Related papers: Radial Density in Apollonian Packings
The theoretically observable limit of electron density distribution by single-crystal X-ray diffraction is discussed. When F_{orb} and {\delta}F are defined as, respectively, the partial structure factor for an orbital and the deviation of…
Dense packings have served as useful models of the structure of liquid, glassy and crystal states of matter, granular media, heterogeneous materials, and biological systems. Probing the symmetries and other mathematical properties of the…
We investigate the radiation from a charged particle rotating around a dielectric cylinder with a negative real part of dielectric permittivity. For the general case of frequency dispersion in dielectric permittivity, expressions are…
(Abridged) The goal of this paper is to quantify the changes on the SF distribution within the disc galaxies in the last ~8 Gyr. We use as a proxy for the SF radial profile the Near-UV surface brightness distributions, allowing suitably for…
Apparent (radiation) radius of neutron star,R_\infty, depends on the star gravitational mass in quite a different way than the standard coordinate radius in the Schwarzschild metric, R. We show that, for a broad set of equations of state of…
The extended hot X-ray emitting gaseous halo of the Milky Way has an optical depth $\sim1$ for the dominant emission lines of \ion{O}{7} and \ion{O}{8}, which are used to infer the halo properties. To improve on halo gas properties, we…
Using the catalog of O'Neil, Bothun, & Schombert (1999), we examine the central surface brightness distribution (phi(mu_B(0))) of galaxies in the 22.0 < mu_B(0) < 25.0 mag arcsec^{-2} range. Taking advantage of having a catalog in which…
The method, proposed in \cite{Za22} to derive the densest packing fraction of random disc and sphere packings, is shown to yield in two dimensions too high a value that (i) violates the very assumption underlying the method and (ii)…
`Conspiracy' between the dark and the baryonic mater prohibits an unambiguous decomposition of disc galaxy rotation curves into the corresponding components. Several methods have been proposed to counter this difficulty, but their results…
We consider the oxygen abundance distributions for a sample of massive spiral galaxies from the MaNGA survey in which the radial abundance gradient flattens to a constant value outside of the outer break radius, Rb,outer. The outer break…
We present scattered light images of the TW Hya disk performed with SPHERE in PDI mode at 0.63, 0.79, 1.24 and 1.62 micron. We also present H2/H3-band ADI observations. Three distinct radial depressions in the polarized intensity…
This is the second in a series of papers giving a proof of the Kepler conjecture, which asserts that the density of a packing of congruent spheres in three dimensions is never greater than $\pi/\sqrt{18}\approx 0.74048...$. This is the…
The physical mechanism through which the outgoing material of massive red supergiants is accelerated above the escape velocity is unclear. Thanks to the transparency of its circumstellar envelope, the nearby red supergiant Betelgeuse gives…
We study the problem of high-dimensional multiple packing in Euclidean space. Multiple packing is a natural generalization of sphere packing and is defined as follows. Let $ N>0 $ and $ L\in\mathbb{Z}_{\ge2} $. A multiple packing is a set…
We determine putative optimal packings of regular spherical polygons via optimization on smooth manifolds. For several cases, we establish maximality by extending the Lov\'asz theta number to Cayley graphs on the special orthogonal group…
We consider $O(1)$ dense loop model in a square lattice wrapped on a cylinder of odd circumference $L$ and calculate the exact densities of loops. These densities of loops are equal to the densities of critical bond percolation clusters on…
We measure the two-point density correlations and Voronoi cell distributions of cyclically sheared granular spheres obtained with a fluorescence technique and compare them with random packing of frictionless spheres. We find that the radial…
We consider two seemingly unconnected problems: first, under what circumstances are arithmetic groups like SL(2,O) generated by elementary matrices; second, when do certain classes of circle/sphere packings fill up space? We show that these…
We present a detailed X-ray spectral analysis of the Circinus Galaxy using archival data obtained with the ASCA satellite. The spectrum shows numerous emission lines in the soft X-ray band from highly ionized ions, as well as Compton…
High precision planet orbital data extracted from direct observation, spacecraft explorations and laser ranging techniques enable to put a strong constraint on the maximal dark matter density of a spherical halo centered around the Sun. The…