Avalanche size distribution in a random walk model

We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches and other self-organized critical phenomena in one dimension. We find scaling laws relating the frequency, size and width of avalanches and an exponent $4/3$ in the size distribution law.Comment: 16 pages Latex, macros included, 3 postscript figure

The phase diagram of an Ising model on a polymerized random surface

We construct a random surface model with a string susceptibility exponent one quarter by taking an Ising model on a random surface and introducing an additional degree of freedom which amounts to allowing certain outgrowths on the surfaces. Fine tuning the Ising temperature and the weight factor for outgrowths we find a triple point where the susceptibility exponent is one quarter. At this point magnetized and nonmagnetized gravity phases meet a branched polymer phase.Comment: Latex file, 10 pages, macros included. Two EPS figure

The inverse conjunction fallacy

If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not in the more specific, but also when they accepted both beliefs, they were inclined to give greater confidence to the more general. It is argued that this effect underlies a number of other demonstrations of fallacious reasoning, particularly in category-based induction. Alternative accounts of the phenomenon are evaluated, and it is concluded that the effect is best interpreted in terms of intensional reasoning [Tversky, A., & Kahneman, D. (1983). Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90, 293–315.]

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

Five-Torsion in the Homology of the Matching Complex on 14 Vertices

J. L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the bottom nonvanishing homology group of the matching complex $M_{14}$ on 14 vertices. Combining our observation with results due to Bouc and to Shareshian and Wachs, we conclude that the case $n=14$ is exceptional; for all other $n$, the torsion subgroup of the bottom nonvanishing homology group has exponent three or is zero. The possibility remains that there is other torsion than 3-torsion in higher-degree homology groups of $M_n$ when $n \ge 13$ and $n \neq 14$.Comment: 11 page

Effect of exchange interaction on superparamagnetic relaxation

We use Langer's approach to calculate the reaction rate of a system of two (classical) spins interacting via the exchange coupling $J$ in a magnetic field $H$, with uniaxial anisotropy of constant $K$. We find a particular value of the exchange coupling, that is $j\equiv J/K = j_c\equiv 1-h^2$, where $h\equiv H/2K$, which separates two regimes corresponding to a two-stage and one-stage switching. For $j\gg j_c$ the N\'eel-Brown result for the one-spin problem is recovered.Comment: 7 pages, 2 eps figures, fig.1 of better quality can be provided upon reques