Related papers: Sphere packings I
We provide an explicit geometric algorithm involving only ruler and compass constructions in order to specify the specular reflection point on the surface of a reflecting sphere of radius $r$ given two focal points $A$ and $B$ lying outside…
Clusters of galaxies acting as gravitational lenses deform the images of background galaxies. For small galaxies the deformation is determined by the local properties of the lens (shear, convergence). Small circular shaped galaxies are seen…
We present high resolution interferometric and single dish observations of molecular gas in the Serpens cluster-forming core. Star formation does not appear to be homogeneous throughout the core, but is localised in spatially- and…
We propose several descriptive measures to characterize the arrangements of planetary masses, periods, and mutual inclinations within exoplanetary systems. These measures are based in complexity theory and capture the global, system-level…
We propose a model to describe the concentration dependence of the viscosity of soft particles. We incorporate in a very simple way the softness of the particles into expressions originally developed for rigid spheres. This is done by…
Apollonian circle packings arise by repeatedly filling the interstices between mutually tangent circles with further tangent circles. It is possible for every circle in such a packing to have integer radius of curvature, and we call such a…
This paper proves that any compact, closed, simply connected and connected three dimensional stellar manifold is stellar equivalent to the three dimensional sphere.
ISO and IUE spectra of the round planetary nebula Me 2-1 are combined with visual spectra taken from the literature to obtain for the first time a complete extinction-corrected spectrum. With this, the physico-chemical characteristics of…
I review the origins and development of the idea of Dyson spheres, their purpose, their engineering, and their detectability. I explicate the ways in which the popular imagining of them as monolithic objects would make them dynamically…
As a star orbits the center of its host galaxy, the trajectory is encompassed within a 3D toroid. The orbit probes all points in this toroid, unless its orbital frequencies exhibit integer ratios (commensurate frequencies), in which case a…
We consider the Keplerian arcs around a fixed Newtonian center joining two prescribed distinct positions in a prescribed flight time. We prove that, putting aside the "opposition case" where infinitely many planes of motion are possible,…
We study dense packings of a large number of congruent non-overlapping circles inside a square by looking for configurations which maximize the packing density, defined as the ratio between the area occupied by the disks and the area of the…
The stellar obliquity of a transiting planetary system can be constrained by combining measurements of the star's rotation period, radius, and projected rotational velocity. Here we present a hierarchical Bayesian technique for recovering…
This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing geometric analysis. A fundamental feature…
Recent surveys of star forming regions have shown that most stars, and probably all massive stars, are born in dense stellar clusters. The mechanism by which a molecular cloud fragments to form several hundred to thousands of individual…
Accurate stellar parameters and precise elemental abundances are vital pieces to correctly characterize discovered planetary systems, better understand planet formation, and trace galactic chemical evolution. We have performed a uniform…
We derive analytic, closed form, numerically stable solutions for the total flux received from a spherical planet, moon or star during an occultation if the specific intensity map of the body is expressed as a sum of spherical harmonics.…
Recent simulation work has successfully captured the formation of the star clusters that have been observed in merging galaxies. These studies, however, tend to focus on studying extreme starbursts, such as the Antennae galaxies. We aim to…
We study the relationship between local and global density for sphere packings, and in particular the convergence of packing densities in large, compact regions to the Euclidean limit. We axiomatize key properties of sphere packing bounds…
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two…