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At least 1,153 records · Page 64

Globular cluster photometry with the Hubble Space Telescope. I - Description of the method and analysis of the core of 47 Tuc

Accurate photometry for individual post-main-sequence stars in the core of the Galactic globular cluster 47 Tuc is presented and analyzed using an empirical point spread function model and Monte Carlo simulations. A V vs. V-I color-magnitude diagrams is constructed which shows several distinct stellar types, including RGB and HB stars. Twenty-four blue straggler stars are detected in 47 Tuc, more concentrated toward the center of the cluster than the giants. This supports the hypothesis is that the stragglers are either coalesced stars or members of binary systems that are more massive than single stars. The radial profile of the projected stellar density is flat in the central region of 47 Tuc with a core radius of 23 +/- 2 arcsec. No signature of a collapsed core is evident. The observed radial cumulative distribution of stars rules out the presence of a massive compact object in the center.

Guhathakurta, Puragra↗

Joint inference of multiplicative and additive systematics in galaxy density fluctuations and clustering measurements

Galaxy clustering measurements are a key probe of the matter density field in the Universe. With the era of precision cosmology upon us, surveys rely on precise measurements of the clustering signal for meaningful cosmological analysis. However, the presence of systematic contaminants can bias the observed galaxy number density, and thereby bias the galaxy two-point statistics. As the statistical uncertainties get smaller, correcting for these systematic contaminants becomes increasingly important for unbiased cosmological analysis. We present and validate a new method for understanding and mitigating both additive and multiplicative systematics in galaxy clustering measurements (two-point function) by joint inference of contaminants in the galaxy overdensity field (one-point function) using a maximum-likelihood estimator (MLE). We test this methodology with Kilo-Degree Survey-like mock galaxy catalogues and synthetic systematic template maps. We estimate the cosmological impact of such mitigation by quantifying uncertainties and possible biases in the inferred relationship between the observed and the true galaxy clustering signal. Our method robustly corrects the clustering signal to the sub-percent level and reduces numerous additive and multiplicative systematics from 1.5σ to less than 0.1σ for the scenarios we tested. In addition, we provide an empirical approach to identifying the functional form (additive, multiplicative, or other) by which specific systematics contaminate the galaxy number density. Even though this approach is tested and geared towards systematics contaminating the galaxy number density, the methods can be extended to systematics mitigation for other two-point correlation measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

AGB sodium abundances in the globular cluster 47 Tucanae (NGC 104)

A recent analysis comparing the [Na/Fe] distributions of red giant branch (RGB) and asymptotic giant branch (AGB) stars in the Galactic globular cluster NGC 6752 found that the ratio of Na-poor to Na-rich stars changes from 30:70 on the RGB to 100:0 on the AGB. The surprising paucity of Na-rich stars on the AGB in NGC 6752 warrants additional investigations to determine if the failure of a significant fraction of stars to ascend the AGB is an attribute common to all globular clusters. Therefore, we present radial velocities, [Fe/H], and [Na/Fe] abundances for 35 AGB stars in the Galactic globular cluster 47 Tucanae (47 Tuc; NGC 104), and compare the AGB [Na/Fe] distribution with a similar RGB sample published previously. The abundances and velocities were derived from high-resolution spectra obtained with the Michigan/Magellan Fiber System and MSpec spectrograph on the Magellan–Clay 6.5 m telescope. We find the average heliocentric radial velocity and [Fe/H] values to be 〈RV{sub helio.}〉 = −18.56 km s{sup −1} (σ = 10.21 km s{sup −1}) and 〈[Fe/H]〉 = −0.68 (σ = 0.08), respectively, in agreement with previous literature estimates. The average [Na/Fe] abundance is 0.12 dex lower in the 47 Tuc AGB sample compared to the RGB sample, and the ratio of Na-poor to Na-rich stars is 63:37 on the AGB and 45:55 on the RGB. However, in contrast to NGC 6752, the two 47 Tuc populations have nearly identical [Na/Fe] dispersion and interquartile range values. The data presented here suggest that only a small fraction (≲20%) of Na-rich stars in 47 Tuc may fail to ascend the AGB, which is a similar result to that observed in M13. Regardless of the cause for the lower average [Na/Fe] abundance in AGB stars, we find that Na-poor stars and at least some Na-rich stars in 47 Tuc evolve through the early AGB phase. The contrasting behavior of Na-rich stars in 47 Tuc and NGC 6752 suggests that the RGB [Na/Fe] abundance alone is insufficient for predicting if a star will ascend the AGB.

