for a 1.4 solar mass NS, whereas the BH fraction shows an approximate monotonic increase in the 4-25 and 12-25 keV energy bands. We calculate the overall ratio of BH to NS to be approximately 1 for 4-25 keV and approximately 2 for 12-25 keV.

Vulic, N.↗

Far Ultraviolot Space Telescope (FAUST)

The Far Ultraviolet Space Telescope is a compact, wide field-of-view, far ultraviolet instrument designed for observations of extended and point sources of astronomical interest. It was originally used in sounding rocket work by both French and American investigators. The instrument was modified for flight on the space shuttle and flew on the Spacelab 1 mission as a joint effort between the Laboratoire d'Astronomie Spatiale and the University of California, Berkeley. The prime experiment objective of this telescope on the Atmospheric Laboratory Applications and Science (ATLAS 1) NASA mission is to observe faint astronomical sources in the far ultraviolet with sensitivities far higher than previously available. The experiment will cover the 1300 to 1800 A band, which is inaccessible to observers on earth. The observing program during the mission consists of obtaining deep sky images during spacecraft nighttime. The targets will include hot stars and nebulae in our own galaxy, faint diffuse galactic features similar to the cirrus clouds seen by the Infrared Astronomical Satellite (IRAS), large nearby galaxies, nearby clusters of galaxies, and objects of cosmological interest such as quasars and the diffuse far ultraviolet background.

Bowyer, S.↗

X-ray QPOs from the Ultra-luminous X-ray Source in M82: Evidence Against Beaming

We report the discovery with the European Photon Imaging Camera (EPIC) CCD cameras onboard XMM-Newton of a 54 mHz quasiperiodic oscillation (QPO) in the greater than 2 keV X-ray flux from the ultra-luminous X-ray source (ULX) X41.4+60 in the starburst galaxy M82. This is the first detection of a QPO in the X-ray flux from an extra-Galactic ULX, and confirms that the source is a compact object. The QPO is detected in the combined PN and MOS data at the approx. 6sigma level, and separately at lower significances in both the PN and MOS instruments. It had a centroid frequency of 54.3 +/- 0.9 mHz, a coherence Q is identical with nu(sub 0)/Delta nu(sub fwhm) is approx. 5, and an amplitude (rms) in the 2 - 10 keV band of 8.5%. Below about 0.2 Hz the power spectrum can be described by a power-law with index approx. 1, and integrated amplitude (rms) of 13.5%. The X-ray spectrum requires a curving continuum, with a disk-blackbody (diskbb) at T = 3.1 keV providing an acceptable, but not unique, fit. A broad Fe line centered at 6.55 keV is required in all fits, but the equivalent width (EW) of the line is sensitive to the choice of continuum model. There is no evidence of a reflection component. The implied bolometric luminosity is approx. 4 - 5 x 10(exp 40) ergs/s. Data from several archival Rossi X-ray Timing Explorer (RXTE) pointings at M82 also show evidence for QPOs in the 50 - 100 mHz frequency range. Several Galactic black hole candidates (BHCs), including GRS 1915+105, GRO J1655-40, and XTE 1550-564, show QPOs in the same frequency range as the 50 - 100 mHz QPOs in X41.4+60, which at first glance suggests a possible connection with such objects. However, strong, narrow QPOs provide solid evidence for disk emission, and thus present enormous theoretical difficulties for models which rely on either geometrically or relativistically beamed emission to account for the high X-ray luminosities. We discuss the implications of our findings for models of the ULX sources.

Strohmayer, Tod E.↗

Assessment of oil and gas fields in California as potential CO 2 storage sites

California's total annual greenhouse gas (GHG) emissions (425.3 MtCO 2 e) in 2018 were about 6.4% of the US total (6,677 MtCO 2 e) and around 1% of global emissions. About 39% of 2018 GHG emissions in California were from the industrial and electrical sectors. Many of these emissions were from large stationary point sources and were suitable for carbon capture retrofit with subsequent storage of the captured carbon dioxide (CO 2 ) in geological formations. Previous studies of California found suitable geology and CO 2 storage resource. This study refines and furthers prior work using a three-stage screening process of oil fields, gas fields, and underground natural gas storage (UGS) sites by combining criteria from previous studies while excluding sites that pose technical risk or are located in regions with surface restrictions including sensitive habitats and dense populations. In the first stage, 129 CO 2 storage sites in California were identified using qualification criteria based upon formation properties including geological conditions and pore pressure. The second stage identified sensitive sites by applying conservative screens including seismic activity, faulting, population density, restricted lands, and sensitive habitats. During the third stage, 61 CO 2 potential storage sites were identified by subtraction of stage 2 areas from stage 1. The potential storage volume in the third stage ranged from 1.0 to 2.0 GtCO 2 . Finally, we applied a scoring system with seven parameters to rank the 61 potential sites based on subsurface technical criteria. The scored sites are classified as high priority, medium priority, and sites for future study. Prospective CO 2 storage sites with high and moderate priority were selected and linked to CO 2 sources. There are 14 prospective sites (above 20 MtCO 2 storage resource per site) with a total storage resource of 1024 MtCO 2 distributed in Northern and Southern California. Of these sites, there are 9 potential CO 2 -EOR sites and 1 depleted oil field with a total estimated CO 2 storage volume of ~800 MtCO 2 in the Southern San Joaquin and Ventura Basin. These 10 prospective sites with a storage resource greater than 20 MtCO 2 could potentially deliver more than 20 years of storage with an average injection rate of 40 MtCO 2 /year. The remaining 4 highly prospective sites are in Northern California. Additionally, study results suggest that saline formations should be re-evaluated in concert with storage in oil, gas, and natural gas storage reservoirs.

