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Showing papers on "Cluster (physics) published in 1977"


Journal ArticleDOI
TL;DR: In this article, a review of properties of clusters of galaxies and some theoretical interpretations are reviewed, including catalogs of clusters, the static properties of rich clusters, cluster dynamics, X-ray emission from clusters, and cluster radio emission.
Abstract: Observational properties of clusters of galaxies and some theoretical interpretations are reviewed. The major subjects of the review include catalogs of clusters, the static properties of rich clusters, cluster dynamics, X-ray emission from clusters of galaxies, and cluster radio emission. Observed static properties discussed are: richness, classification schemes, galactic content, cD galaxies, density profiles, sizes, and the optical luminosity function. Several characteristic time scales of clusters of galaxies are examined along with mass segregation, the dynamical evolution of clusters, cluster masses, mass-to-light ratios, the missing-mass problem, and the mean galactic and cluster mass densities in the universe. The main characteristics of clusters that contain X-ray emission are summarized, emphasizing the relation of the X-ray emission to optical properties. The most important properties of cluster radio emission are outlined, the relation of this emission to the other cluster properties studied is indicated, and evidence suggesting the influence of an intracluster gas on the radio galaxies and their relativistic electrons is noted.

315 citations


Journal ArticleDOI
TL;DR: In this paper, the authors consider self-contained gas flows, in which mass ejected by galaxies in the outer regions of a cluster flows toward the core of the cluster and ultimately accretes onto the central galaxies.
Abstract: Radiation from gas within rich clusters of galaxies may regulate the central gas density to that value at which the cooling time equals the lifetime of the system, since at higher densities mass deposition by cooling in the central regions would exceed mass injection from the member galaxies and mass inflow from the outer regions of the cluster. We argue that in X-ray clusters a steady inflow of material takes place, in which the gravitational energy of the accreting material powers the X-ray luminosity of the source and accounts for the observed spatial extent of the gas distribution.In the present paper we consider self-contained gas flows, in which mass ejected by galaxies in the outer regions of the cluster flows toward the core of the cluster and ultimately accretes onto the central galaxies. This model, which depends only on a single parameter measuring the ratio of the mass-injection rate to the cooling in the central regions, accounts for the observed X-ray luminosities of the clusters, the surface-brightness profiles, and energy spectra in terms of thermal bremsstrahlung emission from the gas. We briefly argue that thermal conduction does not affect the observed properties of the source.We discuss the expected equivalent widthsmore » of observable emission lines, the morphology of the X-ray emission from the Perseus cluster, the formation of cD and active galaxies, and extinction and scattering by dust within the cluster.« less

246 citations


Journal ArticleDOI
TL;DR: In this article, an application of Kubo's linear response theory is used to study the nonequilibrium situation that results from placing a cluster, of vortices in a weak external velocity field, such as that produced by a distant vortex cluster.
Abstract: Equilibrium statistics of a cluster of a large number of positive two-dimensional point vortices in an infinite region and the associated thermodynamic functions, exhibiting negative temperatures, are evaluated analytically and numerically from a microcanonical ensemble. Extensive numerical simulations of vortex motion are performed to verify the predicted equilibrium configurations. An application of Kubo's linear response theory is used to study the nonequilibrium situation that results from placing a cluster, of vortices in a weak external velocity field, such as that produced by a distant vortex cluster. The weak field causes the cluster to grow in size as if there were an effective positive eddy viscosity. When a number of clusters interact, the effect is for each to grow while the distances between them decrease with time. The latter effect is an exhibit of negative viscosity. The application of this to the motion of the atmosphere is discussed.

174 citations


Journal ArticleDOI
TL;DR: In this article, a theory of pair connectedness is developed for fluid as well as lattice systems when the presence of physical clusters of particles in the system is explicitly taken into account.
Abstract: A theory of pair connectedness is developed for fluid as well as lattice systems when the presence of physical clusters of particles in the system is explicitly taken into account. Activity and density expansions, an Ornstein-Zernicke relation and the Percus-Yevick approximation are established in analogy with the theory of the pair-correlation function. A simple application to the percolation problem is given; for a lattice the results are compared with the known solution of the Bethe lattice. For a fluid system the theory is used to investigate the relation of percolation and condensation in a Van der Waals gas, the result shows that an infinite cluster of particles is formed in the gaseous phase, along the coexistence curve, before the critical point is reached.

