相关论文: Proof of Aperiodicity of hat tile using the Golden…
Recent experimental advances in controlling dissipation have brought about unprecedented flexibility in engineering non-Hermitian Hamiltonians in open classical and quantum systems. A particular interest centers on the topological…
Recently there has been developed a reformulation of General Relativity - referred to as {\it the null surface version of GR} - where instead of the metric field as the basic variable of the theory, families of three-surfaces in a…
Every body knows that identical regular triangles or squares can tile the whole plane. Many people know that identical regular hexagons can tile the plane properly as well. In fact, even the bees know and use this fact! Is there any other…
Quasicrystals have intrigued and stimulated research in a large number of disciplines. Mathematicians, physicists, chemists, metallurgists and materials scientists have found in them a fertile ground for new insights and discoveries. In the…
We show that given any tiling of Euclidean space, any geometric patterns of points, we can find a patch of tiles (of arbitrarily large size) so that copies of this patch appear in the tiling nearly centered on a scaled and translated…
We study equilibrium configurations of non-Euclidean plates, in which the reference metric is uniaxially periodic. This work is motivated by recent experiments on thin sheets of composite thermally responsive gels [1]. Such sheets bend…
An irregular vertex in a tiling by polygons is a vertex of one tile and belongs to the interior of an edge of another tile. In this paper we show that for any integer $k\geq 3$, there exists a normal tiling of the Euclidean plane by convex…
The Spectre is an aperiodic monotile for the Euclidean plane that is truly chiral in the sense that it tiles the plane without any need for a reflected tile. The topological and dynamical properties of the Spectre tilings are very similar…
Aperiodic (quasicrystalline) tilings, such as Penrose's tiling, can be built up from e.g. kites and darts, squares and equilateral triangles, rhombi or shield shaped tiles and can have a variety of different symmetries. However, almost all…
Material's geometrical structure is a fundamental part of their properties. The honeycomb geometry of graphene is responsible for the arising of its Dirac cone, while the kagome and Lieb lattice hosts flat bands and pseudospin-1 Dirac…
A tile Hamiltonian (TH) replaces the actual atomic interactions in a quasicrystal with effective interactions between and within tiles. We study Al-Co-Ni and Al-Co-Cu decagonal quasicrystals described as decorated Hexagon-Boat-Star (HBS)…
In contrast to many known results concerning periodic tilings of the Euclidean plane with pentagons, here tilings with rotational symmetry are investigated. A certain class of convex pentagons is introduced. It can be shown that for any…
We show that translational tiling problems in a quotient of $\mathbb{Z}^d$ can be effectively reduced or ``simulated'' by translational tiling problems in $\mathbb{Z}^d$. In particular, for any $d \in \mathbb{N}$, $k < d$ and…
In this work we study the existence of homogeneous Einstein metrics on the total space of homogeneous fibrations such that the fibers are totally geodesic manifolds. We obtain the Ricci curvature of an invariant metric with totally geodesic…
The global monopole solutions which give rise to quite unusual physical phenomena have captured considerable attention. In this paper, we study the Einstein ring of the spherically symmetric AdS black hole solution with a global monopole…
Aperiodic crystals constitute a fascinating class of materials that includes incommensurate (IC) modulated structures and quasicrystals (QCs). Although these two categories share a common foundation in the concept of superspace, the…
We refine the regularity of noncollapsed limits of 5-dimensional manifolds with bounded Ricci curvature. In particular, for noncollapsed limits of Einstein 5-manifolds, we prove that (1) tangent cones are unique of the form…
Solutions to the Einstein equations for Bianchi IX cosmologies are examined through the use of Ellis MacCallum Wainwright (expansion-normalized) variables. Using an iterative map derived from the Einstein equations one can construct an…
In this work, Einstein's view of geometry as physical geometry is taken into account in the analysis of diverse issues related to the notions of inertial motion and inertial reference frame. Einstein's physical geometry enables a…
The gedanken-experiment of Einstein's lift is analyzed in order of determining whether the free-falling observer inside the lift can detect the eventual topological non-triviality of space-time