It is widely recognized that an efficient sample of a spatially distributed resource will have some degree of regularity. For example, locating sample points at the nodes of a regular grid is an optimal model-based design for some semivariograms and domain shapes. Locating points becomes more complicated if the domain has an irregular shape or if the design incorporates existing sample points. ...

Recently proposed constitutive models that describe the mechanical behavior of open-porous cellular materials take into account random pore sizes but not randomness in shapes [1]. In present contribution, a computational model to reconstruct highly irregular structure porous is developed using sphere packing and Laguerre-Voronoi tessellation [2]. The structure-property relationship then investi...

For positive integers p and q with 1/p+1/q < 1/2, a tessellation of type {p, q} is a tessellation of the hyperbolic plane by regular p-gons with q p-gons meeting at each vertex. In this paper, a necessary and sufficient condition on the integers p and q is established to determine when a tessellation of type {p, q} can be realized as a tessellation of the hyperbolic plane by fundamental domains...

We study the weak convergence of β- and β′-Delaunay tessellations in Rd−1 that were introduced part I this paper, as β→∞. The limiting stationary simplicial random tessellation, which is called Gaussian-Delaunay characterized terms a space-time paraboloid hull process Rd−1×R. latter object has previously appeared analysis number shocks solution inviscid Burgers’ equation description local asymp...

Prediction of mechanical properties of carbon nanotube-based composite is one of the important issues which should be addressed reasonably. A proper modeling approach is a multi-scale technique starting from nano scale and lasting to macro scale passing in-between scales of micro and meso. The main goal of this research is to develop a multi-scale modeling approach to extract mechanical propert...

A model for an inhomogeneous Poisson process with high intensity near the edges of a Voronoi tessellation in 2D or 3D is proposed. The model is analysed in a Bayesian setting with priors on nuclei of the Voronoi tessellation and other model parameters. An MCMC algorithm is constructed to sample from the posterior, which contains information about the unobserved Voronoi tessellation and the mode...

In order to detect a motif of local structures in different protein conformations, the Delaunay tessellation is applied to protein structures represented by C(alpha) atoms only. By the Delaunay tessellation the interior space of the protein is uniquely divided up into Delaunay tetrahedra whose vertices are the C(alpha) atom positions. Some edges of the tetrahedra are virtual bonds connecting ad...