Properties of generalized magnetic polarizability tensors
Properties of generalized magnetic polarizability tensors
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DOI：
10.1002/mma.8856
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发表时间：
2022-07
影响因子：
2.9
通讯作者：
P. Ledger;W. Lionheart
中科院分区：
文献类型：
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作者：
P. Ledger;W. Lionheart
对于麦克斯韦系统的涡流近似，我们提出了一种新的替代完全渐近展开式，用于描述导体导电体的尺寸趋于零时，由于导电体的存在而引起的低频磁场扰动。通过引入使用多指数的广义磁极化率张量(GMPTS)，我们的新的替代公式使得众所周知的秩2磁极化率张量(MPT)对象描述能够自然地扩展到高阶张量描述。特别地，我们证明了静磁场的贡献，给出了关于GMPT对称性的新结果，导出了GMPT系数实部和虚部的显式公式，并描述了GMPT系数的光谱行为。我们还引入了调和GMPT(HGMPT)的概念，它比同阶的其他GMPT描述具有更少的系数。我们描述了HGMPT的标度、平移和旋转性质，并描述了一种获得在对称群作用下不变的HGMPT系数的方法。这种方法是在使用HGMPTS进行隐藏目标识别的目标分类中选择特征的一种候选方法。
We present new alternative complete asymptotic expansions for the time harmonic low‐frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation of the Maxwell system. Our new alternative formulations enable a natural extension of the well‐known rank 2 magnetic polarizability tensor (MPT) object characterization to higher order tensor descriptions by introducing generalized MPTs (GMPTs) using multi‐indices. In particular, we identify the magnetostatic contribution, provide new results on the symmetries of GMPTs, derive explicit formulae for the real and imaginary parts of GMPT coefficients and also describe the spectral behavior of GMPT coefficients. We also introduce the concept of harmonic GMPTs (HGMPTs) that have fewer coefficients than other GMPT descriptions of the same order. We describe the scaling, translation and rotational properties of HGMPTs and describe an approach for obtaining those HGMPT coefficients that are invariant under the action of a symmetry group. Such an approach is one candidate for selecting features in object classification for hidden object identification using HGMPTs.