155 citations


Journal ArticleDOI
TL;DR: In this paper, the average thermodynamic properties of small (N?13) clusters of atoms were calculated using the Monte Carlo method and the melting points predicted by these tests did not differ by more than 5%.
Abstract: The Monte Carlo method is used to calculate the average thermodynamic properties of small (N?13) clusters of atoms. All cluster sizes studied exhibit fairly sharp solid–liquid, as well as liquid–gas, transitions. In addition, some of the larger clusters also undergo structural transitions between different isomeric forms. The solid–liquid transition temperature is determined by four independent tests. The melting points predicted by these tests do not differ by more than 5%.

143 citations


Journal ArticleDOI
TL;DR: In this article, the size and shape of bimetallic ruthenium-copper and osmiumcopper clusters and of monometallic RUThenium and Osmium clusters, all dispersed on a silica carrier, have been obtained by high-resolution electron microscopy.

114 citations


Journal ArticleDOI
TL;DR: Raman and depolarization spectra of GeSe 2 alloyed with Se or As 2 Se reveal a sharp vibrational doublet, only one component of which can be attributed to a vibrational excitation of the local atomic cluster as discussed by the authors.

111 citations




Journal ArticleDOI
TL;DR: In this paper, a method for testing the distinctness of two clusters in Euclidean space is described, where the projections of the N 1 and N 2 members of the clusters onto the line joining the cluster centroids are calculated, which corresponds to an index of overlap, VG.
Abstract: A method is described for testing the distinctness of two clusters in Euclidean space. One first calculates the projections, q,of the N1and N2members of the clusters onto the line joining the cluster centroids. From the distributions of qan index of disjunction, W,is calculated, which corresponds to an index of overlap, VG.The quantity W√(N1+N2)is distributed as noncentral tsubject to assumptions on the multivariate normal distribution of the clusters. This allows a test of whether the observed disjunction is significantly greater than a chosen figure, which is equivalent to testing whether the overlap of the clusters is significantly less than a corresponding value of VG.Two clusters that appear distinct may be produced simply by the partitioning of a homogeneous swarm into two contiguous regions. Provided that the clusters form a dichotomy in a dendrogram, and that the clustering method yields geometrically convex clusters, a conservative test of this situation can be derived by determining the excess of Wover the value expected for a rectangular distribution.

88 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used the self-consistent field (SfF) to perform electronic-structure calculations for two series of aluminum clusters containing up to 43 atoms, the largest metal cluster so far treated by this method.
Abstract: The self-consistent-field $X\ensuremath{\alpha}$ scattered-wave molecular-orbital method has been used to perform electronic-structure calculations for two series of aluminum clusters containing up to 43 atoms, the largest metal cluster so far treated by this method. The first series consisted of clusters of 13, 19, and 43 atoms having the ${O}_{h}$ symmetry characteristic of bulk fcc aluminum while the second consisted of 5, 9, and 25 atom clusters having the ${C}_{4v}$ symmetry appropriate to the (100) surface. The convergence of the calculated results as a function of cluster size has been examined. The largest cluster of each series yields an occupied bandwidth of over 90% [$92% ({C}_{4v}),99% ({O}_{h})$] of the bulk band width derived from x-ray emission spectra. These larger clusters also show reasonable agreement with the main features of density-of-states curves derived from band-structure calculations and those inferred from recent photoemission measurements. The differences and similarities between various cluster- and band-theory results are discussed. Examination of projected densities of states for the various atoms provides a possible explanation of the smaller occupied bandwidth observed in the photoemission spectrum, compared with the x-ray or band-structure results. It is also suggested that similar projected density-of-states plots for the case of transition-metal clusters might prove useful for the study of structure sensitivity in heterogeneous catalysis.



