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DOE OSTI2020

Hypernetwork science via high-order hypergraph walks

We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

2p x-ray absorption spectroscopy of 3d transition metal systems

This review provides an overview of the different methods and computer codes that are used to interpret 2p x-ray absorption spectra of 3d transition metal ions. We first introduce the basic parameters and give an overview of the methods used. We start with the semi-empirical multiplet codes and compare the different codes that are available. A special chapter is devoted to the user friendly interfaces that have been written on the basis of these codes. Next we discuss the first principle codes based on band structure, including a chapter on Density Functional theory based approaches. We also give an overview of the first-principle multiplet codes that start from a cluster calculation and we discuss the wavefunction based methods, including multi-reference methods. We end the review with a discussion of the link between theory and experiment and discuss the open issues in the spectral analysis.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Cluster Analysis of Combined EDS and EBSD Data to Solve Ambiguous Phase Identifications

A common problem in analytical scanning electron microscopy (SEM) using electron backscatter diffraction (EBSD) is the differentiation of phases with distinct chemistry but the same or very similar crystal structure. X-ray energy dispersive spectroscopy (EDS) is useful to help differentiate these phases of similar crystal structures but different elemental makeups. However, open, automated, and unbiased methods of differentiating phases of similar EBSD responses based on their EDS response are lacking. This paper describes a simple data analytics-based method, using a combination of singular value decomposition and cluster analysis, to merge simultaneously acquired EDS + EBSD information and automatically determine phases from both their crystal and elemental data. I use hexagonal TiB 2 ceramic contaminated with multiple crystallographically ambiguous but chemically distinct cubic phases to illustrate the method. Code, in the form of a Python 3 Jupyter Notebook, and the necessary data to replicate the analysis are provided as Supplementary material.

47 OTHER INSTRUMENTATION↗

DOE OSTI2016

Reducing uncertainties in nucleation rates: A comparison of measurements and simulations

Recently, large uncertainties in amine nucleation thermodynamics associated with the description of interactions of H{sub 2}SO{sub 4}, the key atmospheric nucleation precursor, with pre-nucleation clusters have been revealed. Here we investigate the formation of (H{sub 2}SO{sub 4}){sub 2}(H{sub 2}O){sub n} (n=0-5) clusters via H{sub 2}O–induced dimerization using conventional RI-MP2 and PW91PW91 methods and recently developed multistep BRIMP2 and B3RICC2 methods widely used in nucleation studies and compare the obtained results with measurements for equilibrium constants of H{sub 2}O–induced dimerization. Variations in K{sub p} and Gibbs free energies predicted by different methods were found to be unexpectedly large, several times of those in hydration free energies commonly used to benchmark computational quantum methods. This means that the common hydration benchmarks are not fully representative of nucleation and that the validation of quantum methods to be recommended for use in nucleation studies is impossible without a thorough assessment of H{sub 2}SO{sub 4}-H{sub 2}SO{sub 4} interactions. We show clearly that only conventional RI-MP2 and PW91PW91 methods are consistent with experiments and that a thorough validation of theoretical predictions against experimental data on H{sub 2}SO{sub 4} clustering is needed prior to recommending a quantum–chemical method for use in nucleation research. We also shows that conclusions about the role of Amine-Enhanced Ternary Homogeneous Nucleation (ATHN) in atmospheric nucleation may be affected by the large uncertainties in nucleation thermodynamics associated with the application of B3RICC2 and BRIMP2 methods and may need a thorough revision.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Quantifying resolution in cosmological N- body simulations using self-similarity

ABSTRACT We demonstrate that testing for self-similarity in scale-free simulations provides an excellent tool to quantify the resolution at small scales of cosmological N-body simulations. Analysing two-point correlation functions measured in simulations using abacus , we show how observed deviations from self-similarity reveal the range of time and distance scales in which convergence is obtained. While the well-converged scales show accuracy below 1 per cent, our results show that, with a small force softening length, the spatial resolution is essentially determined by the mass resolution. At later times, the lower cut-off scale on convergence evolves in comoving units as a−1/2 (a being the scale factor), consistent with a hypothesis that it is set by two-body collisionality. A corollary of our results is that N-body simulations, particularly at high red-shift, contain a significant spatial range in which clustering appears converged with respect to the time-stepping and force softening but has not actually converged to the physical continuum result. The method developed can be applied to determine the resolution of any clustering statistic and extended to infer resolution limits for non-scale-free simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Effect of Carbon Nanofiber Clustering on the Micromechanical Properties of a Cement Paste

