Related papers: What is Aperiodic Order?
The theory of aperiodic order is concerned with the development of ideas stimulated by the discovery of quasicrystals. We give a gentle introduction to some mathematical aspects of aperiodic order, aimed at a more general audience.
This article presents a very gentle introduction to the field of aperiodic order, aimed at a general audience. It is intended to provide a "Snapshot of Modern Mathematics" relating to the Oberwolfach mini-workshop "Dynamical versus…
Spatial aperiodicity occurs in various models and material s. Although today the most well-known examples occur in the area of quasicrystals, other applications might also be of interest. Here we discuss some issues related to the notion…
This article gives a brief survey of the theory and applications of anomalies.
We present here an elementary construction of an aperiodic tile set. Although there already exist dozens of examples of aperiodic tile sets we believe this construction introduces an approach that is different enough to be interesting and…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
This is an introductory article to the theory of multiple gaps.
The purpose of this book is to provide an introduction to period theory and then to place it within the matrix of recursive function theory.
Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order,…
In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the…
In this short article we present some properties regarding the order and the type of an entire function.
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
We give an introduction into diffraction theory for aperiodic order. We focus on an approach via dynamical systems and the phenomenon of pure point diffraction. We review recent results and sketch proofs. We then present a new uniform…
We establish a deterministic technique to investigate transport moments of arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the Lorentz gas with infinite horizon: the typical…
The effects of an aperiodic order or a random disorder on phase transitions in statistical mechanics are discussed. A heuristic relevance criterion based on scaling arguments as well as specific results for Ising models with random disorder…
The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…
This is a survey of the model theory of second order logic.
We give a leisurely introduction into mathematical diffraction theory with a focus on pure point diffraction. In particular, we discuss various characterisations of pure point diffraction and common models arising from cut and project…
Mathematical formula describing the periodicity of the elements in the periodic system is presented.
This is an expository article/encyclopedia entry explaining the history, techniques, and central results in the field of smooth ergodic theory.