论文标题
在随机波动的半空间中，声波辐射传递的边界效应
Boundary effects in Radiative Transfer of acoustic waves in a randomly fluctuating half-space
论文作者
论文摘要
本文涉及辐射传递方程的推导，以在弱散射状态下随机波动的半空间中传播的声波传播，以及通过对波浪溶液的Wigner变换的渐近分析来研究边界效应。这些辐射传递方程式可以通过随机异质性散射来对波能密度的运输进行建模。该方法建立在图像方法的基础上，其中半空间问题扩展到全空间，并具有两个对称源和均匀的机械性能图。然后确定对总能量密度的两个贡献：一个类似于全空间中能量密度传播的贡献，介质特性的统计平稳性缺乏没有前阶效应；一个在边界的一个波长中支撑的一个，它描述了两个对称源产生的波之间的干扰效应。在统一的诺伊曼边界条件的情况下，这种边界效应的强度增加了一倍，而对于均匀的迪里奇边界条件，这种强度取消了这种强度。
This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating half-space in the weak-scattering regime, and the study of boundary effects through an asymptotic analysis of the Wigner transform of the wave solution. These radiative transfer equations allow to model the transport of wave energy density, taking into account the scattering by random heterogeneities. The approach builds on the method of images, where the half-space problem is extended to a full-space, with two symmetric sources and an even map of mechanical properties. Two contributions to the total energy density are then identified: one similar to the energy density propagation in a full-space, for which the resulting lack of statistical stationarity of the medium properties has no leading-order effect; and one supported within one wavelength of the boundary, which describes interference effects between the waves produced by the two symmetric sources. In the case of a homogeneous Neumann boundary conditions, this boundary effect yields a doubling of the intensity, and in the case of homogeneous Dirichlet boundary conditions, a canceling of that intensity.
