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Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…
Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic…
Protest activity, a constitutionally protected right in the United States under the First Amendment, serves as a key tool for individuals with limited individual influence to unite collectively and amplify their impact. Despite its legal…
We analyze mechanisms and regimes of wave packet spreading in nonlinear disordered media. We predict that wave packets can spread in two regimes of strong and weak chaos. We discuss resonance probabilities, nonlinear diffusion equations,…
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…
We investigate in detail two models describing how stresses propagate and fluctuate in granular media. The first one is a scalar model where only the vertical component of the stress tensor is considered. In the continuum limit, this model…
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
We investigate a model for spatial epidemics explicitly taking into account bi-directional movements between base and destination locations on individual mobility networks. We provide a systematic analysis of generic dynamical features of…
Armed conflict data display scaling and universal dynamics in both social and physical properties like fatalities and geographic extent. We propose a randomly branching, armed-conflict model that relates multiple properties to one another…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
The difference diffusion model with two equilibrium states is given by a stochastic equation with two components: the predicted one, which is determined by the regression function of increments with two equilibriums, and the stochastic one,…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose…
We investigate the burst dynamics during drainage going from low to high injection rate at various fluid viscosities. The bursts are identified as pressure drops in the pressure signal across the system. We find that the statistical…
There is a clear distinction between simple laminar and complex turbulent fluids. But in some cases, as for the nocturnal planetary boundary layer, a stable and well-ordered flow can develop intense and sporadic bursts of turbulent activity…
In this paper, we present a computational modeling approach for the dynamics of human crowds, where the spreading of an emotion (specifically fear) has an influence on the pedestrians' behavior. Our approach is based on the methods of the…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms,…