广义立方双色散方程解的渐近性质

本文研究广义立方双色散方程的初边值问题,它包括了几类双色散方程以及Bq,IBq,IMBq方程作为特殊情形,当方程非线性项满足某些条件时,利用等价变换和改进的积分估计法证明了问题整体广义解按时间的指数形式衰减为零.最后,将本文定理结论应用到实际模型中,得到了问题的解具有衰减行为时方程参数应满足的条件.     

Reissner板弯曲问题的渐近解

本文从分析Ｒｅｉｓｓｎｅｒ板理论与Ｋｉｒｃｈｈｏｆｆ板理论的关系入手，导出了对Ｒｅｉｓｓｎｅｒ板问题的求解，可用摄动技术转化为相应边界条件下求解一系列Ｋｉｒｃｈｏｆｆ板问题，最后给出了算例也证明了本文方法具有简单，精度高的特点。     

细胞繁殖反应扩散型方程的渐近解

给出了细胞繁殖反应扩散型方程的渐近解，并讨论了其一致有效性。     

脉冲时滞积分-微分系统解的非振动性和渐近性

讨论了脉冲时滞积分-微分系统解的非振动性和渐近性，得到了时滞积分-微分系统在脉冲扰动下解的非振动性和渐近性的充分条件。     

在奇异性区域上的特征值问题的渐近解

本文考虑Ｈｅｌｍｈｏｔｚ方程△Ｕ＋λＵ＝０，在奇异地依赖于小参数的一个区域上的解。文章采用摄动方法，求出了特征值的二阶渐近解。     

双线性时间序列模型高阶矩的渐近性质

讨论了一般双线性时间序列模型BL（R，r,Q,q）的高阶（2u阶，u=1，2，…）平稳解存在的充分条件，并证明了高阶矩估计量的相和性和渐近正态性。     

求强非线性系统共振解的渐近法

本文通过引入参数变换α=ε/(υ^2 ε),并假设ω0^2=(pv／q)^2 α△，把强非线性系统转化为弱非线性系统，再将解展开为傅氏级数，利用参数待定法可方便地求出强非线性系统的共振解。算例表明近似解与数值解非常接近。     

具有边界层和角层现象的半线性边值问题的渐近解

本文研究二阶半线性速值问题的奇摄动,在出现边界层和角层的现象下,导出边位问题解的n阶一致有效渐近近似式,并分别按最大模和L_2范数作出余项的估计。     

一类具耗散项的非线性四阶波动方程的整体弱解及其渐近性质

本文讨论一类具耗散项的非线性四阶波动方程的初边值问题.该问题来源于不同的物理背景,例如平面中固定金属板的运动、梁的振动,以及水波的相互作用等都涉及这一问题.利用位势井理论和紧致性方法,我们证明了当初始能量为正但有适当上界,非线性项满足假设条件时,该问题整体弱解的存在性.并在此基础上,利用方程中耗散项的作用和一个微分不等式得到了解的渐近性质.     

反应堆用磁致伸缩材料设计

简要介绍了磁致伸缩现象及几类常见的磁致伸缩材料,并对反应堆用磁致伸缩材料做了详尽的设计;特别是对磁致伸缩材料的抗辐照性能、磁致伸缩性能及高温性能做了详尽地分析.     

Existence and global asymptotic behaviour of positive periodic solution of an SI epidemic model with delays

In this paper, a periodic SI model with delays is studied. By utilizing the Lyapunov–Krasovskii functional method, a novel explicit criterion for the existence and uniqueness and global asymptotic stability of positive periodic solution is established. Finally, a numerical example is given to illustrate the effectiveness of the obtained results.     

船用核反应堆提棒外推临界优化研究

因稳定时间受限，传统的倍增公式导出的外推临界公式计算结果大于实测值，偏危险；文中根据新的中子倍增公式导出了外推临界计算的新公式，实例计算表明，该公式比传统的外推临界公式精确且偏安全．     

Development of a path model for human‐induced unplanned reactor trips in nuclear power plants

A simple path model for human‐induced unplanned reactor trips in nuclear power plants (NPPs) is proposed. The path model consists of four plant states and seven transitions between the four plant states, and describes how NPPs in the normal operation state result in unplanned reactor trips due to human errors. By applying the simple path model to historic unplanned reactor trip data, it is found that two out of five paths take more than 80% of the human‐induced unplanned reactor trips. The proposed path model for human‐induced unplanned reactor trips in NPPs is expected to provide insights into how human‐induced unplanned reactor trips can be reduced by cutting the critical paths to human‐induced unplanned reactor trips. Copyright © 2010 John Wiley & Sons, Ltd.     

