Related papers: Radial Density in Apollonian Packings
As part of a stellar population sampling program, a series of photometric probes at various field sizes and depths have been obtained in a low extinction window in the galactic anticentre direction. Such data set strong constraints on the…
We model the positional dependence of the optical polarization (BVRI-bands) in the circumstellar disc of beta Pictoris as observed by Gledhill et al. (1991) and Wolstencroft et al. (1995). The particles are spherical, have a size…
We measure the two-point correlation of free Voronoi volumes in binary disc packings, where the packing fraction $\phi_{\rm avg}$ ranges from 0.8175 to 0.8380. We observe short-ranged correlations over the whole range of $\phi_{\rm avg}$…
We present a high spatial resolution submillimeter continuum survey of 24 circumstellar disks in the Tau-Aur and Oph-Sco star formation regions using the SMA. In the context of a simple model, we use broadband SEDs and submillimeter…
We present the densest known packing of regular tetrahedra with density phi = 4000/4671 = 0.856347... Like the recently discovered packings of Kallus et al. [arXiv:0910.5226] and Torquato-Jiao [arXiv:0912.4210], our packing is crystalline…
The origin of the narrow optical emission bands seen toward the Red Rectangle is not yet understood. In this paper we investigate further the proposal that these are due to luminescence of large carbonaceous molecules. Polarised signals of…
The average distance of the equal hard spheres is introduced to evaluate the density of a given arrangement. The absolute smallest value is two radii because the spheres can not be closer to each other than their diameter. The absolute…
We investigate which conditions of dust attenuation and stellar populations allow models of dusty, continuously star-forming, bulge-less disk galaxies at 0.8<z<3.2 to meet the different colour selection criteria of high-z ``red'' galaxies…
We have studied the packing of congruent disks on a spherical cap, for caps of different size and number of disks, $N$. This problem has been considered before only in the limit cases of circle packing inside a circle and on a sphere…
The packing density of the regular cross-polytope in Euclidean $n$-space is unknown except in dimensions $2$ and $4$ where it is 1. The only non-trivial upper bound is due to Gravel, Elser, and Kallus (2011) who proved that for $n=3$ the…
Predicting the densest random disc packing fraction is an unsolved paradigm problem relevant to a number of disciplines and technologies. One difficulty is that it is ill-defined without setting a criterion for the disorder. Another is that…
We present the first significant detection of relativistic smearing of the X-ray reflection spectrum from the putative accretion disk in the low/hard state of Cyg X-1. The ionization state, and amount of relativistic smearing are…
The article presents the mathematical sequences describing circle packing densities in four different geometric configurations involving a hexagonal lattice based equal circle packing in the Euclidian plane. The calculated sequences take…
The ``Little Red Dots'' (LRDs) are red and compact galaxies detected in JWST deep fields, mainly in the redshift range $z=4-8$. Given their compactness and the inferred stellar masses in the hypothesis that LRDs are starburst galaxies, the…
The radial density profile (RDP) of cluster DOLIDZE 14 provides the radius of 9.8 arcmin, it is based on consideration of first plateau region of RDP. This value is less than the radius which comes through consideration of the second…
We present the results of a wide-field survey for extremely red objects (EROs hereafter), the widest so far, based on Ks and R band imaging. The survey covers 701 arcmin^2 and it is 85% complete to Ks\leq18.8 over the whole area and to…
The radial density profiles of stellar galaxy discs can be well approximated as an exponential. Compared to this canonical form, however, the profiles in the majority of disc galaxies show downward or upward breaks at large radii.…
We use a state-of-the-art physics-based model of electromagnetic scattering to analyze average circular polarization ratios measured for the A and B rings of Saturn at a wavelength of 12.6 cm. This model is directly based on the Maxwell…
We review results about the density of typical lattices in $R^n.$ They state that such density is of the order of $2^{-n}.$ We then obtain similar results for random packings in $R^n$: after taking suitably a fraction $\nu$ of a typical…
The vertical structure of stationary thin accretion discs is calculated from the energy balance equation with heat generation due to microscopic ion viscosity {\eta} and electron heat conductivity {\kappa}, both depending on temperature. In…