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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - A comparison of the factorization approach to temporal and spatial propagation in the case of some acoustic waves
AU - Kinsler, Paul
PY - 2018/2/6
Y1 - 2018/2/6
N2 - The evolution of acoustic waves can be evaluated in two ways: either as a temporal, or a spatial propagation. Propagating in space provides the considerable advantage of being able to handle dispersion and propagation across interfaces with remarkable efficiency; but propagating in time is more physical and gives correctly behaved reflections and scattering without effort. Which shouldbe chosen in a given situation, and what compromises might have to be made? Here the natural behaviors of each choice of propagation are compared and contrasted for an ordinary second order wave equation, the time-dependent diffusion wave equation, an elastic rod wave equation, and the Stokes'/ van Wijngaarden's equations, each case illuminating a characteristic feature of thetechnique. Either choice of propagation axis enables a partitioning the wave equation that gives rise to a directional factorization based on a natural "reference" dispersion relation. The resulting exact coupled bidirectional equations then reduce to a single unidirectional first-order wave equation using a simple "slow evolution" assumption that minimizes effect of subsequent approximations, whileallowing a direct term-to-term comparison between exact and approximate theories.
AB - The evolution of acoustic waves can be evaluated in two ways: either as a temporal, or a spatial propagation. Propagating in space provides the considerable advantage of being able to handle dispersion and propagation across interfaces with remarkable efficiency; but propagating in time is more physical and gives correctly behaved reflections and scattering without effort. Which shouldbe chosen in a given situation, and what compromises might have to be made? Here the natural behaviors of each choice of propagation are compared and contrasted for an ordinary second order wave equation, the time-dependent diffusion wave equation, an elastic rod wave equation, and the Stokes'/ van Wijngaarden's equations, each case illuminating a characteristic feature of thetechnique. Either choice of propagation axis enables a partitioning the wave equation that gives rise to a directional factorization based on a natural "reference" dispersion relation. The resulting exact coupled bidirectional equations then reduce to a single unidirectional first-order wave equation using a simple "slow evolution" assumption that minimizes effect of subsequent approximations, whileallowing a direct term-to-term comparison between exact and approximate theories.
U2 - 10.1088/2399-6528/aaa85c
DO - 10.1088/2399-6528/aaa85c
M3 - Journal article
VL - 2
JO - Journal of Physics Communications
JF - Journal of Physics Communications
SN - 2399-6528
M1 - 025011
ER -