Depinning asymptotics in ergodic media

Arnd Scheel; Sergey Tikhomirov

doi:10.1007/978-3-319-64173-7_6

Depinning asymptotics in ergodic media

Arnd Scheel, Sergey Tikhomirov

School of Mathematics

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

4 Scopus citations

Abstract

We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can prove power-law asymptotics for the speed, with exponent depending on a local dimension of the ergodic measure near extremal values. We also show that our conceptual assumptions are satisfied in a context of weak inhomogeneity of the medium and almost balanced kinetics, and compare asymptotics with numerical simulations.

Original language	English (US)
Title of host publication	Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday
Editors	Pavel Gurevich, Juliette Hell, Arnd Scheel, Bjorn Sandstede
Publisher	Springer New York LLC
Pages	88-108
Number of pages	21
ISBN (Print)	9783319641720
DOIs	https://doi.org/10.1007/978-3-319-64173-7_6
State	Published - 2017
Event	Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016 - Berlin, Germany Duration: Jul 25 2016 → Jul 29 2016

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	205
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016
Country/Territory	Germany
City	Berlin
Period	7/25/16 → 7/29/16

Bibliographical note

Publisher Copyright:
© Springer International Publishing AG 2017.

Keywords

Center manifolds
Ergodic media
Front propagation
Inhomogeneous media
Pinning
Quasiperiodic media

Publisher link

10.1007/978-3-319-64173-7_6

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Depinning asymptotics in ergodic media. / Scheel, Arnd; Tikhomirov, Sergey.
Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday. ed. / Pavel Gurevich; Juliette Hell; Arnd Scheel; Bjorn Sandstede. Springer New York LLC, 2017. p. 88-108 (Springer Proceedings in Mathematics and Statistics; Vol. 205).

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

Scheel, A & Tikhomirov, S 2017, Depinning asymptotics in ergodic media. in P Gurevich, J Hell, A Scheel & B Sandstede (eds), Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday. Springer Proceedings in Mathematics and Statistics, vol. 205, Springer New York LLC, pp. 88-108, Conference on Patterns of Dynamics held in honor of Bernold Fiedler’s 60th Birthday, 2016, Berlin, Germany, 7/25/16. https://doi.org/10.1007/978-3-319-64173-7_6

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AB - We study speeds of fronts in bistable, spatially inhomogeneous media at parameter regimes where speeds approach zero. We provide a set of conceptual assumptions under which we can prove power-law asymptotics for the speed, with exponent depending on a local dimension of the ergodic measure near extremal values. We also show that our conceptual assumptions are satisfied in a context of weak inhomogeneity of the medium and almost balanced kinetics, and compare asymptotics with numerical simulations.

KW - Center manifolds

KW - Ergodic media

KW - Front propagation

KW - Inhomogeneous media

KW - Pinning

KW - Quasiperiodic media

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BT - Patterns of Dynamics - In Honour of Bernold Fiedler’s 60th Birthday

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A2 - Scheel, Arnd

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Y2 - 25 July 2016 through 29 July 2016

ER -

Depinning asymptotics in ergodic media

Abstract

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Bibliographical note

Keywords

Publisher link

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