相关论文: A guide to mathematical quasicrystals

We study quasi-modular pseudometric spaces as asymmetric refinements of modular metric structures. To each such space we associate canonical forward and backward quasi-uniformities and the corresponding directional topologies. We introduce…

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

One-dimensional cut-and-project point sets obtained from the square lattice in the plane are considered from a unifying point of view and in the perspective of aperiodic wavelet constructions. We successively examine their geometrical…

This article is devoted to the study of classical and new results concerning equidistant sets, both from the topological and metric point of view. We start with a review of the most interesting known facts about these sets in the euclidean…

Exact expressions for probability densities of conjugate pair separation in euclidean isometries are obtained, for the cosmic crystallography.These are the theoretical counterparts of the mean histograms arising from computer simulation of…

We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current,…

Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…

We formulate a geometric measurement theory of dynamical classical systems possessing both continuous and discrete degrees of freedom. The approach is covariant with respect to choices of clocks and canonically incorporates laboratories.…

We describe a quasiperiodic optical lattice, created by a physical realization of the abstract cut-and-project construction underlying all quasicrystals. The resulting potential is a generalization of the Fibonacci tiling. Calculation of…

Almost all observed square-triangle quasicrystals in soft-matter systems contain a large number of point-like defects, yet the role these defects play in stabilizing the quasicrystal phase remains poorly understood. In this work, we…

New aspects of a relation between lattice and dislocation structures are examined within a physically transparent theoretical scheme. Predicted features originating from the lattice discreteness include: (i) multiple core dislocation…

In this paper we propose an elementary topological approach which unifies and extends various different results concerning fixed points and periodic points for maps defined on sets homeomorphic to rectangles embedded in euclidean spaces. We…

We provide complete structural theorems for the so-called quasiasymptotic behavior of non-quasianalytic ultradistributions. As an application of these results, we obtain descriptions of quasiasymptotic properties of regularizations at the…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

Quasicrystals remain among the most intriguing materials in physics and chemistry. Their structure results in many unusual properties including anomalously low friction as well as poor electrical and thermal conductivity but it also…

Despite an artificial intelligence-assisted modeling of disordered crystals is a widely used and well-tried method of new materials design, the issues of its robustness, reliability, and stability are still not resolved and even not…

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

I introduce a family of closeness functions between causal Lorentzian geometries of finite volume and arbitrary underlying topology. When points are randomly scattered in a Lorentzian manifold, with uniform density according to the volume…

In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…

A combination of classical density-functional theory and thermodynamic perturbation theory is applied to a survey of finite-temperature trends in the relative stabilities of one-component crystals and quasicrystals interacting via effective…