Two-colorings with many monochromatic cliques in both colors

Color the edges of the n-vertex complete graph in red and blue, and suppose that red k-cliques are fewer than blue k-cliques. We show that the number of red k-cliques is always less than cknk, where ck∈(0, 1) is the unique root of the equation zk=(1-z)k+kz(1-z)k-1. On the other hand, we construct a coloring in which there are at least cknk-O(nk-1) red k-cliques and at least the same number of blue k-cliques. © 2013 Elsevier Inc

On the naturality of the Mathai-Quillen formula

We give an alternative proof for the Mathai-Quillen formula for a Thom form using its natural behaviour with respect to fiberwise integration. We also study this phenomenon in general context.Comment: 6 page

The quadrupole moment of slowly rotating fluid balls

In this paper we use the second order formalism of Hartle to study slowly and rigidly rotating stars with focus on the quadrupole moment of the object. The second order field equations for the interior fluid are solved numerically for different classes of possible equations of state and these solutions are then matched to a vacuum solution that includes the general asymptotically flat axisymmetric metric to second order, using the Darmois-Israel procedure. For these solutions we find that the quadrupole moment differs from that of the Kerr metric, as has also been found for some equations of state in other studies. Further we consider the post-Minkowskian limit analytically. In the paper we also illustrate how the relativistic multipole moments can be calculated from a complex gravitational potential.Comment: 13 pages, 5 figure

The Near-Infrared Number Counts and Luminosity Functions of Local Galaxies

This study presents a wide-field near-infrared (K-band) survey in two fields; SA 68 and Lynx 2. The survey covers an area of 0.6 deg.$^2$, complete to K=16.5. A total of 867 galaxies are detected in this survey of which 175 have available redshifts. The near-infrared number counts to K=16.5 mag. are estimated from the complete photometric survey and are found to be in close agreement with other available studies. The sample is corrected for incompleteness in redshift space, using selection function in the form of a Fermi-Dirac distribution. This is then used to estimate the local near-infrared luminosity function of galaxies. A Schechter fit to the infrared data gives: M$^\ast_K = -25.1 \pm 0.3$, $\alpha = -1.3\pm 0.2$ and $\phi^\ast =(1.5\pm 0.5)\times 10^{-3}$ Mpc$^{-3}$ (for H$_0=50$ Km/sec/Mpc and q$_0=0.5$). When reduced to $\alpha=-1$, this agrees with other available estimates of the local IRLF. We find a steeper slope for the faint-end of the infrared luminosity function when compared to previous studies. This is interpreted as due to the presence of a population of faint but evolved (metal rich) galaxies in the local Universe. However, it is not from the same population as the faint blue galaxies found in the optical surveys. The characteristic magnitude ($M^\ast_K$) of the local IRLF indicates that the bright red galaxies ($M_K\sim -27$ mag.) have a space density of $\le 5\times 10^{-5}$ Mpc$^{-3}$ and hence, are not likely to be local objects.Comment: 24 pages, 8 figures, AASTEX 4.0, published in ApJ 492, 45

Uniform tiling with electrical resistors

The electric resistance between two arbitrary nodes on any infinite lattice structure of resistors that is a periodic tiling of space is obtained. Our general approach is based on the lattice Green's function of the Laplacian matrix associated with the network. We present several non-trivial examples to show how efficient our method is. Deriving explicit resistance formulas it is shown that the Kagom\'e, the diced and the decorated lattice can be mapped to the triangular and square lattice of resistors. Our work can be extended to the random walk problem or to electron dynamics in condensed matter physics.Comment: 22 pages, 14 figure

Dielectric formalism and damping of collective modes in trapped Bose-Einstein condensed gases

We present the general dielectric formalism for Bose-Einstein condensed systems in external potential at finite temperatures. On the basis of a model arising within this framework as a first approximation in an intermediate temperature region for large condensate we calculate the damping of low-energy excitations in the collisionless regime.Comment: 4 pages, no figures, RevTe

Phase-field crystal modelling of crystal nucleation, heteroepitaxy and patterning

We apply a simple dynamical density functional theory, the phase-field-crystal (PFC) model, to describe homogeneous and heterogeneous crystal nucleation in 2d monodisperse colloidal systems and crystal nucleation in highly compressed Fe liquid. External periodic potentials are used to approximate inert crystalline substrates in addressing heterogeneous nucleation. In agreement with experiments in 2d colloids, the PFC model predicts that in 2d supersaturated liquids, crystalline freezing starts with homogeneous crystal nucleation without the occurrence of the hexatic phase. At extreme supersaturations crystal nucleation happens after the appearance of an amorphous precursor phase both in 2d and 3d. We demonstrate that contrary to expectations based on the classical nucleation theory, corners are not necessarily favourable places for crystal nucleation. Finally, we show that adding external potential terms to the free energy, the PFC theory can be used to model colloid patterning experiments.Comment: 21 pages, 16 figure

Phase-field approach to polycrystalline solidification including heterogeneous and homogeneous nucleation

Advanced phase-field techniques have been applied to address various aspects of polycrystalline solidification including different modes of crystal nucleation. The height of the nucleation barrier has been determined by solving the appropriate Euler-Lagrange equations. The examples shown include the comparison of various models of homogeneous crystal nucleation with atomistic simulations for the single component hard-sphere fluid. Extending previous work for pure systems (Gránásy L, Pusztai T, Saylor D and Warren J A 2007 Phys. Rev. Lett. 98 art no 035703), heterogeneous nucleation in unary and binary systems is described via introducing boundary conditions that realize the desired contact angle. A quaternion representation of crystallographic orientation of the individual particles (outlined in Pusztai T, Bortel G and Gránásy L 2005 Europhys. Lett. 71 131) has been applied for modeling a broad variety of polycrystalline structures including crystal sheaves, spherulites and those built of crystals with dendritic, cubic, rhombododecahedral, truncated octahedral growth morphologies. Finally, we present illustrative results for dendritic polycrystalline solidification obtained using an atomistic phase-field model

The First Hour of Extra-galactic Data of the Sloan Digital Sky Survey Spectroscopic Commissioning: The Coma Cluster

On 26 May 1999, one of the Sloan Digital Sky Survey (SDSS) fiber-fed spectrographs saw astronomical first light. This was followed by the first spectroscopic commissioning run during the dark period of June 1999. We present here the first hour of extra-galactic spectroscopy taken during these early commissioning stages: an observation of the Coma cluster of galaxies. Our data samples the Southern part of this cluster, out to a radius of 1.5degrees and thus fully covers the NGC 4839 group. We outline in this paper the main characteristics of the SDSS spectroscopic systems and provide redshifts and spectral classifications for 196 Coma galaxies, of which 45 redshifts are new. For the 151 galaxies in common with the literature, we find excellent agreement between our redshift determinations and the published values. As part of our analysis, we have investigated four different spectral classification algorithms: spectral line strengths, a principal component decomposition, a wavelet analysis and the fitting of spectral synthesis models to the data. We find that a significant fraction (25%) of our observed Coma galaxies show signs of recent star-formation activity and that the velocity dispersion of these active galaxies (emission-line and post-starburst galaxies) is 30% larger than the absorption-line galaxies. We also find no active galaxies within the central (projected) 200 h-1 Kpc of the cluster. The spatial distribution of our Coma active galaxies is consistent with that found at higher redshift for the CNOC1 cluster survey. Beyond the core region, the fraction of bright active galaxies appears to rise slowly out to the virial radius and are randomly distributed within the cluster with no apparent correlation with the potential merger of the NGC 4839 group. [ABRIDGED]Comment: Accepted in AJ, 65 pages, 20 figures, 5 table