一种基于新的区间二型梯形模糊相似测度的多属性群决策方法

本文首先基于区间二型梯形模糊数的周长、面积、负指数距离提出了一种新的区间二型梯形模糊相似测度,讨论了其性质。其次,基于该相似测度公式分别构建了区间二型梯形模糊专家权重和属性权重确定模型,然后通过集结区间二型梯形模糊决策信息与权重信息,给出了一种基于该相似测度的群决策方法。最后,通过投资方案选择实例说明了该方法的合理性和有效性。     

Investigation of the sensitivity of turbulent closures and coupling of hybrid RANS‐LES models for predicting flow fields with separation and reattachment

Hybrid models have found widespread applications for simulation of wall‐bounded flows at high Reynolds numbers. Typically, these models employ Reynolds‐averaged Navier–Stokes (RANS) and large eddy simulation (LES) in the near‐body and off‐body regions, respectively. A number of coupling strategies between the RANS and LES regions have been proposed, tested, and applied in the literature with varying degree of success. Linear eddy‐viscosity models (LEVM) are often used for the closure of turbulent stress tensor in RANS and LES regions. LEVM incorrectly predicts the anisotropy of Reynolds normal stress at the RANS‐LES interface region. To overcome this issue, use of non‐linear eddy‐viscosity models (NLEVM) have started receiving attention. In this study, a generic non‐linear blended modeling framework for performing hybrid simulations is proposed. Flow over the periodic hills is used as the test case for model evaluation. This case is chosen due to complex flow physics with simplified geometry. Analysis of the simulations suggests that the non‐linear hybrid models show a better performance than linear hybrid models. It is also observed that the non‐linear closures are less sensitive to the RANS‐LES coupling and grid resolution. Copyright © 2016 John Wiley & Sons, Ltd.     

Peano's kernel theorem for vector-valued functions and some applications

We extend the well-known Peano Kernel Theorem to a class of linear operators L : Cⁿ⁺¹([a,b];X}→ X, X being a Branch space, which vanish on abstract polynomials of degree ≤ n. We then recover, in the abstract setting, classical estimates of remainders in polynomials interpolation and quadrature formulas. Finally, we present an application to the error analysis of the trapezoidal time discretization scheme for parabolic evolution equations.     

Extension of a class of periodizing variable transformations for numerical Integration

Class variable transformations with integer , for numerical computation of finite-range integrals, were introduced and studied by the author in the paper [A. Sidi, A new variable transformation for numerical integration, Numerical Integration IV, 1993 (H. Brass and G. Hämmerlin, eds.), pp. 359-373.] A representative of this class is the -transformation that has been used with lattice rules for multidimensional integration. These transformations ``periodize' the integrand functions in a way that enables the trapezoidal rule to achieve very high accuracy, especially with even . In the present work, we extend these transformations to arbitrary values of , and give a detailed analysis of the resulting transformed trapezoidal rule approximations. We show that, with suitable , they can be very useful in different situations. We prove, for example, that if the integrand function is smooth on the interval of integration and vanishes at the endpoints, then results of especially high accuracy are obtained by taking to be an odd integer. Such a situation can be realized in general by subtracting from the integrand the linear interpolant at the endpoints of the interval of integration. We also illustrate some of the results with numerical examples via the extended -transformation.

     

A numerical approach for solving an extended Fisher-Kolomogrov-Petrovskii-Piskunov equation

In the present paper a numerical method, based on finite differences and spline collocation, is presented for the numerical solution of a generalized Fisher integro-differential equation. A composite weighted trapezoidal rule is manipulated to handle the numerical integrations which results in a closed-form difference scheme. A number of test examples are solved to assess the accuracy of the method. The numerical solutions obtained, indicate that the approach is reliable and yields results compatible with the exact solutions and consistent with other existing numerical methods. Convergence and stability of the scheme have also been discussed.     

The Time-Scaled Trapezoidal Integration Rule for Discrete Fractional Order Controllers

In this paper, the time-scaled trapezoidal integration rule for discretizing fractional order controllers is discussed. This interesting proposal is used to interpret discrete fractional order control (FOC) systems as control with scaled sampling time. Based on this time-scaled version of trapezoidal integration rule, discrete FOC can be regarded as some kind of control strategy, in which strong control action is applied to the latest sampled inputs by using scaled sampling time. Namely, there are two time scalers for FOC systems: a normal time scale for ordinary feedback and a scaled one for fractional order controllers. A new realization method is also proposed for discrete fractional order controllers, which is based on the time-scaled trapezoidal integration rule. Finally, a one mass position 1/s^k control system, realized by the proposed method, is introduced to verify discrete FOC systems and their robustness against saturation non-linearity.     

永乐大钟梯形木架稳定性初探

对北京市大钟寺悬挂永乐大钟的梯形木架结构的稳定性进行了初步分析. 根据弹性结构稳定 性理论的能量法和中国古建筑结构``卯榫'接头抗弯性能的简化的本构模型,采用``对比法 '分析了二维梯形木架的结构稳定性;结果表明中国古建筑木架结构的``收分'形状设计对 增大木架稳定性有很大作用, 立柱``侧角'越大,稳定性越好. 收分形式设计凸现 中国古代工程技术人员的聪明智慧.     

金属覆层保偏光纤偏振器的五层波导模型及理论分析

对金属履层保偏光纤偏振器建立了五层波导变参量物理模型,设计了自适应套孔爬山法的数值计算方法求解含多层波导本征值的复超越方程,计算结果揭示了金属覆层偏光纤偏振器的物理机制,并对器件进行了优化设计,给出了实验结果。     

曹娥江径流特性及其对河口冲淤的影响

曹娥江径流具有浙闽山溪性强潮河口的若干特征,径流年际、年内变幅较大,洪水暴涨暴落,洪枯比极大,年内存在两个汛期,即梅汛期和台风汛期. 根据曹娥江径流特性,本文讨论了曹娥江河口河床洪冲枯淤变化特性,径流对潮汐大小的间接影响以及径流对曹娥江口门外主槽出口方向的影响.     

浅埋圆形孔洞附近的半圆形凸起对SH波的散射

采用"契合"的思想，给出了地下孔洞与地面上的半圆形凸起地形对SH波散射问题的 解答. 将整个求解区域分割成两部分来处理. 其一为包括半圆形凸起地形在内的一个圆形区 域I，其余为区域II. 在区域I和II中分别构造位移解，并在两个区域的"公共边界"上 实施"契合". 在区域I中构造一个上半部边界应力为零，而其余部分位移、应力任意的驻 波解，在区域II中构造出半圆形凹陷和浅埋圆孔的散射波，且要求它满足水平界面上应力 为零的约束条件. 然后再通过移动坐标，满足"公共边界"的"契合"条件和地下孔洞的边 界条件，建立起求解该问题的无穷代数方程组. 最后，给出了分析例题和数值结果，并 对其进行了讨论.