Tales within Tales and Cutoffs within Cutoffs: What Sets the Mass Scale for Galaxies?

Please answer ``yes'' or ``no'': 1. Does the mass function for clusters of galaxies cut off exponentially? 2. Does the luminosity function for galaxies cut off exponentially? 3. Is the dependence of virial velocity on galaxy luminosity a power law? 4. Does the velocity function for galaxies cut off exponentially?Comment: 10 pages, no figures, contribution to the MPA/ESO/MPE/USM conference "Lighthouses of the Universe", Sunyaev et al. (eds.), ESO Astrophysics Symposia, Springer Verla

Correlated random fields in dielectric and spin glasses

Both orientational glasses and dipolar glasses possess an intrinsic random field, coming from the volume difference between impurity and host ions. We show this suppresses the glass transition, causing instead a crossover to the low $T$ phase. Moreover the random field is correlated with the inter-impurity interactions, and has a broad distribution. This leads to a peculiar variant of the Imry-Ma mechanism, with 'domains' of impurities oriented by a few frozen pairs. These domains are small: predictions of domain size are given for specific systems, and their possible experimental verification is outlined. In magnetic glasses in zero field the glass transition survives, because the random fields are disallowed by time-reversal symmetry; applying a magnetic field then generates random fields, and suppresses the spin glass transition.Comment: minor modifications, final versio

Generic Misalignment Aberration Patterns in Wide-Field Telescopes

Axially symmetric telescopes produce well known "Seidel" off-axis third-order aberration patterns: coma, astigmatism, curvature of field and distortion. When axial symmetry is broken by the small misalignments of optical elements, additional third-order aberration patterns arise: one each for coma, astigmatism and curvature of field and two for distortion. Each of these misalignment patterns is characterized by an associated two-dimensional vector, each of which in turn is a linear combination of the tilt and decenter vectors of the individual optical elements. For an N-mirror telescope, 2(N-1) patterns must be measured to keep the telescope aligned. Alignment of the focal plane may require two additional patterns. For N = 3, as in a three mirror anastigmat, there is a two-dimensional "subspace of benign misalignment" over which the misalignment patterns for third-order coma, astigmatism and curvature of field are identically zero. One would need to measure at least one of the two distortion patterns to keep the telescope aligned. Alternatively, one might measure one of the fifth-order misalignment patterns, which are derived herein. But the fifth-order patterns are rather insensitive to misalignments, even with moderately wide fields, rendering them of relatively little use in telescope alignment. Another alternative would be to use telescope pointing as part of the alignment solution.Comment: 50 pages, 13 figures, Accepted for Publication in PAS