Related papers: Instability of scale-free networks under node-brea…
We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
We analyze a two-dimensional spring network model comprising breakable and unbreakable springs. Computer simulations showed this system to exhibit intermittent stress drops in a larger strain regime, and these stress drops resulted in…
Slip at a frictional interface occurs via intermittent events. Understanding how these events are nucleated, can propagate, or stop spontaneously remains a challenge, central to earthquake science and tribology. In the absence of disorder,…
The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…
Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…
We consider nonequilibrium phase transitions in weighted scale-free networks, in which highly connected nodes, which are created earlier in time are partially immunized. For epidemic spreading we solve the dynamical mean-field equations and…
One explanation for the impressive recent boom in network theory might be that it provides a promising tool for an understanding of complex systems. Network theory is mainly focusing on discrete large-scale topological structures rather…
Modern world builds on the resilience of interdependent infrastructures characterized as complex networks. Recently, a framework for analysis of interdependent networks has been developed to explain the mechanism of resilience in…
We study the robustness of complex networks subject to edge removal. Several network models and removing strategies are simulated. Rather than the existence of the giant component, we use total connectedness as the criterion of breakdown.…
We study a cascading edge failure mechanism on a connected random graph with a prescribed degree sequence, sampled using the configuration model. This mechanism prescribes that every edge failure puts an additional strain on the remaining…
We present a framework to calculate the cascade size evolution for a large class of cascade models on random network ensembles in the limit of infinite network size. Our method is exact and applies to network ensembles with almost arbitrary…
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…
Heterogeneous materials are often organized in a hierarchical manner, where a basic unit is repeated over multiple scales.The structure then acquires a self-similar pattern. Examples of such structure are found in various biological and…
We present an extension of fiber bundle models considering that failed fibers still carry a fraction $0 \leq \alpha \leq 1$ of their failure load. The value of $\alpha$ interpolates between the perfectly brittle failure $(\alpha = 0)$ and…
We study networks of coupled bistable elastic elements, recently proposed as a model for crumpled thin sheets. The networks are poised on the verge of a localized instability, and the model allows unique access to both local and global…
Can the topology of a network that consists of many particles interacting with each other change in complexity when a phase transition occurs? The answer to this question is particularly interesting to understand the nature of phase…
Complex systems are large collections of entities that organize themselves into non-trivial structures that can be represented by networks. A key emergent property of such systems is robustness against random failures or targeted attacks…
Methods connecting dynamical systems and graph theory have attracted increasing interest in the past few years, with applications ranging from a detailed comparison of different kinds of dynamics to the characterisation of empirical data.…
Combining X-ray tomography with simultaneous shear force measurement, we investigate shear-induced granular avalanches using spherical particles with different surface roughness. We find that systems consisting of particles with large…