On the order of singular optimal control problems

In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.Dedicated to R. BellmanThis work was supported by the National Science Foundation under Grant No. ENG-77-16660.     

Optimality conditions at junctions of singular and nonsingular controls

Some necessary conditions for the optimality of junctions between singular and nonsingular subarcs arising in optimal control problems are well established. The second part of McDanell's conjecture has been proved false. The first part still awaits verification or otherwise. This paper briefly summarizes previous work and presents some evidence to suggest that the first part of the conjecture is also false.     

硅色敏器件对复色光色差辨识能力的数值分析

对复色光的光谱功率分布和色敏器件光谱响应的实验曲线进行了函数拟合，采用Mathematica 4．2计算了具有不同峰值波长和半高宽的高斯分布的复色光在色敏器件中产生的电流比．计算结果表明，待测复色光的峰值波长和半高宽变化对两种典型的色敏器件的输出信号影响的权重比分别为100：1和10：1。权重比说明色敏器件的输出电流比随峰值波长和半高宽的变化非常灵敏，但两者权重不同，其中峰值波长的变化影响更为显著，是影响复色光颜色变化的主要因素．数值分析的结果表明，硅双结色敏器件对复色光色差有良好的辨识能力．两种器件权重比的差异说明了器件制作工艺与其辨识能力的关系，为器件合理设计提供了理论依据．     

Homogenization of the Signorini boundary‐value problem in a thick junction and boundary integral equations for the homogenized problem

We consider a mixed boundary‐value problem for the Poisson equation in a thick junction Ω_ε which is the union of a domain Ω₀ and a large number of ε—periodically situated thin cylinders. The non‐uniform Signorini conditions are given on the lateral surfaces of the cylinders. The asymptotic analysis of this problem is done as ε→0, i.e. when the number of the thin cylinders infinitely increases and their thickness tends to zero. We prove a convergence theorem and show that the non‐uniform Signorini boundary conditions are transformed in the limiting variational inequalities in the region that is filled up by the thin cylinders as ε→0. The convergence of the energy integrals is proved as well. The existence and uniqueness of the solution to this non‐standard limit problem is established. This solution can be constructed by using a penalty formulation and successive iteration. For some subclass, these problems can be reduced to an obstacle problem in Ω₀ and an appropriate postprocessing. The equations in Ω₀ finally are also treated with boundary integral equations. Copyright © 2010 John Wiley & Sons, Ltd.     

无序二维约瑟夫森结阵列中磁场引起的涡旋玻璃态相变

采用电阻阻错结的无序二维约瑟夫森结阵列模型,数值研究超导薄膜中垂直磁场引起的涡旋运动.通过分析磁场激发产生的涡旋度Ne及低频电压噪声S₀的变化特性,得到如下结论：在无序超导体中固定温度不变,随着磁场的减弱涡旋液态经过准有序的布拉格相,涡旋玻璃相重新进入到低磁场下的钉扎稀磁液相. 由于在涡旋玻璃相中,电流驱动下的噪声值表现出一个峰,表明系统处于无序与有序相互竞争的亚稳态,并且临界电流应有峰值效应. 计算得到噪声值的变化与Okuma等得到的无序超导Mo_xSi_1-x膜实验现象一致,并能解释磁场降低引起的重新进入钉扎的稀磁液相行为. 关键词： 约瑟夫森结阵列 磁通玻璃 重新进入 峰值效应     

Multimode squeezed states produced by a confocal parametric oscillator

We investigate the spatial behaviour of the quantum-noise-reduction spectrum of the vacuum state emitted by a degenerate optical parametric oscillator below threshold. In view of possible experimental implementations, we consider a mode-degenerate resonator and two matching lenses and show that, for the realistic case of a finite-width pump, significant level of squeezing can be observed in a very small region of the beam. Received 25 September 2002 Published online 11 February 2003     

Output voltage calculations in double barrier magnetic tunnel junctions with asymmetric voltage behavior

In this paper we study the asymmetric voltage behavior (AVB) of the tunnel magnetoresistance (TMR) for single and double barrier magnetic tunnel junctions (MTJs) in range of a quasi-classical free electron model. Numerical calculations of the TMR–V curves, output voltages and I–V characteristics for negative and positive values of applied voltages were carried out using MTJs with CoFeB/MgO interfaces as an example. Asymmetry of the experimental TMR–V curves is explained by different values of the minority and majority Fermi wave vectors for the left and right sides of the tunnel barrier, which arises due to different annealing regimes. Electron tunneling in DMTJs was simulated in two ways: (i) Coherent tunneling, where the DMTJ is modeled as one tunnel system and (ii) consecutive tunneling, where the DMTJ is modeled by two single barrier junctions connected in series.     

Positive and negative Hanbury-Brown and Twiss correlations in normal metal-superconducting devices

In the light of the recent analogs of the Hanbury-Brown and Twiss experiments [1] in mesoscopic beam splitters, negative current noise correlations are recalled to be the consequence of an exclusion principle. Here, positive (bosonic) correlations are shown to exist in a fermionic system, composed of a superconductor connected to two normal reservoirs. In the Andreev regime, the correlations can either be positive or negative depending on the reflection coefficient of the beam splitter. For biases beyond the gap, the transmission of quasiparticles favors fermionic correlations. The presence of disorder enhances positive noise correlations. Potential experimental applications are discussed. Received 1 June 1999