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This work focuses on incorporating pairwise constraints into a spectral clustering algorithm. A new constrained spectral clustering method is proposed, as well as an active constraint acquisition technique and a heuristic for parameter selection. We demonstrate that our constrained spectral clustering method, CSC, works well when the data exhibits what we term local proximity structure.
One metal atom surrounded by its 12 nearest neighbors is considered for both D(3d) (face-centered cubic-like) and D(3h) (hexagonal close-packed-like) geometries. For Al and Be, the neutral cluster and the positive and negative ions are considered for idealized (all bonds equal) and distorted geometries. The D(3d) geometry is found to be the lowest for Be13, while the D(3h) geometry is lower for Al13. This is the reverse of what is expected based upon the bulk metal structures, Be(hcp) and Al(fcc). Al13 is found to have only small distortions, while Be13 shows large distortions for both the D(3d) and D(3h) geometries. The ions have geometries which are similar to those found for the neutral systems. Both all-electron and effective core potential calculations were carried out on the X13 clusters; the agreement is very good.
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The X-ray source in the Perseus cluster has been studied both by the Copernicus satellite and by sounding-rocket instruments flown by Columbia University. The spatial and spectral data from these observations are examined. A surface brightness distribution is obtained which shows that the source consists of a compact core associated with NGC 1275 and a more extended emission volume. The structure of the central core region has been examined by means of an image reconstruction technique, revealing a steeply declining luminosity function and north-south elongation. The spectrum of the emission of the core region is distinguished from that of the surrounding area and found to be consistent with a hydrogen column density of 2.5 x 10 to the 21th/sq cm. A comparison between the isothermal and adiabatic gas sphere models is presented which shows the need for at least two components to provide the X-ray emission.
The purpose of this study was to measure the physical conditions of gas along sight lines toward 6 stars in the core Chi Persei open cluster. These sight lines traverse gas in both the Orion and Perseus spiral arms of the Galaxy, at distances of 500 and 2000 pc, respectively. The stars have angular separations ranging from 45 to 280 arcsec; 60 arcsec corresponds to linear distances of 0.15 and 0.6 pc in the two arms. Thus, abundance variations in these observations would constitute evidence for small-scale variations in the properties of the interstellar medium. Ground-based Na I observations at high resolution (approx. 15 km/sec) toward 172 stars (including the 6 in this study) in the double open cluster h and Chi Persei have revealed complex spatial variation. These variations are especially evident in the gas at velocities of -40 and -55 km/sec, corresponding to the Perseus spiral arm. 21 cm observations of HI emission using the Low Resolution DRAO Survey, with a 12-arcmin beam, also show variations. Averaging the Na I apparent optical depth profiles of neighboring sight lines in order to mimic such a beam size reduces the variation, as compared to the individual Na I measurements, but still show variations larger than seen in the 21 cm profiles. Na I is not the dominant ionization state of Na in the interstellar medium. Thus, it is possible that the variations seen really trace physical structures in the interstellar medium, or they may simply result from variations in the radiation field seen by the gas, or be due to some other environmental circumstance. To distinguish among these possibilities in the present study we obtained FUSE spectra toward the 6 targets in order to measure the molecular hydrogen absorption profiles along these sight lines. The higher J states of H2 are populated by the ambient W radiation field, and thus can provide insight into the environment affecting the gas. If both the high and low J states reveal absorption line profiles with variations similar to that observed in Na I, this would indicate that the variations are due to real structures in the interstellar medium. On the other hand, if the only the high J profiles mimicked the Na I profiles, then the variations may be attributable to environmental effects. We found that the H2 profiles showed considerable variation over the 6 sight lines, and that the profiles, despite having somewhat lower velocity resolution, resemble the Na I profiles. Thus, it appears that the gas really does exhibit variations in physical structures along these sight lines. Useful follow-up work would be to obtain higher signal-to-noise FUSE observations of H2, since the present data are of only moderate quality, and to obtain data on additional targets in this double cluster, in order to map out in more detail the extent and magnitude of the small-scale variations.
