Related papers: Trace formula for activated escape in noisy maps
We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum co-ordinate vary freely and restrict only angle with…
We prove sharp asymptotic estimates for the rate of escape of the two-dimensional simple random walk conditioned to avoid a fixed finite set. We derive it from asymptotics available for the continuous analogue of this process (cf…
We present a novel path-integral method for the determination of time-dependent and time-averaged reaction rates in multidimensional, periodically driven escape problems at weak thermal noise. The so obtained general expressions are…
We investigate the escape dynamics of the doubling map with a time-periodic hole. We use Ulam's method to calculate the escape rate as a function of the control parameters. We consider two cases, oscillating or breathing holes, where the…
We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope of the map by solving Frobenius-Perron…
We study the noise-driven escape of active Brownian particles (ABPs) and run-and-tumble particles (RTPs) from confining potentials. In the small noise limit, we provide an exact expression for the escape rate in term of a variational…
For the enhancement of the transient stability of power systems, the key is to define a quantitative optimization formulation with system parameters as decision variables. In this paper, we model the disturbances by Gaussian noise and…
A theoretical approach for characterising the influence of asymmetry of noise distribution on the escape rate of a multi-stable system is presented. This was carried out via the estimation of an action, which is defined as an exponential…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
Inferring plausible node mobility based only on information from wireless contact traces is a difficult problem. Working with mobility information allows richer protocol simulations, particularly in dense networks, but requires complex…
Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape…
We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complicates the analysis is that rest points are included in the…
For a class of non-uniformly hyperbolic interval maps, we study rates of escape with respect to conformal measures associated with a family of geometric potentials. We establish the existence of physically relevant conditionally invariant…
Numerical computations of bifurcation maps for one dimensional maps show patterns (regular jumps in point density) in the zones of chaotic behaviour. In this work, empiric formulas are given for these patterns for an entire class of maps.
The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighborhood of a given saddlepoint exactly by means of a smooth…
We are exploring two archetypal noise induced escape scenarios: escape from a finite interval and from the positive half-line under the action of the mixture of L\'evy and Gaussian white noises in the overdamped regime, for the random…
In this article we study a piecewise linear discretization schemes for transfer operators (Perron-Frobenius operators) associated with interval maps. We show how these can be used to provide rigorous {\bf pointwise} approximations for…
Suppose a two-dimensional dynamical system has a stable attractor that is surrounded by an unstable limit cycle. If the system is additively perturbed by white noise, the rate of escape through the limit cycle will fall off exponentially as…
Discrete optimal transportation problems arise in various contexts in engineering, the sciences and the social sciences. Often the underlying cost criterion is unknown, or only partly known, and the observed optimal solutions are corrupted…
We address the difficult question of inferring plausible node mobility based only on information from wireless contact traces. Working with mobility information allows richer protocol simulations, particularly in dense networks, but…