62 research outputs found
Levy stable distribution and [0,2] power law dependence of acoustic absorption on frequency
The absorption of acoustic wave propagation in a broad variety of lossy media
is characterized by an empirical power law function of frequency, w^y. It has
long been noted that exponent y ranges from 0 to 2 for diverse media. Recently,
the present author developed a fractional Laplacian wave equation to accurately
model the power law dissipation, which can be further reduced to the fractional
Laplacian diffusion equation. The latter is known underlying the Levy stable
distribution theory. Consequently, the parameters y is found to be the Levy
stability index, which is known bounded within 0<y\le2. This finding first
provides a theoretical explanation of empirical observations 0<y<=2.
Statistically, the frequency-dependent absorption can thus be understood a Levy
stable process, where the parameter y describes the fractal nature of
attenuative media.Comment: Welcome any comments to [email protected]
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