79 ASTRONOMY AND ASTROPHYSICS↗

PHYSICAL PROPERTIES OF THE B AND Be STAR POPULATIONS OF h AND {chi} PERSEI

We present a study of the B and Be star populations of the double cluster h and {chi} Persei. Blue optical spectroscopy is used to first measure projected rotational velocity, V sin i, effective surface temperature, T{sub eff}, and surface gravity, log g, for B-type sample stars, while available Stroemgren photometry is used to calculate T{sub eff} and log g for the Be stars showing emission. In our sample of 104 objects for which we measured these stellar parameters, 28 are known or proposed Be stars. Of these Be stars, 22 show evidence of emission at the times of our observations, and furthermore, we find evidence in our data and the literature for at least 8 transient Be stars in the clusters. We find that the Be stars are not rotating near their critical velocity, contrary to the results of studies of similar open clusters. We compare the results of our analysis with other previous studies and find that the cluster members are more evolved than found by Huang and Gies but still retain much of their initial rotational angular momentum.

79 ASTRONOMY AND ASTROPHYSICS↗

On the physical size of the Milky Way globular cluster NGC 7089 (M2)

ABSTRACT We study the outer regions of the Milky Way globular cluster NGC 7089 based on new Dark Energy Camera observations. The resulting background-cleaned stellar density profile reveals the existence of an extended envelope. We confirm previous results that cluster stars are found out up to ∼1° from the cluster’s centre, which is nearly three times the value of the most robust tidal radii estimations. We also used results from direct N-body simulations in order to compare with the observations. We found a fairly good agreement between the observed and numerically generated stellar density profiles. Because of the existence of gaps and substructures along globular cluster tidal tails, we closely examined the structure of the outer cluster region beyond the Jacobi radius. We extended the analysis to a sample of 35 globular clusters, 20 of them with observed tidal tails. We found that if the stellar density profile follows a power law ∝ r−α, the α slope correlates with the globular cluster present mass, in the sense that, the more massive the globular cluster, the smaller the α value. This trend is not found in globular clusters without observed tidal tails. The origin of such a phenomenon could be related, among other reasons, to the proposed so-called potential escapers or to the formation of globular clusters within dark matter minihaloes.

79 ASTRONOMY AND ASTROPHYSICS↗

The Dynamics of the Wide-angle Tailed (WAT) Galaxy Cluster A562

We present the first in-depth dynamical analysis of the archetypal wide-angle tailed (WAT) cluster A562. We have combined Gemini observations with archival data from the literature to form a sample of 76 cluster members and derived a mean redshift of 0.1088 ± 0.0004 and a velocity dispersion of 919 ± 116 km s{sup −1}. This relatively large velocity dispersion suggests either a very massive cluster (M {sub dyn} > 6.9 × 10{sup 14} M {sub ☉}) and/or a merger system. The merger model is supported by a non-Gaussian galaxy velocity distribution, an elongated spatial distribution of likely cluster members, and an elongated X-ray emitting gas. This scenario would generate the bulk flow motion of the intracluster medium that can exert enough ram pressure to bend the radio jets. Thus, our observations support the model in which a recent off-axis merger event produced the cluster wide conditions needed to shape the WAT in A562.

79 ASTRONOMY AND ASTROPHYSICS↗

Multiresolution edge detection using enhanced fuzzy c-means clustering for ultrasound image speckle reduction

