One-dimensional wave dispersion in layered media
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 ar...
| Main Authors: | , , , |
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| Format: | Journal article |
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Society for Industrial and Applied Mathematics
2015
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| _version_ | 1797090447224471552 |
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| author | Farmer, C Ockendon, H Ockendon, J Allwright, D |
| author_facet | Farmer, C Ockendon, H Ockendon, J Allwright, D |
| author_sort | Farmer, C |
| collection | OXFORD |
| description | 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 |
| first_indexed | 2024-03-07T03:18:44Z |
| format | Journal article |
| id | oxford-uuid:b6b58c3e-5e91-44ea-b44f-8ed83134cc19 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:18:44Z |
| publishDate | 2015 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:b6b58c3e-5e91-44ea-b44f-8ed83134cc192022-03-27T04:42:54ZOne-dimensional wave dispersion in layered mediaJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b6b58c3e-5e91-44ea-b44f-8ed83134cc19Symplectic Elements at OxfordSociety for Industrial and Applied Mathematics2015Farmer, COckendon, HOckendon, JAllwright, DHomogenisation 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 |
| spellingShingle | Farmer, C Ockendon, H Ockendon, J Allwright, D One-dimensional wave dispersion in layered media |
| title | One-dimensional wave dispersion in layered media |
| title_full | One-dimensional wave dispersion in layered media |
| title_fullStr | One-dimensional wave dispersion in layered media |
| title_full_unstemmed | One-dimensional wave dispersion in layered media |
| title_short | One-dimensional wave dispersion in layered media |
| title_sort | one dimensional wave dispersion in layered media |
| work_keys_str_mv | AT farmerc onedimensionalwavedispersioninlayeredmedia AT ockendonh onedimensionalwavedispersioninlayeredmedia AT ockendonj onedimensionalwavedispersioninlayeredmedia AT allwrightd onedimensionalwavedispersioninlayeredmedia |