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Extreme Scattering Events (ESEs) are dramatic variations of the flux density at Gigahertz frequencies caused by ray path distortions within an isolated inhomogeneity ("plasma lens") in the interstellar medium. These events are characterized…
In this work, we report the emergence of extreme events in a damped and driven velocity-dependent mechanical system. We observe that the extreme events emerge at multiple points. We further notice that the extreme events occur symmetrically…
We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…
The statistics of velocity differences between very heavy inertial particles suspended in an incompressible turbulent flow is found to be extremely intermittent. When particles are separated by distances within the viscous subrange, the…
Some sufficient conditions on the algebraic stability of non-homogeneous regime-switching diffusion processes are established. In this work we focus on determining the decay rate of a stochastic system which switches randomly between…
The dynamical behaviour of a weakly diluted fully-inhibitory network of pulse-coupled spiking neurons is investigated. Upon increasing the coupling strength, a transition from regular to stochastic-like regime is observed. In the…
Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…
In the scientific literature, the term emergent phenomena is invoked in the context of a collective behavior observed in a complex adaptive system that exhibits no correspondence with the behavior of the system constituents. Although this…
Intermittency of energy dissipation has long been studied via high-order moments in homogeneous and isotropic turbulence, but not much where the boundary effects are explicitly included. Here, we derive two fundamental Reynolds number…
Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…
We study a spatial diffusion process generated by velocity fluctuations of intermittent nature. We note that intermittence reduces the entropy production rate while enhancing the diffusion strength. We study a case of space-dependent…
We illustrate the interplay between certain discrete and continuous problems, by presenting a method for the study of the asymptotics of a divergent sequence, through consideration of the asymptotics of its continuous analogue
Quantitative estimates for the top Lyapunov exponents for systems of stochastic reaction-diffusion equations are proven. The treatment includes reaction potentials with degenerate minima. The proof relies on an asymptotic expansion of the…
Sheared incompressible flows are usually considered non-dispersive media. As a consequence, the frequency evolution in transients has received much less attention than the wave energy density or growth factor. By carrying out a large number…
We study the asymptotic stability of a dissipative evolution in a Hilbert space subject to intermittent damping. We observe that, even if the intermittence satisfies a persistent excitation condition, if the Hilbert space is…
Fluid dynamics induced by periodically forced flow around a cylinder is analyzed computationally for the case when the forcing frequency is much lower than the von K{\'a}rm{\'a}n vortex shedding frequency corresponding to the constant flow…
Self-interacting diffusions are processes living on a compact Riemannian manifold defined by a stochastic differential equation with a drift term depending on the past empirical measure of the process. The asymptotics of this measure is…
A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…
The purpose of this paper is to establish asymptotic behaviors of time-inhomogeneous multi-scale stochastic differential equations (SDEs). To achieve them, we analyze the evolution system of measures for time-inhomogeneous Markov…
Metastability is a physical phenomenon ubiquitous in first order phase transitions. A fruitful mathematical way to approach this phenomenon is the study of rare transitions Markov chains. For Metropolis chains associated with Statistical…