Searcharxiv⌕ Search

arXiv subjects

Daria Pchelina

Publications and source records attributed to Daria Pchelina.

3 recordsLinked to original sources
arXiv2026

On Dense Tetrahedra in Binary Sphere Packings

This paper considers the density of tetrahedra arising in a specific decomposition of packings of unequal spheres in $\mathbb{R}^3$. It aims to extend a bound obtained in 2D in the 1960s by Florian. The focus is on packings of spheres of sizes $1$ and $\sqrt{2}-1$: the small sphere fits exactly into each octahedral hole of a hexagonal close packing of large spheres, yielding a conjecturally maximally dense packing (for these sizes). The paper slightly improves, by completely different means, the previous best upper bound on the density of such packings. The proof combines geometric insight with challenging interval arithmetic computations, which may be of independent interest.

math.MG↗
arXiv2022

Density of triangulated ternary disc packings

We consider ternary disc packings of the plane, i.e. the packings using discs of three different radii. Packings in which each ''hole'' is bounded by three pairwise tangent discs are called triangulated. There are 164 pairs $(r,s)$, $1{>}r{>}s$, allowing triangulated packings by discs of radii 1, $r$ and $s$. In this paper, we enhance existing methods of dealing with maximal-density packings in order to find ternary triangulated packings which maximize the density among all the packings with the same disc radii. We showed for 16 pairs that the density is maximized by a triangulated ternary packing; for 15 other pairs, we proved the density to be maximized by a triangulated packing using only two sizes of discs; for 40 pairs, we found non-triangulated packings strictly denser than any triangulated one; finally, we classified the remaining cases where our methods are not applicable.

cs.CG↗