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Literature DB >> 25278739

Attenuated Fractional Wave Equations With Anisotropy.

Abstract

This paper develops new fractional calculus models for wave propagation. These models permit a different attenuation index in each coordinate to fully capture the anisotropic nature of wave propagation in complex media. Analytical expressions that describe power law attenuation and anomalous dispersion in each direction are derived for these fractional calculus models.

Entities: Disease

Year: 2014 PMID： 25278739 PMCID： PMC4112933 DOI： 10.1115/1.4025940

Source DB: PubMed Journal: J Vib Acoust ISSN： 1048-9002 Impact factor: 1.583

9 in total

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

Authors: W Chen; S Holm
Journal: J Acoust Soc Am Date: 2004-04 Impact factor: 1.840

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

Authors: Bradley E Treeby; B T Cox
Journal: J Acoust Soc Am Date: 2010-05 Impact factor: 1.840

3. Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory.

Authors: Christian C Anderson; Adam Q Bauer; Mark R Holland; Michal Pakula; Pascal Laugier; G Larry Bretthorst; James G Miller
Journal: J Acoust Soc Am Date: 2010-11 Impact factor: 1.840

2 in total

1. STOCHASTIC SOLUTIONS FOR FRACTIONAL WAVE EQUATIONS.

Authors: Mark M Meerschaert; René L Schilling; Alla Sikorskii
Journal: Nonlinear Dyn Date: 2015-06-01 Impact factor: 5.022

2. Nonlinear attenuation and dispersion in human calcaneus in vitro: statistical validation and relationships to microarchitecture.

Authors: Keith A Wear
Journal: J Acoust Soc Am Date: 2015-03 Impact factor: 2.482

2 in total

Attenuated Fractional Wave Equations With Anisotropy.

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

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

3. Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory.

4. The dependence of ultrasonic properties on orientation in human vertebral bone.

5. Anomalous negative dispersion in bone can result from the interference of fast and slow waves.

6. Anomalous diffusion expressed through fractional order differential operators in the Bloch-Torrey equation.

7. Analytical time-domain Green's functions for power-law media.

8. Velocity dispersion in trabecular bone: influence of multiple scattering and of absorption.

9. A stratified model to predict dispersion in trabecular bone.

1. STOCHASTIC SOLUTIONS FOR FRACTIONAL WAVE EQUATIONS.

2. Nonlinear attenuation and dispersion in human calcaneus in vitro: statistical validation and relationships to microarchitecture.