Related papers: Crossover Behaviour In Driven Cascades
We propose a model of random diffusion to investigate flow fluctuations in complex networks. We derive an analytical law showing that the dependence of fluctuations with the mean traffic in a network is ruled by the delicate interplay of…
The Hawkes process has garnered attention in recent years for its suitability to describe the behavior of online information cascades. Here, we present a fully tractable approach to analytically describe the distribution of the number of…
Fragmentation can be observed in nature and in everyday life on a wide range of length scales and for all kinds of technical applications. Most studies on dynamic failure focus on the behaviour of bulk systems in one, two and three…
Colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high…
The crossover between dispersion patterns has been frequently observed in various systems. Inspired by the pathway-based kinetic model for E. coli chemotaxis that accounts for the intracellular adaptation process and noise, we propose a…
Cross phenomena, representing responses of a system to external stimuli, are ubiquitous from quantum to macro scale. The Onsager theorem is often used to describe them, stating that the coefficient matrix of cross phenomena connecting the…
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods…
The paper studies the behavior of the trajectories of fluid particles in a compressible generalization of the Kraichnan ensemble of turbulent velocities. We show that, depending on the degree of compressibility, the trajectories either…
We study a two-dimensional granular system where external driving force is applied to each particle in the system in such a way that the system is driven into a steady state by balancing the energy input and the dissipation due to inelastic…
Power law is one of the the simplest forms of the relationship between different variables of a system. It leads naturally to the introduction of compound parameters describing physical properties of the system. Often one of the variables…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
Using the linearized DC power flow model, we study cascading failures and their spatial and temporal properties in the US Western Interconnect (USWI) power grid. We also introduce the preferential Degree And Distance Attachment (DADA)…
There is a commonality among contagious diseases, tweets, urban crimes, nuclear reactions, and neuronal firings that past events facilitate the future occurrence of events. The spread of events has been extensively studied such that the…
In this article we investigate the energy spectrum statistics of fractals at the quantum level. We show that the energy-level distribution of a fractal follows a power-law behaviour, if its energy spectrum is a limit set of piece-wise…
A damped chain of particles with harmonic nearest-neighbor interactions in a spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is studied numerically. One end of the chain is pulled slowly which acts as a weak…
A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain…
Sudden failure of a single transmission element in a power grid can induce a domino effect of cascading failures, which can lead to the isolation of a large number of consumers or even to the failure of the entire grid. Here we present…
Cascading failures, wherein the failure of one component triggers subsequent failures in complex interconnected systems, pose a significant risk of disruptions and emerge across various domains. Understanding and mitigating the risk of such…
In a communication scheme, there exist points at the transmitter and at the receiver where the wave is reduced to a finite set of functions of time which describe amplitudes and phases. For instance, the information is summarized in…
Condensation is the phenomenon whereby one of a sum of random variables contributes a finite fraction to the sum. It is manifested as an aggregation phenomenon in diverse physical systems such as coalescence in granular media, jamming in…