Related papers: Noise sustained pattern growth: Bulk versus bounda…
The effect of external fluctuations on the formation of spatial patterns is analysed by means of a stochastic Swift-Hohenberg model with multiplicative space-correlated noise. Numerical simulations in two dimensions show a shift of the…
We investigate a boundary-driven Ginzburg-Landau dynamics with long-range interactions. In the hydrodynamic limit, the macroscopic evolution is governed by a fractional heat equation with Dirichlet boundary conditions, while the…
We develop precise bounds on the growth rates and fluctuation sizes of unbounded solutions of deterministic and stochastic nonlinear Volterra equations perturbed by external forces. The equation is sublinear for large values of the state,…
Critical fluctuations of some order parameter describing a fluid generates long-range forces between boundaries. Here, we discuss fluctuation-induced forces associated to a disordered Landau-Ginzburg model defined in a $d$-dimensional slab…
The influence of small additive noise on structure formation near a forwards and near an inverted bifurcation as described by a cubic and quintic Ginzburg Landau amplitude equation, respectively, is studied numerically for group velocities…
We present an experimental and theoretical study of the effect of spatio-temporal fluctuations in quasi-reversible systems displaying a spatial quintic supercritical bifurcation. The saturation mechanism is drastically changed by the…
The influence of quantized electromagnetic fields on a nonrelativistic charged particle moving near a conducting plate is studied. We give a field-theoretic derivation of the nonlinear, non-Markovian Langevin equation of the particle by the…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
Force fluctuations in granular materials are investigated. A continuum equation is derived starting from a discrete model proposed in the literature. The influence of boundary conditions is investigated. For periodic boundary conditions the…
We study the dynamics of fronts when both inertial effects and external fluctuations are taken into account. Stochastic fluctuations are introduced as multiplicative noise arising from a control parameter of the system. Contrary to the…
We report that population dynamics in fluctuating environment accompanies mathematically equivalent structure to steady state thermodynamics. By employing the structure, population growth in fluctuating environment is decomposed into…
We utilize the externally forced linearized Navier-Stokes equations to study the receptivity of pre-transitional boundary layers to persistent sources of stochastic excitation. Stochastic forcing is used to model the effect of free-stream…
We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…
Using the theory of large deviations, macroscopic fluctuation theory provides a framework to understand the behaviour of non-equilibrium dynamics and steady states in diffusive systems. We extend this framework to a minimal model of…
A subcritical pattern-forming system with nonlinear advection in a bounded domain is recast as a slow-fast system in space and studied using a combination of geometric singular perturbation theory and numerical continuation. Two types of…
We present a general method of analyzing the influence of finite size and boundary effects on the dynamics of localized solutions of non-linear spatially extended systems. The dynamics of localized structures in infinite systems involve…
In the framework of spatially extended dynamical systems, we present three examples in which the presence of walls lead to dynamic behavior qualitatively different from the one obtained in an infinite domain or under periodic boundary…
External fluctuations have a wide variety of constructive effects on the dynamical behavior of spatially extended systems, as described by stochastic partial differential equations. A set of paradigmatic situations exhibiting such effects…
This paper is devoted to investigate the pattern formation of a volume-filling chemotaxis model with logistic cell growth. We first apply the local stability analysis to establish sufficient conditions of destabilization for uniform…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…