A differential scheme is proposed for the calculation of the components of the effective electrical conductivity tensor of a microinhomogeneous material taking into account the Hall effect. The presence of the Hall effect results in an appearance of asymmetry of the components of the conductivity tensor and a dependence of these components on the magnitude of the magnetic field applied to the material. In this case, the differential scheme leads to a system of matrix differential equations that were solved numerically in the current work. This solution was obtained for materials containing spherical or cylindrical inclusions. In the case of cylindrical inclusions, the results were obtained for inclusions with the symmetry axes parallel or orthogonal to the magnetic field. A comparison of the results obtained by the proposed methodology to the low concentration approximation was carried out.

中文翻译：

---

具有霍尔效应的微观非均匀材料有效电导率的微分方案

提出了一种考虑霍尔效应的微分方案，用于计算微观非均匀材料的有效电导率张量的分量。霍尔效应的存在导致电导率张量的分量出现不对称性，并且这些分量依赖于施加到材料的磁场的大小。在这种情况下，微分格式产生了在当前工作中数值求解的矩阵微分方程组。该解决方案是针对含有球形或圆柱形夹杂物的材料而获得的。对于圆柱形夹杂物，结果是针对对称轴平行或正交于磁场的夹杂物获得的。将所提出的方法获得的结果与低浓度近似值进行了比较。