Purpose: Speckle suppression in ultrasound (US) images of various anatomic structures via a novel speckle noise reduction algorithm. Methods: The proposed algorithm employs an enhanced fuzzy c-means (EFCM) clustering and multiresolution wavelet analysis to distinguish edges from speckle noise in US images. The edge detection procedure involves a coarse-to-fine strategy with spatial and interscale constraints so as to classify wavelet local maxima distribution at different frequency bands. As an outcome, an edge map across scales is derived whereas the wavelet coefficients that correspond to speckle are suppressed in the inverse wavelet transform acquiring the denoised US image. Results: A total of 34 thyroid, liver, and breast US examinations were performed on a Logiq 9 US system. Each of these images was subjected to the proposed EFCM algorithm and, for comparison, to commercial speckle reduction imaging (SRI) software and another well-known denoising approach, Pizurica's method. The quantification of the speckle suppression performance in the selected set of US images was carried out via Speckle Suppression Index (SSI) with results of 0.61, 0.71, and 0.73 for EFCM, SRI, and Pizurica's methods, respectively. Peak signal-to-noise ratios of 35.12, 33.95, and 29.78 and edge preservation indices of 0.94, 0.93, and 0.86 were found for the EFCM, SIR, and Pizurica's method, respectively, demonstrating that the proposed method achieves superior speckle reduction performance and edge preservation properties. Based on two independent radiologists’ qualitative evaluation the proposed method significantly improved image characteristics over standard baseline B mode images, and those processed with the Pizurica's method. Furthermore, it yielded results similar to those for SRI for breast and thyroid images significantly better results than SRI for liver imaging, thus improving diagnostic accuracy in both superficial and in-depth structures. Conclusions: A new wavelet-based EFCM clustering model was introduced toward noise reduction and detail preservation. The proposed method improves the overall US image quality, which in turn could affect the decision-making on whether additional imaging and/or intervention is needed.

60 APPLIED LIFE SCIENCES↗

Dark Energy Survey Year 1 results: constraints on intrinsic alignments and their colour dependence from galaxy clustering and weak lensing

Abstract We perform a joint analysis of intrinsic alignments and cosmology using tomographic weak lensing, galaxy clustering, and galaxy–galaxy lensing measurements from Year 1 (Y1) of the Dark Energy Survey. We define early- and late-type subsamples, which are found to pass a series of systematics tests, including for spurious photometric redshift error and point spread function correlations. We analyse these split data alongside the fiducial mixed Y1 sample using a range of intrinsic alignment models. In a fiducial non-linear alignment model analysis, assuming a flat Λ cold dark matter cosmology, we find a significant difference in intrinsic alignment amplitude, with early-type galaxies favouring $A_\mathrm{IA} = 2.38^{+0.32}_{-0.31}$ and late-type galaxies consistent with no intrinsic alignments at $0.05^{+0.10}_{-0.09}$. The analysis is repeated using a number of extended model spaces, including a physically motivated model that includes both tidal torquing and tidal alignment mechanisms. In multiprobe likelihood chains in which cosmology, intrinsic alignments in both galaxy samples and all other relevant systematics are varied simultaneously, we find the tidal alignment and tidal torquing parts of the intrinsic alignment signal have amplitudes $A_1 = 2.66 ^{+0.67}_{-0.66}$, $A_2=-2.94^{+1.94}_{-1.83}$, respectively, for early-type galaxies and $A_1 = 0.62 ^{+0.41}_{-0.41}$, $A_2 = -2.26^{+1.30}_{-1.16}$ for late-type galaxies. In the full (mixed) Y1 sample the best constraints are $A_1 = 0.70 ^{+0.41}_{-0.38}$, $A_2 = -1.36 ^{+1.08}_{-1.41}$. For all galaxy splits and IA models considered, we report cosmological parameter constraints consistent with the results of the main DES Y1 cosmic shear and multiprobe cosmology papers.

79 ASTRONOMY AND ASTROPHYSICS↗

RED SUPERGIANTS AS COSMIC ABUNDANCE PROBES: THE FIRST DIRECT METALLICITY DETERMINATION OF NGC 4038 IN THE ANTENNAE

We present a direct determination of the stellar metallicity in the close pair galaxy NGC 4038 (D = 20 Mpc) based on the quantitative analysis of moderate-resolution KMOS/Very Large Telescope spectra of three super star clusters. The method adopted in our analysis has been developed and optimized to measure accurate metallicities from atomic lines in the J-band of single red supergiant (RSG) or RSG-dominated star clusters. Hence, our metallicity measurements are not affected by the biases and poorly understood systematics inherent to strong line H ii methods, which are routinely applied to massive data sets of galaxies. We find [Z] = +0.07 ± 0.03 and compare our measurements to H ii strong line calibrations. Our abundances and literature data suggest the presence of a flat metallicity gradient, which can be explained as redistribution of metal-rich gas following the strong interaction.

