论文标题
在功率密度的二维Riemannian流形上重建各向异性电导率
Reconstructing anisotropic conductivities on two-dimensional Riemannian manifolds from power densities
论文作者
论文摘要
我们考虑具有光滑边界的导电紧凑型二维Riemannian歧管。该设置定义了歧管上的天然导电laplacian，因此还定义了由合适的边界条件引起的电势，电流场和相应的功率密度。由声音层析造影术的激励，我们表明，如果歧管具有零属并且已知度量，那么各向异性电导率就可以从少数功率密度的知识中唯一和建设性地恢复。我们通过在连钉上重建各向异性电导率，即经典属零属最小的表面在三个空间中进行数值说明。
We consider an electrically conductive compact two-dimensional Riemannian manifold with smooth boundary. This setting defines a natural conductive Laplacian on the manifold and hence also voltage potentials, current fields and corresponding power densities arising from suitable boundary conditions. Motivated by Acousto-Electric Tomography we show that if the manifold has genus zero and the metric is known, then the anisotropic conductivity can be recovered uniquely and constructively from knowledge of a few power densities. We illustrate the procedure numerically by reconstructing an anisotropic conductivity on the catenoid, i.e. the classical genus zero minimal surface in three-space.
