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

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

Long-Lived Double-Barred Galaxies From Pseudo-Bulges

A large fraction of barred galaxies host secondary bars that are embedded in their large-scale primary counterparts. These are common also in gas poor early-type barred galaxies. The evolution of such double-barred galaxies is still not well understood, partly because of a lack of realistic $N$-body models with which to study them. Here we report a new mechanism for generating such systems, namely the presence of rotating pseudo-bulges. We demonstate with high mass and force resolution collisionless $N$-body simulations that long-lived secondary bars can form spontaneously without requiring gas, contrary to previous claims. We find that secondary bars rotate faster than primary ones. The rotation is not, however, rigid: the secondary bars pulsate, with their amplitude and pattern speed oscillating as they rotate through the primary bars. This self-consistent study supports previous work based on orbital analysis in the potential of two rigidly rotating bars. The pulsating nature of secondary bars may have important implications for understanding the central region of double-barred galaxies.Comment: Paper submitted to ApJ

A Constant Bar Fraction out to Redshift z~1 in the Advanced Camera for Surveys Field of the Tadpole Galaxy

Bar-like structures were investigated in a sample of 186 disk galaxies larger than 0.5 arcsec that are in the I-band image of the Tadpole galaxy taken with the HST ACS. We found 22 clear cases of barred galaxies, 21 galaxies with small bars that appear primarily as isophotal twists in a contour plot, and 11 cases of peculiar bars in clump-cluster galaxies, which are face-on versions of chain galaxies. The latter bars are probably young, as the galaxies contain only weak interclump emission. Four of the clearly barred galaxies at z~0.8-1.2 have grand design spirals. The bar fraction was determined as a function of galaxy inclination and compared with the analogous distribution in the local Universe. The bar fraction was also determined as a function of galaxy angular size. These distributions suggest that inclination and resolution effects obscure nearly half of the bars in our sample. The bar fraction was also determined as a function of redshift. We found a nearly constant bar fraction of 0.23+-0.03 from z~0 to z=1.1. When corrected for inclination and size effects, this fraction is comparable to the bar fraction in the local Universe, ~0.4, as tabulated for all bar and Hubble types in the Third Reference Catalogue of Galaxies. The average major axis of a barred galaxy in our sample is ~10 kpc after correcting for redshift with a LambdaCDM cosmology. Galaxy bars were present in normal abundance at least ~8 Gy ago (z~1); bar dissolution cannot be common during a Hubble time unless the bar formation rate is comparable to the dissolution rate.Comment: to appear in ApJ, Sept 1, 2004, Vol 612, 18 pg, 12 figure