Reflection of Surface Plasmon Polaritons by a Corner Reflector of Negative Index Materials

A novel type of corner reflector for the reflection of surface plasmon polariton (SPP) is proposed. The reflector consists of two layers of compensatory media whose permittivity and permeability take opposite signs to that of the corresponding layer of the SP waveguide. By rigorously solving Maxwell's equations, the reflected SPP is proved to exist. The transverse wave vector of the reflected SPP is always antiparallel to that of the incident SPP and no phase retardation is introduced.     

A MICROFOUNDATION OF PREDATOR‐PREY DYNAMICS

ABSTRACT. Predator‐prey relationships account for an important part of all interactions betweenspecies. In this paper we provide a microfoundation for such predator‐prey relations in afood chain. Basic entities of our analysis are representative organisms of species modeled similar to economic households. With prices as indicators of scarcity, organisms are assumed to behave as if they maximize their net biomass subject to constraints which express the organisms' risk of being preyed upon during predation. Like consumers, organisms face a ‘budget constraint’ requiring their expenditure on prey biomass not to exceed their revenue from supplying own biomass. Short‐run ecosystem equilibria are defined and derived. The net biomass acquired by the representative organism in the short term determines the positive or negative population growth. Moving short‐run equilibria constitute the dynamics of the predator‐prey relations that are characterized in numerical analysis. The population dynamics derived here turn out to differ significantly from those assumed in the standard Lotka‐Volterra model.     

The strong relaxation limit of the multidimensional isothermal Euler equations

We construct global smooth solutions to the multidimensional isothermal Euler equations with a strong relaxation. When the relaxation time tends to zero, we show that the density converges towards the solution to the heat equation.

     

Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

On the excitation of a closely spaced array by a line source

An infinite row of periodically spaced, identical rigid circularcylinders is excited by an acoustic line source which is parallelto the generators of the cylinders. A method for calculatingthe scattered field accurately and efficiently is presented.When the cylinders are sufficiently close together, Rayleigh–Blochsurface waves that propagate energy to infinity along the arrayare excited. An expression is derived which enables the amplitudesof these surface waves to be computed without requiring thesolution to the full scattering problem.     

空位在金刚石近(001)表面扩散的分子动力学模拟

用分子动力学方法模拟了空位在金刚石近(001)表面的扩散过程,研究了温度对空位扩散的影响.结果表明,当温度为1000K左右时,位于近表面第二层上的空位开始向表面运动;当温度在1400—2000K时,空位完全扩散到表面.这与实验结果和其他计算结果符合得很好.同时发现,温度为1400—1800K时,空位的扩散经历了两次迁移运动,其分别对应了均方位移图中的两个极大值.在不施加任何约束的条件下得到了空位的动态扩散路径,空位在金刚石近(001)表面的扩散势垒约为042eV.并探讨了一定温度下空位数目增多及其不同排列 关键词： 金刚石 空位 扩散 分子动力学     

CCD摄像机大视场光学镜头的设计

为提高CCD摄像机的成像质量，同时使镜头结构紧凑、小型化，在大视场光学镜头的设计中，引入标准二次曲面和偶次非球面。根据初级像差理论，分析了非球面的位置、初始结构参数的求解规律。通过理论计算和ZEMAX光学设计软件的优化，给出工作波长为0.4～0.7μm、全视场角为80°，相对孔径为1∶1.5的镜头设计实例。该镜头由7块镜片组成，包括一个标准二次曲面和两个8次方非球面；在40lp/mm空间频率处的MTF值超过0.85，全视场畸变小于3％，像质优良     

Estimating Invariant Probability Densities for Dynamical Systems

Knowing a probability density (ideally, an invariant density) for the trajectories of a dynamical system allows many significant estimates to be made, from the well-known dynamical invariants such as Lyapunov exponents and mutual information to conditional probabilities which are potentially more suitable for prediction than the single number produced by most predictors. Densities on typical attractors have properties, such as singularity with respect to Lebesgue measure, which make standard density estimators less useful than one would hope. In this paper we present a new method of estimating densities which can smooth in a way that tends to preserve fractal structure down to some level, and that also maintains invariance. We demonstrate with applications to real and artificial data.     

双面电弧焊接的传热模型

将等离子焊接(PAW)电弧和钨极氩弧焊(TIG)电弧串接,相对作用于工件的正反面形成双面电弧焊接(DSAW)系统,可以引导焊接电流沿工件厚度方向流过小孔,补偿等离子电弧穿透工件时消耗的能量,以有效地提高等离子弧的穿透能力.综合考虑影响双面电弧焊接正反面熔池几何形状的力学因素,建立了熔池表面变形的控制方程,以此为基础并采用帖体曲线坐标系建立了DSAW焊接传热的数学模型,分析了DSAW,PAW焊接传热的差异,从传热的角度解释了DSAW焊接熔深增加的原因.焊接工艺实验表明,计算结果与实测结果吻合良好. 关键词： 双面电弧焊接(DSAW) 传热模型 熔池表面变形模型     

Controlling global stochasticity of Hamiltonian systems by nonlinear perturbation

A method of controlling global stochasticity in Hamiltonian systems by applying nonlinear perturbation is proposed. With the well-known standard map we demonstrate that this control method can convert global stochasticity into regular motion in a wide chaotic region for arbitrary initial condition, in which the control signal remains very weak after a few kicks. The system in which chaos has been controlled approximates to the original Hamiltonian system, and this approach appears robust against small external noise. The mechanism underlying this high control efficiency is intuitively explained. Received 15 January 2002 Published online 6 June 2002