论文标题
弹性波在连续固体中的扩散，并随机固定位错阵列
Diffusion of elastic waves in a continuum solid with a random array of pinned dislocations
论文作者
论文摘要
在连续力力学框架中考虑了许多，随机放置和定向的固定位错段的散射，在三维固体中的不相干弹性能在三维固体中的传播。散射机制是长度为L的弹性字符串，该弹性串是对传入波的反应。因此，散射器不是静态的，而是具有自己的动态。建立了伯特 - 盐（BS）方程，并展示了病房 - 塔卡哈西身份（WTI）。 BS方程将其写入光谱问题，使用WTI在扩散极限中求解。为了领先，确实会产生扩散行为，并获得了扩散系数的明确公式。在没有内在阻尼的情况下，可以在独立的散射近似（ISA）中评估它。它不仅取决于裸露的纵向和横向波速度，还取决于相干波的重新归一化速度以及衰减系数。可以明确识别由L和谐振频率的频率给出的长度尺度的影响，可以明确鉴定。可以确定扩散常数的kubo表示。当单位体积少量数量很少时，以能量传递形式主义获得的先前的通用结果将回收。这包括扩散能量密度的平气，但是，这通常不存在。形式主义与电磁波在介质分布的介质中具有许多相似之处。然而，弹性相互作用取决于动量。
The propagation of incoherent elastic energy in a three-dimensional solid due to the scattering by many, randomly placed and oriented, pinned dislocation segments, is considered in a continuum mechanics framework. The scattering mechanism is that of an elastic string of length L that re-radiates as a response to an incoming wave. The scatterers are thus not static but have their own dynamics. A Bethe-Salpeter (BS) equation is established, and a Ward-Takahashi Identity (WTI) is demonstrated. The BS equation is written as a spectral problem that, using the WTI, is solved in the diffusive limit. To leading order a diffusion behavior indeed results, and an explicit formula for the diffusion coeffcient is obtained. It can be evaluated in an Independent Scattering Approximation (ISA) in the absence of intrinsic damping. It depends not only on the bare longitudinal and transverse wave velocities but also on the renormalized velocities, as well as attenuation coeffcients, of the coherent waves. The influence of the length scale given by L, and of the resonant behavior for frequencies near the resonance frequency of the strings, can be explicitly identified. A Kubo representation for the diffusion constant can be identified. Previous generic results, obtained with an energy transfer formalism, are recovered when the number of dislocations per unit volume is small. This includes the equipartition of diffusive energy density which, however, does not hold in general. The formalism bears a number of similarities with the behavior of electromagnetic waves in a medium with a random distribution of dielectric scatterers; the elastic interaction, however, is momentum dependent.
