Related papers: Escape dynamics through a continuously growing lea…
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…
In order to simulate observational and experimental situations, we consider a leak in the phase space of a chaotic dynamical system. We obtain an expression for the escape rate of the survival probability applying the theory of transient…
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties…
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…
The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When…
One or more small holes provide non-destructive windows to observe corresponding closed systems, for example by measuring long time escape rates of particles as a function of hole sizes and positions. To leading order the escape rate of…
We investigate the dependence of the escape rate on the position of a hole placed in uniformly hyperbolic systems admitting a finite Markov partition. We derive an exact periodic orbit formula for finite size Markov holes which differs from…
The escape dynamics in an analytical gravitational model which describes the motion of stars in a binary system of interacting dwarf spheroidal galaxies is investigated in detail. We conduct a numerical analysis distinguishing between…
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…
We use an effective Hamiltonian to characterize particle dynamics and find escape rates in a periodically kicked Hamiltonian. We study a model of particles in storage rings that is described by a chaotic symplectic map. Ignoring the…
A natural question of how the survival probability depends upon a position of a hole was seemingly never addressed in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related…
Atmosphere escape is one key process controlling the evolution of planets. However, estimating the escape rate in any detail is difficult because there are many physical processes contributing to the total escape rate. Here we show that as…
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…
Anomalous kinetics of infective (e.g., autocatalytic) reactions in open, nonhyperbolic chaotic flows are important for many applications in biological, chemical, and environmental sciences. We present a scaling theory for the singular…
This paper discusses possible approaches to the escape rate in infinite lattices of weakly coupled maps with uniformly expanding repeller. It is proved that computed-via-volume rates of spatially periodic approximations grow linearly with…
The escape dynamics in a simple analytical gravitational model which describes the motion of stars in a Seyfert galaxy is investigated in detail. We conduct a thorough numerical analysis distinguishing between regular and chaotic orbits as…
We analyze a pair of diffusion equations which are derived in the infinite system--size limit from a microscopic, individual--based, stochastic model. Deviations from the conventional Fickian picture are found which ultimately relate to the…
This study presents a novel analytical framework for modeling unsteady gas dynamics in parallel pipeline systems under leakage conditions. The proposed method introduces a time-dependent leakage mass flow rate function, which dynamically…
The bounded rationality plays a vital role in the collective behavior of the evacuation process. Also investigating human behavior in such an extreme situation is a continuing concern within social psychology. In this paper, we construct a…
We investigate in detail the escape dynamics in an analytical gravitational model which describes the motion of stars in a quasar galaxy with a disk and a massive nucleus. We conduct a thorough numerical analysis distinguishing between…