Measurement of the Mass Profile of Abell 1689

In this letter we present calibrated mass and light profiles of the rich cluster of galaxies Abell 1689 out to 1 $h^{-1}$ Mpc from the center. The high surface density of faint blue galaxies at high redshift, selected by their low surface brightness, are unique tools for mapping the projected mass distribution of foreground mass concentrations. The systematic gravitational lens distortions of $10^4$ of these background galaxies in 15\arcmin\ fields reveal detailed mass profiles for intervening clusters of galaxies, and are a direct measure of the growth of mass inhomogeneity. The mass is measured directly, avoiding uncertainties encountered in velocity or X-ray derived mass estimates. Mass in the rich cluster Abell 1689 follows smoothed light, outside 100 h$^{-1}$ kpc, with a rest-frame V band mass-to-light ratio of $400 \pm 60$ $h^{-1} (M/L_V)_\odot$. Near the cluster center, mass appears to be more smoothly distributed than light. Out to a radius of 1 $h^{-1}$ Mpc the total mass follows a steeper than isothermal profile. Comparing with preliminary high resolution N-body clustering simulations for various cosmogonies on these scales, these data are incompatible with hot dark matter, a poor fit to most mixed dark matter models, and favor open or $\Lambda > 0$ cold dark matter. Substructure is seen in both the mass and the light, but detailed correspondence is erased on scales less than 100 $h^{-1}$ kpc.Comment: 13 pages, uuencoded, compressed postscript file, 2 figures included additional 1Mbyte figure available on request. Only change is that in original errorbars on Fig. 5 were a factor of 2 too big

Topics in the Dynamics or General Relativity

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An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur

Studying pion effects on the chiral phase transition

We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a five percent change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed.Comment: 2 pages, 2 figures, talk given by J.A.M. at the 30th International School of Nuclear Physics, Erice, Sicily from 16 - 24 September 200

Adjustable tension wire guide Patent

Adjustable spiral wire winding devic

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

Outflanking and securely using the PIN/TAN-System

The PIN/TAN-system is an authentication and authorization scheme used in e-business. Like other similar schemes it is successfully attacked by criminals. After shortly classifying the various kinds of attacks we accomplish malicious code attacks on real World Wide Web transaction systems. In doing so we find that it is really easy to outflank these systems. This is even supported by the users' behavior. We give a few simple behavior rules to improve this situation. But their impact is limited. Also the providers support the attacks by having implementation flaws in their installations. Finally we show that the PIN/TAN-system is not suitable for usage in highly secure applications.Comment: 7 pages; 2 figures; IEEE style; final versio

Neutrino emissivities and bulk viscosity in neutral two-flavor quark matter

We study thermodynamic and transport properties for the isotropic color-spin-locking (iso-CSL) phase of two-flavor superconducting quark matter under compact star constraints within a NJL-type chiral quark model. Chiral symmetry breaking and the phase transition to superconducting quark matter leads to a density dependent change of quark masses, chemical potentials and diquark gap. A self-consistent treatment of these physical quantities influences on the microscopic calculations of transport properties. We present results for the iso-CSL direct URCA emissivities and bulk viscosities, which fulfill the constraints on quark matter derived from cooling and rotational evolution of compact stars. We compare our results with the phenomenologically successful, but yet heuristic 2SC+X phase. We show that the microscopically founded iso-CSL phase can replace the purely phenomenological 2SC+X phase in modern simulations of the cooling evolution for compact stars with color superconducting quark matter interior.Comment: 15 pages, 6 figures, references added, text improve

Dynamically induced scalar quark confinement

We employ a functional approach to investigate the confinement problem in quenched Landau gauge QCD. We demonstrate analytically that a linear rising potential between massive quarks is generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities is driven by the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken. We have thus uncovered a novel mechanism that directly links chiral symmetry breaking with confinement.Comment: 12 pages, 2 figures; v2: clarifications added and typos corrected, version to be published by MPL