Fourier acceleration of iterative processes in disordered systems

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.     

Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

基于激光雷达的垂直能见度反演算法及其误差评估

针对大气垂直方向上消光系数分布不均匀难以用传统方法直接测量垂直能见度的问题,提出了一种基于激光雷达探测垂直能见度的计算方法。根据大气辐射传输基本原理,借助于辐射传输方程,推导出了垂直能见度的计算公式;然后利用激光雷达原理方程和Klett算法反演出大气垂直方向上的消光系数分布,基于此提出了垂直能见度的迭代算法。最后,利用灰色模型GM(1,1)和批统计算法,对激光雷达反演得到的后向散射系数进行了评估,给出了误差置信区间为（0.760±0.339）×10⁻⁴（srad·km）⁻¹。结果表明,该方法是一种特别有效的计算垂直能见度的方法,符合探测的基本需求,且误差小精度高。     

Shifting the Superparamagnetic Limit of Nanosized Copper Iron Spinel

In this paper we analyze trend of EFG values measured at Cd impurity in a group of semiconducting delafossites with chemical formula CuBO₂ (B = Al, Fe, Cr, Nd). We conclude that this trend reveals one of the most subtle details in electronic spectrum of the compounds: if impurity states are formed within or out of the band gap. In CuAlO₂ and CuFeO₂ the Cd EFG exhibits larger value than in CuCrO₂ and CuNdO₂, when Cd substitutes the Cu atom. This occurs because in the first two compounds the Cd forms shallow band within the gap, and in the second two compounds does not. When Cd occupies the B position it exhibits almost the same EFG in all delafossites. In this case, Cd does not form its states within the gap in none of the compounds. To arrive to these conclusions we analyzed and calculated various systems (Cd-doped CuAlO₂ and CuCrO₂ compounds, fictitious molecules), using the FP-LAPW method.     

折射率梯度引起反转的光自旋霍尔效应研究

从经典电动力学出发,研究了由折射率梯度导致的反转光自旋霍尔效应。通过分析光从光疏介质入射到光密介质和从光密介质入射到光疏介质两种情况,揭示了光自旋霍尔效应中的横移与偏振态、折射率梯度以及入射角等因素的定性关系。当入射角一定时,光从光疏介质入射到光密介质时的水平偏振横移绝对值大于垂直偏振横移,而从光密介质入射到光疏介质的情况正好与之相反,并且传输场的横移方向取决于折射率梯度方向,增大入射角能明显增强光自旋霍尔效应,对某一特定的线偏振光束,其左、右旋圆偏振光分量的横移等值反向。这些研究结果为调控光自旋霍尔效应提供了有效途径。     

质子注入能量对垂直腔面发射激光器的阈值和功率的影响

文章研究了如何兼顾质子注入型垂直腔面发射激光器的功率和阈值性能.从模拟和实验两方面分析了质子注入能量与器件功率和阈值特性的关系.发现注入能量过高时,损伤有源区,降低了功率性能.而能量过低则会减弱对注入电流的限制,增加阈值.计算和实验结果表明,对于文中的器件结构,315 keV的注入能量是合适的.在10μm的注入孔径下获得器件的阈值为4.3 mA,功率为1.7 mW.     

A Two-Level Preconditioned Conjugate-Gradient Method in Distorted and Structured Grids

In this paper, we propose a new two-level preconditioned C-G method which uses the quadratic smoothing and the linear correction in distorted but topologically structured grid. The CPU time of this method is less than that of the multigrid preconditioned C-G method (MGCG) using the quadratic element, but their accuracy is almost the same. Numerical experiments and eigenvalue analysis are given and the results show that the proposed two-level preconditioned method is efficient.     

地层静温预测的非牛顿流体数学模型

根据热力学参数、泥浆参数及井筒结构参数等，先选定一个地层温度梯度进行计算，得出泥浆出口温度.将此计算值与实测温度值比较，按照比较结果再修正所选的地层温度梯度.如此反复，直到得出合理的地层温度梯度.在此基础上，从热力学及流体力学等有关方程出发， 经过推演得到井壁上温度随深度变化以及地层温度分布的数学模型.由于钻井过程中泥浆、 岩石及其温度场间是相互作用、相互影响的，这为研究热 流 固耦合渗流过程的理论与应 用提供了一种新的方法. 关键词： 温度梯度 非牛顿流体 数学模型     

Phase diagram of speed gradient model with an on-ramp

In this paper, phase transitions are investigated in speed gradient model with an on-ramp. Phase diagrams of traffic flow composed of manually driven vehicles and adaptive cruise control (ACC) vehicles are studied, respectively. The traffic flow composed of ACC vehicles is modeled by enhancing propagation speed of small disturbance. The phase diagram of traffic flow composed of manually driven vehicles is similar to that in previous works, in which such states as pinned localized cluster (PLC), moving localized cluster (MLC), triggered stop-and-go traffic (TSG), oscillatory congested traffic (OCT), and homogeneous congested traffic (HCT) are reproduced. In the phase diagram of traffic flow composed of ACC vehicles, traffic stability is enhanced and such states as PLC, MLC, and TSG disappear. Furthermore, some interesting phenomena, such as stationary OCT upstream of on-ramp and appearance of second OCT in HCT, are identified.