Related papers: Resolution dependence of most probable pathways wi…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…
Optimal paths for the classical Onsager-Machlup function determining most probable paths between points on a manifold are only explicitly identified for specific processes, for example the Riemannian Brownian motion. This leaves out large…
Turing instabilities of reaction-diffusion systems can only arise if the diffusivities of the chemical species are sufficiently different. This threshold is unphysical in most systems with $N=2$ diffusing species, forcing experimental…
In many practically important problems which rely on particles' transport in realistic corrugated channels, one is interested to know the probability that either of the extremities, (e.g., the one containing a chemically active site, or…
Deterministic chaotic dynamics presumes that the state space can be partitioned arbitrarily finely. In a physical system, the inevitable presence of some noise sets a finite limit to the finest possible resolution that can be attained. Much…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes,…
We consider the motion planning problem for stochastic nonlinear systems in uncertain environments. More precisely, in this problem the robot has stochastic nonlinear dynamics and uncertain initial locations, and the environment contains…
We study robust nonlinear filtering for stochastic models driven by L\'evy processes, where the signal and observation processes are coupled through common Brownian and jump noise. Robustness, defined as the continuous dependence of the…
In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…
We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the noise goes to zero relative to the homogenization parameter, we…
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…
Networks of channels conveying particles are often subject to blockages due to the limited carrying capacity of the individual channels. If the channels are coupled, blockage of one causes an increase in the flux entering the remaining open…
In this paper we study the stochastic Navier-Stokes equations on the $d$-dimensional torus with transport noise, which arise in the study of turbulent flows. Under very weak smoothness assumptions on the data we prove local well-posedness…
Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to…
Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input…
We examine most-likely paths between initial and final states for diffusive quantum trajectories in continuously monitored pure-state qubits, obtained as extrema of a stochastic path integral. We demonstrate the possibility of "multipaths"…
We present a model of diffusion in heterogeneous environment, which qualitatively reflects the transport properties of a polymeric membrane with carbon nanotubes. We derived Fokker-Planck equation from system of stochastic equations,…
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…