دورية أكاديمية
A proof that multiple waves propagate in ensemble-averaged particulate materials.
| العنوان: | A proof that multiple waves propagate in ensemble-averaged particulate materials. |
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| المؤلفون: | Gower, Artur L, Abrahams, I David, Parnell, William J |
| بيانات النشر: | //dx.doi.org/10.1098/rspa.2019.0344 Proc Math Phys Eng Sci The Royal Society |
| سنة النشر: | 2019 |
| المجموعة: | Apollo - University of Cambridge Repository |
| مصطلحات موضوعية: | Wiener–Hopf, backscattering, ensemble averaging, multiple scattering, random media, wave propagation |
| الوصف: | Effective medium theory aims to describe a complex inhomogeneous material in terms of a few important macroscopic parameters. To characterize wave propagation through an inhomogeneous material, the most crucial parameter is the effective wavenumber. For this reason, there are many published studies on how to calculate a single effective wavenumber. Here, we present a proof that there does not exist a unique effective wavenumber; instead, there are an infinite number of such (complex) wavenumbers. We show that in most parameter regimes only a small number of these effective wavenumbers make a significant contribution to the wave field. However, to accurately calculate the reflection and transmission coefficients, a large number of the (highly attenuating) effective waves is required. For clarity, we present results for scalar (acoustic) waves for a two-dimensional material filled (over a half-space) with randomly distributed circular cylindrical inclusions. We calculate the effective medium by ensemble averaging over all possible inhomogeneities. The proof is based on the application of the Wiener-Hopf technique and makes no assumption on the wavelength, particle boundary conditions/size or volume fraction. This technique provides a simple formula for the reflection coefficient, which can be explicitly evaluated for monopole scatterers. We compare results with an alternative numerical matching method. |
| نوع الوثيقة: | article in journal/newspaper |
| وصف الملف: | Print-Electronic; application/pdf |
| اللغة: | English |
| العلاقة: | https://www.repository.cam.ac.uk/handle/1810/297015Test |
| DOI: | 10.17863/CAM.44056 |
| الإتاحة: | https://doi.org/10.17863/CAM.44056Test https://www.repository.cam.ac.uk/handle/1810/297015Test |
| حقوق: | Attribution 4.0 International ; https://creativecommons.org/licenses/by/4.0Test/ |
| رقم الانضمام: | edsbas.E9D3F5CA |
| قاعدة البيانات: | BASE |
| DOI: | 10.17863/CAM.44056 |
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