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Many physical systems can be modeled as large sets of domains "glued" together along boundaries - biological cells meet along cell membranes, soap bubbles meet along thin films, countries meet along geopolitical boundaries, and metallic…
Many physical systems are composed of polyhedral cells of varying sizes and shapes. These structures are simple in the sense that no more than three faces meet at an edge and no more than four edges meet at a vertex. This means that…
An open question in studying normal grain growth concerns the asymptotic state to which microstructures converge. In particular, the distribution of grain topologies is unknown. We introduce a thermodynamic-like theory to explain these…
Voronoi tessellations of Poisson point processes are widely used for modeling many types of physical and biological systems. In this paper, we analyze simulated Poisson-Voronoi structures containing a total of 250,000,000 cells to provide…
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…
Topology optimization is able to maximally leverage the high DOFs and mechanical potentiality of porous foams but faces three fundamental challenges: conforming to free-form outer shapes, maintaining geometric connectivity between adjacent…
Faces-classes of grains, often referred to as topological features, largely dictate the evolution of polycrystalline microstructures during grain growth. Realising these topological features is generally an arduous task, often demanding…
Cellular structures manifest their outstanding mechanical properties in many biological systems. One key challenge for designing and optimizing these geometrically complicated structures lies in devising an effective geometric…
Voronoi tessellations of scale-invariant fractal sets are characterized by topological and metrical properties that are significantly different from those of natural cellular structures. As an example we analyze Voronoi diagrams of…
Voronoi Tessellations form an attractive and versatile geometrical asymptotic model for the foamlike cosmic distribution of matter and galaxies. In the Voronoi model the vertices are identified with clusters of galaxies. For a substantial…
Poisson point processes provide a versatile framework for modeling the distributions of random points in space. When the space is partitioned into cells, each associated with a single generating point from the Poisson process, there appears…
A linear bubble model of grain growth is introduced to study the conditions under which an isolated grain can grow to a size much larger than the surrounding matrix average (abnormal growth). We first consider the case of bubbles of two…
Grain growth experiments on thin metallic films have shown the geometric and topological characteristics of the grain structure to be universal and independent of many experimental conditions. The universal size distribution, however, is…
Grain growth is a ubiquitous and fundamental phenomenon observed in the cellular structures with the grain assembly separated by a network of grain boundaries, including metals and ceramics. However, the underlying mechanism of grain growth…
The properties of interstellar grains can now be defined by a rapidly growing wealth of observational data. We rely upon models to combine these data with unobserved properties such as the size distribution of grains, their structure and…
Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three dimensional…
A simple model for the solidification of globular grains in metallic alloys is presented. Based on the Voronoi diagram of the nuclei centers, it accounts for the curvature of the grains near triple junctions. The predictions of this model…
The topological transitions that occur to the grain boundary network during grain growth in a material with uniform grain boundary energies are believed to be known. The same is not true for more realistic materials, since more general…
Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply-connected. This…
We present a two-dimensional granular model for the mechanical behavior of an ensemble of globular grains, during solidification. The grain structure is produced by a Voronoi tessellation based on an array of predefined nuclei. We consider…