Related papers: Density of binary disc packings: lower and upper b…
Maximum disc decompositions of rotation curves place a dynamical upper limit to the mass attributable to stars in galaxies. The precise definition of this term, however, can be vague and varies in usage. We develop an algorithm to robustly…
In previous work a probabilistic approach to controlling difficulties of density in hyperbolic space led to a workable notion of optimal density for packings of bodies. In this paper we extend an ergodic theorem of Nevo to provide an…
We give sharp upper bounds on the maximal injectivity radius of finite-area hyperbolic surfaces and use them, for each g at least 2, to identify a constant r_{g-1,2} with the property that the set of closed genus-g hyperbolic surfaces with…
We use a smoothed particle hydrodynamics (SPH) code to examine the effects of misaligned binary companions on Be star discs. We systematically vary the degree of misalignment between the disc and the binary orbit, as well as the disc…
We obtain new linear programming (LP) and constructive bounds for the covering radius of binary orthogonal arrays of strength $2k$. Our LP bounds develop in two alternative scenarios. First, if a point $y \in F_2^n$, where the covering…
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…
We show that there exists a lattice covering of $\mathbb{R}^n$ by Eucledian spheres of equal radius with density $O\big(n \ln^{\beta} n \big)$ as $n\to\infty$, where \begin{align*} \beta := \frac{1}{2} \log_2 \left(\frac{8 \pi…
We analyse the global structure of the old stellar discs in 34 edge-on spiral galaxies. The radial and vertical exponential scale parameters of the discs are obtained by applying an improved two-dimensional decomposition technique to our…
The relaxed motion of stars and gas in galactic discs is well approximated by a rotational velocity that is a function of radial position only, implying that individual components have lost any information about their prior states.…
By a compact packing of the plane by discs, $P$, we mean a collection of closed discs in the plane with pairwise disjoint interior so that, for every disc $C\in P$, there exists a sequence of discs $D_{0},\ldots,D_{m-1}\in P$ so that each…
We study two related quantities which generalize the concept of upper Banach density of a set to two measurable subsets of the plane. The first of them allows us to generalize a classic result on sufficiently large distances realized in a…
We prove sphere packing density bounds in hyperbolic space (and more generally irreducible symmetric spaces of noncompact type), which were conjectured by Cohn and Zhao and generalize Euclidean bounds by Cohn and Elkies. We work within the…
Random arrangements of points in the plane, interacting only through a simple hard core exclusion, are considered. An intensity parameter controls the average density of arrangements, in analogy with the Poisson point process. It is proved…
[ABRIDGED] We study supermassive black hole binary mergers driven by angular momentum loss to small-scale gas discs. Such binaries form after major galaxy mergers, but their fate is unclear since hardening through stellar scattering becomes…
We discuss optimal constants in a recent result of Rudelson and Vershynin on marginal densities. We show that if $f$ is a probability density on $\R^n$ of the form $f(x)=\prod_{i=1}^n f_i(x_i)$, where each $f_i$ is a density on $\R$, say…
We study the duality of moduli of k- and (n-k)-dimensional slices of euclidean n-cubes, and establish the optimal upper bound 1.
We observe that upper densities and spherical Federer densities may differ on all two dimensional surfaces of the sub-Riemannian Heisenberg group. This provides an entire class of intrinsic rectifiable sets having upper density strictly…
The density bound for schedulability for general pinwheel instances is $\frac{5}{6}$, but density bounds better than $\frac{5}{6}$ can be shown for cases in which the minimum element $m$ of the instance is large. Several recent works have…
We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…
We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the…