Voronoi Network Research Articles

Invasion percolation on a random lattice

The author uses the technique of invasion percolation to compute the critical points and critical exponents of percolation on a random lattice which is the dual of a Voronoi network.

On the distribution of cell areas in a Voronoi network

Abstract The distribution of cell areas for a Voronoi network is examined by computer simulation, and a rough argument is presented as to how this form of distribution may be derived analytically. The resulting form is a gamma function as was previously used by Kiang (1966) to fit numerical data of cell areas. Computer-generated distributions for large samples of cells are here used to test this suggested function more stringently than in Kiang's work.

Simulation of interstitial diffusion in an amorphous structure

The authors investigate the random walk of an interstitial atom through an amorphous structure. The interaction between the diffusing particle and the atoms in the matrix is defined through a model potential which can be used in any disordered material and has strong interrelations with the corresponding Voronoi network. The stochastic process is carefully described as consisting of two random walks: one on the net of interstitial sites, the other on the time axis. Thus, the authors can perform a Monte-Carlo experiment on a simulated amorphous sample. They show that the concept of percolation greatly reduces the complexity of the problem: one can define a percolation threshold for the saddle points, such that only those which are near to this value need be considered. Numerical results are obtained which show the gaussian character of the motion. Finally, the diffusion coefficient is evaluated and shown to be a little higher than in crystalline materials.

Percolation and conduction on the 3D Voronoi and regular networks: a second case study in topological disorder

To assess the effect of random coordination percolation properties of the three-dimensional (3D) Voronoi network and the body-centred cubic with second-nearest-neighbour bonding (BCC2) are calculated by Monte Carlo simulation and compared. The accessible fraction, backbone fraction and effective conductivity of the Voronoi network and regular networks are qualitatively the same. Moreover, when enough bonds are removed from the Voronoi network to make the average coordination match that of the BCC2 network the difference between the conductivities of the two networks is less than 0.002. Finite-size scaling theory is used to estimate percolation thresholds and critical exponents. The bond percolation thresholds of the Voronoi and BCC2 networks are 0.082 and 0.0991, whereas the site percolation thresholds are 0.145 and 0.169. The correlation length, backbone and conductivity exponents of the Voronoi network are v=0.88, beta '=1.06 and t=2.02, in good agreement with the values accepted for regular 3D networks. The effective conductivity of the network derived from a crude finite-element approximation to the Voronoi tessellation is only slightly different from that of the same network with the conductances redistributed at random.

Percolation and conduction on Voronoi and triangular networks: a case study in topological disorder

The network generated from a Voronoi tessellation of space is a natural prototype for topologically random networks. To assess the effects of random coordination, the percolation and conduction properties of the Voronoi network and of its closest kin among regular networks, the triangular network, are calculated and compared by means of Monte Carlo simulations.