相关论文: Roundness of grains in cellular microstructures
Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally…
Polycrystalline materials undergoing coarsening can be represented as evolving networks of grain boundaries, whose statistical characteristics determine macroscopic materials properties. The process of formation of various statistical…
The material properties of polycrystals are strongly affected by the evolution and coarsening of their internal grain structures. Yet, studying this process is challenging due to the complex interactions within grain boundary networks.…
The problem of ring formation in solutions of cylindrical micelles is reinvestigated theoretically, taking into account a finite bending rigidity of the self-assembled linear objects. Transitions between three regimes are found when the…
We consider the Voronoi diagram generated by $n$ i.i.d. $\mathbb{R}^{d}$-valued random variables with an arbitrary underlying probability density function $f$ on $\mathbb{R}^{d}$, and analyse the asymptotic behaviours of certain geometric…
The Voronoi tessellation of a homogeneous Poisson point process in the lower half-plane gives rise to a family of vertical elongated cells in the upper half-plane. The set of edges of these cells is ruled by a Markovian branching mechanism…
Space-saving design is a requirement that is encountered in biological systems and the development of modern technological devices alike. Many living organisms dynamically pack their polymer chains, filaments or membranes inside of…
Two-dimensional simulations are used to explore topological transitions that occur during the formation of films grown from grains that are seeded on substrates. This is done for a relatively large range of the initial value $\Phi_s$ of the…
Numerical simulations of assemblies of grains under cyclic loading exhibit ``granular ratcheting'': a small net deformation occurs with each cycle, leading to a linear accumulation of deformation with cycle number. We show that this is due…
We investigate the spatial structure of cohesive granular matter with spheres floating at an air-liquid interface that form disordered close packings with pores in between. The interface is slowly lowered in a conical container to uniformly…
Current transport in polysilicon is a complicated process with many factors to consider. The inhomogeneous nature of polysilicon with its differently shaped and sized grains is one such consideration. We have developed a method that…
Connecting the collective behavior of disordered systems with local structure on the particle scale is an important challenge, for example in granular and glassy systems. Compounding complexity, in many scientific and industrial…
According to classical grain growth laws, grain growth is driven by the minimization of surface energy and will continue until a single grain prevails. These laws do not take into account the lattice anisotropy and the details of the…
By means of numerical simulations, we study the influence of confinement on three-dimensional random close packed (RCP) granular materials subject to gravity. The effects of grain shape (spherical or polyhedral) and polydispersity on this…
In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure plays a pivotal role in determining the macroscopic physical properties. Here, we analyse local structure metrics derived from…
Most technologically useful materials spanning multiple length scales are polycrystalline. Polycrystalline microstructures are composed of a myriad of small crystals or grains with different lattice orientations which are separated by…
For grain growth to proceed effectively and lead to planet formation a number of barriers to growth must be overcome. One such barrier, relevant for compact grains in the inner regions of the disc, is the `bouncing barrier' in which large…
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…
The Hilbert basis is fundamental in describing the structure of the integer points of a polyhedral cone. The face-centered cubic grid is one of the densest packing of the 3-dimensional space. The cycles of a grid satisfy the constraint set…
Many composite materials, both natural and fabricated, process a Voronoi like architecture or microstructure. Furthermore, the stochasticity and connectivity of Voronoi tessellation endow the composite materials constructed by this kind of…