Related papers: Dense Dirac combs in Euclidean space with pure poi…

The spectral density of euclidean Dirac operator is investigated in partially quenched QCD with arbitrary quark masses. A representation of scalar and pseudoscalar correlators in terms of the spectral density is discussed. The spectral…

In this paper the problem of the theory of a quasicrystal structures - the determination of coordinates of each atom of quasicrystal in analytical form - is solved. Within the framework of the proposed model a periodic crystal can be…

The paper studies the relationship between diffraction and dynamics for uniformly discrete ergodic point processes in real spaces. This relationship takes the form of an isometric embedding of two L^2 spaces. Diffraction (or equivalently…

We study the isoperimetric problem for Euclidean space endowed with a continuous density. In dimension one, we characterize isoperimetric regions for a unimodal density. In higher dimensions, we prove existence results and we derive…

We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of…

Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging over large patches, and are well defined only in the…

We propose a notion of discrete elastic and area-constrained elastic curves in 2-dimensional space forms. Our definition extends the well-known discrete Euclidean curvature equation to space forms and reflects various geometric properties…

We compute the Parisi overlap distribution for paperfolding sequences. It turns out to be discrete, and to live on the dyadic rationals. Hence it is a pure point measure whose support is the full interval [-1; +1]. The space of paperfolding…

Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible…

Describing the deviation of a real structure from a hypothetical higher-symmetry ideal can be a powerful tool to understand and interpret phase transitions. Here we introduce a simple yet effective metric that quantifies the degree of unit…

We propose a unified framework for dealing with matching rules of quasiperiodic patterns, relevant for both tiling models and real world quasicrystals. The approach is intended for extraction and validation of a minimal set of matching…

A well-known object in classical Euclidean geometry is the circumcenter of a triangle, i.e., the point that is equidistant from all vertices. The purpose of this paper is to provide a systematic study of the circumcenter of sets containing…

Recent studies of holographic tensor network models defined on regular tessellations of hyperbolic space have not yet addressed the underlying discrete geometry of the boundary. We show that the boundary degrees of freedom naturally live on…

In the second paper of this series we extend our Bayesian reanalysis of the evidence for a cosmic variation of the fine structure constant to the semi-parametric modelling regime. By adopting a mixture of Dirichlet processes prior for the…

The existence of normal deterministic diffusion in dynamical systems with a two-dimensional phase space tiled by regular triangles (or their unions into regular hexagons) is proven.

This paper develops the theory of discrete Dirac reduction of discrete Lagrange-Dirac systems with an abelian symmetry group acting on the configuration space. We begin with the linear theory and, then, we extend it to the nonlinear setting…

We prove discrete-to-continuum convergence of interaction energies defined on lattices in the Euclidean space (with interactions beyond nearest neighbours) to a crystalline perimeter, and we discuss the possible Wulff shapes obtainable in…

The Dirac combs of primitive Pisot--Vijayaraghavan (PV) inflations on the real line or, more generally, in $\mathbb{R}^d$ are analysed. We construct a mean-orthogonal splitting for such Dirac combs that leads to the classic Eberlein…

The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that representing instead the $\mathit{logarithm}$ of the density…

The diffraction pattern of a single non-periodic compact object, such as a molecule, is continuous and is proportional to the square modulus of the Fourier transform of that object. When arrayed in a crystal, the coherent sum of the…