Journal ArticleDOI
TL;DR: In this paper, a general formalism is developed to obtain series expansions of the average number of physical clusters of particles in the framework of Mayer's theory and some preliminary results are given on the relation between percolation and condensation in fluid systems in the lowest approximation.
Abstract: A general formalism is developed to obtain series expansions of the average number of physical clusters of particles in the framework of Mayer's theory. The special case of lattice systems is investigated in more detail and some preliminary results are given on the relation between percolation (namely the formation of an infinite cluster) and condensation in fluid systems in the lowest approximation (summation of chain diagrams).





Journal ArticleDOI
TL;DR: In this article, the multishell method is presented for exact determination of the Green's function of a cluster embedded in a given effective medium, which is applicable even to systems with off-diagonal disorder, extended-range hopping, multiple bands and/or hybridization.
Abstract: A method is presented for the exact determination of the Green's function of a cluster embedded in a given effective medium. This method, the multishell method, is applicable even to systems with off-diagonal disorder, extended-range hopping, multiple bands and/or hybridization, and is computationally practicable for any system described by a tight-binding or interpolation-scheme Hamiltonian. It allows one to examine the effects of local environment on the densities of states and site spectral weight functions of disordered systems. For any given analytic effective medium characterized by a non-negative density of states the method yields analytic cluster Green's functions and non-negative site spectral weight functions. Previous methods used for the calculation of the Green's function of a cluster embedded in a given effective medium have not been exact. The results of numerical calculations for model systems show that even the best of these previous methods can lead to substantial errors, at least for small clusters in two- and three- dimensional lattices. These results also show that fluctuations in local environment have large effects on site spectral weight functions, even in cases in which the single-site coherent-potential approximation yields an accurate overall density of states.

Journal ArticleDOI
TL;DR: Extended-Huckel calculations on model M6H6(M = Co or Ir) cluster compounds with octahedral, bicapped-tetrahedral, and trigonal-prismatic geometries are reported in this article.
Abstract: Extended-Huckel calculations on model M6H6(M = Co or Ir) cluster compounds with octahedral, bicapped-tetrahedral, and trigonal-prismatic geometries are reported. The theoretical basis of the polyhedral skeletal electron-pair theory is discussed and the important role played by terminal and bridging ligands in such clusters is emphasised. The capping principle which has been used to rationalise the geometries of metal cluster compounds such as [Os6(CO)18] and [Os7(CO)21] is shown to have a quite general quantum-mechanical basis.




Journal ArticleDOI
TL;DR: In this article, a series of tetrameric mixed-metal clusters with carbonyl-metalates is presented, and several of the reported reactions appear to be adaptable to design.
Abstract: : Transition metal cluster complexes have become a very important class of compounds, principally because of their potential in catalysis. Clusters have been shown to behave as catalysts in their own right and they hold considerable promise for serving as models for catalytic surfaces. Clusters comprised of two or more different transition metals in the cluster framework are particularly interesting in this regard because of possible bimetallic effects. Further, mixed-metal clusters have non-equivalent bonding sites. As such they are ideally suited for modeling studies which employ variable temperature NMR to follow the movements of substrates over their surfaces. One of the problems which has hampered studies of mixed-metal clusters is their relative lack of availability. Only a very few isostructural series have been achieved, and general synthetic methods for mixed-metal clusters are lacking. Carbonylmetalates have been widely used as synthetic reagents in cluster chemistry and several of the reported reactions appear to be adaptable to design. This is particularly true of the reactions of Knight and Mays who prepared a series of Group 7 - Group 8 tetrameric mixed-metal clusters through the addition of a carbonylmetalate to a closed M3(CO)12 trimer.






Journal ArticleDOI
TL;DR: The properties of cluster ions and the processes in which they participate are examined in this paper, and the experimental rate constants for these processes are given for the processes that involve cluster ions in the upper atmosphere of the Earth.
Abstract: The properties of cluster ions and the processes in which they participate are examined. Information is given on the bond-dissociation energies of cluster ions. Processes that give rise to compound and cluster ions in ternary collisions, dissociative recombination of a cluster ion and an electron, and ion-molecule reactions involving cluster ions are studied, and the experimental rate constants are given for these processes. The processes that involve cluster ions in the upper atmosphere of the Earth are analyzed.