Related papers: Packing Disks into Disks with Optimal Worst-Case D…
Kernel density estimators with circular data have been studied extensively for decades, as they allow flexible estimations even when the shape of the underlying density is complex. Many recent studies have examined bias correction methods;…
In this work we extend recent study of the properties of the dense packing of "superdisks," by Y. Jiao, F. H. Stillinger and S. Torquato, Phys. Rev. Lett. 100, 245504 (2008), to the jammed state formed by these objects in random sequential…
Kernel density estimation is a convenient way to estimate the probability density of a distribution given the sample of data points. However, it has certain drawbacks: proper description of the density using narrow kernels needs large data…
Two dimensional particle disks in proximity to a planet are numerically integrated to determine when a planet in a circular orbit can truncate a particle disk. Collisions are treated by giving each particle a series of velocity…
The opacity of a spiral disk due to dust absorption influences every measurement we make of it in the UV and optical. Two separate techniques directly measure the total absorption by dust in the disk: calibrated distant galaxy counts and…
In this paper we review the main and the most recent evidence for the presence of a core radius in the distribution of the dark matter around spiral galaxies. Their rotation curves, coadded according to the galaxy luminosity, conform to an…
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…
While the total interior mass of a galaxy is reasonably well determined by a good rotation curve, the relative contributions from disk, bulge and halo are only weakly constrained by one-dimensional data. Barred galaxies are intrinsically…
We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…
It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the…
We use current observations on the number statistics of gravitationally lensed optical arcs towards galaxy clusters to derive an upper limit on the cosmological mass density of the Universe. The gravitational lensing statistics due to…
We present a performance analysis of the DiskMass Survey. The survey uses collisionless tracers in the form of disk stars to measure the surface-density of spiral disks, to provide an absolute calibration of the stellar mass-to-light ratio,…
We calculate the mean density profiles for luminous and dark matter on distance scales $D \sim(1 - 100)$ Mpc around us using recent all-sky catalogs of galaxy groups. Within the Local Volume $( D < 11 ~\rm Mpc)$ we derived the mean stellar…
Given a set of $n$ points in the plane, the Unit Disk Cover (UDC) problem asks to compute the minimum number of unit disks required to cover the points, along with a placement of the disks. The problem is NP-hard and several approximation…
Exact analytical solutions are given for the three finite disks with surface density $\Sigma_n=\sigma_0 (1-R^2/\alpha^2)^{n-1/2} \textrm{with} n=0, 1, 2$. Closed-form solutions in cylindrical co-ordinates are given using only elementary…
Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…
We present a perfect simulation of the hard disks model via the partial rejection sampling method. Provided the density of disks is not too high, the method produces exact samples in $O(\log n)$ rounds, and total time $O(n)$, where $n$ is…
We use high-quality optical rotation curves of 9 low-luminosity disk galaxies to obtain the velocity profile of the surrounding dark matter halos. We find that they increase linearly with radius at least out to the stellar disk edge,…
In this paper we will discuss optimal lower and upper density of non-parallel cylinder packings in $R^{3}$ and similar problems. The main result of the paper is a proof of the conjecture of K. Kuperberg for upper density (existence of a…
We present an algorithm to simulate random sequential adsorption (random "parking") of discs on constant-curvature surfaces: the plane, sphere, hyperboloid, and projective plane, all embedded in three-dimensional space. We simulate complete…