The stable roommates problem with globally-ranked pairs

We introduce a restriction of the stable roommates problem in which roommate pairs are ranked globally. In contrast to the unrestricted problem, weakly stable matchings are guaranteed to exist, and additionally, they can be found in polynomial time. However, it is still the case that strongly stable matchings may not exist, and so we consider the complexity of finding weakly stable matchings with various desirable properties. In particular, we present a polynomial-time algorithm to find a rank-maximal (weakly stable) matching. This is the first generalization of an algorithm due to [Irving et al. 06] to a nonbipartite setting. Also, we describe several hardness results in an even more restricted setting for each of the problems of finding weakly stable matchings that are of maximum size, are egalitarian, have minimum regret, and admit the minimum number of weakly blocking pairs

A spin-boson thermal rectifier

Rectification of heat transfer in nanodevices can be realized by combining the system inherent anharmonicity with structural asymmetry. we analyze this phenomenon within the simplest anharmonic system -a spin-boson nanojunction model. We consider two variants of the model that yield, for the first time, analytical solutions: a linear separable model in which the heat reservoirs contribute additively, and a non-separable model suitable for a stronger system-bath interaction. Both models show asymmetric (rectifying) heat conduction when the couplings to the heat reservoirs are different.Comment: 5 pages, 3 figures, RevTeX

The Visibility of Galactic Bars and Spiral Structure At High Redshifts

We investigate the visibility of galactic bars and spiral structure in the distant Universe by artificially redshifting 101 B-band CCD images of local spiral galaxies from the Ohio State University Bright Spiral Galaxy Survey. Our artificially redshifted images correspond to Hubble Space Telescope I-band observations of the local galaxy sample seen at z=0.7, with integration times matching those of both the very deep Northern Hubble Deep Field data, and the much shallower Flanking Field observations. The expected visibility of galactic bars is probed in two ways: (1) using traditional visual classification, and (2) by charting the changing shape of the galaxy distribution in "Hubble space", a quantitative two-parameter description of galactic structure that maps closely on to Hubble's original tuning fork. Both analyses suggest that over 2/3 of strongly barred luminous local spirals i.e. objects classified as SB in the Third Reference Catalog) would still be classified as strongly barred at z=0.7 in the Hubble Deep Field data. Under the same conditions, most weakly barred spirals (classified SAB in the Third Reference Catalog) would be classified as regular spirals. The corresponding visibility of spiral structure is assessed visually, by comparing luminosity classifications for the artificially redshifted sample with the corresponding luminosity classifications from the Revised Shapley Ames Catalog. We find that for exposures times similar to that of the Hubble Deep Field spiral structure should be detectable in most luminous low-inclination spiral galaxies at z=0.7 in which it is present. [ABRIDGED]Comment: Accepted for publication in The Astronomical Journa

Non-LTE, Relativistic Accretion Disk Fits to 3C~273 and the Origin of the Lyman Limit Spectral Break

We fit general relativistic, geometrically thin accretion disk models with non-LTE atmospheres to near simultaneous multiwavelength data of 3C~273, extending from the optical to the far ultraviolet. Our model fits show no flux discontinuity associated with a hydrogen Lyman edge, but they do exhibit a spectral break which qualitatively resembles that seen in the data. This break arises from relativistic smearing of Lyman emission edges which are produced locally at tens of gravitational radii in the disk. We discuss the possible effects of metal line blanketing on the model spectra, as well as the substantial Comptonization required to explain the observed soft X-ray excess. Our best fit accretion disk model underpredicts the near ultraviolet emission in this source, and also has an optical spectrum which is too red. We discuss some of the remaining physical uncertainties, and suggest in particular that an extension of our models to the slim disk regime and/or including nonzero magnetic torques across the innermost stable circular orbit may help resolve these discrepancies.Comment: Accepted for publication in Ap

An eigenfunction method for particle acceleration at ultra-relativistic shocks

We adapt and modify the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock front via the first-order Fermi process (Kirk, J.G., Schneider, P., Astrophysical Journal 315, 425 (1987)) to apply to shocks of arbitrarily high Lorentz factor. The power-law index of accelerated particles undergoing isotropic small-angle scattering at an ultrarelativistic, unmagnetized shock is found to be s=4.23 +/- 0.2 (where s=d\ln f/ d\ln p, with f the Lorentz-invariant phase-space density and p the momentum), in agreement with the results of Monte-Carlo simulations. We present results for shocks in plasmas with different equations of state and for Lorentz factors ranging from 5 to infinity.Comment: 4 pages, 2 figures, contribution to the Proceedings of the 5th Huntsville GRB Symposiu

Particle Acceleration at Ultra-Relativistic Shocks and the Spectra of Relativistic Fireballs

We examine Fermi-type acceleration at relativistic shocks, and distinguish between the initial boost of the first shock crossing cycle, where the energy gain per particle can be very large, and the Fermi process proper with repeated shock crossings, in which the typical energy gain is of order unity. We calculate by means of numerical simulations the spectrum and angular distribution of particles accelerated by this Fermi process, in particular in the case where particle dynamics can be approximated as small-angle scattering. We show that synchrotron emission from electrons or positrons accelerated by this process can account remarkably well for the observed power-law spectra of GRB afterglows and Crab-like supernova remnants. In the context of a decelerating relativistic fireball, we calculate the maximum particle energy attainable by acceleration at the external blast wave, and discuss the minimum energy for this acceleration process and its consequences for the observed spectrum.Comment: To appear in Proceedings of the 5th Huntsville Gamma-Ray Burst Symposium. LaTeX, 6 pages, 2 figures, uses aipproc.sty and epsfi

Peace by Piece: (Re) imagining Division in Belfast’s Contested Spaces through Memory

This paper investigates processes and actions of diversifying memories of division in Northern Ireland’s political conflict known as the Troubles. Societal division is manifested in its built fabric and territories that have been adopted by predominant discourses of a fragmented society in Belfast; the unionist east and the nationalist west. The aim of the paper is to explore current approaches in planning contested spaces that have changed over time, leading to success in many cases. The argument is that divided cities, like Belfast, feature spatial images and memories of division that range from physical, clear-cut segregation to manifested actions of violence and have become influential representations in the community’s associative memory. While promoting notions of ‘re-imaging’ by current councils demonstrates a total erasure of the Troubles through cleansing its local collective memory, there yet remains an attempt to communicate a different tale of the city’s socio-economic past, to elaborate its supremacy for shaping future lived memories. Yet, planning Belfast’s contested areas is still suffering from a poor understanding of the context and its complexity against overambitious visions

Solitons in (1,1)-supersymmetric massive sigma model

We find the solitons of massive (1,1)-supersymmetric sigma models with target space the groups $SO(2)$ and $SU(2)$ for a class of scalar potentials and compute their charge, mass and moduli space metric. We also investigate the massive sigma models with target space any semisimple Lie group and show that some of their solitons can be obtained from embedding the $SO(2)$ and $SU(2)$ solitons.Comment: Phyzzx.tex, 32 pp, 3 fig