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 a 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 〈k〉 of the graph, on the number of nodes N in the system, and the tolerance parameter α of the Motter and Lai model.

Distribution of blackouts in the power grid and the Motter and Lai model.

Carreras, Dobson, and colleagues have studied empirical data on the sizes of the blackouts in real grids and modeled them with computer simulations using the direct current approximation. They have found that the resulting blackout sizes are distributed as a power law and suggested that this is because the grids are driven to the self-organized critical state. In contrast, more recent studies found that the distribution of cascades is bimodal resulting in either a very small blackout or a very large blackout, engulfing a finite fraction of the system.

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 Erdős-Rényi random graphs.

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 a function of the strength of the initial attack, measured by the fraction of nodes p that survive the initial attack for different values of tolerance α in random regular and Erdös-Renyi graphs. We find the existence of a first-order phase-transition line p_{t}(α) on a p-α plane, such that if pp_{t}, p_{f} is large and the giant component of the network is still present.

Interdependent lattice networks in high dimensions.

We study the mutual percolation of two interdependent lattice networks ranging from two to seven dimensions, denoted as D. We impose that the length (measured as chemical distance) of interdependency links connecting nodes in the two lattices be less than or equal to a certain value, r. For each value of D and r, we find the mutual percolation threshold, p_{c}[D,r], below which the system completely collapses through a cascade of failures following an initial destruction of a fraction (1-p) of the nodes in one of the lattices.