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A comparison of the factorization approach to temporal and spatial propagation in the case of some acoustic waves

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A comparison of the factorization approach to temporal and spatial propagation in the case of some acoustic waves. / Kinsler, Paul.

In: Journal of Physics Communications, Vol. 2, 025011, 06.02.2018.

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@article{ed7cf11958ec4dcfacedea9166304769,
title = "A comparison of the factorization approach to temporal and spatial propagation in the case of some acoustic waves",
abstract = "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.",
author = "Paul Kinsler",
year = "2018",
month = feb,
day = "6",
doi = "10.1088/2399-6528/aaa85c",
language = "English",
volume = "2",
journal = "Journal of Physics Communications",
issn = "2399-6528",
publisher = "IOP Science",

}

RIS

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 -