Linear Momentum Density in Quasistatic Electromagnetic Systems

We discuss a couple of simple quasistatic electromagnetic systems in which the density of electromagnetic linear momentum can be easily computed. The examples are also used to illustrate how the total electromagnetic linear momentum, which may also be calculated by using the vector potential, can be understood as a consequence of the violation of the action-reaction principle, because a non-null external force is required to maintain constant the mechanical linear momentum. We show how one can avoid the divergence in the interaction linear electromagnetic momentum of a system composed by an idealization often used in textbooks (an infinite straight current) and a point charge.Comment: 22 pages, 5 figures, to appear in Eur. J. Phy

Twin paradox and space topology

If space is compact, then a traveller twin can leave Earth, travel back home without changing direction and find her sedentary twin older than herself. We show that the asymmetry between their spacetime trajectories lies in a topological invariant of their spatial geodesics, namely the homotopy class. This illustrates how the spacetime symmetry invariance group, although valid {\it locally}, is broken down {\it globally} as soon as some points of space are identified. As a consequence, any non--trivial space topology defines preferred inertial frames along which the proper time is longer than along any other one.Comment: 6 pages, latex, 3 figure

Rifting of the oceanic Azores Plateau with episodic volcanic activity

Extension of the Azores Plateau along the Terceira Rift exposes a lava sequence on the steep northern flank of the Hirondelle Basin. Unlike typical tholeiitic basalts of oceanic plateaus, the 1.2 km vertical submarine stratigraphic profile reveals two successive compositionally distinct basanitic to alkali basaltic eruptive units. The lower unit is volumetrically more extensive with similar to 1060 m of the crustal profile forming between similar to 2.02 and similar to 1.66 Ma, followed by a second unit erupting the uppermost similar to 30 m of lavas in similar to 100 kyrs. The age of similar to 1.56 Ma of the youngest in-situ sample at the top of the profile implies that the 35 km-wide Hirondelle Basin opened after this time along normal faults. This rifting phase was followed by alkaline volcanism at D. JoAo de Castro seamount in the basin center indicating episodic volcanic activity along the Terceira Rift. The mantle source compositions of the two lava units change towards less radiogenic Nd, Hf, and Pb isotope ratios. A change to less SiO2-undersaturated magmas may indicate increasing degrees of partial melting beneath D. JoAo de Castro seamount, possibly caused by lithospheric thinning within the past 1.5 million years. Our results suggest that rifting of oceanic lithosphere alternates between magmatically and tectonically dominated phases.Peer reviewe

Topological Lattice Gravity Using Self-Dual Variables

Topological gravity is the reduction of general relativity to flat space-times. A lattice model describing topological gravity is developed starting from a Hamiltonian lattice version of B\w F theory. The extra symmetries not present in gravity that kill the local degrees of freedom in $B\wedge F$ theory are removed. The remaining symmetries preserve the geometrical character of the lattice. Using self-dual variables, the conditions that guarantee the geometricity of the lattice become reality conditions. The local part of the remaining symmetry generators, that respect the geometricity-reality conditions, has the form of Ashtekar's constraints for GR. Only after constraining the initial data to flat lattices and considering the non-local (plus local) part of the constraints does the algebra of the symmetry generators close. A strategy to extend the model for non-flat connections and quantization are discussed.Comment: 22 pages, revtex, no figure

SDSS-RASS: Next Generation of Cluster-Finding Algorithms

We outline here the next generation of cluster-finding algorithms. We show how advances in Computer Science and Statistics have helped develop robust, fast algorithms for finding clusters of galaxies in large multi-dimensional astronomical databases like the Sloan Digital Sky Survey (SDSS). Specifically, this paper presents four new advances: (1) A new semi-parametric algorithm - nicknamed ``C4'' - for jointly finding clusters of galaxies in the SDSS and ROSAT All-Sky Survey databases; (2) The introduction of the False Discovery Rate into Astronomy; (3) The role of kernel shape in optimizing cluster detection; (4) A new determination of the X-ray Cluster Luminosity Function which has bearing on the existence of a ``deficit'' of high redshift, high luminosity clusters. This research is part of our ``Computational AstroStatistics'' collaboration (see Nichol et al. 2000) and the algorithms and techniques discussed herein will form part of the ``Virtual Observatory'' analysis toolkit.Comment: To appear in Proceedings of MPA/MPE/ESO Conference "Mining the Sky", July 31 - August 4, 2000, Garching, German

Schumpeterian economic dynamics as a quantifiable minimum model of evolution

We propose a simple quantitative model of Schumpeterian economic dynamics. New goods and services are endogenously produced through combinations of existing goods. As soon as new goods enter the market they may compete against already existing goods, in other words new products can have destructive effects on existing goods. As a result of this competition mechanism existing goods may be driven out from the market - often causing cascades of secondary defects (Schumpeterian gales of destruction). The model leads to a generic dynamics characterized by phases of relative economic stability followed by phases of massive restructuring of markets - which could be interpreted as Schumpeterian business `cycles'. Model timeseries of product diversity and productivity reproduce several stylized facts of economics timeseries on long timescales such as GDP or business failures, including non-Gaussian fat tailed distributions, volatility clustering etc. The model is phrased in an open, non-equilibrium setup which can be understood as a self organized critical system. Its diversity dynamics can be understood by the time-varying topology of the active production networks.Comment: 21 pages, 11 figure

A Serendipitous Galaxy Cluster Survey with XMM: Expected Catalogue Properties and Scientific Applications

