On A Parabolic Equation in MEMS with An External Pressure

The parabolic problem $u_t-\Delta u=\frac{\lambda f(x)}{(1-u)^2}+P$ on a bounded domain $\Omega$ of $R^n$ with Dirichlet boundary condition models the microelectromechanical systems(MEMS) device with an external pressure term. In this paper, we classify the behavior of the solution to this equation. We first show that under certain initial conditions, there exists critical constants $P^*$ and $\lambda_P^*$ such that when $0\leq P\leq P^*$, $0<\lambda\leq \lambda_P^*$, there exists a global solution, while for $0\leq P\leq P^*,\lambda>\lambda_P^*$ or $P>P^*$, the solution quenches in finite time. The estimate of voltage $\lambda_P^*$, quenching time $T$ and pressure term $P^*$ are investigated. The quenching set $\Sigma$ is proved to be a compact subset of $\Omega$ with an additional condition, provided $\Omega\subset R^n$ is a convex bounded set. In particular, if $\Omega$ is radially symmetric, then the origin is the only quenching point. Furthermore, we not only derive the two-side bound estimate for the quenching solution, but also study the asymptotic behavior of the quenching solution in finite time.Comment: 35 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1402.0066 by other author

Analysis of Bs→ϕννˉB_s\to\phi\nu\bar{\nu} at CEPC

The rare $b\to s\nu\bar{\nu}$ decays are sensitive to contributions of new physics (NP) and helpful to resolve the puzzle of multiple $B$ flavor anomalies. In this work, we propose to study the $b\to s\nu\bar{\nu}$ transition at a future lepton collider operating at the $Z$ pole through the $B_s \to \phi\nu\bar{\nu}$ decay. Using the $B_s\to\phi$ decay form factors from lattice simulations, we first update the SM prediction of BR($B_s \to \phi\nu\bar{\nu})_{\mathrm{SM}}=(9.93\pm 0.72)\times 10^{-6}$ and the corresponding $\phi$ longitudinal polarization fraction $F_{L,{\mathrm{SM}}}=0.53\pm 0.04$. Our analysis uses the full CEPC simulation samples with a net statistic of $\mathcal{O}(10^9)$ $Z$ decays. Precise $\phi$ and $B_s$ reconstructions are used to suppress backgrounds. The results show that BR($B_s \to \phi\nu\bar{\nu})$ can be measured with a statistical uncertainty of $\mathcal{O}(\%)$ and an $S/B$ ratio of $\mathcal{O}(1)$ at the CEPC. The quality measures for the event reconstruction are also derived. By combining the measurement of BR($B_s \to \phi\nu\bar{\nu})$ and $F_L$, the constraints on the effective theory couplings at low energy are given.Comment: 12 pages, 15 figures, 3 table

Integration of renewable energy sources: reliability-constrained power system planning and operations using computational intelligence

Renewable sources of energy such as wind turbine generators and solar panels have attracted much attention because they are environmentally friendly, do not consume fossil fuels, and can enhance a nation’s energy security. As a result, recently more significant amounts of renewable energy are being integrated into conventional power grids. The research reported in this dissertation primarily investigates the reliability-constrained planning and operations of electric power systems including renewable sources of energy by accounting for uncertainty. The major sources of uncertainty in these systems include equipment failures and stochastic variations in time-dependent power sources. Different energy sources have different characteristics in terms of cost, power dispatchability, and environmental impact. For instance, the intermittency of some renewable energy sources may compromise the system reliability when they are integrated into the traditional power grids. Thus, multiple issues should be considered in grid interconnection, including system cost, reliability, and pollutant emissions. Furthermore, due to the high complexity and high nonlinearity of such non-traditional power systems with multiple energy sources, computational intelligence based optimization methods are used to resolve several important and challenging problems in their operations and planning. Meanwhile, probabilistic methods are used for reliability evaluation in these reliability-constrained planning and design. The major problems studied in the dissertation include reliability evaluation of power systems with time-dependent energy sources, multi-objective design of hybrid generation systems, risk and cost tradeoff in economic dispatch with wind power penetration, optimal placement of distributed generators and protective devices in power distribution systems, and reliability-based estimation of wind power capacity credit. These case studies have demonstrated the viability and effectiveness of computational intelligence based methods in dealing with a set of important problems in this research arena

Capital market reaction to corporate restructuring announcements : an empirical test in the Shanghai Stock Exchange (SSE)

1 online resource (iii, 28 p.) : col. ill.Includes abstract and appendix.Includes bibliographical references (p. 25-26).The paper utilizes an event study to test whether there is an abnormal return from corporate restructuring announcements in the Shanghai Stock Exchange. We obtain data of abnormal returns and cumulative abnormal return using the Market Model. In the study two term event windows are applied, and after the t-test and bootstrap test, the relationship between the abnormal return and corporate restructuring announcements is confirmed