金属基复合材料热弹塑性变分渐近细观力学模型

基于变分渐近法建立具有周期性微结构的金属基复合材料（MMCs）细观力学模型及相应的增量方程,以准确预测其典型的热弹塑性行为和初始屈服面。利用细、宏观尺度比很小的特点,对单胞变分能量泛函变化进行渐近扩展,计算得到有效瞬时弹塑性刚度矩阵和热应力矩阵;利用迭代均质化及局域化技术模拟MMCs的非线性热弹塑性性能,并通过有限元技术实现相应的数值模型。算例分析表明:该模型能较好地预测MMCs的初始屈服面,并模拟热弹塑性耦合行为,研究成果为MMCs的进一步研究和实际应用提供了技术支撑。      

Computation of flow and thermal fields in a model CVD reactor

Mixing of coaxial jets within a tube in the presence of blockage has been numerically studied. This configuration is encountered during the modelling of flow and heat transfer in CVD (chemical vapour deposition) reactors. For the conditions prevailing in the reactor, the Reynolds numbers are low and flow can be taken to be laminar and incompressible. The unsteady forms of the governing equations have been solved by a finite volume method that can treat complex three-dimensional geometries. The algorithm is a two-step procedure, wherein the first step predicts the velocity field using an assumed pressure field. The second step corrects the fields using a Poisson equation to obtain the pressure corrections. Advection terms have been treated by a hybrid upwind-central difference technique. The computer code developed is fully three-dimensional, though most computations of the present study have been carried out for two-dimensional geometry. Results have been obtained in the form of velocity vector plots, wall shear stress variation on the block and the tube wall, isotherms and temperature profiles. The flow and heat transfer characteristics of jet mixing have been explored in terms of the Reynolds number, the jet velocity ratio, the axial position of the block, and the blockage ratio. The results obtained show that a proper combination of the process parameters can lead to an improved performance of the CVD reactor.     

一类具阻尼项的三阶非线性中立型泛函微分方程的振动性和渐近性

研究一类具阻尼项的三阶非线性中立型连续分布时滞泛函微分方程解的振动性和渐近性,利用广义Riccati变换、积分平均技巧和一些分析技巧,对α≠β的情况,建立了一组保证该方程每一解振动或者收敛到零的充分条件,所得结果改进和推广了最新文献中的一些熟知的准则.     

Geometric method for global stability and repulsion in Kolmogorov systems

A class of autonomous Kolmogorov systems that are dissipative and competitive with the origin as a repellor are considered when each nullcline surface is either concave or convex. Geometric method is developed by using the relative positions of the upper and lower planes of the nullcline surfaces for global asymptotic stability of an interior or a boundary equilibrium point. Criteria are also established for global repulsion of an interior or a boundary equilibrium point on the carrying simplex. This method and the theorems can be viewed as a natural extension of those results for Lotka-Volterra systems in the literature.     

On the Laplace transform of a matrix of fundamental solutions for thermoelastic plates

The Laplace transform of a matrix D(x,t) of fundamental solutions for the partial differential operator describing the time-dependent bending of thermoelastic plates with transverse shear deformation is constructed, and its asymptotic behavior near the origin is investigated. The differential system is reduced to an algebraic one through the application of the Laplace and then Fourier transformations, and all possible cases of roots of the determinant of the latter system are considered. It is shown that in every case, the asymptotic expansion of near the origin has the same dominant term. This is an important step in the construction of boundary-element methods for the above time-dependent model because it determines the nature of the singularity of the kernel of the boundary-integral-equations associated with various initial-boundary-value problems for the governing system.     

Global asymptotic stability in a model of networks

Global asymptotic stability is of importance from a theoretical as well as an application point of view in several fields. We study a system of cubic polynomials that models biological networks. We classify the equilibria and show that the property that the interconnection matrix is Lyapunov diagonally stable is a key feature that determines convergence to a single equilibrium. The results are applied to chains of negative edges, cycles, and to interconnected graphs. We give numerical examples and study network graphs obtained from a model of the Drosophila circadian clock.