Ensemble distribution for immiscible two-phase flow in porous media

Entropic transport in a crowded medium

To know how liquid matter moves through a crowded medium due to the action of a force constitutes currently a problem of great practical importance, present in cases as diverse as the transport of particles through a cell membrane and through a particulate porous medium. To calculate the mass flow through the system, we present an approach that emulates the texture of the medium by using entropic barriers that the particles must overcome in order to move. The model reproduces the scaling behavior of the velocity with the force found in many systems in order to show how the scaling exponent depends on the micro-structure of the medium. Our model offers a new perspective that is able to characterize the flow of matter through the medium and may be useful in studies of nano-fluids, oil recovery, soil drainage, tissue engineering, and drug delivery.

Absorbing random walks interpolating between centrality measures on complex networks

Centrality, which quantifies the importance of individual nodes, is among the most essential concepts in modern network theory. As there are many ways in which a node can be important, many different centrality measures are in use. Here, we concentrate on versions of the common betweenness and closeness centralities. The former measures the fraction of paths between pairs of nodes that go through a given node, while the latter measures an average inverse distance between a particular node and all other nodes. Both centralities only consider shortest paths (i.e., geodesics) between pairs of nodes. Here we develop a method, based on absorbing Markov chains, that enables us to continuously interpolate both of these centrality measures away from the geodesic limit and toward a limit where no restriction is placed on the length of the paths the walkers can explore. At this second limit, the interpolated betweenness and closeness centralities reduce, respectively, to the well-known current-betweenness and resistance-closeness (information) centralities. The method is tested numerically on four real networks, revealing complex changes in node centrality rankings with respect to the value of the interpolation parameter. Nonmonotonic betweenness behaviors are found to characterize nodes that lie close to intercommunity boundaries in the studied networks.