Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation.
Radiative transfer of acoustic waves in continuous complex media: Beyond the Helmholtz equation.
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连续复杂介质中声波的辐射传输：超越亥姆霍兹方程。
DOI：
10.1103/physreve.94.053005
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
A. Derode
中科院分区：
文献类型：
--
作者：
Ibrahim Baydoun;Diego Baresch;R. Pierrat;A. Derode
在波动方程中，不均匀性可以用一个随机势来解释。对于密度和压缩性都有波动的流体中的声波（以及介电常数和磁导率都有波动的介质中的电磁波），随机势需要标量和算子的贡献。为了简单起见，后者通常在多重散射理论中被忽略：无论波的类型如何，这种简化相当于考虑具有取决于位置r的声速c的亥姆霍兹方程。在这项工作中，辐射传输方程推导出的波动方程，以研究通过多重散射介质的能量传输。特别是，各种运输参数上的运营商项的影响进行了研究，基于多次散射的图解方法。分析结果得到的基本数量的传输理论，如传输平均自由程<$^{*}，散射相函数f，和各向异性因子g。丢弃波动方程中的算子项被证明对f和g有显著影响，但仅限于低频区域，即，当无序的关联长度λ_{c}小于或等于波长λ时，更令人惊讶的是，丢弃算子部分对传输平均自由程有显著影响，无论频率范围如何。当标量项和算符项具有相同的振幅时，在低频区，输运平均自由程的差异约为300%，而当λ_{c}/λ=10^{3}时，无论无序涨落多么微弱，差异仍在30%以上。波动方程的数值模拟和Monte Carlo模拟支持分析结果。
Heterogeneity can be accounted for by a random potential in the wave equation. For acoustic waves in a fluid with fluctuations of both density and compressibility (as well as for electromagnetic waves in a medium with fluctuation of both permittivity and permeability) the random potential entails a scalar and an operator contribution. For simplicity, the latter is usually overlooked in multiple scattering theory: whatever the type of waves, this simplification amounts to considering the Helmholtz equation with a sound speed c depending on position r. In this work, a radiative transfer equation is derived from the wave equation, in order to study energy transport through a multiple scattering medium. In particular, the influence of the operator term on various transport parameters is studied, based on the diagrammatic approach of multiple scattering. Analytical results are obtained for fundamental quantities of transport theory such as the transport mean-free path ℓ^{*}, scattering phase function f, and anisotropy factor g. Discarding the operator term in the wave equation is shown to have a significant impact on f and g, yet limited to the low-frequency regime, i.e., when the correlation length of the disorder ℓ_{c} is smaller than or comparable to the wavelength λ. More surprisingly, discarding the operator part has a significant impact on the transport mean-free path ℓ^{*} whatever the frequency regime. When the scalar and operator terms have identical amplitudes, the discrepancy on the transport mean-free path is around 300% in the low-frequency regime, and still above 30% for ℓ_{c}/λ=10^{3} no matter how weak fluctuations of the disorder are. Analytical results are supported by numerical simulations of the wave equation and Monte Carlo simulations.