Friction causing unpredictability

Joshua Oldham; Stefan Weigert

doi:10.1088/1751-8113/49/12/125102

Friction causing unpredictability

Joshua Oldham, Stefan Weigert

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the effect of friction on the dynamics of a classical point particle in a onedimensional double-well potential. It is shown that finite uncertainty in the initial conditions of the particle may prevent us from reliably predicting the well in which the particle will come to rest. This difficulty – to make reliable long-term predictions – originates from the layered structure of phase-space regions sending the particle to the left and the right well, respectively. Similar structures are known to arise, for example, in models used to described the tossing of a coin where friction is, however, not the root cause of the phenomenon.

Original language	English
Article number	125102
Number of pages	11
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	49
Issue number	12
Early online date	15 Feb 2016
DOIs	https://doi.org/10.1088/1751-8113/49/12/125102
Publication status	Published - 29 Mar 2016

Bibliographical note

© 2016 IOP Publishing Ltd. 11 pages, 3 figures. Embargo period: 12 months. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

Keywords

nlin.CD
sensitivity to initial conditions
double-well potential
friction
basins of attraction
randomness

Access to Document

10.1088/1751-8113/49/12/125102

2016-01-07Friction(toJPArevised)
© 2016 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details
Accepted author manuscript, 225 KB

Cite this

@article{62fd0cde005e449cb0b0dddd65056af9,

title = "Friction causing unpredictability",

abstract = "We study the effect of friction on the dynamics of a classical point particle in a onedimensional double-well potential. It is shown that finite uncertainty in the initial conditions of the particle may prevent us from reliably predicting the well in which the particle will come to rest. This difficulty – to make reliable long-term predictions – originates from the layered structure of phase-space regions sending the particle to the left and the right well, respectively. Similar structures are known to arise, for example, in models used to described the tossing of a coin where friction is, however, not the root cause of the phenomenon.",

keywords = "nlin.CD, sensitivity to initial conditions, double-well potential, friction, basins of attraction, randomness",

author = "Joshua Oldham and Stefan Weigert",

note = "{\textcopyright} 2016 IOP Publishing Ltd. 11 pages, 3 figures. Embargo period: 12 months. This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy. Further copying may not be permitted; contact the publisher for details",

year = "2016",

month = mar,

day = "29",

doi = "10.1088/1751-8113/49/12/125102",

language = "English",

volume = "49",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing",

number = "12",

}

TY - JOUR

T1 - Friction causing unpredictability

AU - Oldham, Joshua

AU - Weigert, Stefan

N1 - © 2016 IOP Publishing Ltd. 11 pages, 3 figures. Embargo period: 12 months. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

PY - 2016/3/29

Y1 - 2016/3/29

N2 - We study the effect of friction on the dynamics of a classical point particle in a onedimensional double-well potential. It is shown that finite uncertainty in the initial conditions of the particle may prevent us from reliably predicting the well in which the particle will come to rest. This difficulty – to make reliable long-term predictions – originates from the layered structure of phase-space regions sending the particle to the left and the right well, respectively. Similar structures are known to arise, for example, in models used to described the tossing of a coin where friction is, however, not the root cause of the phenomenon.

AB - We study the effect of friction on the dynamics of a classical point particle in a onedimensional double-well potential. It is shown that finite uncertainty in the initial conditions of the particle may prevent us from reliably predicting the well in which the particle will come to rest. This difficulty – to make reliable long-term predictions – originates from the layered structure of phase-space regions sending the particle to the left and the right well, respectively. Similar structures are known to arise, for example, in models used to described the tossing of a coin where friction is, however, not the root cause of the phenomenon.

KW - nlin.CD

KW - sensitivity to initial conditions

KW - double-well potential

KW - friction

KW - basins of attraction

KW - randomness

U2 - 10.1088/1751-8113/49/12/125102

DO - 10.1088/1751-8113/49/12/125102

M3 - Article

SN - 1751-8113

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 12

M1 - 125102

ER -