The geometries of B+n clusters for n less than 14 have been optimized using density functional theory with the B3LYP functional. The most stable structure for each cluster is planar or quasi-planar. The B3LYP fragmentation energies are calibrated using coupled cluster theory. Overall, our corrected fragmentation energies are in reasonable agreement with experiment. Our results are compared with previous theoretical results.
We present a detailed gravitational mass measurement based on the XMM-Newton imaging spectroscopy analysis of the lensing cluster of galaxies CL0024+17 at $z = 0.395$. The emission appears approximately symmetric. However, on the scale of $r\sim3.3'$, some indication of elongation is visible in the northwest-southeast direction from the hardness ratio map. Within $3'$, we measure a global gas temperature of $3.52\pm0.17$ keV, metallicity of $0.22\pm0.07$, and a bolometric luminosity of $2.9\pm0. l\times10(exp 44)$ erg/s. We derive a temperature distribution with an isothermal temperature of 3.9 keV up to a radius of $1.5'$ and a strong temperature gradient in the outskirts ($1.3' less than r less than 3.3'$). Under the assumption of hydrostatic equilibrium, we measure the gravitational mass and gas mass fraction to be $M-{200} = 2.0\pm0.3\times 10(exp 14)$ solar masses and $f-{gas} = 0.20\pm0.03$ at $r-{200} = 1.05$ Mpc (all for a Hubble constant of 70 km/sec/Mpc) using the observed gas temperature profile. The complex core structure is the key to explaining the discrepancy between the gravitational mass determined from the XMM-Newton observations and HST optical lensing measurements.
We have completed our analysis of the temperature structure of clusters of galaxies. The next to last paper to be supported by this project has been published in the Astrophysical Journal. The analysis for the final paper is nearly complete, but has been delayed by the high priority demands of Chandra Mission Planning and Chandra Calibration which have required more than the expected amount of work by Forman and Donnelly. For this paper, a final check of the 55 member cluster sample identified several clusters for which X-ray luminosities are needed. We also verified the ASCA analysis and the novel method we use for the derivation of the temperature maps against XMM-Newton observations for a few clusters which are publicly available in the XMM-Newton archives We find excellent agreement. This final paper is expected to be submitted by November 2002. It will provide a large, well-defined sample of clusters for comparison to large numerical simulations which can help clarify the evolution of the largest collapsed systems in the Universe.
The 3α phenomenological model describes the structure of the carbon-12 nucleus as a cluster of three alpha particles. This model includes a pairwise α–α interaction and a three-body force. To fit the three-body potential, the 12 C data are used, while ensuring that the pair potential reproduces the α–α scattering data. Alternatively, the mass-energy compensation (MEC) effect can be used to simulate the effect of the three-body potential by adjusting the mass of the α particle within the effective-mass approach. We demonstrate the MEC effect for the 3α ground state by numerically solving the differential Faddeev equation, in which the α–α interaction is described by the Ali-Bodmer potential. The effective masses of α particles are evaluated for the ground and excited 0 + and bound 2 + states. Here, we demonstrate a coupling between the ground and first excited 0 + states, indicated by an anti-crossing of these energy levels in the energy–mass coordinates. A correspondence between the effective mass and a three-body potential is demonstrated. We discuss the results of the 0$^{+}_{2}$ calculations for various models of the α–α interaction.
Analysis of radial velocities in the coma cluster (many of them new) in conjunction with previous data on the density distribution. The cluster extends more than 200 min in radius, with bright and faint galaxies distributed in nearly the same way. Some spirals are members. Several different determinations of M/L give values around 250. The cluster is stabilized by a 'missing mass' some seven times the mass of the galaxies, which must be distributed in the same way as the galaxies.
The temperature dependence of the energies of the isomers of a seven-particle system is studied with a view toward understanding ergodicity problems in Monte Carlo simulations. It is found that the phase space of particles in a cluster is not ergodic at lower temperatures.
