Signatures of Interstellar-Intracluster Medium Interactions: Spiral Galaxy Rotation Curves in Abell 2029

We investigate the rich cluster Abell 2029 (z~0.08) using optical imaging and long-slit spectral observations of 52 disk galaxies distributed throughout the cluster field. No strong emission-line galaxies are present within ~400 kpc of the cluster center, a region largely dominated by the similarly-shaped X-ray and low surface brightness optical envelopes centered on the giant cD galaxy. However, two-thirds of the galaxies observed outside the cluster core exhibit line emission. H-alpha rotation curves of 14 cluster members are used in conjunction with a deep I band image to study the environmental dependence of the Tully-Fisher relation. The Tully-Fisher zero-point of Abell 2029 matches that of clusters at lower redshifts, although we do observe a relatively larger scatter about the Tully-Fisher relation. We do not observe any systematic variation in the data with projected distance to the cluster center: we see no environmental dependence of Tully-Fisher residuals, R-I color, H-alpha equivalent width, and the shape and extent of the rotation curves.Comment: 22 pages, 6 figures, 3 tables; to appear in the August 2000 Astronomical Journa

Stability and symmetry-breaking bifurcation for the ground states of a NLS with a δ′\delta^\prime interaction

We determine and study the ground states of a focusing Schr\"odinger equation in dimension one with a power nonlinearity $|\psi|^{2\mu} \psi$ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) $\delta^\prime$ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) $\omega$. More precisely, there exists a critical value \om^* of the nonlinear eigenvalue \om, such that: if \om_0 < \om < \om^*, then there is a single ground state and it is an odd function; if \om > \om^* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for \om < \om^*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (\om =\om^*+0), ground states are stable if $\mu$ does not exceed a value $\mu^\star$ that lies between 2 and 2.5, and become unstable for $\mu > \mu^*$. Finally, for $\mu > 2$ and \om \gg \om^*, all ground states are unstable. The branch of odd ground states for \om \om^*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non standard techniques have to be used to establish the needed properties of linearization operators.Comment: 46 pages, 5 figure

Explaining the entropy excess in clusters and groups of galaxies without additional heating

The X-ray luminosity and temperature of clusters and groups of galaxies do not scale in a self-similar manner. This has often been interpreted as a sign that the intracluster medium has been substantially heated by non-gravitational sources. In this paper, we propose a simple model which, instead, uses the properties of galaxy formation to explain the observations. Drawing on available observations, we show that there is evidence that the efficiency of galaxy formation was higher in groups than in clusters. If confirmed, this would deplete the low-entropy gas in groups, increase their central entropy and decrease their X-ray luminosity. A simple, empirical, hydrostatic model appears to match both the luminosity-temperature relation of clusters and properties of their internal structure as well.Comment: 5 pages, 4 figures, accepted in ApJL; added one reference, otherwise unchange

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

Environmental Dependence of the Fundamental Plane of Galaxy Clusters

Galaxy clusters approximate a planar (FP) distribution in a three-dimensional parameter space which can be characterized by optical luminosity, half-light radius, and X-ray luminosity. Using a high-quality catalog of cluster redshifts, we find the nearest neighbor cluster for those common to an FP study and the cluster catalog. Examining scatter about the FP, we find 99.2% confidence that it is dependent on nearest neighbor distance. Our study of X-Ray clusters finds that those with high central gas densities are systematically closer to neighbor clusters. If we combine results here with those of Fritsch and Buchert, we find an explanation for some of our previous conclusions: Clusters in close proximity to other clusters are more likely to have massive cooling flows because they are more relaxed and have higher central gas densities.Comment: Accepted for publication in Astrophysical Journal Letters. Moderate revisions, including more statistical analysis and discussion. Latex, 7 page