This paper describes a serendipitous galaxy cluster survey that we plan to conduct with the XMM X-ray satellite. We have modeled the expected properties of such a survey for three different cosmological models, using an extended Press-Schechter (Press & Schechter 1974) formalism, combined with a detailed characterization of the expected capabilities of the EPIC camera on board XMM. We estimate that, over the ten year design lifetime of XMM, the EPIC camera will image a total of ~800 square degrees in fields suitable for the serendipitous detection of clusters of galaxies. For the presently-favored low-density model with a cosmological constant, our simulations predict that this survey area would yield a catalogue of more than 8000 clusters, ranging from poor to very rich systems, with around 750 detections above z=1. A low-density open Universe yields similar numbers, though with a different redshift distribution, while a critical-density Universe gives considerably fewer clusters. This dependence of catalogue properties on cosmology means that the proposed survey will place strong constraints on the values of Omega-Matter and Omega-Lambda. The survey would also facilitate a variety of follow-up projects, including the quantification of evolution in the cluster X-ray luminosity-temperature relation, the study of high-redshift galaxies via gravitational lensing, follow-up observations of the Sunyaev-Zel'dovich effect and foreground analyses of cosmic microwave background maps.Comment: Accepted to ApJ. Minor changes, e.g. presentation of temperature errors as a figure (rather than as a table). Latex (20 pages, 6 figures, uses emulateapj.sty

The Bright SHARC Survey: The Cluster Catalog

We present the Bright SHARC (Serendipitous High-Redshift Archival ROSAT Cluster) Survey, which is an objective search for serendipitously detected extended X-ray sources in 460 deep ROSAT PSPC pointings. The Bright SHARC Survey covers an area of 178.6 sq.deg and has yielded 374 extended sources. We discuss the X-ray data reduction, the candidate selection and present results from our on-going optical follow-up campaign. The optical follow-up concentrates on the brightest 94 of the 374 extended sources and is now 97% complete. We have identified thirty-seven clusters of galaxies, for which we present redshifts and luminosities. The clusters span a redshift range of 0.0696<z<0.83 and a luminosity range of 0.065<Lx<8.3e44 erg/s [0.5-2.0 keV] (assuming Ho = 50 km/s/Mpc and qo=0.5). Twelve of the clusters have redshifts greater than z=0.3, eight of which are at luminosities brighter than Lx=3e44 erg/s. Seventeen of the 37 optically confirmed Bright SHARC clusters have not been listed in any previously published catalog. We also report the discovery of three candidate ``fossil groups'' of the kind proposed by Ponman et al. (1994).Comment: Minor revisions: References updated and typos corrected. Shortened by use of emulateapj.st

The Evolution of Central Volcanoes in Ultraslow Rift Systems : Constraints From D. Joao de Castro Seamount, Azores

The Dom Joao de Castro seamount in the Hirondelle Basin (Azores) is a central volcano on the ultraslow diverging Terceira Rift axis. The combination of structural and geochemical data provides insights into the evolution of central volcanoes in oceanic rift systems above the Azores melting anomaly. The orientation of fault scarps and volcanic structures at D. Joao de Castro and the adjacent Castro fissure zone indicate that the regional SW-NE extending stress field dominates the morphology of the NW Hirondelle Basin. The regional tectonic stress field controls the crustal melt pathways and leads to dike emplacement along fissure zones and the prevalent eruption of mafic lavas. The occurrence of mafic to felsic lavas at D. Joao de Castro gives evidence for both a deep and a shallow crustal melt reservoir generating a subordinate local stress field at the seamount. New Sr-Nd-Pb isotope data along with incompatible trace element ratios indicate that D. Joao de Castro and the Castro Ridges originated from similarly heterogeneous mantle source but did not form simultaneously. Our new model implies that central volcanoes along the Terceira Rift form by the growth of volcanic ridges and transitioned into circular edifices after magmatic systems generate local changes in the regional lithospheric stress field. The geometry of D. Joao de Castro and other magmatic systems along the Terceira Rift combined with the alkaline nature of the erupted lavas, and the large lithosphere thickness indicates that young oceanic rifts are more similar to continental rifts rather than mid-ocean ridges.Peer reviewe

The ROSAT All-Sky Survey: a Catalog of Clusters of Galaxies in a Region of 1 Ster around the South Galactic Pole

A field of 1.013 ster in the ROSAT all-sky survey (RASS), centered on the south galactic pole (SGP), has been searched in a systematic, objective manner for clusters of galaxies. The procedure relied on a correlation of the X-ray positions and properties of ROSAT sources with the distribution of galaxies in the COSMOS digitised data base, which was obtained by scanning the plates of the UK Schmidt IIIa-J optical southern sky survey. The study used the second ROSAT survey data base (RASS-2) and included several optical observing campaigns to measure redshifts. The search, a precursor to the larger REFLEX survey of the whole southern sky, reached the detection limits of the RASS and the COSMOS data, and yielded a catalog of 186 clusters in which the lowest flux is 1.5e-12 erg/cm2/s in the 0.1-2.4 keV band. Of these 157 have measured redshifts. Using a limit of 3.0e-12 erg/cm2/s a complete subset of 112 clusters was obtained, of which 110 have measured redshifts. The spatial distribution of the X-ray clusters out to z = 0.15 shows an extension of the Local Supercluster to the Pisces-Cetus supercluster (z<~0.07), and a more distant orthogonal structure at 0.07<z<0.15.Comment: To be published in ApJ Supplements in February 2002: 53 pages: 18 figure