Journal article

One-dimensional wave dispersion in layered media

Abstract:: Homogenisation theory reveals that long one-dimensional waves propagating in a medium with spatially periodic wave speed can behave like dispersive waves in an appropriately homogenised medium. However the precise time and length scales over which this dispersive behaviour is a good approximation are not clear. This paper describes what happens in a specific case when the sound speed and initial conditions allow the problem to be reduced to a finite system of difference equations which can be solved exactly. The long-time asymptotics are compared with the predictions of homogenisation theory and new light is shed on the dispersion phenomenon

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Farmer, C., Ockendon, H., Ockendon, J., & Allwright, D. (2015). One-dimensional wave dispersion in layered media. SIAM Journal on Applied Mathematics, 75(5), 2128–2146.

MLA Style

Farmer, C., et al. “One-Dimensional Wave Dispersion in Layered Media.” SIAM Journal on Applied Mathematics, vol. 75, no. 5, Society for Industrial and Applied Mathematics, 2015, pp. 2128–46.

Chicago Style

Farmer, C, H Ockendon, J Ockendon, and D Allwright. 2015. “One-Dimensional Wave Dispersion in Layered Media.” SIAM Journal on Applied Mathematics 75 (5): 2128–46.
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Files:: One-dimensional wave dispersion in layered media.pdf

(Preview, Accepted manuscript, pdf, 528.9KB, Terms of use)

Publisher copy:: 10.1137/15M101138X

Authors

+ Farmer, C More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Mathematical Institute
Role:: Author

+ Ockendon, H More by this author

Role:: Author

+ Ockendon, J More by this author

Role:: Author

+ Allwright, D More by this author

Role:: Author

Publisher:: Society for Industrial and Applied Mathematics
Journal:: SIAM Journal on Applied Mathematics More from this journal
Volume:: 75
Issue:: 5
Pages:: 2128–2146
Publication date:: 2015-01-01
DOI:: 10.1137/15M101138X
EISSN:: 1095-712X
ISSN:: 0036-1399

Keywords:: homogenization

dispersion

multiple scales

wave propagation

periodic media
Pubs id:: pubs:538176
UUID:: uuid:b6b58c3e-5e91-44ea-b44f-8ed83134cc19
Local pid:: pubs:538176
Source identifiers:: 538176
Deposit date:: 2015-08-13

Terms of use

Copyright holder:: Society for Industrial and Applied Mathematics
Copyright date:: 2015
Notes:: Copyright © 2015, Society for Industrial and Applied Mathematics.

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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