Related papers: Scaling of spin avalanches in growing networks
The Ising model on a $restricted$ scale-free network (SFN) has been studied employing Monte Carlo simulations. This network is described by a power-law degree distribution in the form $P(k)~k^{-\alpha}$, and is called restricted, because…
We calculate numerically the sizes S of jumps (avalanches) between successively pinned configurations of an elastic line (d=1) or interface (d=2), pulled by a spring of (small) strength m^2 in a random-field landscape. We obtain strong…
Scale-free (SF) networks and small world networks have been found to occur in very diverse contexts. It is this striking universality which makes one look for widely applicable mechanisms which lead to the formation of such networks. In…
Recent studies of attacks on complex networks suggest that small initial breakdowns can lead to global cascades of overload failures in communication, economic trading, and supply-transportation systems, considering the defense methods is…
The nonequilibrium Ising model on a restricted scale-free network has been studied with one- and two-spin flip competing dynamics employing Monte Carlo simulations. The dynamics present in the system can be defined by the probability $q$ in…
It has been well-known that many real networks are scale-free (SF) but extremely vulnerable against attacks. We investigate the robustness of connectivity and the lengths of the shortest loops in randomized SF networks with realistic…
Scale-free networks are a recently developed approach to model the interactions found in complex natural and man-made systems. Such networks exhibit a power-law distribution of node link (degree) frequencies n(k) in which a small number of…
This article addresses the degree distribution of subnetworks, namely the number of links between the nodes in each subnetwork and the remainder of the structure (cond-mat/0408076). The transformation from a subnetwork-partitioned model to…
As shown recently (arXiv:0801.3056), several types of neuronal complex networks involving non-linear integration-and-fire dynamics exhibit an abrupt activation along their transient regime. Interestingly, such an avalanche of activation has…
We study several probability distributions relevant to the avalanche dynamics of elastic interfaces driven on a random substrate: The distribution of size, duration, lateral extension or area, as well as velocities. Results from the…
Given a connected network, it can be augmented by applying a growing strategy (e.g. random or scale-free rules) over the previously existing structure. Another approach for augmentation, recently introduced, involves incorporating a direct…
We introduce a simple model for the size distribution of avalanches based on the idea that the front of an avalanche can be described by a directed random walk. The model captures some of the qualitative features of earthquakes, avalanches…
Dynamical processes exhibiting absorbing states are essential in the modeling of a large variety of situations from material science to epidemiology and social sciences. Such processes exhibit the possibility of avalanching behavior upon…
We consider a growing network, whose growth algorithm is based on the preferential attachment typical for scale-free constructions, but where the long-range bonds are disadvantaged. Thus, the probability to get connected to a site at…
We simulate Barkhausen avalanches on fractal clusters in a two-dimensional diluted Ising ferromagnet with an effective Gaussian random field. We vary the concentration of defect sites $c$ and find a scaling region for moderate disorder,…
We study the correlations between avalanches in the depinning dynamics of elastic interfaces driven on a random substrate. In the mean field theory (the Brownian force model), it is known that the avalanches are uncorrelated. Here we obtain…
The Internet, as well as many other networks, has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the…
We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) ~ k^-a, i.e. the probability of having k links outgoing from a site. In contrast to the diameter of regular…
We reveal the nature of the avalanche collapse of the giant viable component in multiplex networks under perturbations such as random damage. Specifically, we identify latent critical clusters associated with the avalanches of random…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…