The use of carbon nanofibers (CNFs) in cement systems has received significant interest over the last decade due to their nanoscale reinforcing potential. However, despite many reports on the formation of localized CNF clusters, their effect on the cement paste micromechanical properties and relation to the mechanical response at the macroscopic scale are still not fully understood. In this study, grid nanoindentation coupled with scanning electron microscopy and energy dispersive spectroscopy was used to determine the local elastic indentation modulus and hardness of a portland cement paste containing 0.2% CNFs with sub-micro and microscale CNF clusters. The presence of low stiffness and porous assemblage of phases (modulus of 15–25 GPa) was identified in the cement paste with CNFs and was attributed primarily to the interfacial zone surrounding the CNF clusters. The CNFs favored the formation of higher modulus C–S–H phases (>30 GPa) in the bulk paste at the expense of the lower stiffness C–S–H. Nanoindentation results combined with a microscale–macroscale upscaling homogenization method further revealed an elastic modulus of the CNF clusters in the range from 18 to 21 GPa, indicating that the CNF clusters acted as compliant inclusions relative to the cement paste.

36 MATERIALS SCIENCE↗

DOE OSTI2014

Open clusters in the Kepler field. II. NGC 6866

We have developed a maximum-likelihood procedure to fit theoretical isochrones to the observed cluster color-magnitude diagrams of NGC 6866, an open cluster in the Kepler spacecraft field of view. The Markov chain Monte Carlo algorithm permits exploration of the entire parameter space of a set of isochrones to find both the best solution and the statistical uncertainties. For clusters in the age range of NGC 6866 with few, if any, red giant members, a purely photometric determination of the cluster properties is not well-constrained. Nevertheless, based on our UBVRI photometry alone, we have derived the distance, reddening, age, and metallicity of the cluster and established estimates for the binary nature and membership probability of individual stars. We derive the following values for the cluster properties: (m – M) {sub V} = 10.98 ± 0.24, E(B – V) = 0.16 ± 0.04 (so the distance = 1250 pc), age =705 ± 170 Myr, and Z = 0.014 ± 0.005.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1981

The use of adaptive grids in conjunction with shock capturing methods

The use of shock capturing finite-difference techniques in computing flow fields containing shocks results in a smeared or oscillatory solution in the vicinity of the shocks. This smearing or oscillatory behavior is due to the discretized form of the governing differential equations used to compute the solution. The discretization error can be reduced by a proper clustering of mesh points in the region of the shock and by using shock aligned grids. This paper uses a simple method that was developed earlier to cluster points near the shocks and serves to introduce a new method of generating a shock aligned mesh. Applications to the one-dimensional inviscid Burgers' equation, supersonic flow over a wedge with the associated straight oblique shock, one- and two-dimensional inviscid flows through an expanding duct and the problem of a straight oblique shock in a uniform supersonic freestream are presented. Significant reduction in the oscillatory behavior of the solution is demonstrated.

Rai, M. M.↗

DOE OSTI2013

OB ASSOCIATIONS AT THE UPPER END OF THE MILKY WAY LUMINOSITY FUNCTION

The Milky Way's most luminous, young, and massive (M {approx}> 10{sup 4} M{sub Sun }) star clusters and OB associations have largely evaded detection despite knowledge of their surrounding H II regions. We search for these clusters and associations within the 40 star-forming complexes from Rahman and Murray in the 13 most luminous Wilkinson Microwave Anisotropy Probe (WMAP) free-free emission sources of the Galaxy. Selecting for objects with the dust-reddened colors of OB stars, we identify new candidate associations using the Two Micron All Sky Survey point-source catalog. In 40 star-forming complexes searched, 22 contain cluster/association candidates with sizes and masses in the range of 3'-26' and 10{sup 2.3}-10{sup 5} M{sub Sun }. Of the 22 candidates, at least seven have estimated masses {approx}> 10{sup 4} M{sub Sun }, doubling the number of such massive clusters known in the Galaxy. Only one of the searched WMAP sources remains without a candidate. Applying our method to a statistically similar set of test locations, we estimate that 3.0 {+-} 0.6 of our 22 candidate associations are unrelated to the star-forming complexes. In addition, the apparent extinctions of our candidate associations correlate well with the predictions from a Galactic model. These facts, along with the clear detection of a known OB association and the previous spectral verification of one cluster found by this method, validate our method. In eight of the most luminous WMAP sources, the candidate associations can account for the observed free-free flux. With our new compilation, the Galactic census of young, massive stellar associations may now be about half complete.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Non-pairwise additivity of the leading-order dispersion energy

