Escape dynamics through a continuously growing leak

Tamás Kovács, József Vanyó

Research output: Contribution to journalArticle

Abstract

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 describes the planetary accretion. In order to study the dynamics generally, the standard map is investigated in two cases when the dynamics is fully hyperbolic and in the presence of Kolmogorov-Arnold-Moser islands. In addition to the numerical calculations, an analytic solution to the temporal behavior of the model is also derived. We show that in the early phase of the leak expansion, as long as there are enough particles in the system, the number of survivors deviates from the well-known exponential decay. Furthermore, the analytic solution returns the classical result in the limiting case when the number of particles does not affect the leak size.

Original languageEnglish
Article number062218
JournalPhysical Review E
Volume95
Issue number6
DOIs
Publication statusPublished - Jun 20 2017

Fingerprint

escape
Analytic Solution
Standard Map
Accretion
Exponential Decay
falling
Numerical Calculation
Chaotic System
astrophysics
Limiting
expansion
decay
Model

ASJC Scopus subject areas

  • Statistics and Probability
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Escape dynamics through a continuously growing leak. / Kovács, Tamás; Vanyó, József.

In: Physical Review E, Vol. 95, No. 6, 062218, 20.06.2017.

Research output: Contribution to journalArticle

@article{b769f24553a64e9cbb0157affe7bec4a,
title = "Escape dynamics through a continuously growing leak",
abstract = "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 describes the planetary accretion. In order to study the dynamics generally, the standard map is investigated in two cases when the dynamics is fully hyperbolic and in the presence of Kolmogorov-Arnold-Moser islands. In addition to the numerical calculations, an analytic solution to the temporal behavior of the model is also derived. We show that in the early phase of the leak expansion, as long as there are enough particles in the system, the number of survivors deviates from the well-known exponential decay. Furthermore, the analytic solution returns the classical result in the limiting case when the number of particles does not affect the leak size.",
author = "Tam{\'a}s Kov{\'a}cs and J{\'o}zsef Vany{\'o}",
year = "2017",
month = "6",
day = "20",
doi = "10.1103/PhysRevE.95.062218",
language = "English",
volume = "95",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "6",

}

TY - JOUR

T1 - Escape dynamics through a continuously growing leak

AU - Kovács, Tamás

AU - Vanyó, József

PY - 2017/6/20

Y1 - 2017/6/20

N2 - 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 describes the planetary accretion. In order to study the dynamics generally, the standard map is investigated in two cases when the dynamics is fully hyperbolic and in the presence of Kolmogorov-Arnold-Moser islands. In addition to the numerical calculations, an analytic solution to the temporal behavior of the model is also derived. We show that in the early phase of the leak expansion, as long as there are enough particles in the system, the number of survivors deviates from the well-known exponential decay. Furthermore, the analytic solution returns the classical result in the limiting case when the number of particles does not affect the leak size.

AB - 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 describes the planetary accretion. In order to study the dynamics generally, the standard map is investigated in two cases when the dynamics is fully hyperbolic and in the presence of Kolmogorov-Arnold-Moser islands. In addition to the numerical calculations, an analytic solution to the temporal behavior of the model is also derived. We show that in the early phase of the leak expansion, as long as there are enough particles in the system, the number of survivors deviates from the well-known exponential decay. Furthermore, the analytic solution returns the classical result in the limiting case when the number of particles does not affect the leak size.

UR - http://www.scopus.com/inward/record.url?scp=85021397993&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85021397993&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.95.062218

DO - 10.1103/PhysRevE.95.062218

M3 - Article

VL - 95

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 6

M1 - 062218

ER -