79 ASTRONOMY AND ASTROPHYSICS↗

Accelerating the Structure Exploration of Diverse Bi–Pt Nanoclusters via Physics‐Informed Machine Learning Potential and Particle Swarm Optimization

Bimetallic Bi–Pt nanoclusters exhibit diverse structural motifs, including core-shell, Janus, and mixed alloy configurations, due to the unique bonding characteristics between Bi and Pt atoms. Using density functional theory refinements from ChIMES physically machine-learned potential and CALYPSO particle swarm optimization global searches, 34 Bi20-Pt20 nanoclusters are systematically classified. The results reveal that Bi atoms predominantly occupy surface sites, driven by charge transfer effects. Cohesive energy trends alone prove insufficient for structure differentiation, necessitating a data-driven approach employing principal component analysis and K-means clustering. Furthermore, vibrational, electronic, and infrared spectral analyses provide additional insights into structure-property relationships. The findings offer an original framework for the automated classification and analysis of bimetallic nanoclusters, enhancing the understanding of their stability and functional properties.

bimetallic nanoparticles↗

The Aemulus Project. III. Emulation of the Galaxy Correlation Function

Using the N-body simulations of the Aemulus Project, we construct an emulator for the nonlinear clustering of galaxies in real and redshift space. We construct our model of galaxy bias using the halo occupation framework, accounting for possible velocity bias. The model includes 15 parameters, including both cosmological and galaxy bias parameters. We demonstrate that our emulator achieves ~1% precision at the scales of interest, 0.1 h -1 Mpc < r < 10 h -1 Mpc, and recovers the true cosmology when tested against independent simulations. Our primary parameters of interest are related to the growth rate of structure, f, and its degenerate combination, fσ 8 . Using this emulator, we show that the constraining power on these parameters monotonically increases as smaller scales are included in the analysis, all the way down to 0.1 h -1 Mpc. For a BOSS-like survey, the constraints on fσ 8 from r < 30 h -1 Mpc scales alone are nearly a factor of two tighter than those from the fiducial BOSS analysis of redshift-space clustering using perturbation theory at larger scales. The combination of real- and redshift-space clustering allows us to break the degeneracy between f and σ 8, yielding an 11% constraint on f alone for a BOSS-like analysis. The current Aemulus simulations limit this model to surveys of massive galaxies. Future simulations will allow this framework to be extended to all galaxy target types, including emission-line galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

High‐fidelity detection of crop biomass quantitative trait loci from low‐cost imaging in the field

Abstract Field‐based, rapid, and nondestructive techniques for assessing plant productivity are needed to accelerate the discovery of genotype‐to‐phenotype relationships in next‐generation biomass grass crops. The use of hemispherical imaging and light attenuation modeling was evaluated against destructive harvest measures with respect to their ability to accurately capture phenotypic and genotypic relationships in a field‐grown grass crop. Plant area index ( PAI ) estimated from below‐canopy hemispherical images, as well as a suite of thirteen traits assessed by manual destructive harvests, were measured in a Setaria recombinant inbred line mapping population segregating for aboveground productivity and architecture. A significant correlation was observed between PAI and biomass production across the population at maturity ( r 2 = .60), as well as for select diverse genotypes sampled repeatedly over the growing season ( r 2 = .79). Twenty‐seven quantitative trait loci ( QTL ) were detected for manually collected traits associated with biomass production. Of these, twenty‐one were found in four clusters of colocalized QTL . Analysis of image‐based estimates of PAI successfully identified all four QTL hot spots for biomass production. QTL for PAI had greater overlap with those detected for traits associated with biomass production than with those for plant architecture and biomass partitioning. Hemispherical imaging is an affordable and scalable method, which demonstrates how high‐throughput phenotyping can identify QTL related to biomass production of field trials in place of destructive harvests that are labor, time, and material intensive.

