Non-Analyticity and the van der Waals Limit

We study the analyticity properties of the free energy f_\ga(m) of the Kac model at points of first order phase transition, in the van der Waals limit \ga\searrow 0. We show that there exists an inverse temperature $\beta_0$ and \ga_0>0 such that for all $\beta\geq \beta_0$ and for all \ga\in(0,\ga_0), f_\ga(m) has no analytic continuation along the path $m\searrow m^*$ ($m^*$ denotes spontaneous magnetization). The proof consists in studying high order derivatives of the pressure p_\ga(h), which is related to the free energy f_\ga(m) by a Legendre transform

Photometric and dynamic evolution of an isolated disc galaxy simulation

We present a detailed analysis of the evolution of a simulated isolated disc galaxy. The simulation includes stars, gas, star formation and simple chemical yields. Stellar particles are split in two populations: the old one is present at the beginning of the simulation and is calibrated according to various ages and metallicities; the new population borns in the course of the simulation and inherits the metallicity of the gas particles. The results have been calibrated in four wavebands with the spectro-photometric evolutionary model GISSEL2000 (Bruzual & Charlot 1993). Dust extinction has also been taken into account. A rest-frame morphological and bidimensional photometric analysis has been performed on simulated images, with the same tools as for observations. The effects of the stellar bar formation and the linked star formation episode on the global properties of the galaxy (mass and luminosity distribution, colours, isophotal radii) have been analysed. In particular, we have disentangled the effects of stellar evolution from dynamic evolution to explain the cause of the isophotal radii variations. We show that the dynamic properties (e.g. mass) of the area enclosed by any isophotal radius depends on the waveband and on the level of star formation activity. It is also shown that the bar isophotes remain thinner than mass isodensities a long time (> 0.7 Gyr) after the maximum of star formation rate. We show that bar ellipticity is very wavelength dependent as suggested by real observations. Effects of dust extinction on photometric and morphological measurements are systematically quantified.Comment: 14 pages, 16 figures (13 in eps, 3 in jpg format). Accepted for publication in A&

A combined representation method for use in band structure calculations. 1: Method

A representation was described whose basis levels combine the important physical aspects of a finite set of plane waves with those of a set of Bloch tight-binding levels. The chosen combination has a particularly simple dependence on the wave vector within the Brillouin Zone, and its use in reducing the standard one-electron band structure problem to the usual secular equation has the advantage that the lattice sums involved in the calculation of the matrix elements are actually independent of the wave vector. For systems with complicated crystal structures, for which the Korringa-Kohn-Rostoker (KKR), Augmented-Plane Wave (APW) and Orthogonalized-Plane Wave (OPW) methods are difficult to apply, the present method leads to results with satisfactory accuracy and convergence