Related papers: Voronoi chords in flat cosmology
The transition from ordered to disordered structures in Voronoi tessellation is obtained by perturbing the seeds that were originally identified with two types of lattice in 2D and one type in 3D. The area in 2D and the volume in 3D are…
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.…
Any system of bisectors (in the sense of abstract Voronoi diagrams) defines an arrangement of simple curves in the plane. We define Voronoi-like graphs on such an arrangement, which are graphs whose vertices are locally Voronoi. A vertex…
Most of the non-Abelian string-vortices studied so far are characterized by two-dimensional \cpn models with various degrees of supersymmetry on their world sheet. We generalize this construction to "composite" non-Abelian strings…
We discuss Vassiliev invariants for virtual knots, expanding upon the theory of quantum virtual knot invariants developed in arXiv:1509.00578. In particular, following the theory of quantum invariants we work with 'rotational' virtual…
We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which…
Let $p\_n$ be the probability for a planar Poisson-Voronoi cell to have exactly $n$ sides. We construct the asymptotic expansion of $\log p\_n$ up to terms that vanish as $n\to\infty$. We show that {\it two independent biased random walks}…
We study percolation in the following random environment: let $Z$ be a Poisson process of constant intensity in the plane, and form the Voronoi tessellation of the plane with respect to $Z$. Colour each Voronoi cell black with probability…
We study the problem of computing the Voronoi diagram of a set of $n^2$ points with $O(\log n)$-bit coordinates in the Euclidean plane in a substantially sublinear in $n$ number of rounds in the congested clique model with $n$ nodes.…
A rainbow-ladder truncation of QCD's Dyson-Schwinger equations is used to calculate rho- and phi-meson valence-quark (twist-two parton) distribution amplitudes (PDAs) via a light-front projection of their Bethe-Salpeter wave functions,…
We extend the theory of logarithmic Voronoi cells to Gaussian statistical models. In general, a logarithmic Voronoi cell at a point on a Gaussian model is a convex set contained in its log-normal spectrahedron. We show that for models of ML…
We observe stationary random tessellations $X=\{\Xi_n\}_{n\ge1}$ in $\mathbb{R}^d$ through a convex sampling window $W$ that expands unboundedly and we determine the total $(k-1)$-volume of those $(k-1)$-dimensional manifold processes which…
According to the Cosmological Principle, the matter distribution on very large scales should have a kinematic dipole that is aligned with that of the CMB. We determine the dipole anisotropy in the number counts of two all-sky surveys of…
We have recently developed a mean-field theory to estimate the packing fraction of non-spherical particles [A. Baule et al., Nature Commun. (2013)]. The central quantity in this framework is the Voronoi excluded volume, which generalizes…
This review gives an update on virtual Compton scattering (VCS) off the nucleon, $\gamma^* N \to N \gamma$, in the low-energy regime. We recall the theoretical formalism related to the generalized polarizabilities (GPs) and model…
Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point. We compute the algebraic boundaries of these…
The use of the tensor virial theorem (TVT) as a diagnostic of anisotropic velocity distributions in galaxies is revisited. The TVT provides a rigorous global link between velocity anisotropy, rotation and shape, but the quantities appearing…
We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear…
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…
In this paper, we review the computational aspects of a multiscale dissipative particle dynamics model for complex fluid simulations based on the feature-rich geometry of the Voronoi tessellation. The geometrical features of the model are…