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How does a steady state with strong intermittency develop in time from an initial state which is statistically random? For passive sliders driven by various fluctuating surfaces, we show that the approach involves an indefinitely growing…
We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a time-periodic drift term, which vanishes on two stable and one unstable equilibrium branches. Each of…
We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a…
Spatial resolution of stimulated emission depletion (STED) microscopy varies with sample labeling techniques and microscope components, e.g., lasers, lenses, and photo-detectors. Fluctuations in the intensity of the depletion laser decrease…
The dynamic scaling of curved interfaces presents features that are strikingly different from those of the planar ones. Spherical surfaces above one dimension are flat because the noise is irrelevant in such cases. Kinetic roughening is…
Minimal models of self-propelled particles with short-range volume exclusion interactions have been shown to exhibit signatures of phase separation. Here I show that the observed interfacial stability and fluctuations in motility-induced…
In this article, we consider the stochastic wave equation in spatial dimension $d=1$, with linear term $\sigma(u)=u$ multiplying the noise. This equation is driven by a Gaussian noise which is white in time and fractional in space with…
We study the steady state properties of a phenomenological two-state predator model in presence of correlated Gaussian white noise. Based on the corresponding Fokker-Planck equation for probability distribution function the steady state…
A mass ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large…
Elastic interfaces display scale-invariant geometrical fluctuations at sufficiently large lengthscales. Their asymptotic static roughness then follows a power-law behavior, whose associated exponent provides a robust signature of the…
In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered…
We study the scaling properties of a one-dimensional interface at equilibrium, at finite temperature and in a disordered environment with a finite disorder correlation length. We focus our approach on the scalings of its geometrical…
In this work we study the likelihood of survival of single-species in the context of hostile and disordered environments. Population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average…
Spatial and temporal noise power spectra of stripe patterns are investigated, using as a model a Swift-Hohenberg equation with a stochastic term. In particular, the analytical and numerical investigations show: 1) the temporal noise spectra…
We study the density of specular reflection points in the geometrical optics limit when light scatters off fluctuating interfaces and membranes in thermodynamic equilibrium. We focus on the statistical mechanics of both capillary-gravity…
Natural ecosystems are characterized by striking diversity of form and functions and yet exhibit deep symmetries emerging across scales of space, time and organizational complexity. Species-area relationships and species-abundance…
We study the focusing stochastic nonlinear Schr\"odinger equation in one spatial dimension with multiplicative noise, driven by a Wiener process white in time and colored in space, in the $L^2$-critical and supercritical cases. The mass…
Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and…
We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a…
The dynamics of a two-species community of $N$ competing individuals is considered, with an emphasis on the role of environmental variations that affect coherently the fitness of entire populations. The chance of fixation of a mutant…