Generalized wave-front reconstruction algorithm applied in a Shack-Hartmann test

A generalized numerical wave-front reconstruction method is proposed that is suitable for diversified irregular pupil shapes of optical systems to be measured. That is, to make a generalized and regular normal equation set, the test domain is extended to a regular square shape. The compatibility of this method is discussed in detail, and efficient algorithms (such as the Cholesky method) for solving this normal equation set are given. In addition, the authors give strict analyses of not only the error propagation in the wave-front estimate but also of the discretization errors of this domain extension algorithm. Finally, some application examples are given to demonstrate this algorithm

Asymptotic behavior of solutions to the Yamabe equation with an asymptotically flat metric

We prove that any positive solution of the Yamabe equation on an asymptotically flat $n$-dimensional manifold of flatness order at least $\frac{n-2}{2}$ and $n\le 24$ must converge at infinity either to a fundamental solution of the Laplace operator on the Euclidean space or to a radial Fowler solution defined on the entire Euclidean space. The flatness order $\frac{n-2}{2}$ is the minimal flatness order required to define ADM mass in general relativity; the dimension $24$ is the dividing dimension of the validity of compactness of solutions to the Yamabe problem. We also prove such alternatives for bounded solutions when $n>24$. We prove these results by establishing appropriate asymptotic behavior near an isolated singularity of solutions to the Yamabe equation when the metric has a flatness order of at least $\frac{n-2}{2}$ at the singularity and $n<24$, also when $n>24$ and the solution grows no faster than the fundamental solution of the flat metric Laplacian at the singularity. These results extend earlier results of L. Caffarelli, B. Gidas and J. Spruck, also of N. Korevaar, R. Mazzeo, F. Pacard and R. Schoen, when the metric is conformally flat, and work of C.C. Chen and C. S. Lin when the scalar curvature is a non-constant function with appropriate flatness at the singular point, also work of F. Marques when the metric is not necessarily conformally flat but smooth, and the dimension of the manifold is three, four, or five, as well as recent similar results by the second and third authors in dimension six.Comment: 51 page

A patch-based method for the evaluation of dense image matching quality

Airborne laser scanning and photogrammetry are two main techniques to obtain 3D data representing the object surface. Due to the high cost of laser scanning, we want to explore the potential of using point clouds derived by dense image matching (DIM), as effective alternatives to laser scanning data. We present a framework to evaluate point clouds from dense image matching and derived Digital Surface Models (DSM) based on automatically extracted sample patches. Dense matching errors and noise level are evaluated quantitatively at both the local level and whole block level. In order to demonstrate its usability, the proposed framework has been used for several example studies identifying the impact of various factors onto the DIM quality. One example study proves that the overall quality on smooth ground areas improves when oblique images are used in addition. This framework is then used to compare the dense matching quality on three different terrain types. In another application of the framework, a bias between the point cloud and the DSM generated from a photogrammetric workflow is identified. The framework is also used to reveal inhomogeneity in the distribution of the dense matching errors caused by overfitting the bundle network to ground control points

Study on an adaptive multi-model predictive controller for the thermal management of a SOFC-GT hybrid system

A SOFC temperature control system based on adaptive multimodel predictive control (MMPC) method is designed for a solid oxide fuel cell-gas turbine (SOFC-GT) hybrid system with anode and cathode ejectors. Two multi-input and multi-output MPCs (under 100% and 90% load) are designed to control the anode and cathode inlet temperatures. The accuracy of the identified linear models are both more than 95%. The control performance of the designed MMPC is compared with a single MPC and traditional PI. The comparison results demonstrate that the proposed MMPC is most effective and competitive in SOFC thermal management. During the load following, the controller overshoot is less than 1.19K. The settling time is about 2000s, and the integral of time-weighted absolute error is less than 472