Fractional Laplacian time-space models for linear and nonlinear lossy media exhibiting arbitrary frequency power-law dependency.

By Wen Chen, Sverre Holm. 2004

351 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Statistical and Nonlinear Physics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

1. G. Em Karniadakis
2. Lu Lu
3. Wen Chen
4. Guofei Pang
5. W. Chen
6. Sverre Holm
7. Sven Peter Näsholm
8. Zhiping Mao

In Statistical and Nonlinear Physics

1. Lu Lu
2. G. Em Karniadakis
3. Guofei Pang
4. Wen Chen
5. W. Chen
6. Xuhui Meng
7. Maizar Raissi
8. Zhiping Mao

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.”
• A speculative study of 23-order fractional Laplacian modeling of turbulence: some thoughts and conjectures. (2006, methodology): “1 = − ∇ + Δ − − Δ ∂ ∂ + ⋅ ∂ ∂ υ γ ρ . ( 17 ) Here the fractional Laplacian ( ) 3”
• Comparison of fractional wave equations for power law attenuation in ultrasound and elastography. (2013, background): “(10), with a fractional Laplacian attenuation operator first proposed by Chen and Holm (2004).”
• Fractional Differential Mask: A Fractional Differential-Based Approach for Multiscale Texture Enhancement (2010, background): “It has been proven by scientific findings that many fractional order or dimensional mathematic approaches are the best description for natural phenomena [27]–[30].”
• 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”
• Time-space fabric underlying anomalous diffusion (2005, background): “where s is the physical quantity of interest (e.g., temperature in anomalous heat conduction), c the corresponding physical coefficient, (� $2)b represents the symmetric fractional Laplacian [ 14 ], and a and b can be real numbers.”