相关论文: Escape Rates and Singular Limiting Distributions f…

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…

For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from integro-differential (nonlocal) equations. We develop an efficient and convergent…

We study the asymptotic behaviour of the escape rate of a Gibbs measure supported on a conformal repeller through a small hole. There are additional applications to the convergence of Hausdorff dimension of the survivor set.

We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by {\it white L\'evy noise} in a dynamical regime where inertial effects can safely be neglected. The…

Intermittency of energy dissipation has long been studied via high-order moments in homogeneous and isotropic turbulence, but not much where the boundary effects are explicitly included. Here, we derive two fundamental Reynolds number…

Populations experience a complex interplay of continuous and discrete processes: continuous growth and interactions are punctuated by discrete reproduction events, dispersal, and external disturbances. These dynamics can be modeled by…

In dissipative dynamical systems phase space volumes contract, on average. Therefore, the invariant measure on the attractor is singular with respect to the Lebesgue measure. As noted by Ruelle, a generic perturbation pushes the state out…

In this manuscript we show that a noise-activated escape phenomenon occurs in closed Hamiltonian systems. Due to the energy fluctuations generated by the noise, the isopotential curves open up and the particles can eventually escape in…

We establish general moment estimates for the discrete and continuous exit times of a general It\^o process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the…

Chaotic orbits of mushroom billiards display intermittent behaviors. We investigate statistical properties of this system by constructing an infinite partition on the chaotic part of a Poincar\'e surface which illustrates details of chaotic…

Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…

We consider random walks on a non-elementary hyperbolic group endowed with a word distance. To a probability measure on the group are associated two numerical quantities, the rate of escape and the entropy. On the set of admissible…

We consider chaotic (hyperbolic) dynamical systems which have a generating Markov partition. Then, open dynamical systems are built by making one element of a Markov partition a hole through which orbits escape. We compare various estimates…

We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an…

We investigate the rate of convergence of the iterates of an n-dimensional quasiregular mapping within the basin of attraction of a fixed point of high local index. A key tool is a refinement of a result that gives bounds on the distortion…

The escape mechanism of the four hill potential is explored. A thorough numerical investigation takes place in several types of two-dimensional planes and also in a three-dimensional subspace of the entire four-dimensional phase space in…

Thermally activated escape over a potential barrier in the presence of periodic driving is considered. By means of novel time-dependent path-integral methods we derive asymptotically exact weak-noise expressions for both the instantaneous…

The paper considers a process of escape of classical particle from a one-dimensional potential well by virtue of an external harmonic forcing. We address a particular model of the infinite-range potential well that allows independent…

We study deterministic escape dynamics in the framework of the discrete Klein-Gordon modelwith a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and…

We show that an escape from the potential minimum of Fabry-Perot interferometers can be detected measuring the associated sudden change of reflectivity. We demonstrate that the loss of information that occurs retaining only the sequence of…