Comparison of the solutions from a novel variational method with numerical results for the study of beam propagation in a Kerr medium with nonlinear absorption

We present results from a novel variational method for the study of beam propagation in a Kerr medium with nonlinear absorption. This new method combines the variational method and a nonlinear absorption equation and gives a concise expression for the combination. The results obtained with this method show good quantitative agreement with numerical solutions obtained with the finite-difference method. It is shown that the variational method takes much less time than a numerical simulation with the finite-difference method for analysis of beam propagation in a thick medium with nonlinear absorption and nonlinear refraction. The new method makes detailed analysis of beam propagation in a Kerr medium with nonlinear absorption very simple and fast.     

Tone Image Classification and Weighted Learning for Visible and NIR Image Fusion

In this paper, to improve the slow processing speed of the rule-based visible and NIR (near-infrared) image synthesis method, we present a fast image fusion method using DenseFuse, one of the CNN (convolutional neural network)-based image synthesis methods. The proposed method applies a raster scan algorithm to secure visible and NIR datasets for effective learning and presents a dataset classification method using luminance and variance. Additionally, in this paper, a method for synthesizing a feature map in a fusion layer is presented and compared with the method for synthesizing a feature map in other fusion layers. The proposed method learns the superior image quality of the rule-based image synthesis method and shows a clear synthesized image with better visibility than other existing learning-based image synthesis methods. Compared with the rule-based image synthesis method used as the target image, the proposed method has an advantage in processing speed by reducing the processing time to three times or more.     

Comparative experimental study on absolute measurement of spherical surface with two-sphere method

The two-sphere method with multiple confocal measurements and a “cat's-eye” measurement is used widely in high accuracy interferometry, which can obtain the absolute surface data of the tested spherical surface. We provide a comparative experimental study on absolute testing procedures for spherical surface with two-sphere method, which include the classical Jensen method with three position measurements, the Zygo method with five position measurements and a variant of the Jensen method. The variant of the Jensen method can combine the multiple “three-position” measurements based on the fiducial method and averaging method. The repeatability of the involved absolute measurement methods is also studied by the five set experiments, and the corresponding Zernike fitting coefficients are compared in detail. The experimental results are meaningful for implementation of two-sphere method with higher repeatability in practice.     

一类延迟混沌系统沿主轴方向上Lyapunov指数的计算方法

提出了一种计算延迟混沌系统沿主轴方向上Lyapunov指数的方法：矩阵迭代法.给出了其计算方法的原理及推导过程;同时推导了一类泰勒展开法,介绍了已有的Wolf替代法计算延迟混沌系统的Lyapunov指数.分析了三种不同计算方法的优缺点,最后进行了数值模拟,验证方法的有效性. 关键词： Lyapunov指数 延迟混沌系统 矩阵迭代法 泰勒展开法     

求解随机振动结构声辐射的统计边界元方法

机器的机械振动在音频范围内大多是具有明显随机性的随机过程,普通边界元方法不能计算这类具有随机边界条件的结构声辐射问题。本文提出将边界元方法和统计方法相结合的统计边界元方法,导出了求解随机振动物体所辐射噪声声场的计算公式。通过求解随机声场算例的计算,表明本文所提出的方法是正确的。     

Full-Field Determination of Principal-Stress Directions Using Photoelasticity with Plane-Polarized RGB Lights

In this paper, we propose a new three-wavelength method for automatic measurement of principal-stress directions over an entire model on the basis of four-step phase shift method. This method uses four fringe patterns captured by a color charge-coupled devices (CCD) camera corresponding to four angular position arrangements of polaroids in a dark-field plane polariscope. The principal-stress directions can be determined by a single calculation. The method is applied to a circular disc under compression. The principal-stress direction distributions obtained from the proposed method are compared with those obtained from a conventional method and theory. It can be obviously seen that the proposed method accurately yields the principal-stress directions compared with the conventional method.     

Output functions and fractal dimensions in dynamical systems

We present a novel method for the calculation of the fractal dimension of boundaries in dynamical systems, which is in many cases many orders of magnitude more efficient than the uncertainty method. We call it the output function evaluation (OFE) method. We show analytically that the OFE method is much more efficient than the uncertainty method for boundaries with D<0.5, where D is the dimension of the intersection of the boundary with a one-dimensional manifold. We apply the OFE method to a scattering system, and compare it to the uncertainty method. We use the OFE method to study the behavior of the fractal dimension as the system's dynamics undergoes a topological transition.     

