相关论文: Double site-bond percolation model for biomaterial…

Percolation is a model for random damage to a network. It is one of the simplest models that displays a phase transition: when the network is severely damaged, it falls apart in many small connected components, while if the damage is light,…

Bone is a living material. It adapts, in an optimal sense, to loading by changing its density and trabeculae architecture - a process termed remodelling. Implanted orthopaedic devices can significantly alter the loading on the surrounding…

Continuum bone remodelling is an important tool for predicting the effects of mechanical stimuli on bone density evolution. While the modelling of only cancellous bone is considered in many studies based on continuum bone remodelling, this…

Through large-scale numerical simulations, we study the phase ordering kinetics of the $2d$ Ising Model after a zero-temperature quench from a high-temperature homogeneous initial condition. Analysing the behaviour of two important…

The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…

This preliminary study focuses on the development of a medical image segmentation algorithm based on artificial intelligence for calculating bone growth in contact with metallic implants. %as a result of the problem of estimating the growth…

By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder -- either random bonds or random fields -- we show that a critical percolation structure forms in an early stage and…

A useful result about leftmost and rightmost paths in two dimensional bond percolation is proved. This result was introduced without proof in \cite{G} in the context of the contact process in continuous time. As discussed here, it also…

We study a simplified stochastic model for the vascularization of a growing tumor, incorporating the formation of new blood vessels at the tumor periphery as well as their regression in the tumor center. The resulting morphology of the…

Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…

Cementless implants have become widely used for total hip replacement surgery. The long-term stability of these implants is achieved by bone growing around and into the porous surface of the implant, a process called osseointegration.…

We study the effects of nonreciprocity and network structure on percolation. To this end, we investigate nonreciprocal random networks - directed networks for which the probability of a link occurring from node i to node j differs from the…

We present an exact mathematical framework able to describe site-percolation transitions in real multiplex networks. Specifically, we consider the average percolation diagram valid over an infinite number of random configurations where…

Formation of random network of DNA strands is simulated on a two-dimensional triangular lattice. We investigate the size distribution of pores in the network. The results are interpreted within theory of percolation on Bethe lattice.

We consider the 2D quenched--disordered $q$--state Potts ferromagnets and show that at self--dual points any amalgamation of $q-1$ species will fail to percolate despite an overall (high) density of $1-q^{-1}$. Further, in the dilute bond…

According to the scaling theory of localization, all quantum electronic states are localized in two-dimensional (2D) systems. One consequence of the theory is that there is no quantum percolation transition in 2D. However, in a real system…

Bone remodeling involves the coordinated removal of bone by osteoclasts and addition of bone by osteoblasts, a process that is modulated by the prevailing mechanical environment. In this paper a fully coupled model of bone remodeling is…

Analytical approaches to model the structure of complex networks can be distinguished into two groups according to whether they consider an intensive (e.g., fixed degree sequence and random otherwise) or an extensive (e.g., adjacency…

It is shown that a two-component percolation model can explain an experimentally observed behavior, namely that a network built up by a mixture of sintered nanocrystalline semiconducting n- and p-grains can exhibit selective behavior, i.e.…

We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome and diced…