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In this study, an alloy phase-field model is used to simulate solidification microstructures at different locations within a solidified molten pool. The temperature gradient $G$ and the solidification velocity $V$ are obtained from a…
Effective transport properties of heterogeneous structures are predicted by geometric microstructural parameters, but these can be difficult to calculate. Here, a boundary element code with a recurrent series method accurately and…
The progress of image processing during recent years allows the measurement of pedestrian characteristics on a "microscopic" scale with low costs. However, density and flow are concepts of fluid mechanics defined for the limit of infinitely…
The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define…
For a group of pedestrians without any spatial boundaries, the methods of density estimation is a wide area of research. Besides, there is a specific difficulty when the density along one given pedestrian trajectory is needed in order to…
We introduce two new methods to obtain reliable velocity field statistics from N-body simulations, or indeed from any general density and velocity fluctuation field sampled by discrete points. These methods, the {\it Voronoi tessellation…
A voxelization based post-processing algorithm is proposed to analyze the packing of non-spherical particle assemblies simulated using the Discrete Element Method. Voxelization of the particle data allows for isolating the geometric…
Modeling microstructures is an interesting problem not just in Materials Science but also in Mathematics and Statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive…
Polyhedral meshes are increasingly becoming an attractive option with particular advantages over traditional meshes for certain applications. What has been missing is a robust polyhedral meshing algorithm that can handle broad classes of…
We present a numerical study of sidebranching of a solidifying dendrite by means of a phase--field model. Special attention is paid to the regions far from the tip of the dendrite, where linear theories are no longer valid. Two regions have…
A Voronoi diagram is a basic geometric structure that partitions the space into regions associated with a given set of sites, such that all points in a region are closer to the corresponding site than to all other sites. While being…
We consider the Voronoi tessellation based on a homogeneous Poisson point process in $\mathbf{R}^{d}$. For a geometric characteristic of the cells (e.g. the inradius, the circumradius, the volume), we investigate the point process of the…
We introduce a framework for the generation of grid-shell structures that is based on Voronoi diagrams and allows us to design tessellations that achieve excellent static performances. We start from an analysis of stress on the input…
We describe the development of a new software tool, called "Pomelo", for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to…
We investigate Voronoi-like tessellations of bipartite quadrangulations on surfaces of arbitrary genus, by using a natural generalization of a bijection of Marcus and Schaeffer allowing to encode such structures into labeled maps with a…
In this study the Voronoi interpolation is used to interpolate a set of points drawn from a topological space with higher homology groups on its filtration. The technique is based on Voronoi tessellation, which induces a natural dual map to…
The application of Voronoi and Delaunay tessellation based methods for reconstructing continuous fields from discretely sampled data sets is discussed. The succesfull operation as ``multidimensional interpolation'' method is corroborated…
This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the Crystal Structure Prediction, because the…
The work proposes an image segmentation algorithm that isolates slender regions in three-dimensional microstructures. Characterizing slender regions in material microstructures is an extremely important aspect in material science because…
The multi-scale nature of architectured materials raises the need for advanced experimental methods suitable for the identification of their effective properties, especially when their size is finite and they undergo extreme deformations.…