Related papers: Crossover Behaviour In Driven Cascades

Integrated cyber-physical systems (CPSs), such as the smart grid, are increasingly becoming the underpinning technology for major industries. A major concern regarding such systems are the seemingly unexpected large-scale failures, which…

Propagation of chaos for interacting particle systems has been an active research topic over decades. We propose an alternative approach to study the mean-field limit of the stochastic interacting particle systems via tools from information…

We study precursors of failure in hierarchical random fuse network models which can be considered as idealizations of hierarchical (bio)materials where fibrous assemblies are held together by multi-level (hierarchical) cross-links. When…

The critical behaviour of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described…

The standard theoretical treatment of collisional cascades derives a steady-state size distribution assuming a single constant velocity dispersion for all bodies regardless of size. Here we relax this assumption and solve self-consistently…

Complex contagion models have been developed to understand a wide range of social phenomena such as adoption of cultural fads, the diffusion of belief, norms, and innovations in social networks, and the rise of collective action to join a…

We make the first steps towards a generic theory for energy spreading and quantum dissipation. The Wall formula for the calculation of friction in nuclear physics and the Drude formula for the calculation of conductivity in mesoscopic…

Uncovering the mechanism behind the scaling law in human trajectories is of fundamental significance in understanding many spatio-temporal phenomena. In combination of the exploration and the preferential returns, we propose a simple…

We discuss the combined effects of overdamped motion in a quenched random potential and diffusion, in one dimension, in the limit where the diffusion coefficient is small. Our analysis considers the statistics of the mean first-passage time…

Consider growing a network, in which every new connection is made between two disconnected nodes. At least one node is chosen randomly from a subset consisting of $g$ fraction of the entire population in the smallest clusters. Here we show…

We propose a new mechanism for generating power laws. Starting from a random walk, we first outline a simple derivation of the Fokker-Planck equation. By analogy, starting from a certain Markov chain, we derive a master equation for power…

We propose a mathematical framework to systematically explore the propagation properties of a class of continuous in time nonlinear neural network models comprising a hierarchy of processing areas, mutually connected according to the…

In many situations we are interested in the propagation of energy in some portions of a three dimensional system with dilute long-range links. In this paper sandpile model is defined on the three-dimensional small world network with real…

We study the mutual percolation of a system composed of two interdependent random regular networks. We introduce a notion of distance to explore the effects of the proximity of interdependent nodes on the cascade of failures after an…

Electrical power systems are one of the most important infrastructures that support our society. However, their vulnerabilities have raised great concern recently due to several large-scale blackouts around the world. In this paper, we…

We analyze the statistics of water droplet avalanches in a continuously driven system. Distributions are obtained for avalanche size, lifetime, and time between successive avalanches, along with power spectra and return maps. For low flow…

We introduce a model for granular avalanching which exhibits both stretched exponential and power law avalanching over its parameter range. Two modes of transport are incorporated, a rolling layer consisting of individual particles and the…

Arrival processes to service systems often display fluctuations that are larger than anticipated under the Poisson assumption, a phenomenon that is referred to as overdispersion. Motivated by this, we analyze a class of discrete stochastic…

Understanding how complex behaviors, opinions, and innovations spread in online social networks remains a central challenge in computational social science. Existing models of complex contagion typically rely on stylized threshold…

We study the percolation in coupled networks with both inner-dependency and inter-dependency links, where the inner- and inter-dependency links represent the dependencies between nodes in the same or different networks, respectively. We…