An efficient pseudo‐spectral Legendre–Galerkin method for solving a nonlinear partial integro‐differential equation arising in population dynamics

The pseudo‐spectral Legendre–Galerkin method (PS‐LGM) is applied to solve a nonlinear partial integro‐differential equation arising in population dynamics. This equation is a competition model in which similar individuals are competing for the same resources. It is a kind of reaction–diffusion equation with integral term corresponding to nonlocal consumption of resources. The proposed method is based on the Legendre–Galerkin formulation for the linear terms and interpolation operator at the Chebyshev–Gauss–Lobatto (CGL) points for the nonlinear terms. Also, the integral term, which is a kind of convolution, is directly computed by a fast and accurate method based on CGL interpolation operator, and thus, the use of any quadrature formula in its computation is avoided. The main difference of the PS‐LGM presented in the current paper with the classic LGM is in treating the nonlinear terms and imposing boundary conditions. Indeed, in the PS‐LGM, the nonlinear terms are efficiently handled using the CGL points, and also the boundary conditions are imposed strongly as collocation methods. Combination of the PS‐LGM with a semi‐implicit time integration method such as second‐order backward differentiation formula and Adams‐Bashforth method leads to reducing the complexity of computations and obtaining a linear algebraic system of equations with banded coefficient matrix. The desired equation is considered on one and two‐dimensional spatial domains. Efficiency, accuracy, and convergence of the proposed method are demonstrated numerically in both cases. Copyright © 2012 John Wiley & Sons, Ltd.     

Two-dimensional threshold voltage model of a nanoscale silicon-on-insulator tunneling field-effect transistor

The tunneling field-effect transistor(TFET) is a potential candidate for the post-CMOS era.In this paper,a threshold voltage model is developed for this new kind of device.First,two-dimensional(2D) models are used to describe the distributions of potential and electric field in the channel and two depletion regions.Then based on the physical definition of threshold voltage for the nanoscale TFET,the threshold voltage model is developed.The accuracy of the proposed model is verified by comparing the calculated results with the 2D device simulation data.It has been demonstrated that the effects of varying the device parameters can easily be investigated using the model presented in this paper.This threshold voltage model provides a valuable reference to TFET device design,simulation,and fabrication.     

高重复频率脉冲激光能量测量（英文）

设计了一种用于高重复频率脉冲激光能量测量的峰值保持电路。电路由电荷积分器、2阶低通滤波器、时间延迟触发器和峰值保持器组成,通过将光电流脉冲转换成电压脉冲,电压脉冲的峰值与对应电流脉冲所包含的能量成正比。实验测量结果表明：该电路可以测量脉宽〈10 ns,重复频率≥2 kHz的重频窄脉冲激光的脉冲能量,且工作稳定,其线性动态范围≥140倍。该电路可应用于光电阵列探测系统中,能实现较高的空间分辨力。     

基于径向基逼近的KdV方程的无网格辛算法

基于径向基逼近理论,本文为KdV方程构造了一个无网格辛算法.首先借助径向基空间离散Hamilton函数以及Poisson括号,把KdV方程转化成一个有限维的Hamilton系统.然后用辛积分子离散有限维系统,得到辛算法.文章进一步讨论了所构造辛算法的收敛性和误差界.数值例子验证了理论分析.     

基于DSP交替式积分器设计

在DSP扣除斜率算法的基础上,设计了一种新型交替式积分器。该积分器利用DSP进行逻辑控制,使两个模拟积分器交替工作,减小两个积分器的积分时间,从而有效克服由于电容和温漂带来的误差,实现了对信号的长时间积分。同时采用Iqmath库函数实现定点处理器的运算来提高实时精度,很方便地实现了实时而准确的积分处理。     

约束多体系统动力学分析的改进的离散零空间算法

通过对已有离散零空间矩阵计算方法的改进,构造了改进的离散零空间等效变换公式,该公式可不依赖于特定的积分方法,能简洁、方便的与多种数值积分方法相结合。基于改进公式,提出了改进的离散零空间算法框架,并将该框架与一般变分积分法结合,构造了约束多体系统动力学分析的改进的离散零空间算法。通过曲柄滑块机构的数值实验,验证了改进的离散零空间等效变换公式的正确性,示例了其与数值积分算法的良好结合性,说明了改进算法的可行性和有效性。     

An efficient explicit full-discrete scheme for strong approximation of stochastic Allen–Cahn equation

In Becker and Jentzen (2019) and Becker et al. (2017), an explicit temporal semi-discretization scheme and a space–time full-discretization scheme were, respectively, introduced and analyzed for the additive noise-driven stochastic Allen–Cahn type equations, with strong convergence rates recovered. The present work aims to propose a different explicit full-discrete scheme to numerically solve the stochastic Allen–Cahn equation with cubic nonlinearity, perturbed by additive space–time white noise. The approximation is easily implementable, performing the spatial discretization by a spectral Galerkin method and the temporal discretization by a kind of nonlinearity-tamed accelerated exponential integrator scheme. Error bounds in a strong sense are analyzed for both the spatial semi-discretization and the spatio-temporal full discretization, with convergence rates in both space and time explicitly identified. It turns out that the obtained convergence rate of the new scheme is, in the temporal direction, twice as high as existing ones in the literature. Numerical results are finally reported to confirm the previous theoretical findings.     

X射线成像积分滤波模型与实验

X射线数字化成像系统的不足主要表现在成像末端耦合约束、微焦点约束瓶颈以及单光子成像缺陷与量子噪声约束等方面,利用传统的数字图像处理手段很难实现有效的图像滤波,而复杂的滤波算法进一步限制了其工程使用效果。为了提高X射线成像系统的光学传递能力与系统抗噪声能力,本文首先以热激发X辐射源与X射线像增强器为例,从系统层面探索成像遇到的诸多技术瓶颈,并在此基础上提出了一种针对X射线成像的积分滤波方法。然后,将空间频率固定的铅制光栅作为被测目标,通过改变中继光学耦合系统的物像关系使得像方空间频率在一定区间内连续改变,进而通过大量的实验数据实现在不同积分时间条件下的光学传递函数精确拟合。接着,分别从光学传递函数积分效果与归一化后的基频传递特性的角度验证了该滤波方法可以有效压制热触发源引入的量子噪声,避免图像产生单光子成像缺陷。实验数据表明:该方法可以提升系统成像的光学传递能力。最后,通过帧叠加与积分滤波的对比效果验证了该滤波方法的优越性。