The leading-order (i.e., dipole-dipole) dispersion energy is calculated for one-dimensional (1D) and two-dimensional (2D) infinite lattices, and an infinite 1D array of infinitely long lines, of doubly occupied locally harmonic wells. The dispersion energy is decomposed into pairwise and non-pairwise additive components. By varying the force constant and separation of the wells, the non-pairwise additive contribution to the dispersion energy is shown to depend on the overlap of density between neighboring wells. As well separation is increased, the non-pairwise additivity of the dispersion energy decays. The different rates of decay for 1D and 2D lattices of wells is explained in terms of a Jacobian effect that influences the number of nearest neighbors. For an array of infinitely long lines of wells spaced 5 bohrs apart, and an inter-well spacing of 3 bohrs within a line, the non-pairwise additive component of the leading-order dispersion energy is −0.11 kJ mol{sup −1} well{sup −1}, which is 7% of the total. The polarizability of the wells and the density overlap between them are small in comparison to that of the atomic densities that arise from the molecular density partitioning used in post-density-functional theory (DFT) damped dispersion corrections, or DFT-D methods. Therefore, the nonadditivity of the leading-order dispersion observed here is a conservative estimate of that in molecular clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

CODEX clusters

Context: Large area catalogs of galaxy clusters constructed from ROSAT All-Sky Survey provide the basis for our knowledge of the population of clusters thanks to long-term multiwavelength efforts to follow up observations of these clusters. Aims: The advent of large area photometric surveys superseding previous, in-depth all-sky data allows us to revisit the construction of X-ray cluster catalogs, extending the study to lower cluster masses and higher redshifts and providing modeling of the selection function. Methods: We performed a wavelet detection of X-ray sources and made extensive simulations of the detection of clusters in the RASS data. We assigned an optical richness to each of the 24 788 detected X-ray sources in the 10 382 square degrees of the Baryon Oscillation Spectroscopic Survey area using red sequence cluster finder redMaPPer version 5.2 run on Sloan Digital Sky Survey photometry. We named this survey COnstrain Dark Energy with X-ray (CODEX) clusters. Results: We show that there is no obvious separation of sources on galaxy clusters and active galactic nuclei (AGN) based on the distribution of systems on their richness. This is a combination of an increasing number of galaxy groups and their selection via the identification of X-ray sources either by chance or by groups hosting an AGN. To clean the sample, we use a cut on the optical richness at the level corresponding to the 10% completeness of the survey and include it in the modeling of the cluster selection function. We present the X-ray catalog extending to a redshift of 0.6. Conclusions: The CODEX suvey is the first large area X-ray selected catalog of northern clusters reaching fluxes of 10 –13 ergs s –1 cm –2 . We provide modeling of the sample selection and discuss the redshift evolution of the high end of the X-ray luminosity function (XLF). Our results on z < 0.3 XLF agree with previous studies, while we provide new constraints on the 0.3 < z < 0.6 XLF. We find a lack of strong redshift evolution of the XLF, provide exact modeling of the effect of low number statistics and AGN contamination, and present the resulting constraints on the flat ΛCDM.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Efficient and accurate treatment of electron correlations with correlation matrix renormalization theory

We present an efficient method for calculating the electronic structure and total energy of strongly correlated electron systems. The method extends the traditional Gutzwiller approximation for one-particle operators to the evaluation of the expectation values of two particle operators in the many-electron Hamiltonian. The method is free of adjustable Coulomb parameters, and has no double counting issues in the calculation of total energy, and has the correct atomic limit. We demonstrate that the method describes well the bonding and dissociation behaviors of the hydrogen and nitrogen clusters, as well as the ammonia composed of hydrogen and nitrogen atoms. We also show that the method can satisfactorily tackle great challenging problems faced by the density functional theory recently discussed in the literature. The computational workload of our method is similar to the Hartree-Fock approach while the results are comparable to high-level quantum chemistry calculations.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS2013

Orbit Clustering Based on Transfer Cost

We propose using cluster analysis to perform quick screening for combinatorial global optimization problems. The key missing component currently preventing cluster analysis from use in this context is the lack of a useable metric function that defines the cost to transfer between two orbits. We study several proposed metrics and clustering algorithms, including k-means and the expectation maximization algorithm. We also show that proven heuristic methods such as the Q-law can be modified to work with cluster analysis.

combinatorial optimization↗

DOE OSTI2015

Sloan Digital Sky Survey III photometric quasar clustering: Probing the initial conditions of the Universe

Here, the Sloan Digital Sky Survey has surveyed 14,555 square degrees of the sky, and delivered over a trillion pixels of imaging data. We present the large-scale clustering of 1.6 million quasars between z=0.5 and z=2.5 that have been classified from this imaging, representing the highest density of quasars ever studied for clustering measurements. This data set spans 0~ 11,00 square degrees and probes a volume of 80 h –3 Gpc 3 . In principle, such a large volume and medium density of tracers should facilitate high-precision cosmological constraints. We measure the angular clustering of photometrically classified quasars using an optimal quadratic estimator in four redshift slices with an accuracy of ~ 25% over a bin width of δ l ~ 10–15 on scales corresponding to matter-radiation equality and larger (0ℓ ~ 2–3).

