Spherical radially transverse isotropic heterogeneous inclusions in homogeneous isotropic conductive host media are considered. The volume integral equation for the field in the medium with an isolated inclusion subjected to a constant external field is solved using Mellin-transform technique. The method allows revealing tensor structure of the solution with precision to one scalar function of radial coordinate. Differential equation for this function arises in the process of realization of the method. For multilayered radially transverse isotropic inclusions, an efficient algorithm of solution is presented. Neutral inclusions that do not disturb constant external fields in the host medium are considered. For neutral inclusions, relations between the conductivity coefficients of the inclusion and the host medium are indicated. It is shown that homogeneous inclusions with a layer of other material at the inclusion interface can be neutral (invisible for external observers). For neutral inclusions, thin boundary layers can be changed with specific boundary conditions at the inclusion interface (singular models of thin layers). Parameters of the singular models are indicated in terms of conductivity coefficients of the inclusion, layer, and host medium. The effective field method is used for calculation of the effective conductivity of homogeneous isotropic media containing random sets of radially transverse isotropic inclusions. Influence of volume fractions and conductivity coefficients of the inclusions on the effective conductivity of the composite is studied.

考虑均匀各向同性导电主体介质中的球形径向横向各向同性异质夹杂物。使用梅林变换技术求解具有恒定外场的孤立夹杂物介质中场的体积积分方程。该方法允许精确地揭示径向坐标的一个标量函数解的张量结构。该函数的微分方程是在该方法的实现过程中产生的。对于多层径向横向各向同性夹杂物，提出了一种有效的求解算法。考虑不干扰宿主介质中恒定外部场的中性夹杂物。对于中性夹杂物，显示了夹杂物和基质介质的电导率系数之间的关系。结果表明，在夹杂物界面处具有一层其他材料的均质夹杂物可以是中性的（对于外部观察者来说是不可见的）。对于中性夹杂物，薄边界层可以随着夹杂物界面处的特定边界条件而改变（薄层的奇异模型）。奇异模型的参数以夹杂物、层和主体介质的电导率系数表示。有效场法用于计算包含随机径向横向各向同性夹杂组的均匀各向同性介质的有效电导率。研究了夹杂物的体积分数和电导系数对复合材料有效电导率的影响。