A Complete Classification of Tractability in RCC-5

We investigate the computational properties of the spatial algebra RCC-5 which is a restricted version of the RCC framework for spatial reasoning. The satisfiability problem for RCC-5 is known to be NP-complete but not much is known about its approximately four billion subclasses. We provide a complete classification of satisfiability for all these subclasses into polynomial and NP-complete respectively. In the process, we identify all maximal tractable subalgebras which are four in total.Comment: See http://www.jair.org/ for an online appendix and other files accompanying this articl

A Solvable 2D Quantum Gravity Model with \GAMMA >0

We consider a model of discretized 2d gravity interacting with Ising spins where phase boundaries are restricted to have minimal length and show analytically that the critical exponent $\gamma= 1/3$ at the spin transition point. The model captures the numerically observed behavior of standard multiple Ising spins coupled to 2d gravity.Comment: Latex, 9 pages, NBI-HE-94-0

Non-equilibrium dynamics in a 3d spin-glass

Non-equilibrium dynamics in a Ag(11%Mn) spin-glass has been studied by low frequency ac-susceptibility and magnetic relaxation experiments. The results unequivocally show that spin structures that memorize the cooling process are imprinted in the system. These imprinted structures disclose themselves through dramatic changes of the dynamics on re-heating the spin-glass through the temperatures where intermittent stops or changes of the cooling rate have been imposed. We can qualitatively interpret our results in terms of the droplet spin-glass model developed by Fisher and Huse [Phys. Rev. B 38 (1988) 373; 386].Comment: 9 pages RevTex, 11 postscript figure

Simulations of Dust in Interacting Galaxies

A new Monte-Carlo radiative-transfer code, Sunrise, is used to study the effects of dust in N-body/hydrodynamic simulations of interacting galaxies. Dust has a profound effect on the appearance of the simulated galaxies. At peak luminosities, about 90% of the bolometric luminosity is absorbed, and the dust obscuration scales with luminosity in such a way that the brightness at UV/visual wavelengths remains roughly constant. A general relationship between the fraction of energy absorbed and the ratio of bolometric luminosity to baryonic mass is found. Comparing to observations, the simulations are found to follow a relation similar to the observed IRX-Beta relation found by Meurer et al (1999) when similar luminosity objects are considered. The highest-luminosity simulated galaxies depart from this relation and occupy the region where local (U)LIRGs are found. This agreement is contingent on the presence of Milky-Way-like dust, while SMC-like dust results in far too red a UV continuum slope to match observations. The simulations are used to study the performance of star-formation indicators in the presence of dust. The far-infrared luminosity is found to be reliable. In contrast, the H-alpha and far-UV luminosity suffer severely from dust attenuation, and dust corrections can only partially remedy the situation.Comment: 4 pages, 5 figures, to appear in the proceedings of the conference "The Spectral Energy Distribution of Gas-Rich Galaxies", eds. C.C. Popescu & R.J. Tuffs (Heidelberg, October 2004

Inertial forces and the foundations of optical geometry

Assuming a general timelike congruence of worldlines as a reference frame, we derive a covariant general formalism of inertial forces in General Relativity. Inspired by the works of Abramowicz et. al. (see e.g. Abramowicz and Lasota, Class. Quantum Grav. 14 (1997) A23), we also study conformal rescalings of spacetime and investigate how these affect the inertial force formalism. While many ways of describing spatial curvature of a trajectory has been discussed in papers prior to this, one particular prescription (which differs from the standard projected curvature when the reference is shearing) appears novel. For the particular case of a hypersurface-forming congruence, using a suitable rescaling of spacetime, we show that a geodesic photon is always following a line that is spatially straight with respect to the new curvature measure. This fact is intimately connected to Fermat's principle, and allows for a certain generalization of the optical geometry as will be further pursued in a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61). For the particular case when the shear-tensor vanishes, we present the inertial force equation in three-dimensional form (using the bold face vector notation), and note how similar it is to its Newtonian counterpart. From the spatial curvature measures that we introduce, we derive corresponding covariant differentiations of a vector defined along a spacetime trajectory. This allows us to connect the formalism of this paper to that of Jantzen et. al. (see e.g. Bini et. al., Int. J. Mod. Phys. D 6 (1997) 143).Comment: 42 pages, 7 figure

The Spectrum of the Loop Transfer Matrix on Finite Lattice

We consider the model of random surfaces with extrinsic curvature term embedded into 3d Euclidean lattice $Z^3$. On a 3d Euclidean lattice it has equivalent representation in terms of transfer matrix $K(Q_{i},Q_{f})$, which describes the propagation of loops $Q$. We study the spectrum of the transfer matrix $K(Q_{i},Q_{f})$ on finite dimensional lattices. The renormalisation group technique is used to investigate phase structure of the model and its critical behaviour.Comment: 10 pages, 5 figures, Latex, psfi