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

Typical properties of optimal growth in the Von Neumann expanding model for large random economies

We calculate the optimal solutions of the fully heterogeneous Von Neumann expansion problem with $N$ processes and $P$ goods in the limit $N\to\infty$. This model provides an elementary description of the growth of a production economy in the long run. The system turns from a contracting to an expanding phase as $N$ increases beyond $P$. The solution is characterized by a universal behavior, independent of the parameters of the disorder statistics. Associating technological innovation to an increase of $N$, we find that while such an increase has a large positive impact on long term growth when $N\ll P$, its effect on technologically advanced economies ($N\gg P$) is very weak.Comment: 8 pages, 1 figur

Analysis of Collectivism and Egoism Phenomena within the Context of Social Welfare

Comparative benefits provided by the basic social strategies including collectivism and egoism are investigated within the framework of democratic decision-making. In particular, we study the mechanism of growing "snowball" of cooperation.Comment: 12 pages, 5 figures. Translated from Russian. Original Russian Text published in Problemy Upravleniya, 2008, No. 4, pp. 30-3

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

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

New evidence on Allyn Young's style and influence as a teacher

This paper publishes the hitherto unpublished correspondence between Allyn Abbott Young's biographer Charles Blitch and 17 of Young's former students or associates. Together with related biographical and archival material, the paper shows the way in which this adds to our knowledge of Young's considerable influence as a teacher upon some of the twentieth century's greatest economists. The correspondents are as follows: James W Angell, Colin Clark, Arthur H Cole, Lauchlin Currie, Melvin G de Chazeau, Eleanor Lansing Dulles, Howard S Ellis, Frank W Fetter, Earl J Hamilton, Seymour S Harris, Richard S Howey, Nicholas Kaldor, Melvin M Knight, Bertil Ohlin, Geoffrey Shepherd, Overton H Taylor, and Gilbert Walker

Fluctuations in the coarsening dynamics of the O(N) model: are they similar to those in glassy systems?

We study spatio-temporal fluctuations in the non-equilibrium dynamics of the d dimensional O(N) in the large N limit. We analyse the invariance of the dynamic equations for the global correlation and response in the slow ageing regime under transformations of time. We find that these equations are invariant under scale transformations. We extend this study to the action in the dynamic generating functional finding similar results. This model therefore falls into a different category from glassy problems in which full time-reparametrisation invariance, a larger symmetry that emcompasses time scale invariance, is expected to be realised asymptotically. Consequently, the spatio-temporal fluctuations of the large N O(N) model should follow a different pattern from that of glassy systems. We compute the fluctuations of local, as well as spatially separated, two-field composite operators and responses, and we confront our results with the ones found numerically for the 3d Edwards-Anderson model and kinetically constrained lattice gases. We analyse the dependence of the fluctuations of the composite operators on the growing domain length and we compare to what has been found in super-cooled liquids and glasses. Finally, we show that the development of time-reparametrisation invariance in glassy systems is intimately related to a well-defined and finite effective temperature, specified from the modification of the fluctuation-dissipation theorem out of equilibrium. We then conjecture that the global asymptotic time-reparametrisation invariance is broken down to time scale invariance in all coarsening systems.Comment: 57 pages, 5 figure

Two Interacting Electrons in a Quasiperiodic Chain

We study numerically the effect of on-site Hubbard interaction U between two electrons in the quasiperiodic Harper's equation. In the periodic chain limit by mapping the problem to that of one electron in two dimensions with a diagonal line of impurities of strength U we demonstrate a band of resonance two particle pairing states starting from E=U. In the ballistic (metallic) regime we show explicitly interaction-assisted extended pairing states and multifractal pairing states in the diffusive (critical) regime. We also obtain localized pairing states in the gaps and the created subband due to U, whose number increases when going to the localized regime, which are responsible for reducing the velocity and the diffusion coefficient in the qualitatively similar to the non-interacting case ballistic and diffusive dynamics. In the localized regime we find propagation enhancement for small U and stronger localization for larger U, as in disordered systems.Comment: 14 pages Revtex file, 8 figures (split into 19 jpg figures). (postscript versions of the jpg figures are also available upon request) submitted to PR

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