Related papers: Sequential Voronoi diagram calculations using simp…
Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…
Volatility-dependent fractionation of the rock-forming elements at high temperatures is an early, widespread process during formation of the earliest solids in protoplanetary disks. Equilibrium condensation calculations allow prediction of…
We prove a Voronoi formula for coefficients of a large class of $L$-functions including Maass cusp forms, Rankin-Selberg convolutions, and certain isobaric sums. Our proof is based on the functional equations of $L$-functions twisted by…
We prove that the supercritical phase of Voronoi percolation on $\mathbb{R}^d$, $d\geq 3$, is well behaved in the sense that for every $p>p_c(d)$ local uniqueness of macroscopic clusters happens with high probability. As a consequence,…
A model for a monolayer of two types of particles spontaneously forming ordered patterns is studied by a mesoscopic theory and by MC simulations. We assume hard-cores of the same size for both components, short-range attraction long-range…
A two-step reaction scheme for the production of extremely neutron-rich radioactive beams, fission followed by cold fragmentation, is considered. The cross sections of the second step, the cold fragmentation of neutron-rich fission…
This paper presents a combined numerical-theoretical study of the macroscopic behavior and local field distributions in a special class of two-dimensional periodic composites with viscoplastic phases. The emphasis is on strongly nonlinear…
The typical cell of a Voronoi tessellation generated by $n+1$ uniformly distributed random points on the $d$-dimensional unit sphere $\mathbb S^d$ is studied. Its $f$-vector is identified in distribution with the $f$-vector of a beta'…
In this thesis we study sets of points in the plane and their Voronoi diagrams, in particular when the points coincide. We bring together two ways of studying point sets that have received a lot of attention in recent years: Voronoi…
We show that one can employ well-established numerical continuation methods to efficiently calculate the phase diagram for thermodynamic systems. In particular, this involves the determination of lines of phase coexistence related to first…
Topological physics desires stable methods to measure the polarization singularities in optical vector fields. Here a periodic plasmonic metasurface is proposed to perform divergence computation of vectorial paraxial beams. We design such…
There are very few results on mixed finite element methods on surfaces. A theory for the study of such methods was given recently by Holst and Stern, using a variational crimes framework in the context of finite element exterior calculus.…
Multiphase shear flows often show banded structures that affect the global behavior of complex fluids e.g. in microdevices. Here we investigate numerically the banding of emulsions, i.e. the formation of regions of high and low volume…
In this article, we investigate vacuum leakage detection problems in composite manufacturing. Our approach uses Voronoi diagrams, a well-known structure in discrete geometry. The Voronoi diagram of the vacuum connection positions partitions…
Machine learning has emerged as a powerful tool for the analysis of mesoscopic and atomically resolved images and spectroscopy in electron and scanning probe microscopy, with the applications ranging from feature extraction to information…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
General models of Gibbs Delaunay-Voronoi tessellations, which can be viewed as extensions of Ord's process, are considered. The interaction may occur on each cell of the tessellation and between neighbour cells. The tessellation may also be…
We have developed a novel method of determining 2D radial density profiles for astronomical systems of discrete objects using Voronoi tessellations. This Voronoi-based method was tested against the standard annulus-based method on 5…
Formaldehyde is a key precursor in the formation routes of many complex organic molecules (COMs) in space. It is also an intermediate step in CO hydrogenation sequence that leads to methanol formation on the surface of interstellar grains…
The binary Voronoi mixture is a fluid model whose interactions are local and many-body. Here we perform molecular-dynamics (MD) simulations of an equimolar mixture that is weakly polydisperse and additive. For the first time we study the…