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Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…

The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern "random", Poisson-Voronoi tessellations (PVT), or "non-random", Non Poisson-Voronoi…

Dendrite core is the center point of the dendrite. The information of dendrite core is very helpful for material scientists to analyze the properties of materials. Therefore, detecting the dendrite core is a very important task in the…

Voronoi mosaics inspired by the seed points placed on the Archimedes Spirals are reported. Voronoi entropy was calculated for these patterns. Equidistant and non-equidistant patterns are treated. Voronoi mosaics built from cells of equal…

We use a simple fragmentation model to describe the statistical behavior of the Voronoi cell patterns generated by a set of points in 1D and in 2D. In particular, we are interested in the distribution of sizes of these Voronoi cells. Our…

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 demonstrate numerical techniques for automatic identification of individual spiral arms in hydrodynamic simulations of astrophysical discs. Building on our earlier work, which used tensor classification to identify regions that were…

As the need for miniaturized structural and functional materials has increased,the need for precise materials characterizaton has also expanded. Nanoindentation is a popular method that can be used to measure material mechanical behavior…

Materials characterization using electron backscatter diffraction (EBSD) requires indexing the orientation of the measured region from Kikuchi patterns. The quality of Kikuchi patterns can degrade due to pattern overlaps arising from two or…

We investigate the problem of image retrieval based on visual queries when the latter comprise arbitrary regions-of-interest (ROI) rather than entire images. Our proposal is a compact image descriptor that combines the state-of-the-art in…

This paper presents a range of results in partial differential equations (PDEs) in which Voronoi patterns arise. We investigate the connection between the solution to an elliptic equation and its probabilistic interpretation as a stochastic…

The multifaceted physics of oxides is shaped by their composition and the presence of defects, which are often accompanied by the formation of polarons. The simultaneous presence of polarons and defects, and their complex interactions, pose…

This paper considers a class of deploy and search strategies for multi-robot systems and evaluates their performance. The application framework used is a system of autonomous mobile robots equipped with required sensors and communication…

Although Poisson-Voronoi diagrams have interesting mathematical properties, there is still much to discover about the geometrical properties of its grains. Through simulations, many authors were able to obtain numerical approximations of…

We study the problem of decomposing a volume bounded by a smooth surface into a collection of Voronoi cells. Unlike the dual problem of conforming Delaunay meshing, a principled solution to this problem for generic smooth surfaces remained…

We revisit a new type of a Voronoi diagram, in which distance is measured from a point to a pair of points. We consider a few more such distance functions, based on geometric primitives, and analyze the structure and complexity of the…

The Hilbert metric is a distance function defined for points lying within a convex body. It generalizes the Cayley-Klein model of hyperbolic geometry to any convex set, and it has numerous applications in the analysis and processing of…

Deformation microstructure heterogeneities play a pivotal role during dislocation patterning and interface network restructuring. Thus, they affect indirectly how an alloy recrystallizes if at all. Given this relevance, it has become common…

We tackle the problem of estimating the spatial distribution of mobile phones from Mobile Network Operator (MNO) data, namely Call Detail Record (CDR) or signalling data. The process of transforming MNO data to a density map requires…

Precise assessment of the mechanical properties of soft biological systems at the nanoscale is crucial for understanding physiology, pathology, and developing relevant drugs. Conventional atomic force microscopy (AFM)-based indentation…