Cascading traffic jamming in a two-dimensional Motter and Lai model

We study the cascading traffic jamming on a two-dimensional random geometric graph using the Motter and Lai model. The traffic jam is caused by a localized attack incapacitating circular region or a line of a certain size, as well as a dispersed attack on an equal number of randomly selected nodes. We investigate if there is a critical size of the attack above which the network becomes completely jammed due to cascading jamming, and how this critical size depends on the average degree $\langle k\rangle$ of the graph, on the number of nodes $N$ in the system, and the tolerance parameter $\alpha$ of the Motter and Lai model.Comment: 14 pages, 9 figure

Network Overload due to Massive Attacks

We study the cascading failure of networks due to overload, using the betweenness centrality of a node as the measure of its load following the Motter and Lai model. We study the fraction of survived nodes at the end of the cascade $p_f$ as function of the strength of the initial attack, measured by the fraction of nodes $p$, which survive the initial attack for different values of tolerance $\alpha$ in random regular and Erd\"os-Renyi graphs. We find the existence of first order phase transition line $p_t(\alpha)$ on a $p-\alpha$ plane, such that if $p <p_t$ the cascade of failures lead to a very small fraction of survived nodes $p_f$ and the giant component of the network disappears, while for $p>p_t$, $p_f$ is large and the giant component of the network is still present. Exactly at $p_t$ the function $p_f(p)$ undergoes a first order discontinuity. We find that the line $p_t(\alpha)$ ends at critical point $(p_c,\alpha_c)$ ,in which the cascading failures are replaced by a second order percolation transition. We analytically find the average betweenness of nodes with different degrees before and after the initial attack, investigate their roles in the cascading failures, and find a lower bound for $p_t(\alpha)$. We also study the difference between a localized and random attacks

Spatial wave intensity correlations in quasi-one-dimensional wires

Spatial intensity correlations between waves transmitted through random media are analyzed within the framework of the random matrix theory of transport. Assuming that the statistical distribution of transfer matrices is isotropic, we found that the spatial correlation function can be expressed as the sum of three terms, with distinctive spatial dependences. This result coincides with the one obtained in the diffusive regime from perturbative calculations, but holds all the way from quasi-ballistic transport to localization. While correlations are positive in the diffusive regime, we predict a transition to negative correlations as the length of the system decreases.Comment: 10 pages, 3 figures. Submitted to Physical Review Letter

Interdependent networks with correlated degrees of mutually dependent nodes

We study a problem of failure of two interdependent networks in the case of correlated degrees of mutually dependent nodes. We assume that both networks (A and B) have the same number of nodes $N$ connected by the bidirectional dependency links establishing a one-to-one correspondence between the nodes of the two networks in a such a way that the mutually dependent nodes have the same number of connectivity links, i.e. their degrees coincide. This implies that both networks have the same degree distribution $P(k)$. We call such networks correspondently coupled networks (CCN). We assume that the nodes in each network are randomly connected. We define the mutually connected clusters and the mutual giant component as in earlier works on randomly coupled interdependent networks and assume that only the nodes which belong to the mutual giant component remain functional. We assume that initially a $1-p$ fraction of nodes are randomly removed due to an attack or failure and find analytically, for an arbitrary $P(k)$, the fraction of nodes $\mu(p)$ which belong to the mutual giant component. We find that the system undergoes a percolation transition at certain fraction $p=p_c$ which is always smaller than the $p_c$ for randomly coupled networks with the same $P(k)$. We also find that the system undergoes a first order transition at $p_c>0$ if $P(k)$ has a finite second moment. For the case of scale free networks with $2<\lambda \leq 3$, the transition becomes a second order transition. Moreover, if $\lambda<3$ we find $p_c=0$ as in percolation of a single network. For $\lambda=3$ we find an exact analytical expression for $p_c>0$. Finally, we find that the robustness of CCN increases with the broadness of their degree distribution.Comment: 18 pages, 3 figure

Inter-similarity between coupled networks

Recent studies have shown that a system composed from several randomly interdependent networks is extremely vulnerable to random failure. However, real interdependent networks are usually not randomly interdependent, rather a pair of dependent nodes are coupled according to some regularity which we coin inter-similarity. For example, we study a system composed from an interdependent world wide port network and a world wide airport network and show that well connected ports tend to couple with well connected airports. We introduce two quantities for measuring the level of inter-similarity between networks (i) Inter degree-degree correlation (IDDC) (ii) Inter-clustering coefficient (ICC). We then show both by simulation models and by analyzing the port-airport system that as the networks become more inter-similar the system becomes significantly more robust to random failure.Comment: 4 pages, 3 figure

Random sequential adsorption on Euclidean, fractal, and random lattices

Irreversible adsorption of objects of different shapes and sizes on Euclidean, fractal, and random lattices is studied. The adsorption process is modeled by using random sequential adsorption algorithm. Objects are adsorbed on one-, two-, and three-dimensional Euclidean lattices, on Sierpinski carpets having dimension d between 1 and 2, and on Erdos-Rényi random graphs. The number of sites is M=Ld for Euclidean and fractal lattices, where L is a characteristic length of the system. In the case of random graphs, such a characteristic length does not exist, and the substrate can be characterized by a fixed set of M vertices (sites) and an average connectivity (or degree) g. This paper concentrates on measuring (i) the probability WL(M)(θ) that a lattice composed of Ld(M) elements reaches a coverage θ and (ii) the exponent νj characterizing the so-called jamming transition. The results obtained for Euclidean, fractal, and random lattices indicate that the quantities derived from the jamming probability WL(M)(θ), such as (dWL/dθ)max and the inverse of the standard deviation ΔL, behave asymptotically as M1/2. In the case of Euclidean and fractal lattices, where L and d can be defined, the asymptotic behavior can be written as M1/2=Ld/2=L1/νj, with νj=2/d.Fil: Pasinetti, Pedro Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaFil: Ramírez, Lucía Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaFil: Centres, Paulo Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaFil: Ramirez Pastor, Antonio Jose. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich". Universidad Nacional de San Luis. Facultad de Ciencias Físico Matemáticas y Naturales. Instituto de Física Aplicada "Dr. Jorge Andrés Zgrablich"; ArgentinaFil: Cwilich, Gabriel. Yeshiva University; Estados Unido