Method and System for Synchronizing Electronic Program Guides

A method (500) for generating a time scheduling (150) of a contents stream (140) distributed to a plurality of terminals (120) is provided. The contents stream is segmented in consecutive segments, each segment defining a corresponding program (Pi). The method includes receiving auxiliary meta data comprising a planned time scheduling of the content stream which has been set in advance and monitoring at least a portion of a segment of the contents stream to extract corresponding content features there from. The method further includes generating a corresponding fingerprint based on the extracted content features and assessing at least one among an actual start time and an actual end time of such segment based on a comparison between said fingerprint and a reference fingerprint associated with such segment. The method still further includes updating the planned time scheduling based on the assessed at least one among the actual start time and the actual end time so as to generate a time scheduling synchronized with the contents stream

SPATION: Services Platforms and Applications for Transparent Information management in an in-hOme Network

The characteristics of PCs, huge storage capacity, tremendous processing power, and high flexibility are becoming available for consumer devices like set-top boxes, TVs, and VCRs. Interconnection of these devices and wireless communication with various portable devices will create a complex home system with the capacity to store many types of data and offer new ways of interacting with it. To offer the user high flexibility and ease of use, new solutions are required. Advanced retrieval methods are needed to support accessing data stored anywhere in the home system from any device. Meta-data obtained through analysis, services, and logging user behaviour is needed to support these functions. Transfer of data must be easy, and transfer and adaptation of accompanying meta-data must be transparent to the user. The combination of broadcast, storage, and internet will open the way to new types of applications and interactions with the home system. A large distributed storage space will be available in future home networks consisting of CE equipment, PCs and handheld devices. The objective of the project is to find innovative solutions for the movement, organization and retrieval of information in such a heterogeneous home system. Three major technical issues are under consideration: 1) New Meta-data computing methods are needed to support advanced retrieval methods. This means ways to solve how to generate meta-data by analysing the content, howto combine meta-data from various sources and how to transform meta-data for use by different devices; 2) New services providing meta-data, applications and UIs to make retrieval of information easier for non-IT-expert users; 3) Standards for inter-storage communication need to be extended in the area of handheld devices, meta-data storage and services

An extension of the SHARC survey

We report on our search for distant clusters of galaxies based on optical and X-ray follow up observations of X-ray candidates from the SHARC survey. Based on the assumption that the absence of bright optical or radio counterparts to possibly extended X-ray sources could be distant clusters. We have obtained deep optical images and redshifts for several of these objects and analyzed archive XMM-Newton or Chandra data where applicable. In our list of candidate clusters, two are probably galaxy structures at redshifts of z$\sim$0.51 and 0.28. Seven other structures are possibly galaxy clusters between z$\sim$0.3 and 1. Three sources are identified with QSOs and are thus likely to be X-ray point sources, and six more also probably fall in this category. One X-ray source is spurious or variable. For 17 other sources, the data are too sparse at this time to put forward any hypothesis on their nature. We also serendipitously detected a cluster at z=0.53 and another galaxy concentration which is probably a structure with a redshift in the [0.15-0.6] range. We discuss these results within the context of future space missions to demonstrate the necessity of a wide field of view telescope optimized for the 0.5-2 keV range.Comment: Accepted in A&

A family of diameter-based eigenvalue bounds for quantum graphs

We establish a sharp lower bound on the first non-trivial eigenvalue of the Laplacian on a metric graph equipped with natural (i.e., continuity and Kirchhoff) vertex conditions in terms of the diameter and the total length of the graph. This extends a result of, and resolves an open problem from, [J. B. Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17 (2016), 2439--2473, Section 7.2], and also complements an analogous lower bound for the corresponding eigenvalue of the combinatorial Laplacian on a discrete graph. We also give a family of corresponding lower bounds for the higher eigenvalues under the assumption that the total length of the graph is sufficiently large compared with its diameter. These inequalities are sharp in the case of trees.Comment: Substantial revision of v1. The main result, originally for the first eigenvalue, has been generalised to the higher ones. The title has been changed and the proofs substantially reorganised to reflect the new result, and a section containing concluding remarks has been adde