ArticleThe Journal of the Acoustical Society of America2016
Approximate analytical time-domain Green's functions for the Caputo fractional wave equation.
Article in The Journal of the Acoustical Society of America, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed.
- Numerical spatial impulse response calculations for a circular piston radiating in a lossy medium.The Journal of the Acoustical Society of America · 2022Article
- Exact and approximate analytical time-domain Green's functions for space-fractional wave equations.The Journal of the Acoustical Society of America · 2019Article
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2 authors.
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Abstract
The Caputo fractional wave equation [Geophys. J. R. Astron. Soc. 13, 529-539 (1967)] models power-law attenuation and dispersion for both viscoelastic and ultrasound wave propagation. The Caputo model can be derived from an underlying fractional constitutive equation and is causal. In this study, an approximate analytical time-domain Green's function is derived for the Caputo equation in three dimensions (3D) for power law exponents greater than one. The Green's function consists of a shifted and scaled maximally skewed stable distribution multiplied by a spherical spreading factor 1/(4πR). The approximate one dimensional (1D) and two dimensional (2D) Green's functions are also computed in terms of stable distributions. Finally, this Green's function is decomposed into a loss component and a diffraction component, revealing that the Caputo wave equation may be approximated by a coupled lossless wave equation and a fractional diffusion equation.
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