A geometric analysis of logarithmic switchback phenomena

N Popovic

doi:10.1088/1742-6596/22/1/011

A geometric analysis of logarithmic switchback phenomena

N Popovic^*

^*Corresponding author for this work

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract / Description of output

One common characteristic of many classical singular perturbation problems is the occurrence of logarithmic (switchback) terms in the corresponding asymptotic expansions. We discuss two such problems well known to give rise to logarithmic switchback: first, Lagerstrom's equation, a model related to the asymptotic treatment of low Reynolds number flow from fluid mechanics, and second, the Evans function approach to the stability of degenerate shock waves in (scalar) reaction-diffusion equations. We show how asymptotic expansions for these two problems can be obtained by means of methods from dynamical systems theory as well as of the blow-up technique. We identify the structure of these expansions and demonstrate that the occurrence of the logarithmic switchback terms therein is in fact caused by a resonance phenomenon.

Original language	English
Title of host publication	International Workshop on Hysteresis & Multi-scale Asymptotics
Editors	MP Mortell, RE OMalley, AV Pokrovskii, VA Sobolev
Publisher	IOP Publishing
Pages	164-173
Number of pages	10
DOIs	https://doi.org/10.1088/1742-6596/22/1/011
Publication status	Published - 2005
Event	International Workshop on Hysteresis and Multi-scale Asymptotics - Cork, Ireland Duration: 17 Mar 2004 → 21 Mar 2004

Publication series

Name	JOURNAL OF PHYSICS CONFERENCE SERIES
Publisher	IOP PUBLISHING LTD
Volume	22
ISSN (Print)	1742-6588

Conference

Conference	International Workshop on Hysteresis and Multi-scale Asymptotics
Country/Territory	Ireland
Period	17/03/04 → 21/03/04

Keywords / Materials (for Non-textual outputs)

SMALL REYNOLDS NUMBERS
ASYMPTOTIC EXPANSIONS
SHOCK-WAVES
STABILITY

Access to Document

10.1088/1742-6596/22/1/011

Cite this

@inproceedings{2086132e2cb143a6a12e35392ace9d28,

title = "A geometric analysis of logarithmic switchback phenomena",

abstract = "One common characteristic of many classical singular perturbation problems is the occurrence of logarithmic (switchback) terms in the corresponding asymptotic expansions. We discuss two such problems well known to give rise to logarithmic switchback: first, Lagerstrom's equation, a model related to the asymptotic treatment of low Reynolds number flow from fluid mechanics, and second, the Evans function approach to the stability of degenerate shock waves in (scalar) reaction-diffusion equations. We show how asymptotic expansions for these two problems can be obtained by means of methods from dynamical systems theory as well as of the blow-up technique. We identify the structure of these expansions and demonstrate that the occurrence of the logarithmic switchback terms therein is in fact caused by a resonance phenomenon.",

keywords = "SMALL REYNOLDS NUMBERS, ASYMPTOTIC EXPANSIONS, SHOCK-WAVES, STABILITY",

author = "N Popovic",

year = "2005",

doi = "10.1088/1742-6596/22/1/011",

language = "English",

series = "JOURNAL OF PHYSICS CONFERENCE SERIES",

publisher = "IOP Publishing",

pages = "164--173",

editor = "MP Mortell and RE OMalley and AV Pokrovskii and VA Sobolev",

booktitle = "International Workshop on Hysteresis & Multi-scale Asymptotics",

note = "International Workshop on Hysteresis and Multi-scale Asymptotics ; Conference date: 17-03-2004 Through 21-03-2004",

}

Popovic, N 2005, A geometric analysis of logarithmic switchback phenomena. in MP Mortell, RE OMalley, AV Pokrovskii & VA Sobolev (eds), International Workshop on Hysteresis & Multi-scale Asymptotics. JOURNAL OF PHYSICS CONFERENCE SERIES, vol. 22, IOP Publishing, pp. 164-173, International Workshop on Hysteresis and Multi-scale Asymptotics, Ireland, 17/03/04. https://doi.org/10.1088/1742-6596/22/1/011

TY - GEN

T1 - A geometric analysis of logarithmic switchback phenomena

AU - Popovic, N

PY - 2005

Y1 - 2005

N2 - One common characteristic of many classical singular perturbation problems is the occurrence of logarithmic (switchback) terms in the corresponding asymptotic expansions. We discuss two such problems well known to give rise to logarithmic switchback: first, Lagerstrom's equation, a model related to the asymptotic treatment of low Reynolds number flow from fluid mechanics, and second, the Evans function approach to the stability of degenerate shock waves in (scalar) reaction-diffusion equations. We show how asymptotic expansions for these two problems can be obtained by means of methods from dynamical systems theory as well as of the blow-up technique. We identify the structure of these expansions and demonstrate that the occurrence of the logarithmic switchback terms therein is in fact caused by a resonance phenomenon.

AB - One common characteristic of many classical singular perturbation problems is the occurrence of logarithmic (switchback) terms in the corresponding asymptotic expansions. We discuss two such problems well known to give rise to logarithmic switchback: first, Lagerstrom's equation, a model related to the asymptotic treatment of low Reynolds number flow from fluid mechanics, and second, the Evans function approach to the stability of degenerate shock waves in (scalar) reaction-diffusion equations. We show how asymptotic expansions for these two problems can be obtained by means of methods from dynamical systems theory as well as of the blow-up technique. We identify the structure of these expansions and demonstrate that the occurrence of the logarithmic switchback terms therein is in fact caused by a resonance phenomenon.

KW - SMALL REYNOLDS NUMBERS

KW - ASYMPTOTIC EXPANSIONS

KW - SHOCK-WAVES

KW - STABILITY

U2 - 10.1088/1742-6596/22/1/011

DO - 10.1088/1742-6596/22/1/011

M3 - Conference contribution

T3 - JOURNAL OF PHYSICS CONFERENCE SERIES

SP - 164

EP - 173

BT - International Workshop on Hysteresis & Multi-scale Asymptotics

A2 - Mortell, MP

A2 - OMalley, RE

A2 - Pokrovskii, AV

A2 - Sobolev, VA

PB - IOP Publishing

T2 - International Workshop on Hysteresis and Multi-scale Asymptotics

Y2 - 17 March 2004 through 21 March 2004

ER -

A geometric analysis of logarithmic switchback phenomena

Abstract / Description of output

Publication series

Conference

Keywords / Materials (for Non-textual outputs)

Access to Document

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Cite this