Zobrazeno 1 - 10
of 226
pro vyhledávání: '"Domokos, Gabor"'
In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the
Externí odkaz:
http://arxiv.org/abs/2402.17765
A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp corners and flat
Externí odkaz:
http://arxiv.org/abs/2402.04190
We prove that every homogeneous convex polyhedron with only one unstable equilibrium (known as a mono-unstable convex polyhedron) has at least $7$ vertices. Although it has been long known that no mono-unstable tetrahedra exist, and mono-unstable pol
Externí odkaz:
http://arxiv.org/abs/2401.17906
In Gale Crater near Mars' equator, dunes and ripples of sand stand out from the general orderless, rocky terrain. In addition, images from Curiosity, the Mars Science Laboratory rover, reveal more subtle orderly forms: widespread, meter-scale domains
Externí odkaz:
http://arxiv.org/abs/2312.13818
Autor:
Bárány, Imre, Domokos, Gábor
Given a polytope $P\subset R^3$ and a non-zero vector $z \in R^3$, the plane $\{x\in R^3:zx=t\}$ intersects $P$ in convex polygon $P(z,t)$ for $t \in [t^-,t^+]$ where $t^-=\min \{zx: x \in P\}$ and $t^+=\max \{zx: x\in P\}$, $zx$ is the scalar produc
Externí odkaz:
http://arxiv.org/abs/2310.18960
The monostatic property of polyhedra (i.e. the property of having just one stable or unstable static equilibrium point) has been in a focus of research ever since Conway and Guy \cite{Conway} published the proof of the existence of the first such obj
Externí odkaz:
http://arxiv.org/abs/2304.06984
Autor:
Ludmány, Balázs, Domokos, Gábor
While three-dimensional measurement technology is spreading fast, its meaningful application to sedimentary geology still lacks content. Classical shape descriptors (such as axis ratios, circularity of projection) were not inherently three-dimensiona
Externí odkaz:
http://arxiv.org/abs/2303.05285
In the study of monostatic polyhedra, initiated by John H. Conway in 1966, the main question is to construct such an object with the minimal number of faces and vertices. By distinguishing between various material distributions and stability types, t
Externí odkaz:
http://arxiv.org/abs/2302.04252
We introduce and study a general framework for modeling the evolution of crack networks. The evolution steps are triggered by exponential clocks corresponding to local micro-events, and thus reflect the state of the pattern. In an appropriate simulta
Externí odkaz:
http://arxiv.org/abs/2301.09503
Autor:
Regős, Krisztina, Pawlak, Rémy, Wang, Xing, Meyer, Ernst, Decurtins, Silvio, Domokos, Gábor, Novoselov, Kostya S., Liu, Shi-Xia, Aschauer, Ulrich
Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by the covalent, hydrogen or van der Waals interactions - self-assembly of alike molecules results in a large variety of c
Externí odkaz:
http://arxiv.org/abs/2208.03964