A 0.5-1.5-keV X-ray image of the Perseus cluster of galaxies was obtained with a focusing telescope system aboard a sounding rocket. The source consists of a region of diffuse emission plus a superposed central source in the vicinity of NGC 1275 smaller than 4 arcmin in diameter that accounts for one-quarter of the total intensity within a radius of 25 arcmin. The results for the diffuse source are consistent with the isothermal-hydrostatic picture in which the hot gas has a core radius of 17 arcmin and is approximately symmetric about NGC 1275. Several isothermal-hydrostatic models are considered which relate the size and temperature of the diffuse X-ray source with the core radius of the galaxies and their velocity dispersion. Fixing the velocity dispersion at values measured by Chincarini and Rood (1971) requires the core radius of the galaxies to be 28 + or - 9 arcmin, which is larger than present measurements. Conversely, fixing the core radius of the galaxies at 8 arcmin requires a smaller velocity dispersion or a condition in which the velocity distribution is anisotropic. Upper limits on the intrinsic X-ray absorption of the central source place the bulk of its X-ray emission beyond the nuclear region of NGC 1275.
Results are reported for an observation of the Coma cluster with an imaging X-ray telescope system aboard a sounding rocket. A two-dimensional X-ray map of the cluster in the energy range from 0.15 to 2.0 keV is presented. The radial distribution, granularity, and ellipticity of the X-ray surface brightness are investigated, and the spectrum and flux within the field of view are analyzed. These properties are then examined quantitatively by comparing the observations with models through the use of a chi-squared test. It is found that: (1) no single galaxy contributes more than a few percent of the total X-ray flux of the Coma cluster; (2) the X-ray source is diffuse but granular on a scale of several arcmin, particularly in the central region; (3) the centroid of the X-ray source is at a local intensity minimum; and (4) the data are most consistent with an isothermal hydrostatic model.
The X-ray sources in the Perseus cluster have been studied by many authors. Available data on the spatial and spectral distributions are examined and summarized. Based on these observations, a consistent model is proposed for the production of X-rays and gamma-rays in the region around NGC 1275. It is shown that good agreement with observations is obtained by assuming the emission of soft X-rays for thermal bremsstrahlung and of hard X-rays and gamma-rays from the inverse Compton process.
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The globular cluster omega Centauri contains the largest known population of very hot horizontal branch (HB) stars. We have used the Hubble Space Telescope to obtain a far-UV/optical color-magnitude diagram of three fields in omega Cen. We find that over 30% of the HB objects are "extreme" HB or hot post-HB stars. A wide gap in the color distribution of the hot HB stars may correspond to gaps found earlier in several other clusters, which argues for a common mass loss mechanism. The diagram contains a significant population of hot sub-HB stars, which we interpret as the "blue-hook" objects predicted by D'Cruz (1996a). These are produced by late He-flashes in stars which have undergone unusually large giant branch mass loss. Omega Cen has a well-known spread of metal abundance, and the diagram is consistent with a giant branch mass loss efficiency which increases with metallicity. There is no evidence for a dynamical origin of the hot HB stars.
Near-term quantum devices require wavefunction ansätze that are expressive while also of shallow circuit depth in order to both accurately and efficiently simulate molecular electronic structure. While the unitary coupled cluster ansatz (e.g., UCCSD) has become a standard, the high gate count associated with the implementation of this limits its feasibility on noisy intermediate-scale quantum (NISQ) hardware. k -Fold unitary cluster Jastrow (uCJ) ansätze mitigate this challenge by providing O( kN 2 ) circuit scaling and favorable linear depth circuit implementation. Previous work has focused on the real orbitalrotation (Re-uCJ) variant of uCJ, which allows an exact (Trotter-free) implementation. Here we extend and generalize the k -fold uCJ framework by introducing two new variants, Im-uCJ and g-uCJ, which incorporate imaginary and fully complex orbital rotation operators, respectively. Similar to Re-uCJ, both of the new variants achieve quadratic gate-count scaling. Our results focus on the simplest k = 1 model, and show that the uCJ models frequently maintain energy errors within chemical accuracy (∼1 kcal mol −1 ). Both g-uCJ and Im-uCJ are more expressive in terms of capturing electron correlation and are also more accurate than the earlier Re-uCJ ansatz. We further show that Im-uCJ and g-uCJ circuits can also be implemented exactly, without any Trotter decomposition. Numerical tests using k = 1 on H 2 , H 3 + , Be 2 , C 2 H 4 , C 2 H 6 and C 6 H 6 in various basis sets confirm the practical feasibility of these shallow Jastrow-based ansätze for applications on near-term quantum hardware.