Explosive metallic breakdown

We investigate the metallic breakdown of a substrate on which highly conducting particles are adsorbed and desorbed with a probability that depends on the local electric field. We find that, by tuning the relative strength $q$ of this dependence, the breakdown can change from continuous to explosive. Precisely, in the limit in which the adsorption probability is the same for any finite voltage drop, we can map our model exactly onto the $q$-state Potts model and thus the transition to a jump occurs at $q=4$. In another limit, where the adsorption probability becomes independent of the local field strength, the traditional bond percolation model is recovered. Our model is thus an example of a possible experimental realization exhibiting a truly discontinuous percolation transition.

Searching for superspreaders of information in real-world social media

A number of predictors have been suggested to detect the most influential spreaders of information in online social media across various domains such as Twitter or Facebook. In particular, degree, PageRank, k-core and other centralities have been adopted to rank the spreading capability of users in information dissemination media. So far, validation of the proposed predictors has been done by simulating the spreading dynamics rather than following real information flow in social networks. Consequently, only model-dependent contradictory results have been achieved so far for the best predictor. Here, we address this issue directly. We search for influential spreaders by following the real spreading dynamics in a wide range of networks. We find that the widely-used degree and PageRank fail in ranking users influence. We find that the best spreaders are consistently located in the k-core across dissimilar social platforms such as Twitter, Facebook, Livejournal and scientific publishing in the American Physical Society. Furthermore, when the complete global network structure is unavailable, we find that the sum of the nearest neighbors degree is a reliable local proxy for users influence. Our analysis provides practical instructions for optimal design of strategies for viral information dissemination in relevant applications.

Optimal box-covering algorithm for fractal dimension of complex networks

The self-similarity of complex networks is typically investigated through computational algorithms the primary task of which is to cover the structure with a minimal number of boxes. Here we introduce a box-covering algorithm that not only outperforms previous ones, but also finds optimal solutions. For the two benchmark cases tested, namely, the E. Coli and the WWW networks, our results show that the improvement can be rather substantial, reaching up to 15% in the case of the WWW network.

A micromechanical model of collapsing quicksand

The discrete element method constitutes a general class of modeling techniques to simulate the microscopic behavior (i.e. at the particle scale) of granular/soil materials. We present a contact dynamics method, accounting for the cohesive nature of fine powders and soils. A modification of the model adjusted to capture the essential physical processes underlying the dynamics of generation and collapse of loose systems is able to simulate quicksand behavior of a collapsing soil material, in particular of a specific type, which we call living quicksand. We investigate the penetration behavior of an object for varying density of the material. We also investigate the dynamics of the penetration process, by measuring the relation between the driving force and the resulting velocity of the intruder, leading to a power law behavior with exponent 1/2, i.e. a quadratic velocity dependence of the drag force on the intruder.

Tricritical point in explosive percolation

The suitable interpolation between classical percolation and a special variant of explosive percolation enables the explicit realization of a tricritical percolation point. With high-precision simulations of the order parameter and the second moment of the cluster size distribution a fully consistent tricritical scaling scenario emerges yielding the tricritical crossover exponent $1/phi_t=1.8pm0.1$.

Laws of Population Growth

An important issue in the study of cities is defining a metropolitan area, as different definitions affect the statistical distribution of urban activity. A commonly employed method of defining a metropolitan area is the Metropolitan Statistical Areas (MSA), based on rules attempting to capture the notion of city as a functional economic region, and is constructed using experience. The MSA is time-consuming and is typically constructed only for a subset (few hundreds) of the most highly populated cities. Here, we introduce a new method to designate metropolitan areas, denoted the City Clustering Algorithm (CCA). The CCA is based on spatial distributions of the population at a fine geographic scale, defining a city beyond the scope of its administrative boundaries. We use the CCA to examine Gibrats law of proportional growth, postulating that the mean and standard deviation of the growth rate of cities are constant, independent of city size. We find that the mean growth rate of a cluster utilizing the CCA exhibits deviations from Gibrats law, and that the standard deviation decreases as a power-law with respect to the city size. The CCA allows for the study of the underlying process leading to these deviations, shown to arise from the existence of long-range spatial correlations in the population growth. These results have socio-political implications, such as those pertaining to the location of new economic development in cities of varied size.