58 GEOSCIENCES↗

Using TDRSS as an orbiting VLBI observatory

The procedures and results of experimental VLBI astronomical observations performed using TDRSE, the first deployed satellite of the NASA TDRSS, as one of the network telescopes are reviewed. The other two elements of the VLBI network were the high-sensitivity 64-m antennas of the NASA DSN in Australia and of ISAS in Japan, with a 25-m Japanese antenna used to check their performance. The E configuration of the Mark III recording system at White Sands was used to record seven contiguous 2-MHz channels centered at 2.27799 GHz during five 3-h periods in July-August 1986. Although satellite pointing failures and ground-station problems limited the number of useful observations to six, interferometric fringes of the sources were obtained in all of these observations, demonstrating the feasibility of the approach.

Ulvestad, James S.↗

Orbit determination error analysis and comparison of station-keeping costs for Lissajous and halo-type libration point orbits and sensitivity analysis using experimental design techniques

Spacecraft in orbit near libration point L1 in the Sun-Earth system are excellent platforms for research concerning solar effects on the terrestrial environment. One spacecraft mission launched in 1978 used an L1 orbit for nearly 4 years, and future L1 orbital missions are also being planned. Orbit determination and station-keeping are, however, required for these orbits. In particular, orbit determination error analysis may be used to compute the state uncertainty after a predetermined tracking period; the predicted state uncertainty levels then will impact the control costs computed in station-keeping simulations. Error sources, such as solar radiation pressure and planetary mass uncertainties, are also incorporated. For future missions, there may be some flexibility in the type and size of the spacecraft's nominal trajectory, but different orbits may produce varying error analysis and station-keeping results. The nominal path, for instance, can be (nearly) periodic or distinctly quasi-periodic. A periodic 'halo' orbit may be constructed to be significantly larger than a quasi-periodic 'Lissajous' path; both may meet mission requirements, but perhaps the required control costs for these orbits are probably different. Also for this spacecraft tracking and control simulation problem, experimental design methods can be used to determine the most significant uncertainties. That is, these methods can determine the error sources in the tracking and control problem that most impact the control cost (output); it also produces an equation that gives the approximate functional relationship between the error inputs and the output.

Gordon, Steven C.↗

Spontaneous Raman–LIF–CO–OH measurements of species concentration in turbulent spray flames

This paper presents new measurements of species concentrations, temperature and mixture fraction in selected regions of a turbulent ethanol spray flame. The line-Raman–LIF–COsingle bondOH setup developed at the Sandia's Combustion Research Facility is utilised to probe regions of a spray flame where laser breakdown of liquid droplets is avoided and the remaining interferences can be corrected. The spray flame is stabilised on the piloted Sydney needle spray burner, where axial translation of the liquid injecting needle in the air-blast stream can transition the spray from dilute to dense. The solution to obtaining successful measurements is found to be multifaceted and includes: the appropriate selection of flame conditions; high sensitivity of the Raman detection system permitting reduced laser energies; development of a pre-processing algorithm to reject strong droplet interferences; and application of the hybrid matrix inversion method combined with wavelet denoising to account for interference corrections and noise at the very low signal levels obtained. Unique and necessary for the successful measurements reported in this paper, a pre-processing algorithm is outlined that removes data points corrupted with strong interferences from droplets. These interferences arise from a range of sources, but the most intense are due to the laser interaction with surrounding mist or liquid fragments, such that measurements near the jet centreline are corrupted and hence discarded. Reliable measurements of mixture fraction, temperature obtained from the sum of the species number densities, and species mole fractions are reported for regions in the flames sufficiently far from the centreline. The paper demonstrates the feasibility of the judicious use of Raman scattering in turbulent spray flames, the results of which will be extremely useful for validating numerical simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