相关论文: Tiling models for metadislocations in AlPdMn appro…

We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the…

Metric embeddings are a widely used method in algorithm design, where generally a ``complex'' metric is embedded into a simpler, lower-dimensional one. Historically, the theoretical computer science community has focused on bi-Lipschitz…

Aperiodic tilings with a small number of prototiles are of particular interest, both theoretically and for applications in crystallography. In this direction, many people have tried to construct aperiodic tilings that are built from a…

Phyllotactic patterns possess the quasicrystalline structure of the quasiperiodic Penrose tiling pattern. The author has shown that quasicrystalline structure of the quasiperiodic Penrose tiling pattern underlie iterative growth processes…

We consider a mesoscale model for nano-sized metaparticles (MPs) composed of a central sphere decorated by polymer chains with laterally attached spherocylinder. The latter mimics the mesogenic (e.g., cyanobiphenyl) group. Molecular…

Vacancy swelling of quasicrystals under irradiation is considered. In quasicrystals, the evolution of dislocations is accompanied by the formation of phasons which are localized topological defects of the vacancy and interstitial types. At…

Using computer simulations and theory, we investigate the ultrasoft interactions between dendrimers formed of a central polymer connected by stiff linkers to a corona of flexible polymers, forming `pompoms' at the ends of the linkers. We…

It has recently been argued that individual 1D quasicrystals can be ascribed 2D topological quantum numbers and a corresponding set of topologically protected edge modes. Here, we demonstrate the equivalence of such 1D quasicrystals to a…

Scanning tunnelling microscopy has been used to study the formation of a Bi monolayer deposited on the five-fold surface of i-Al70Pd21Mn9. Upon deposition of low sub-monolayer coverages, the nucleation of pentagonal clusters of Bi adatoms…

Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects.…

We use molecular dynamics simulations to study the driven phases of particles such as vortices or colloids moving over a decagonal quasiperiodic substrate. In the regime where the pinned states have quasicrystalline ordering, the driven…

We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk,…

In the present paper, as we did previously in [7], we investigate the relations between the geometric properties of tilings and the algebraic properties of associated relational structures. Our study is motivated by the existence of…

Advancements in the synthesis of faceted nanoparticles and colloids have spurred interest in the phase behavior of polyhedral shapes. Regular tetrahedra have attracted particular attention because they prefer local symmetries that are…

We introduce tessellation of the filled Julia sets for hyperbolic and parabolic quadratic maps. Then the dynamics inside their Julia sets are organized by tiles which work like external rays outside. We also construct continuous families of…

Disordered metasurfaces provide a versatile platform for harnessing near- and far-field scattered light. Most research has focused on either particulate topologies composed of individual, well-identified metaatoms or, to a lesser extent,…

It has long been established that certain higher-dimensional topological phases of matter support extended objects like quasi-strings and quasi-membranes in their bulk states. In this study, we investigate the physics of these topological…

We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar…

In this expository article we show how the concepts of manifolds with corners, blow-ups and resolutions can be used effectively for the construction of quasimodes, i.e. approximate eigenfunctions of the Laplacian on certain families of…

We investigate a two-dimensional tiling model. Even though the degrees of freedom in this model are discrete, it has a hidden continuous global symmetry in the infinite lattice limit, whose corresponding Goldstone modes are the…