An approximate method for determining the static deflection and natural frequency of a cracked beam

This paper provides an approximate method to determine the stiffness and the fundamental frequency of a cracked beam. The cracked beam is first represented as an un-cracked beam with equivalent reduced sections around the cracks. The effect of the cracks is explained, visualised and quantified using the equivalence concept developed for stepped beams with periodically variable cross-sections. Then an alternative expression of the improved Rayleigh method is provided to calculate the natural frequencies of a beam with a variable stiffness distribution along its length. As the method is insensitive to the assumed mode shapes, it avoids the difficulty in choosing appropriate mode shapes and yields accurate results. This is shown using several examples to compare the results determined using the proposed method and the Finite Element method (FEM). The method greatly simplifies the calculation of cracked beams with complicated configurations, such as a beam with several cracks, a cracked beam with concentrated masses, a beam with cracks close to each other, and a beam with periodically distributed cracks.     

积分节点迎风偏移的节点积分无单元Galerkin方法

建立求解稳态对流-扩散方程的-种稳定、高效的无单元Galerkin方法.该方法计算积分时采用基于局部Taylor展开的节点积分,并根据对流占优的程度对积分节点进行自适应迎风偏移.与传统的使用稳定化的无单元Galerkin方法相比,该方法是-种不依赖于背景网格积分的纯无网格方法,具有更好的稳定性和较高的计算效率,其程序实施更为简便.     

Two-stage mode finder for waveguides with a 2D cross-section

We present a fast and efficient method to find the vectorial eigenmodes of waveguides with an arbitrary 2D cross-section. The method can deal with both material losses and radiation losses (through perfectly matched layer boundary conditions). In the first stage of the method, a coarse estimate of the propagation constants is found using a plane-wave method. In the second stage, these estimates are refined using a mode-matching method.     

Scattering of light by axially symmetric particles: Modification of the point-matching method

The approach based on the separation of the fields into two parts with definite properties and the proper choice of special scalar potentials for each of them is applied to the point-matching method. Earlier, such a procedure carried out within the framework of the method of separation of variables for spheroids allowed us to obtain a solution that is considerably more efficient for strongly prolate and strongly oblate particles than solutions obtained with other versions of this method. It was found that the replacement of the summation over points on the particle surface in the point-matching method by the corresponding integral leads to a faster and more exact algorithm. The applicability of the proposed method is considered in comparison with the related method of extended boundary conditions. For spheroids and Chebyshev particles with a maximum-to-minimum-size ratio exceeding 1.5–2, the efficiency of the point-matching method is not high. For other Chebyshev particles, the point-matching method is undoubtedly preferable to the commonly used method of extended boundary conditions since it allows one to increase the accuracy of calculations by several orders of magnitude. Moreover, whereas the latter method is in principle inapplicable to certain Chebyshev particles, the former lacks this disadvantage.     

Finite Element Iterative Methods for the Stationary Double-Diffusive Natural Convection Model

In this paper, we consider the stationary double-diffusive natural convection model, which can model heat and mass transfer phenomena. Based on the fixed point theorem, the existence and uniqueness of the considered model are proved. Moreover, we design three finite element iterative methods for the considered problem. Under the uniqueness condition of a weak solution, iterative method I is stable. Compared with iterative method I, iterative method II is stable with a stronger condition. Moreover, iterative method III is stable with the strongest condition. From the perspective of viscosity, iterative method I displays well in the case of a low viscosity number, iterative method II runs well with slightly low viscosity, and iterative method III can deal with high viscosity. Finally, some numerical experiments are presented for testing the correctness of the theoretic analysis.     

基于离散变分原理的耗散动力学模拟方法：模拟三维囊泡形状

将基于离散变分原理的耗散动力学模拟方法应用到三维囊泡体系,通过优化囊泡的弯曲能求解其平衡态形状. 该方法的优点之一是不需要预先假定对称性. 针对特定约化自发曲率的囊泡体系,该方法模拟获得了一系列轴对称形状,模拟结果与文献中预先假定轴对称条件的计算方法所报道的结果一致,这验证了该模拟方法的可靠性及精确性. 此外,使用该方法研究了两个差别巨大的平衡态形状之间的转变动力学,在转变过程中观察到了多个非轴对称的中间形状. 研究结果表明该方法不仅可以模拟囊泡的非轴对称结构,而且具备模拟囊泡在剧烈形变下演化过程的能力. 为研究更复杂的囊泡体系,特别是生物膜的形变提供了一个重要的理论模拟方法. 关键词： 生物膜 离散空间变分法 耗散动力学 三角网格划分     

