24 citations · 143 across the 29 of their papers we have counts for
5 papers · 1 filter
When different norms lead to same billiard trajectories?
Arseniy Akopyan, Roman Karasev
In this paper, extending the works of Milena Radnović and Serge Tabachnikov, we establish conditions for two different non-symmetric norms to define the same billiard reflection la…
On mutually diagonal nets on (confocal) quadrics and 3-dimensional webs
Arseniy V. Akopyan, Alexander I. Bobenko, Wolfgang K. Schief +1
Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics an…
The Weighted Mean Curvature Derivative of a Space-Filling Diagram
Arseniy Akopyan, Herbert Edelsbrunner
Representing an atom by a solid sphere in -dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its moti…
The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram
Arseniy Akopyan, Herbert Edelsbrunner
The morphometric approach [HRC13,RHK06] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of…
The Regge symmetry, confocal conics, and the Schläfli formula
Arseniy Akopyan, Ivan Izmestiev
The Regge symmetry is a set of remarkable relations between two tetrahedra whose edge lengths are related in a simple fashion. It was first discovered as a consequence of an asympt…