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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| Summary: | 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 |
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