Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian.

By Bradley E. Treeby, B. Cox. 2010

330 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Mechanics of Materials

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In Biomedical Engineering

In Mechanics of Materials

Citations in the corpus

fPINNs: Fractional Physics-Informed Neural Networks (2018, background): “Among these are solute transport in fractured and porous media [2, 3], acoustic wave propagation with frequency-dependent dissipation [4, 5, 6, 7], laminar and turbulent flows [8, 9, 10], viscoelastic constitutive laws [11], just to mention a few.”
Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians (2014, neutral): “…α and the phase velocity are calculated by the amplitude spectral ratio in decibels/meter and the phase change at each frequency (Buttkus, 2000; Treeby and Cox, 2010): αðωÞ ¼ −20 log10 A2 A1 ∕d; (20) cðωÞ ¼ ωd ϕ1 − ϕ2 ; (21) where A1;2 are the amplitude spectra at two receivers, ϕ1;2 are…”
What is the fractional Laplacian? A comparative review with new results (2018, neutral): “Fractional equation Domain Diffusion-reaction [6] ∂t u + (− )α/2u + c(t, x)u = 0 (0,+∞) ×Rd Quasi-geostrophic [7] ∂tθ + u · ∇θ + κ(− )α/2θ = f [0, T ] ×R2 Cahn-Hilliard [8–10] ∂t u + (− )α/2(−ε2 u + f (u)) = 0 (0, T ] × (0,2π)2 Porous medium [8,11] ∂t u + (− )α/2(|u|m−1signu) = 0 (0,+∞) ×Rd Schrödin”
A Petrov–Galerkin finite element method for variable-coefficient fractional diffusion equations (2015, background): “(1) can be viewed as a generalized elasticity equation obtained by incorporating a fractional Hooke’s law into a classical force balance equation to take into account of the nonlocal interaction [19–22], which provides a fractional analogue to an alternative nonlocal elasticity model, i.”
Analytical solutions for the multi-term time–space Caputo–Riesz fractional advection–diffusion equations on a finite domain (2012, methodology): “[40] proposed modeling power-law absorption and dispersion for acoustic propagation using the fractional Laplacian.”
Comparison of fractional wave equations for power law attenuation in ultrasound and elastography. (2013, background): “This is caused by the differences in the sign of the Fourier transform kernel between Treeby and Cox (2010) and this paper, see the Appendix A.”