相关论文: Poresizes in random line networks
The simplest null models for networks, used to distinguish significant features of a particular network from {\it a priori} expected features, are random ensembles with the degree sequence fixed by the specific network of interest. These…
We study the distribution of diameters d of Erd\"os-R\'enyi random graphs with average connectivity c. The diameter d is the maximum among all shortest distances between pairs of nodes in a graph and an important quantity for all dynamic…
A quantitative comparison of the pore space geometry for three natural sandstones is presented. The comparison is based on local porosity theory which provides a geometric characterization of stochastic microstructures. The characterization…
Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with…
Porous media are often modelled as systems of overlapping obstacles, which leads to the problem of two percolation thresholds in such systems, one for the porous matrix and the other one for the void space. Here we investigate these…
Networks provide a popular representation of complex data. Often, different types of relational measurements are taken on the same subjects. Such data can be represented as a \textit{multislice network}, a collection of networks on the same…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…
We investigate wrinkling of two-dimensional random and triangular semiflexible polymer networks under shear. Both types of semiflexible networks exhibit wrinkling above a small critical shear angle, which scales with an exponent of the…
We consider a three dimensional spatial network, where $N$ nodes are randomly distributed within a cube $L\times L\times L$. Each two nodes are connected if their mutual distance does not excess a given cutoff $a$. We analyse numerically…
Many biological tissues feature a heterogeneous network of fibers whose tensile and bending rigidity contribute substantially to these tissues' elastic properties. Rigidity percolation has emerged as a important paradigm for relating these…
We define a dynamic model of random networks, where new vertices are connected to old ones with a probability proportional to a sublinear function of their degree. We first give a strong limit law for the empirical degree distribution, and…
Continuum models of porous media use macroscopic parameters and state variables to capture essential features of pore-scale physics. We propose a macroscopic property "accessivity" ($\alpha$) to characterize the network connectivity of…
The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and…
Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…
A theoretical approach to estimating stable drainage front widths in three-dimensional random porous media under gravitational and capillary effects is presented. Based on the frontier of the infinite cluster in gradient percolation, we…
A common way of classifying network connectivity is the association of the nodal degree distribution to specific probability distribution models. During the last decades, researchers classified many networks using the Poisson or Pareto…
In this paper, we are concerned with the simulation of blood flow in microvascular networks and the surrounding tissue. To reduce the computational complexity of this issue, the network structures are modeled by a one-dimensional graph,…
The study of real-life network modeling has become very popular in recent years. An attractive model is the scale-free percolation model on the lattice $\mathbb{Z}^d$, $d\ge1$, because it fulfills several stylized facts observed in large…
We present a generalized network model for simulating capillary-dominated two-phase flow through porous media at the pore scale. Three-dimensional images of the pore space are discretized using a generalized network -- described in a…
Past work has shown that ions can pass through a membrane more readily in one direction than the other. We demonstrate here in a model and an experiment that for a mixture of small and large particles such asymmetric diffusion can arise…