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Scattering mean free path in continuous complex media: beyond the Helmholtz equation
Ibrahim Baydoun1, Diego Baresch1, Romain Pierrat1
1ESPCI ParisTech, PSL Research University, CNRS, Univ Paris Diderot, Sorbonne Paris Cité, Institut Langevin, 1 rue Jussieu, F-75005, Paris, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 15, 2015
Summary
Standard models incorrectly calculate wave propagation in heterogeneous media. Our findings reveal that accounting for both scalar and operator potentials is crucial for accurate acoustic wave scattering mean free path calculations.
Area of Science:
- Physics
- Wave Propagation
- Acoustics
Background:
- Heterogeneous media are often modeled with a scalar random potential, simplifying wave speed variations.
- This simplification in Helmholtz' equation can lead to inaccuracies in wave field calculations.
Purpose of the Study:
- To present theoretical calculations of the ensemble-averaged wave field in heterogeneous media.
- To correct inaccuracies in the calculation of the scattering mean free path for acoustic waves.
Main Methods:
- Theoretical calculations of the coherent wave field using a random process model.
- Incorporating both scalar and operator parts in the random potential.
- Utilizing the diagrammatic approach of multiple scattering with Bourret's and on-shell approximations.
Main Results:
- The standard scalar potential approach yields incorrect scattering mean free path results.
- A detailed calculation requires both scalar and operator components in the random potential.
- The scattering mean free path is over 4 times smaller (13/3) in the low-frequency limit when both potential parts are considered.
Conclusions:
- The simplified scalar potential model is inadequate for accurate acoustic wave scattering calculations.
- Accurate modeling of heterogeneous media requires a more complex random potential.
- Theoretical results are validated by numerical experiments, confirming the revised scattering mean free path.
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