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首页> 外文会议>Conference on Subsurface and Surface Sensing Technologies and Applications Ⅲ Jul 30-Aug 1, 2001, San Diego, USA >Combining fractional time derivative loss models and the similarity transformation technique to turn lossless configurations into lossy ones
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Combining fractional time derivative loss models and the similarity transformation technique to turn lossless configurations into lossy ones

机译：结合分数时间导数损失模型和相似度转换技术，将无损配置转换为有损配置

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摘要

A method is presented by which a complicated space-time domain electromagnetic wavefield in a lossless configuration may afterwards be transformed into the space-time domain field of a lossy configuration with a prescribed quality factor Q. The method is applicable to inhomogeneous and anisotropic media. Moreover, it may be employed to fields in 1D, 2D, and 3D spatial configurations. The first step is the introduction of a specific loss model into the lossless Maxwell's equations. Two loss models will be presented. These are generalizations to the electromagnetic case of the elastodynamic Scott-Blair stress-strain law and the elastodynamic Power Law, which yield a quality factor Q that is (nearly) constant over a long frequency range. Both loss models introduce fractional time derivatives in Maxwell's equations. The second step of the method relates the lossless and the lossy time domain Green's tensors by means of the similarity transformation technique. This approach has the benefit that an existing time domain wavefield for a lossless but otherwise intricate medium can be converted to the relevant lossy situation by a simple postprocessing step. Next, numerical results for both loss models will be shown. These will be compared with the results for a third loss model that is guaranteed to yield the correct arrival time. It is observed that the former two loss models cause deviations from the exact arrival time. However, these deviations are small except for high losses. As far as the shape of the time evolution of the fields is concerned, both loss models perform equally well, even in case of high losses.
机译：提出了一种方法，通过该方法可以将具有无损配置的复杂时空电磁波场随后转换为具有规定品质因数Q的有损配置的时空场。该方法适用于非均匀和各向异性的介质。此外，它可用于1D，2D和3D空间配置中的字段。第一步是将特定的损失模型引入无损麦克斯韦方程。将介绍两种损失模型。这些是弹性动力学斯科特-布莱尔应力应变定律和弹性力学幂定律的电磁情况的概括，它们产生的品质因数Q在很长的频率范围内（几乎）恒定。两种损耗模型都在麦克斯韦方程中引入了分数时间导数。该方法的第二步通过相似变换技术将无损和时域格林的张量关联起来。这种方法的好处是，可以通过简单的后处理步骤将现有的无损但复杂的介质时域波场转换为相关的有损情况。接下来，将显示两个损耗模型的数值结果。将这些与第三损失模型的结果进行比较，以确保产生正确的到达时间。可以观察到，前两个损耗模型会导致与实际到达时间的偏差。但是，除了高损耗之外，这些偏差很小。就场的时间演化形状而言，即使在高损失的情况下，两种损失模型的性能也一样好。

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