Existence of nontrivial solutions for periodic Schrodinger equations with new nonlinearities

We study the Schr\"{o}dinger equation: \begin{eqnarray} - \Delta u+V(x)u+f(x,u)=0,\qquad u\in H^{1}(\mathbb{R}^{N}),\nonumber \end{eqnarray} where $V$ is periodic and $f$ is periodic in the $x$-variables, $0$ is in a gap of the spectrum of the operator $-\Delta+V$. We prove that under some new assumptions for $f$, this equation has a nontrivial solution. Our assumptions for the nonlinearity $f$ are very weak and greatly different from the known assumptions in the literature.Comment: arXiv admin note: substantial text overlap with arXiv:1310.239

Distributed Contingency Analysis over Wide Area Network among Dispatch Centers

Traditionally, a regional dispatch center uses the equivalent method to deal with external grids, which fails to reflect the interactions among regions. This paper proposes a distributed N-1 contingency analysis (DCA) solution, where dispatch centers join a coordinated computation using their private data and computing resources. A distributed screening method is presented to determine the Critical Contingency Set (DCCS) in DCA. Then, the distributed power flow is formulated as a set of boundary equations, which is solved by a Jacobi-Free Newton-GMRES (JFNG) method. During solving the distributed power flow, only boundary conditions are exchanged. Acceleration techniques are also introduced, including reusing preconditioners and optimal resource scheduling during parallel processing of multiple contingencies. The proposed method is implemented on a real EMS platform, where tests using the Southwest Regional Grid of China are carried out to validate its feasibility.Comment: 5 pages, 6 figures, 2017 IEEE PES General Meetin

The computational method of substructure’s frequency response function in transfer path analysis

The multi-degree-of-freedom coupled vibration system with “engine-mount-body” as the transfer path was divided into active substructure (engine), passive substructure (body) and linking components (mounts) between active and passive substructure. According to the dynamic equation of multi-degree-of-freedom coupling vibration system, the computational method of the substructure’s Frequency Response Function (FRF) was proposed. For the coupled vibration system of the real vehicle’s transfer path, the computational method of the substructure’s FRF was used to obtain the FRF of substructure and dynamic mount stiffness based on the FRF of system obtained by the hammering test. Combining the dynamic mount stiffness with the vibration acceleration of the active and passive sides of the mount, the operating load was identified based on the mount-stiffness method of the transfer path analysis. Combining the operating load with the FRF of substructure to analyze the contribution of the transfer path, the contribution of each path to the target location (the Z-direction of the front floor of the cab) was presented. The correctness of the computational method of the substructure’s FRF was presented by calculating the vibration isolation ratio of the mount, which provided theoretical support for the research of dynamic characteristics of the substructure and linking components