Related papers: Hyperuniformity on spherical surfaces
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…
Arrays of nanoparticles exploited in light scattering applications commonly only feature either a periodic or a rather random arrangement of its constituents. For the periodic case, light scattering is mostly governed by the strong spatial…
Disordered many-particle hyperuniform systems are exotic amorphous states characterized by anomalous suppression of large-scale density fluctuations. Here we substantially broaden the hyperuniformity concept along four different directions.…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
Disordered hyperuniformity is a description of hidden correlations in point distributions revealed by an anomalous suppression in fluctuations of local density at various coarse-graining length scales. In the absorbing phase of models…
We introduce decorated piecewise hyperbolic and spherical surfaces and discuss their discrete conformal equivalence. A decoration is a choice of circle about each vertex of the surface. Our decorated surfaces are closely related to…
In this note we will consider the question when from the appropriate behavior of a sequence of points on caps we can conclude that the sequence is uniformly distributed on the sphere.
We develop a theory for distributed branch points and investigate their role in determining the shape and influencing the mechanics of thin hyperbolic objects. We show that branch points are the natural topological defects in hyperbolic…
We investigate lower asymptotic bounds of number variances for invariant locally square-integrable random measures on Euclidean and real hyperbolic spaces. In the Euclidean case we show that there are subsequences of radii for which the…
In this paper we study hyperuniformity on flat tori. Hyperuniform point sets on the unit sphere have been studied by J.~Brauchart, P.~Grabner, W.~Kusner and J.~Ziefle. It is shown that point sets which are hyperuniform for large balls,…
Hyperuniform disorder is a type of correlated disorder characterized by vanishing spectral density at small wavevectors, making the configuration effectively homogeneous on long length scales. In photonics, hyperuniform disorder is…
A model of randomly distributed overlapping spheres of different radii is represented to describe a heterogeneous porous medium. Two-particle correlation function of the relative position of pores of different radii in the medium space was…
With the help of hyper-ideal circle pattern theory, we have developed a discrete version of the classical uniformization theorems for surfaces represented as finite branched covers over the Riemann sphere as well as compact polyhedral…
Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the…
The use of coherent wave phenomena to enhance device performance is a cornerstone of modern optics. In juxtaposition to (locally) periodic metasurfaces, their disordered counterparts exhibit an interplay of destructive and constructive…
We explore quantitative descriptors that herald when a many-particle system in $d$-dimensional Euclidean space $\mathbb{R}^d$ approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative…
The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the…
Due to the lack of long-range order, it remains challenging to characterize the structure of disordered solids and understand the nature of the glass transition. Here we propose a new structural order parameter by taking into account…
The concept of hyperuniformity has been introduced by Torquato and Stillinger in 2003 as a notion to detect structural behaviour intermediate between amorphous disorder and crystalline order. The present paper studies a generalisation of…
Hyperuniform metasurfaces promise an unusual form of wave control: the suppression of elastic scattering over extended angular ranges without periodic order. Here, we present a comprehensive experimental and theoretical study of 2D stealthy…