09 BIOMASS FUELS↗

Subsurface microbial communities as a tool for characterizing regional-scale groundwater flow

Subsurface microbial community distribution patterns are influenced by biogeochemical and groundwater fluxes and may inform hydraulic connections along groundwater-flow paths. This study examined the regional-scale microbial community of the Death Valley Regional Flow System and evaluated whether subsurface communities can be used to identify groundwater-flow paths between recharge and discharge areas. Samples were collected from 36 sites in three groundwater basins: Pahute Mesa–Oasis Valley (PMOV), Ash Meadows (AM), and Alkali Flat–Furnace Creek Ranch (AFFCR). Microbial diversity within and between communities varied by location, and communities were separated into two overall groups that affiliated with the AM and PMOV/AFFCR basins. Network analysis revealed patterns between clusters of common microbes that represented groundwaters with similar geochemical conditions and largely corroborated hydraulic connections between recharge and discharge areas. Null model analyses identified deterministic and stochastic ecological processes contributing to microbial community assemblages. Most communities were more different than expected and governed by dispersal limitation, geochemical differences, or undominating processes. However, certain communities from sites located within or near the Nevada National Security Site were more similar than expected and dominated by homogeneous dispersal or selection. Overall, the (dis)similarities between the microbial communities of DVRFS recharge and discharge areas supported previously documented hydraulic connections between: (1) Spring Mountains and Ash Meadows; (2) Frenchman and Yucca Flat and Amargosa Desert; and (3) Amargosa Desert and Death Valley. However, only a portion of the flow path between Pahute Mesa and Oasis Valley could be supported by microbial community analyses, likely due to well-associated artifacts in samples from the two Oasis Valley sites. This study demonstrates the utility of combining microbial data with hydrologic, geologic, and water-chemistry information to comprehensively characterize groundwater systems, highlighting both strengths and limitations of this approach.

54 ENVIRONMENTAL SCIENCES↗

Thiohalorhabdus methylotropha sp. nov., an extremely halophilic autotrophic methylotiotroph from hypersaline lakes

So far, there have been no reports of trimethylamine (TMA)-utilizing extremely halophilic microorganisms in hypersaline habitats. Our aerobic enrichments at 4 M total Na + with 5 mM TMA inoculated with surface sediments from hypersaline soda (at pH 9.5) or chloride-sulfate (at pH 7) lakes in southwestern Siberia were successful only for the latter. The initial enrichment included both bacteria and haloarchaea but only the bacterial component was able to grow as a pure culture with TMA. Strain Cl-TMA forms a new-species lineage within the genus Thiohalorhabdus which includes extremely halophilic and obligate lithoautotrophic sulfur-oxidizing gammaproteobacteria. Cl-TMA can grow methyloautotrophically utilizing TMA, dimethylamine (DMA) and methanol (MeOH) as the electron donors or chemolithoautotrophically with thiosulfate. Mixotrophic growth was also observed with the three methyl compounds and thiosulfate. Carbon is assimilated autotrophically via the Calvin-Benson-Basham pathway. Unlike the type species of Thiohalorhabdus, T. denitrificans , Cl-TMA was incapable of anaerobic growth via denitrification. The isolate belongs to extreme halophiles growing between 2.5 and 5 M NaCl with an optimum at 3–3.5 M. Genome analysis identified two gene clusters coding for PQQ-dependent methanol dehydrogenases (MxaFI and XoxF), four homologues of the formaldehyde activating enzymes (Faes), a TMA/DMA oxidation locus, and two cluster of genes encoding an N-methylglutamate dehydrogenase pathway (NMGP) for methylamine oxidation. The first steps of C 1 -subtrate conversions are followed by the tetrahydrofolate (THF)-linked and tetrahydromethanopterin (H4MPT)-linked formaldehyde oxidation pathways and two formate dehydrogenases. All of those signatures of methylotrophy were absent in T. denitrificans . In contrast, genes for two key sulfur oxidation enzymes, thiosulfate dehydrogenase TsdAB and sulfide dehydrogenase FccAB, that are present in the type species are missing in Cl-TMA. Thiosulfate is oxidized to sulfate by a combination of an incomplete Sox cycle and an sHdr system. Strain Cl-TMA T (JCM 35977 = UQM 41915) is proposed to be classified as Thiohalorhabdus methylotrophus sp. nov.

