Comparison of fractional wave equations for power law attenuation in ultrasound and elastography.
By Sverre Holm, Sven Peter Näsholm. 2013
71 citations recorded by the source corpus.
A set of wave equations with fractional loss operators in time and space are analyzed. The fractional Szabo equation, the power law wave equation and the causal fractional Laplacian wave equation are all found to be low-frequency approximations of the fractional Kelvin-Voigt wave equation and the more general fractional Zener wave equation. The latter two equations are based on fractional constitutive equations, whereas the former wave equations have been derived from the desire to model power law attenuation in applications like medical ultrasound. This has consequences for use in modeling and simulation, especially for applications that do not satisfy the low-frequency approximation, such as shear wave elastography. In such applications, the wave equations based on constitutive equations are the viable ones.
Subfields: Civil and Structural Engineering, Mechanics of Materials, Modeling and Simulation
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In Civil and Structural Engineering
- Lu Lu
- G. Em Karniadakis
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- Xiaoliang Wan
- Dongbin Xiu
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- Xiang Ma
- Sharif Rahman
In Mechanics of Materials
In Modeling and Simulation
Citations in the corpus
- fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “Among these are solute transport in fractured and porous media [1, 43], acoustic wave propagation with frequency-dependent dissipation [5, 15], laminar and turbulent flows [41, 4], and viscoelastic constitutive laws [25], just to mention a few.”