Related papers: Methodology to Construct Large Realizations of Per…
Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities.…
Studies of random organization models of monodisperse spherical particles have shown that a hyperuniform state is achievable when the system goes through an absorbing phase transition to a critical state. Here we investigate to what extent…
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure…
Disordered hyperuniform structures are an exotic state of matter having vanishing long-wavelength density fluctuations similar to perfect crystals but without long-range order. Although its importance in materials science has been brought…
Many physical systems can be studied as collections of particles embedded in space, evolving through deterministic evolution equations. Natural questions arise concerning how to characterize these arrangements - are they ordered or…
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…
Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights:…
We study, via the replica method of disordered systems, the packing problem of hard-spheres with a square-well attractive potential when the space dimensionality, d, becomes infinitely large. The phase diagram of the system exhibits…
Disordered stealthy hyperuniform (SHU) two-phase media are a special subset of hyperuniform structures with novel physical properties due to their hybrid crystal-liquid nature. We have previously shown that the strong-contrast expansion of…
Disordered hyperuniform materials with vanishing long-wavelength density fluctuations are attracting attention due to their unique physical properties. In these systems, the large-scale density fluctuations are strongly suppressed as in a…
We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces $ \mathbb{H}_{d}$ for $d \geq 2$. In contrast to the Euclidean setting, a limiting nontrivial ideal tessellation $ \mathcal{V}_{d}$ appears as the…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
The concept of a hyperuniformity disorder length $h$ was recently introduced for analyzing volume fraction fluctuations for a set of measuring windows. This length permits a direct connection to the nature of disorder in the spatial…
Purpose: The purpose of this work is to investigate the hypothesis that uniform sampling measurements that are endowed with antipodal symmetry play an important role when the raw data and image data are related through the Fourier…
Hyperuniform materials, characterized by anomalously suppressed long-wavelength density fluctuations, exhibit unique optical and photonic properties distinct from both crystalline and random media. While most prior studies have focused on…
We extend our theory of amorphous packings of hard spheres to binary mixtures and more generally to multicomponent systems. The theory is based on the assumption that amorphous packings produced by typical experimental or numerical…
In this paper, we study the problem of hyperball (hypersphere) packings in $n$-dimensional hyperbolic space ($n \ge 4$). We prove that to each $n$-dimensional congruent saturated hyperball packing, there is an algorithm to obtain a…
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…
Hyperuniform states are an efficient way to fill up space for disordered systems. In these states the particle distribution is disordered at the short scale but becomes increasingly uniform when looked at large scales. Hyperuniformity…