Traveling length and minimal traveling time for flow through percolation networks with long-range spatial correlations

We study the distributions of traveling length l and minimal traveling time t through two-dimensional percolation porous media characterized by long-range spatial correlations. We model the dynamics of fluid displacement by the convective movement of tracer particles driven by a pressure difference between two fixed sites (''wells'') separated by Euclidean distance r. For strongly correlated pore networks at criticality, we find that the probability distribution functions P(l) and P(t) follow the same scaling Ansatz originally proposed for the uncorrelated case, but with quite different scaling exponents. We relate these changes in dynamical behavior to the main morphological difference between correlated and uncorrelated clusters, namely, the compactness of their backbones. Our simulations reveal that the dynamical scaling exponents for correlated geometries take values intermediate between the uncorrelated and homogeneous limiting cases

The Complex Topology of Chemical Plants

We show that flowsheets of oil refineries can be associated to complex network topologies that are scale-free, display small-world effect and possess hierarchical organization. The emergence of these properties from such man-made networks is explained as a consequence of the currently used principles for process design, which include heuristics as well as algorithmic techniques. We expect these results to be valid for chemical plants of different types and capacities.Comment: 7 pages, 5 figures and 1 tabl

Transition from Knudsen to molecular diffusion in activity of absorbing irregular interfaces

We investigate through molecular dynamics the transition from Knudsen to molecular diffusion transport towards 2d absorbing interfaces with irregular geometry. Our results indicate that the length of the active zone decreases continuously with density from the Knudsen to the molecular diffusion regime. In the limit where molecular diffusion dominates, we find that this length approaches a constant value of the order of the system size, in agreement with theoretical predictions for Laplacian transport in irregular geometries. Finally, we show that all these features can be qualitatively described in terms of a simple random-walk model of the diffusion process.Comment: 4 pages, 4 figure

Planar and Poly-Arc Lombardi Drawings

In Lombardi drawings of graphs, edges are represented as circular arcs, and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing, and not every planar graph has a planar Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be drawn with k circular arcs, noting that every graph has a smooth 2-Lombardi drawing. We show that every planar graph has a smooth planar 3-Lombardi drawing and further investigate topics connecting planarity and Lombardi drawings.Comment: Expanded version of paper appearing in the 19th International Symposium on Graph Drawing (GD 2011). 16 pages, 8 figure

Distributed flow optimization and cascading effects in weighted complex networks

We investigate the effect of a specific edge weighting scheme $\sim (k_i k_j)^{\beta}$ on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow model: current flow in random resistor networks. By the tuning of control parameter $\beta$ and by considering two general cases of relative node processing capabilities as well as the effect of bandwidth, we show the dependence of transport efficiency upon the correlations between the topology and weights. By studying the severity of cascades for different control parameter $\beta$, we find that network resilience to cascading overloads and network throughput is optimal for the same value of $\beta$ over the range of node capacities and available bandwidth