Related papers: Controlling Escape in the Standard Map
We study the escape dynamics in the presence of a hole of a standard family of intermittent maps of the unit interval with neutral fixed point at the origin (and finite absolutely continuous invariant measure). Provided that the hole (is a…
We show that particle transport in a uniform, quantum multi-baker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semi-classical limit leads to diffusion. Random…
We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…
We derive a general exact formula for the mean first passage time (MFPT) from a fixed point inside a planar domain to an escape region on its boundary. The underlying mixed Dirichlet-Neumann boundary value problem is conformally mapped onto…
We present some new results on sample path optimality for the ergodic control problem of a class of non-degenerate diffusions controlled through the drift. The hypothesis most often used in the literature to ensure the existence of an a.s.…
In this paper, we study McKean-Vlasov SDE living in $\mathbb{R}^d$ in the reversible case without assuming any type of convexity assumptions for confinement or interaction potentials. Kramers' type law for the exit-time from a domain of…
The rates of activated processes, such as escape from a metastable state and nucleation, are exponentially sensitive to an externally applied field. We describe how this applies to modulation by high-frequency fields and illustrate it with…
The time needed for a particle to exit a confining domain through a small window, called the narrow escape time (NET), is a limiting factor of various processes, such as some biochemical reactions in cells. Obtaining an estimate of the mean…
In this work we characterize the escape of orbits from the phase space of the Riemann-Liouville (RL) fractional standard map (fSM). The RL-fSM, given in action-angle variables, is derived from the equation of motion of the kicked rotor when…
We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
Motivated in part by a problem in simulated tempering (a form of Markov chain Monte Carlo) we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin…
In this paper we study the fluctuations from the limiting behavior of small noise random perturbations of diffusions with multiple scales. The result is then applied to the exit problem for multiscale diffusions, deriving the limiting law…
Physical notions of stochastic resonance for potential diffusions in periodically changing double-well potentials such as the spectral power amplification have proved to be defective. They are not robust for the passage to their effective…
We study a class of two-sided optimal control problems of general linear diffusions under a so-called Poisson constraint: the controlling is only allowed at the arrival times of an independent Poisson signal processes. We give a weak and…
For a stopped diffusion process in a multidimensional time-dependent domain $\D$, we propose and analyse a new procedure consisting in simulating the process with an Euler scheme with step size $\Delta$ and stopping it at discrete times…
We study and compare three characteristic times of the standard map, the Lyapunov time t_L, the Poincare recurrence time t_r and the stickiness (or escape) time t_{st}. The Lyapunov time is the inverse of the Lyapunov characteristic number…
We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which…
Statistical properties for the recurrence of particles in an oval billiard with a hole in the boundary are discussed. The hole is allowed to move in the boundary under two different types of motion: (i) counterclockwise periodic circulation…
In this paper we consider the problem of avoided crossings (level repulsion) in phononic crystals and suggest a computationally efficient strategy to distinguish them from normal cross points. This process is essential for the correct…