这是一份andrews圣安德鲁斯大学 MT2501作业代写的成功案例
where $Z_{i}$ is the coordination number of site $i$. We now introduce a site-site Green function $G_{i j}$ defined by
$$
Z_{i} G_{i k}-\sum_{j} G_{j k}=-\delta_{i k},
$$
where, physically, $G_{i j}$ is the field at $j$ as a result of injecting a unit flux at $i$. With the aid of the Green function, Eq. (35) becomes
$$
P_{i}=P_{i}^{0}+\sum_{j} \sum_{k} G_{i j} \Delta_{j k}\left(P_{j}-P_{k}\right)
$$
$$
Q_{i j}=Q_{i j}^{0}+\sum_{[l k]} Q_{l k}\left(G_{i l}+G_{j k}-G_{j l}-G_{i k}\right),
$$
where $[l k]$ indicates that the bond connecting nearest-neighbor sites $l$ and $k$ is counted only once in the sum. We denote bonds with Greek letters and assign direction to them and let
$$
\gamma_{\alpha \beta}=\left(G_{i l}+G_{j k}\right)-\left(G_{j l}+G_{i k}\right),
$$
MT2501 COURSE NOTES ：
The MG approximation can be generalized to macroscopically-anisotropic materials that consist of $n-1$ different types of unidirectionally aligned isotropic inclusions of the same shape, and is given by
$$
\sum_{i=1}^{n} \phi_{i}\left(\mathbf{C}{e}-\mathbf{C}{1}\right) \cdot \mathbf{T}{i}^{(1)}=\mathbf{0} $$ where $$ \mathbf{T}{i}^{(1)}=\left[\mathbf{U}+\mathcal{S}: \mathbf{C}{1}^{-1}:\left(\mathbf{C}{i}-\mathbf{C}_{1}\right)\right]^{-1}
$$