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A bifurcating system subject to multiplicative noise can exhibit on-off intermittency close to the instability threshold. For a canonical system, we discuss the dependence of this intermittency on the Power Spectrum Density (PSD) of the…
We study the most probable way an interface moves on a macroscopic scale from an initial to a final position within a fixed time in the context of large deviations for a stochastic microscopic lattice system of Ising spins with Kac…
Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The…
We are interested in viscous scalar conservation laws with a white-in-time but spatially correlated stochastic forcing. The equation is assumed to be one-dimensional and periodic in the space variable, and its flux function to be locally…
We have studied front dynamics for the discrete $A+A \leftrightarrow A$ reaction-diffusion system, which in the continuum is described by the (stochastic) Fisher-Kolmogorov-Petrovsky-Piscunov equation. We have revisited this discrete model…
Motivated by stochastic models of climate phenomena, the steady-state of a linear stochastic model with additive Gaussian white noise is studied. Fluctuation theorems for nonequilibrium steady-states provide a constraint on the character of…
There are two main universality classes for depinning of elastic interfaces in disordered media: quenched Edwards-Wilkinson (qEW), and quenched Kardar-Parisi-Zhang (qKPZ). The first class is relevant as long as the elastic force between two…
We consider the stochastic evolution of a 1+1-dimensional interface (or polymer) in presence of a substrate. This stochastic process is a dynamical version of the homogeneous pinning model. We start from a configuration far from…
Liquid-gas phase coexistence in a boundary-driven diffusive system is studied by analyzing fluctuating hydrodynamics of a density field defined on a one-dimensional lattice with a space interval $\Lambda$. When an interface width $\ell$ is…
We study the spatiotemporal dynamics of random spatially distributed noninfinitesimal perturbations in one-dimensional chaotic extended systems. We find that an initial perturbation of finite size $\epsilon_0$ grows in time obeying the…
We study the dynamics of a system of hard-core particles sliding downwards on a one dimensional fluctuating interface, which in a special case can be mapped to the problem of a passive scalar advected by a Burgers fluid. Driven by the…
The effect of small noise in a smooth dynamical system is negligible on any finite time interval. Here we study situations when it persists on intervals increasing to infinity. Such asymptotic regime occurs when the system starts from…
We consider the dynamic evolution of a coupled array of N multiplicative random variables. The magnitude of each is constrained by a lower bound w_0 and their sum is conserved. Analytical calculation shows that the simplest case, N=2 and…
We study the one-dimensional Bak-Sneppen model for the evolution of species in an ecosystem. Of particular interest are the temporal fluctuations in the fitness variables. We numerically compute the power spectral density and apply the…
We analyze the effects of additive, spatially extended noise on spatiotemporal patterns in continuum neural fields. Our main focus is how fluctuations impact patterns when they are weakly coupled to an external stimulus or another…
The dissipative dynamics of Gaussian squeezed states (GSS) and coherent superposition states (CSS) are analytically obtained and compared. Time scales for sustaining different quantum properties such as squeezing, negativity of the Wigner…
The precision of reaction-diffusion models for mesoscopic physical systems is limited by fluctuations. To account for this uncertainty, Van Kampen derived a stochastic Langevin-like reaction-diffusion equation that incorporates…
We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density…
We have performed small-angle light-scattering measurements of the static structure factor of a critical binary mixture undergoing diffusive partial remixing. An uncommon scattering geometry integrates the structure factor over the sample…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…