Ensemble separation and stickiness influence in a driven stadium-like billiard: A Lyapunov exponents analysis

Matheus S. Palmero; André L.P. Livorati; Iberê L. Caldas; Edson D. Leonel

doi:10.1016/j.cnsns.2018.05.024

Ensemble separation and stickiness influence in a driven stadium-like billiard: A Lyapunov exponents analysis

Matheus S. Palmero^*, André L.P. Livorati, Iberê L. Caldas, Edson D. Leonel

^*Corresponding author for this work

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

Abstract

The dynamics of an ensemble of non-interacting particles suffering elastic collisions inside a driven stadium-like billiard is investigated through a four-dimensional nonlinear mapping. The system presents a resonance velocity, which plays an important role on the ensemble separation according to the initial velocities. The idea is to use the Lyapunov exponents to study the ensemble separation. We compare two different methods: (i) Finite Time Lyapunov Exponents and (ii) Wolf Linearization Algorithm. Results from both methods show good agreement regarding the separation of ensembles. Our results give support for the fact that stickiness influences the dynamics providing a crucial effect in the ensemble separation of the velocities for the time-dependent stadium-like billiard.

Original language	English
Pages (from-to)	248-259
Number of pages	12
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	65
Early online date	28 May 2018
DOIs	https://doi.org/10.1016/j.cnsns.2018.05.024
Publication status	Published - 1 Dec 2018

Access to Document

10.1016/j.cnsns.2018.05.024

Link to publication in Scopus

Fingerprint Dive into the research topics of 'Ensemble separation and stickiness influence in a driven stadium-like billiard: A Lyapunov exponents analysis'. Together they form a unique fingerprint.

Cite this

@article{953d9342a92d4c77aa4997382491ff37,

title = "Ensemble separation and stickiness influence in a driven stadium-like billiard: A Lyapunov exponents analysis",

abstract = "The dynamics of an ensemble of non-interacting particles suffering elastic collisions inside a driven stadium-like billiard is investigated through a four-dimensional nonlinear mapping. The system presents a resonance velocity, which plays an important role on the ensemble separation according to the initial velocities. The idea is to use the Lyapunov exponents to study the ensemble separation. We compare two different methods: (i) Finite Time Lyapunov Exponents and (ii) Wolf Linearization Algorithm. Results from both methods show good agreement regarding the separation of ensembles. Our results give support for the fact that stickiness influences the dynamics providing a crucial effect in the ensemble separation of the velocities for the time-dependent stadium-like billiard.",

author = "Palmero, {Matheus S.} and Livorati, {Andr{\'e} L.P.} and Caldas, {Iber{\^e} L.} and Leonel, {Edson D.}",

year = "2018",

month = dec,

day = "1",

doi = "10.1016/j.cnsns.2018.05.024",

language = "English",

volume = "65",

pages = "248--259",

journal = "Communications in Nonlinear Science and Numerical Simulation",

issn = "1007-5704",

publisher = "Amsterdam:Elsevier",

}

Ensemble separation and stickiness influence in a driven stadium-like billiard : A Lyapunov exponents analysis. / Palmero, Matheus S.; Livorati, André L.P.; Caldas, Iberê L.; Leonel, Edson D.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 65, 01.12.2018, p. 248-259.

Research output: Contribution to journal › Article (Academic Journal) › peer-review

TY - JOUR

T1 - Ensemble separation and stickiness influence in a driven stadium-like billiard

T2 - A Lyapunov exponents analysis

AU - Palmero, Matheus S.

AU - Livorati, André L.P.

AU - Caldas, Iberê L.

AU - Leonel, Edson D.

PY - 2018/12/1

Y1 - 2018/12/1

N2 - The dynamics of an ensemble of non-interacting particles suffering elastic collisions inside a driven stadium-like billiard is investigated through a four-dimensional nonlinear mapping. The system presents a resonance velocity, which plays an important role on the ensemble separation according to the initial velocities. The idea is to use the Lyapunov exponents to study the ensemble separation. We compare two different methods: (i) Finite Time Lyapunov Exponents and (ii) Wolf Linearization Algorithm. Results from both methods show good agreement regarding the separation of ensembles. Our results give support for the fact that stickiness influences the dynamics providing a crucial effect in the ensemble separation of the velocities for the time-dependent stadium-like billiard.

AB - The dynamics of an ensemble of non-interacting particles suffering elastic collisions inside a driven stadium-like billiard is investigated through a four-dimensional nonlinear mapping. The system presents a resonance velocity, which plays an important role on the ensemble separation according to the initial velocities. The idea is to use the Lyapunov exponents to study the ensemble separation. We compare two different methods: (i) Finite Time Lyapunov Exponents and (ii) Wolf Linearization Algorithm. Results from both methods show good agreement regarding the separation of ensembles. Our results give support for the fact that stickiness influences the dynamics providing a crucial effect in the ensemble separation of the velocities for the time-dependent stadium-like billiard.

UR - http://www.scopus.com/inward/record.url?scp=85047851903&partnerID=8YFLogxK

U2 - 10.1016/j.cnsns.2018.05.024

DO - 10.1016/j.cnsns.2018.05.024

M3 - Article (Academic Journal)

AN - SCOPUS:85047851903

VL - 65

SP - 248

EP - 259

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

SN - 1007-5704

ER -