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Cosmology relies on the Cosmological Principle, i.e., the hypothesis that the Universe is homogeneous and isotropic on large scales. This implies in particular that the counts of galaxies should approach a homogeneous scaling with volume at…
Quasicrystals have a higher degree of rotational and point-reflection symmetry than conventional crystals. As a result, quasicrystalline heterostructures fabricated from dielectric materials with micrometer-scale features exhibit…
We propose a novel method of determination of the dust particle spatial distribution in dust clouds that form in three-dimensional (3D) complex plasmas under microgravity conditions. The method utilizes the data obtained during the 3D…
We study the spatial distribution of point sets on the sphere obtained from the representation of a large integer as a sum of three integer squares. We examine several statistics of these point sets, such as the electrostatic potential,…
In this exploratory article, we present a constructive method for scattering points on the surface of $d$ dimensional spheres which we believe is new and of interest. Indeed, the problem of uniformly distributing points on spheres is an…
Spherical collapse predicts that a single value of the turnaround density (average matter density within the scale on which a structure detaches from the Hubble flow) characterizes all cosmic structures at the same redshift. It has been…
We present a new theory for partitioning simulations of periodic and solid-state systems into physically sound atomic contributions at the level of Kohn-Sham density functional theory. Our theory is based on spatially localized linear…
Let Y be a surface with only finitely many singularities all of which are cusps. A set of cusps on Y is called three-divisible, if there is a cyclic global triple cover of Y branched precisely over these cusps. The aim of this note is to…
Understanding the structure of the matter distribution in the Universe due to the action of the gravitational instability -- the cosmic web -- is complicated by lack of direct analytic access to the nonlinear domain of structure formation.…
The mode problem on the factored 3--sphere is applied to field theory calculations for massless fields of spin 0, 1/2 and 1. The degeneracies on the factors, including lens spaces, are neatly derived in a geometric fashion. Vacuum energies…
We present a new model of the three-dimensional distribution of molecular gas in the Milky Way Galaxy, based on CO line data. Our analysis is based on a gas-flow simulation of the inner Galaxy using smoothed-particle hydrodynamics (SPH)…
Cosmic microwave background (CMB) temperature and polarization observations indicate that in the best-fit $\Lambda$ Cold Dark Matter model of the Universe, the local geometry is consistent with at most a small amount of positive or negative…
Symmetric teleparallel gravity is one among the general relativistic trinity which deals with the non-metricity scalar $Q$. In the Einstein Hilbert action, a function of $Q$ is chosen to be the main contributory part of the Lagrangian and a…
The properties of spatial distribution of luminous matter are investigated analysing all the available three dimensional catalogues of galaxies. In standard view, galaxies are believed to have a fractal distribution at small scale with a…
We introduce a statistical quantity, known as the $K$ function, related to the integral of the two--point correlation function. It gives us straightforward information about the scale where clustering dominates and the scale at which…
A nontrivial topology of the spatial section of the universe is an observable, which can be probed for all locally homogeneous and isotropic universes, without any assumption on the cosmological density parameters. We discuss how one can…
We construct an analytical model of Population III star formation that connects the cosmological radiation background to sub-AU protostellar disk fragmentation, a dynamic range inaccessible to any single simulation. Our approach is based on…
Let $X$ be a K3 surface defined over a number field $K$. Assume that $X$ admits a structure of an elliptic fibration or an infinite group of automorphisms. Then there exists a finite extension $K'/K$ such that the set of $K'$-rational…
Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…
Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…