59 BASIC BIOLOGICAL SCIENCES↗

The miR-183 family cluster alters zinc homeostasis in benign prostate cells, organoids and prostate cancer xenografts

The miR-183 cluster, which is comprised of paralogous miRs-183, -96 and -182, is overexpressed in many cancers, including prostate adenocarcinoma (PCa). Prior studies showed that overexpression of individual pre-miRs-182, -96 and -183 in prostate cells decreased zinc import, which is a characteristic feature of PCa tumours. Zinc is concentrated in healthy prostate 10-fold higher than any other tissue, and an >80% decrease in zinc is observed in PCa specimens. Here, we studied the effect of overexpression of the entire 4.8 kb miR-183 family cluster, including the intergenic region which contains highly conserved genomic regions, in prostate cells. This resulted in overexpression of mature miR-183 family miRs at levels that mimic cancer-related changes. Overexpression of the miR-183 cluster reduced zinc transporter and intracellular zinc levels in benign prostate cells, PCa xenografts and fresh prostate epithelial organoids. Microarray analysis of miR-183 family cluster overexpression in prostate cells showed an enrichment for cancer-related pathways including adhesion, migration and wound healing. An active secondary transcription start site was identified within the intergenic region of the miR-183 cluster, which may regulate expression of miR-182. Taken together, this study shows that physiologically relevant expression of the miR-183 family regulates zinc levels and carcinogenic pathways in prostate cells.

Science & Technology - Other Topics↗

Crystal genes in a marginal glass-forming system of Ni 50 Zr 50

Glass-forming motifs with B2 traits are found. A perfect Ni-centered B33 motif deteriorates the glass-forming ability of Ni 50 Zr 50 . The marginal glass-forming ability (GFA) of binary Ni-Zr system is an issue to be explained considering the numerous bulk metallic glasses (BMGs) found in the Cu-Zr system. Using molecular dynamics, the structures and dynamics of Ni 50 Zr 50 metallic liquid and glass are investigated at the atomistic level. To achieve a well-relaxed glassy sample, sub-T g annealing method is applied and the final sample is closer to the experiments than the models prepared by continuous cooling. With the state-of-the-art structural analysis tools such as cluster alignment and pair-wise alignment methods, two glass-forming motifs with some mixed traits of the metastable B2 crystalline phase and the crystalline Ni-centered B33 motif are found to be dominant in the undercooled liquid and glass samples. A new chemical order characterization on each short-range order (SRO) structure is accomplished based on the cluster alignment method. The significant amount of the crystalline motif and the few icosahedra in the glassy sample deteriorate the GFA.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Communication: Newton homotopies for sampling stationary points of potential energy landscapes

One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small enough) solutions but they all exhibit characteristic problems. Moreover, traditional methods can break down if the system contains singular solutions. Here, we propose an efficient implementation of Newton homotopies, which can sample a large number of the stationary points of complicated many-body potentials. We demonstrate how the procedure works by applying it to the nearest-neighbor ϕ{sup 4} model and atomic clusters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Delocalization and stretch-bend mixing of the HOH bend in liquid water

Liquid water’s rich sub-picosecond vibrational dynamics arise from the interplay of different high- and low-frequency modes evolving in a strong yet fluctuating hydrogen bond network. Recent studies of the OH stretching excitations of H 2 O indicate that they are delocalized over several molecules, raising questions about whether the bending vibrations are similarly delocalized. In this paper, we take advantage of an improved 50 fs time-resolution and broadband infrared (IR) spectroscopy to interrogate the 2D IR lineshape and spectral dynamics of the HOH bending vibration of liquid H2O. Indications of strong bend-stretch coupling are observed in early time 2D IR spectra through a broad excited state absorption that extends from 1500 cm -1 to beyond 1900 cm -1 , which corresponds to transitions from the bend to the bend overtone and OH stretching band between 3150 and 3550 cm -1 . Pump-probe measurements reveal a fast 180 fs vibrational relaxation time, which results in a hot-ground state spectrum that is the same as observed for water IR excitation at any other frequency. The fastest dynamical time scale is 80 fs for the polarization anisotropy decay, providing evidence for the delocalized or excitonic character of the bend. Finally, normal mode analysis conducted on water clusters extracted from molecular dynamics simulations corroborate significant stretch-bend mixing and indicate delocalization of δ HOH on 2-7 water molecules.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