Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations

One of the main challenges in computational simulations of gas detonation propagation is that negative density or negative pressure may emerge during the time evolution, which will cause blow-ups. Therefore, schemes with provable positivity-preserving of density and pressure are desired. First order and second order positivity-preserving schemes were well studied, e.g., [6], [10]. For high order discontinuous Galerkin (DG) method, even though the characteristicwise TVB limiter in [1], [2] can kill oscillations, it is not sufficient to maintain the positivity. A simple solution for arbitrarily high order positivity-preserving schemes solving Euler equations was proposed recently in [22]. In this paper, we first discuss an extension of the technique in [22], [23], [24] to design arbitrarily high order positivity-preserving DG schemes for reactive Euler equations. We then present a simpler and more robust implementation of the positivity-preserving limiter than the one in [22]. Numerical tests, including very demanding examples in gaseous detonations, indicate that the third order DG scheme with the new positivity-preserving limiter produces satisfying results even without the TVB limiter.     

Fringe pattern denoising using averaging based on nonlocal self-similarity

Digital image processing for fringe patterns is an important procedure in optical interferometry. Filtering off noise from fringe patterns is one of the key tasks for extraction of the phase field. Spin filters proposed by Yu et al. [Appl. Opt. 33(1994), 41(2002), et al.] have been proven to be effective denoising methods. In this paper, we develop a nonlocal self-similarity filter, which averages similar pixels searched for in whole image instead of in a local fringe direction as the spin filters do. Although simple and free of the fringe orientation estimation, involving more pixels with higher similarity levels, our algorithm has stronger robustness against noise and thus denoises fringe patterns more effectively. Simulation and experimental results show that our algorithm outperforms related filters both in preserving smooth fringes and in reducing blurring effects and quantitative errors.     

Quantum information splitting of an arbitrary three-qubit state via the cavity input–output process

We propose a realizable quantum information splitting (QIS) scheme for an arbitrary three-qubit state via the cavity input–output process. In our scheme, a four-qubit cluster state and a three-qubit Greenberger–Horne–Zeilinge (GHZ) state are used as quantum channel. The sender and controller only need to perform Bell-state measurements and a single-qubit measurement, respectively. The receiver can reconstruct the arbitrary three-qubit state by classical communication and local operations. Compared with the scheme in Nie et al. [Optics Communications 284 (2011) 1457], the quantum resources and classical information in our scheme are decreased by 5 qubits and 1 bit, respectively. Moreover, we replace the W-state category measurement in the former with Bell-state measurements and a single-qubit measurement, which is more simple and feasible in experiment.     

Quasi-fractional Talbot effect of resonant diffraction grating

The Fresnel diffraction of resonant diffraction grating is studied on the basis of the modal method, and it shows that the conventional fractional Talbot effect can still occur by choosing appropriate parameters. The Fresnel diffraction distributions of the resonant diffraction gratings with periods between λ and 4λ are analyzed, and the diffraction fields exhibit periodicity in both grating direction and the propagating direction. The experiment is carried out to verify the simulation results of the quasi-fractional Talbot effect of the resonant diffraction grating. This effect has potential application in lithography for high-resolution patterning.     

Unique geometric and electronic structure of CO adsorbed on Ge(100): A DFT study

CO adsorption on the Ge(100) surface has been investigated using a slab model with density functional theory implemented in SIESTA. CO was found to be exclusively adsorbed on the asymmetric dimer with C attaching on the lower Ge dimer atom. The adsorption process is barrierless. The calculated adsorption energy and vibration frequencies are comparable to previous experimental results. The crystal orbital Hamilton analysis showed that the bonding between Ge and CO is mainly attributable to the Ge 4p_z orbital overlapping with C 2 s, or with CO molecular orbitals 3σ and 4σ. The repulsive energy between adsorbed CO molecules is less than 1 kcal/mol. The diffusion barrier of CO on the Ge(100) surface is about 14 kcal/mol.     

Growth and vibrational properties of MnOx thin films on Rh(111)

The growth, structures, and vibrational properties of ultrathin manganese oxide films on Rh(111) had been investigated using high-resolution electron energy loss spectroscopy (HREELS), X-ray photoelectron spectroscopy (XPS), low energy electron diffraction (LEED), low energy ion scattering spectroscopy (LEIS) and Auger electron spectroscopy (AES). MnO_x grew in a layer-by-layer fashion on the Rh(111) surface. HREELS phonon features and XPS binding energies showed that an OMnO like tri-layer formed initially. Which was stable on the Rh(111) surface with MnO_x coverage less than one monolayer. At above one monolayer, Mn₃O₄ was preferred as indicated from a four-phonon feature peaked at 13.3, 39, 68 and 83 meV in HREELS. Higher temperature oxidation and annealing were found to improve the long-range order of the MnO_x films.     

Preservation of entanglement in a two-qubit-spin coupled system

A theoretical scheme for preserving the entanglement in a two-qubit-spin coupled system in the presence of Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interaction is proposed. On the basis of a sequence of operations performed periodically on the system, the scheme can preserve the entanglement of the system starting from any initial state with any desired high precision for any desired long duration.     

A class of hybrid DG/FV methods for conservation laws I: Basic formulation and one-dimensional systems

By comparing the discontinuous Galerkin (DG) and the finite volume (FV) methods, a concept of ‘static reconstruction’ and ‘dynamic reconstruction’ is introduced for high-order numerical methods. Based on the new concept, a class of hybrid DG/FV schemes is presented for one-dimensional conservation law using a ‘hybrid reconstruction’ approach. In the hybrid DG/FV schemes, the lower-order derivatives of a piecewise polynomial solution are computed locally in a cell by the DG method based on Taylor basis functions (called as ‘dynamic reconstruction’), while the higher-order derivatives are re-constructed by the ‘static reconstruction’ of the FV method, using the known lower-order derivatives in the cell itself and its adjacent neighboring cells. The hybrid DG/FV methods can greatly reduce CPU time and memory required by the traditional DG methods with the same order of accuracy on the same mesh, and they can be extended directly to unstructured and hybrid grids in two and three dimensions similar to the DG and/or FV methods. The hybrid DG/FV methods are applied to one-dimensional conservation law, including linear and non-linear scalar equation and Euler equations. In order to capture the strong shock waves without spurious oscillations, a simple shock detection approach is developed to mark ‘trouble cells’, and a moment limiter is adopted for higher-order schemes. The numerical results demonstrate the accuracy, and the super-convergence property is shown for the third-order hybrid DG/FV schemes. In addition, by analyzing the eigenvalues of the semi-discretized system in one dimension, we discuss the spectral properties of the hybrid DG/FV schemes to explain the super-convergence phenomenon.     

时滞对一类单位负反馈二阶振荡系统的正面作用分析

针对一类被控对象具有二阶系统标准形式的振荡系统进行了稳定性分析,讨论了闭环系统为单位负反馈时信号传输时滞对控制系统性能的影响.通过绘制和分析相对阻尼系数在不同取值区间的Nyquist曲线,得出了时滞与闭环系统稳定性的关系,并对各种情况进行了单位阶跃响应的实例仿真.仿真结果表明了分析的正确性.     

结构与参量不确定的网络与网络之间的混沌同步

进行了结构与参量不确定的网络与网络之间的混沌同步研究．通过设计适当的控制输入,不但实现了两个复杂网络之间的混沌同步,而且网络节点状态方程中的未知参量和网络内部节点之间的耦合强度也被同时确定．通过采用具有调制损耗的CO2激光器的状态方程进行仿真实验,发现网络与网络之间的同步性能非常稳定．