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1974

ERTS-1 imagery and native plant distributions

A method is developed for using ERTS spectral signature data to determine plant community distribution and phenology without resolving individual plants. An Exotech ERTS radiometer was used near ground level to obtain spectral signatures for a desert plant community, including two shrub species, ground covered with live annuals in April and dead ones in June, and bare ground. It is shown that comparisons of scene types can be made when spectral signatures are expressed as a ratio of red reflectivity to IR reflectivity or when they are plotted as red reflectivity vs. IR reflectivity, in which case the signature clusters of each component are more distinct. A method for correcting and converting the ERTS radiance values to reflectivity values for comparison with ground truth data is appended.

Musick, H. B.↗

DOE OSTI2025

Production of alternate realizations of DESI fiber assignment for unbiased clustering measurement in data and simulations

A critical requirement of spectroscopic large scale structure analyses is correcting for selection of which galaxies to observe from an isotropic target list. This selection is often limited by the hardware used to perform the survey which will impose angular constraints of simultaneously observable targets, requiring multiple passes to observe all of them. In SDSS this manifested solely as the collision of physical fibers and plugs placed in plates. In DESI, there is the additional constraint of the robotic positioner which controls each fiber being limited to a finite patrol radius. A number of approximate methods have previously been proposed to correct the galaxy clustering statistics for these effects, but these generally fail on small scales. To accurately correct the clustering we need to upweight pairs of galaxies based on the inverse probability that those pairs would be observed (Bianchi & Percival 2017). This paper details an implementation of that method to correct the Dark Energy Spectroscopic Instrument (DESI) survey for incompleteness. To calculate the required probabilities, we need a set of alternate realizations of DESI where we vary the relative priority of otherwise identical targets. These realizations take the form of alternate Merged Target Ledgers (AMTL), the files that link DESI observations and targets. We present the method used to generate these alternate realizations and how they are tracked forward in time using the real observational record and hardware status, propagating the survey as though the alternate orderings had been adopted. We detail the first applications of this method to the DESI One-Percent Survey (SV3) and the DESI year 1 data. We include evaluations of the pipeline outputs, estimation of survey completeness from this and other methods, and validation of the method using mock galaxy catalogs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2014

A RIGOROUS FREE-FORM LENS MODEL OF A2744 TO MEET THE HUBBLE FRONTIER FIELDS CHALLENGE

Hubble Frontier Fields (HFF) imaging of the most powerful lensing clusters provides access to the most magnified distant galaxies. The challenge is to construct lens models capable of describing these complex massive, merging clusters so that individual lensed systems can be reliably identified and their intrinsic properties accurately derived. We apply the free-form lensing method (WSLAP+) to A2744, providing a model independent map of the cluster mass, magnification, and geometric distance estimates to multiply lensed sources. We solve simultaneously for a smooth cluster component on a pixel grid, together with local deflections by the cluster member galaxies. Combining model prediction with photometric redshift measurements, we correct and complete several systems recently claimed and identify four new systems totaling 65 images of 21 systems spanning a redshift range of 1.4 < z < 9.8. The reconstructed mass shows small enhancements in the directions where significant amounts of hot plasma can be seen in X-ray. We compare photometric redshifts with ''geometric redshifts'', finding a high level of self-consistency. We find excellent agreement between predicted and observed fluxes with a best-fit slope of 0.999 ± 0.013 and an rms of ∼0.25 mag, demonstrating that our magnification correction of the lensed background galaxies is very reliable. Intriguingly, few multiply lensed galaxies are detected beyond z ≅ 7.0, despite the high magnification and the limiting redshift of z ≅ 11.5 permitted by the HFF filters. With the additional HFF clusters, we can better examine the plausibility of any pronounced high-z deficit with potentially important implications for the reionization epoch and the nature of dark matter.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2020

A Classification of Ice Crystal Habits Using Combined Lidar and Scanning Polarimeter Observations during the SEAC4RS Campaign

Using collocated NASA Cloud Physics Lidar (CPL) and Research Scanning Polarimeter (RSP) data from the Studies of Emissions and Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC4RS) campaign, a new observational-based method was developed which uses a K-means clustering technique to classify ice crystal habit types into seven categories: column, plates, rosettes, spheroids, and three different type of irregulars. Intercompared with the collocated SPEC, Inc., Cloud Particle Imager (CPI) data, the frequency of the detected ice crystal habits from the proposed method presented in the study agrees within 5% with the CPI-reported values for columns, irregulars, rosettes, and spheroids, with more disagreement for plates. This study suggests that a detailed ice crystal habit retrieval could be applied to combined space-based lidar and polarimeter observations such as CALIPSO and POLDER in addition to future missions such as the Aerosols, Clouds, Convection, and Precipitation (A-CCP).

Natalie Midzak↗