Topology of some tiling spaces without finite local complexity, Discrete Contin - Frank, Sadun () Citation Context ...tiling space Ω is defined as the closure in an appropriate Gromov-Hausdorff topology on the space of translations of the tiling. Then the space Ω is a matchbox manifold ...
of elements of some subfamily of U;“Hausdorff” refers to a topological space where for any two distinct points there exist neighbourhoods of each which are disjoint from each other, and “homeomorphic” means the existence of a homeomorphism, a continuous function between topological spaces that...
The theory of hyperbolic band topology with second Chern numbers We start to design a tight-binding lattice model in the 2D hyperbolic space. Figure1aillustrates the Bravais lattice of designed hyperbolic model in a Poincaré disk, where the translational symmetry of a {8,8} hyperbolic tiling exi...
found by relaxing the design space. This means the use of a continuous composite material description using a characteristic unit-cell length\(\epsilon \rightarrow 0\), allowing for much more detail than a single-scale discretized point-wise material or void description. Here, the theory of hom...
Rμη−12gμηR=−KTμηIt is well known that in order to reach his conclusions, Einstein had to modify our notion of space–time in the large and used the curved Riemanian geometry in describing the left hand side of his equation. On the right hand side we have the mass tensor....
Chemical and physical transformations by milling are attracting enormous interest for their ability to access new materials and clean reactivity, and are central to a number of core industries, from mineral processing to pharmaceutical manufacturing. Whi
To understand on aperiodic tiling (or a quasicrystal modeled on an aperiodic tiling), we construct a space of similar tilings, on which the group of translations acts naturally. This space is then an (abstract) dynamical system. Dynamical properties of the space (such as mixing, or the ...
A tiling space is a closed subset of that is invariant under this action. The chapter explains the concepts of topological rigidity and the topological structure of tiling spaces. It also explains about deformations of tiling spaces.Alex Clark...
occurs on the boundary of the Eden model at least a number of times proportional to an isoperimetric profile of the graph. Using this, we can extend the results about the topology of the Eden model to non-Euclidean spaces, such as hyperbolicn-space and universal covers of certain Riemannian...
TilingHomeomorphy to a disk05B4552C2020H15We study self-affine tiles which tile the n-dimensional real vector space with respect to a crystallographic group. First we define classes of graphs that allow to determine the neighbors of a given tile algorithmically. In the case of plane tiles ...