论文标题
广义磁化性张量的性能
Properties of Generalised Magnetic Polarizability Tensors
论文作者
论文摘要
我们在时间谐波低 - 低频磁场扰动的时间内提出了新的替代性完整渐近扩展，这是由于导电渗透对象的存在引起的，因为对于Maxwell系统的涡流近似值趋于零。我们的新替代配方可以通过使用多个指标引入通用MPT（GMPTS）来对众所周知的等级2磁性极化张量（MPT）对象表征进行自然扩展。特别是，我们确定磁静力的贡献，为GMPT的对称性提供了新的结果，为GMPT系数的实际和虚构部分提供了明确的公式，并描述了GMPT系数的光谱行为。我们还介绍了比其他GMPT对同一顺序的描述更少的谐波GMPTS（HGMPTS）的概念。我们描述了HGMPTS的缩放，翻译和旋转特性，并描述了一种在对称组的作用下获得不变的HGMPT系数的方法。这种方法是一种用于选择对象分类中的特征，以使用HGMPTS进行隐藏的对象识别。
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 characterisation to higher order tensor descriptions by introducing generalised 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 behaviour 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.
