Chirality for crooked curves

Autor: Dietler, Giovanni, Kusner, Robert, Kusner, Wöden, Rawdon, Eric, Szymczak, Piotr

Chiral objects rotate when placed in a collimated flow or wind. We exploit this hydrodynamic intuition to construct a tensorial chirality measure for rigid filaments and curves. This tensor is trace-free, so if a curve has a right-handed twist about

Externí odkaz: http://arxiv.org/abs/2004.10338

Hyperuniform point sets on the sphere: probabilistic aspects

Autor: Brauchart, Johann S., Grabner, Peter J., Kusner, Wöden B., Ziefle, Jonas

Publikováno v: Monatshefte f\"ur Mathematik 2020

The concept of hyperuniformity has been introduced by Torquato and Stillinger in 2003 as a notion to detect structural behaviour intermediate between amorphous disorder and crystalline order. The present paper studies a generalisation of this concept

Externí odkaz: http://arxiv.org/abs/1809.02645

Configuration Spaces of Equal Spheres Touching a Given Sphere: The Twelve Spheres Problem

Autor: Kusner, Rob, Kusner, Wöden, Lagarias, Jeffrey C., Shlosman, Senya

Publikováno v: pp. 219--277 in: G. Ambrus, I. Barany, K. J. Boroczky, G. Fejes-Toth, J. Pach (Eds.) New Trends in Intuitive Geometry, Bolyai Society Mathematical Studies No. 27, Springer-Verlag GMBH, Germany 2018

The problem of twelve spheres is to understand, as a function of $r \in (0,r_{max}(12)]$, the configuration space of $12$ non-overlapping equal spheres of radius $r$ touching a central unit sphere. It considers to what extent, and in what fashion, to

Externí odkaz: http://arxiv.org/abs/1611.10297

The local optimality of the double lattice packing

Autor: Kallus, Yoav, Kusner, Wöden

Publikováno v: Discrete & Computational Geometry 56:2, 449-471 (2016)

This paper introduces a technique for proving the local optimality of packing configurations. Applying this technique to a general convex polygon, we prove that the construction of the optimal double lattice packing by Kuperberg and Kuperberg is also

Externí odkaz: http://arxiv.org/abs/1509.02241

Upper bounds on packing density for circular cylinders with high aspect ratio

Autor: Kusner, Wöden

Publikováno v: Discrete & Computational Geometry, 52:4, 964-978 (2014)

In the early 1990s, A. Bezdek and W. Kuperberg used a relatively simple argument to show a surprising result: The maximum packing density of circular cylinders of infinite length in $\mathbb{R}^3$ is exactly $\pi/\sqrt{12}$, the planar packing densit

Externí odkaz: http://arxiv.org/abs/1309.6996