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Linking multiple relaxation, power-law attenuation, and fractional wave equations
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10.1121/1.3641457
/content/asa/journal/jasa/130/5/10.1121/1.3641457
http://aip.metastore.ingenta.com/content/asa/journal/jasa/130/5/10.1121/1.3641457

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Top panels: Frequency-dependent attenuation for τσ  = 1000τε with the fractional derivative orders α = 0.3 (top left), and α = 0.8 (top right). The attenuation curves displayed show α k ,Z(ω) from Eq. (16) as predicted by the fractional Zener model, and as predicted for the approximate ML-NSW model by α k, ML(ω) in Eq. (23) for a set of Ω1 and Ω2 choices as displayed in the legends. The horizontal axis represents normalized frequency. For visualization convenience, each absorption curve is normalized to α k  = 1 at ωτσ = 1. Bottom panels: The corresponding normalized effective compressibilities κν ML(Ω) of the continuum of relaxation processes as a function of normalized relaxation frequency Ω·τσ for α = 0.3 (bottom left), and α = 0.8 (bottom right) of the approximate ML-NSW model with Ω limits as described in the legends.

Image of FIG. 2.
FIG. 2.

(Color online) Frequency-dependent speed of sound for τσ = 1000τε with the fractional derivative orders α = 0.3 (left pane), and α = 0.8 (right pane). The curves display c Z(ω) from Eq. (17) as predicted by the fractional Zener model, and as predicted by c ML(ω) in Eq. (24) for a set of Ω1 and Ω2 choices as displayed in the legends. The horizontal axis represents normalized frequency.

Image of FIG. 3.
FIG. 3.

(Color online) Comparison of resulting attenuation modeled in Ref. 7 (thick solid line), fractional Zener model (dashed line), and the approximate ML-NSW model by use of κν ML(Ω) (thin solid line) of Eq. (19) . The medium parameters are displayed in Table I . The fractional Zener and approximate ML-NSW parameters are listed in Table II .

Tables

Generic image for table
TABLE I.

Medium parameters for the attenuation power-law fit, similar to the Yang and Cleveland parameters in Ref. 7.

Generic image for table
TABLE II.

Fitted fractional Zener and ML-NSW model parameters corresponding to the Yang and Cleveland attenuation properties as reproduced in Table I. The resulting attenuation is displayed in Fig. 3.

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/content/asa/journal/jasa/130/5/10.1121/1.3641457
2011-11-16
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Linking multiple relaxation, power-law attenuation, and fractional wave equations
http://aip.metastore.ingenta.com/content/asa/journal/jasa/130/5/10.1121/1.3641457
10.1121/1.3641457
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