共形单步交替方向隐式时域有限差分方法及其改进

提出了一种基于共形网格技术的共形单步交替方向隐式时域有限差分(CLeapfrog ADI-FDTD)方法。与常规FDTD方法相比,此方法能够减小由于目标边界不契合网格划分而引入的阶梯近似误差,提高算法计算不规则目标时的精度;同时算法稳定性更强,计算效率更高。由于引入共形技术后显著降低了原差分法的无条件稳定性,本文利用增长矩阵本征值方法理论分析了算法的稳定性,然后采用了一种改进的共形面积计算方法,在此基础上提出了一种稳定性更高的改进的共形单步交替方向隐式时域有限差分(ICLeapfrog ADI-FDTD)方法。数值算例验证了ICLeapfrog ADI-FDTD是一种具有高稳定性和高精度的高效算法。     

定向耦合法测量非标准接口元件驻波系数

 利用网络分析仪,根据需要在设定的频率范围进行扫频测量,网络分析仪的端口1输出的微波信号经过微波传输转换器进入与待测非标准元件匹配连接的连接段（如波导）;网络分析仪的端口2连接定向耦合器,用于监测传输段内的反射微波信号。首先,在非标准接口端面连接短路面,通过网络分析仪测量反射信号在设定频点的相对幅度值;然后去掉短路面,在非标准接口端面连接待测元件,再次测量反射信号在特定频点的相对幅度值;最后根据本文推导的公式得出驻波系数。该方法的测量误差与定向耦合器的方向性（方向性系数越大越好）和待测元件驻波系数有关。将该方法运用在非标准接口匹配负载驻波系数的测量中,定向耦合器方向性系数取为40 dB,测得其驻波系数小于1.2,误差小于20%。该方法简便可行,可以用于测量常用的非标准接口元件尤其是非标准低驻波系数元件的驻波系数。     

A global strategy for solving reactive transport equations

Reactive transport models are complex nonlinear Partial Differential Algebraic Equations (PDAE), coupling the transport engine with the geochemical operator. We propose an efficient and robust global numerical method, based on a method of lines and Differential Algebraic Equations (DAE) solvers, combined with a Newton method using a powerful sparse linear solver. Numerical experiments show the performances of the method. We also propose a unified framework to describe classical methods such as Sequential Non-Iterative Approach, Sequential Iterative Approach, Direct Substitution Approach and compare them with our global method.     

无网格方法中结点搜索算法的改进

在采用无网格方法进行数值计算时,常常涉及到结点搜索问题.在处理复杂区域问题时,求解区域中分布的结点数量非常大.如果用传统的全局结点搜索算法时计算量将十分巨大,因此,提出了求解域分解法以减小结点搜索的计算量.采用该方法时,结点搜索的范围就可以由整个求解域缩减到几个相关的子域中,从而大大地减少了无网格方法计算中的结点搜索时间.用该方法对理想流体的位势流动进行了数值模拟,发现:随结点数的增加,无网格方法所用时间与有限元方法相比越来越大;但与全局结点搜索无网格方法相比,本方法大大节省了计算时间.     

定向耦合法测量非标准接口元件驻波系数

利用网络分析仪,根据需要在设定的频率范围进行扫频测量,网络分析仪的端口1输出的微波信号经过微波传输转换器进入与待测非标准元件匹配连接的连接段（如波导）;网络分析仪的端口2连接定向耦合器,用于监测传输段内的反射微波信号。首先,在非标准接口端面连接短路面,通过网络分析仪测量反射信号在设定频点的相对幅度值;然后去掉短路面,在非标准接口端面连接待测元件,再次测量反射信号在特定频点的相对幅度值;最后根据本文推导的公式得出驻波系数。该方法的测量误差与定向耦合器的方向性（方向性系数越大越好）和待测元件驻波系数有关。将该方法运用在非标准接口匹配负载驻波系数的测量中,定向耦合器方向性系数取为40 dB,测得其驻波系数小于1.2,误差小于20%。该方法简便可行,可以用于测量常用的非标准接口元件尤其是非标准低驻波系数元件的驻波系数。     

HL-RBWO-冷腔特性的一种快速算法

在传统谐振法基础上发展了一种计算慢性结构（SWS）冷腔参数的脉冲响应法,它的主要思想是利用有丰富谐波成分的窄脉冲作为激励源来代替实验系统中的扫频源,从而使得获取RBWO的色散曲线速度大大加快。这种方法使得脉冲响应法成为计算SWS冷腔参数的一种快速数值算法,更加适合于数值计算,并在研究HL-RBWO时得到有效的应用。     

HL-RBWO-冷腔特性的一种快速算法

 在传统谐振法基础上发展了一种计算慢性结构（SWS）冷腔参数的脉冲响应法，它的主要思想是利用有丰富谐波成分的窄脉冲作为激励源来代替实验系统中的扫频源，从而使得获取RBWO的色散曲线速度大大加快。这种方法使得脉冲响应法成为计算SWS冷腔参数的一种快速数值算法，更加适合于数值计算，并在研究HL-RBWO时得到有效的应用。