研究弹性正碰的一个代数技巧及其几何解释

给出处理弹性正碰的一个代数技巧及其几何解释,不需要具体求解方程组,可以直接得到方程组的解.     

线性代数方程迭代解法的几何解释

对线性代数方程组Ｊａｃｏｂｉ迭代解法及Ｇａｕｓｓ－Ｓｅｉｄｅｌ迭代解法的迭代格式，主对角元素限制及收敛条件等给出几何解释。     

麦克斯韦方程组超定问题的解释

麦克斯韦方程组有6个未知量,8个方程,是超定方程组.对于超定问题一般这样解释:认为两个散度方程是不独立的,只需初始时刻满足即可,之后自动满足。所以计算电磁学中只求解旋度方程,而不求解散度方程。文中指出这种解释有一个循环逻辑缺陷,从而导致此种解释不正确;在计算电磁学中两个散度方程必须求解。推广的线性相关概念用以解释偏微分方程超定问题。在这个推广的线性相关定义下,原来众多"表面"超定方程都变成了适定方程,避免了一些歧义。     

用三角函数法获得非线性Boussinesq方程的广义孤子解

找到一个合适的代换——三角函数法，将非线性Boussinesq微分方程转换为非线性代数方程组.用吴消元法求解该非线性代数方程组，从而获得一般形式Boussinesq微分方程的广义孤子解. 关键词： Boussinesq方程 吴消元法 非线性代数方程组 孤子解     

不同多边形网格计算性能的比较

利用基于多边形网格的有限容积法计算程序,考察了由三角形网格生成的三种多边形网格用于求解层流N-S方程组的数值特征.结果表明,收敛特性与多边形的构造方法无关,但计算结果的精度与网格类型有关,满足局部正交的PEBI网格精度最高,而由三角形形心相连构成的多边形精度较差.就方腔自然对流问题而言,在边界附近铺几层正交网格有利于提高努谢尔特数的精度.     

非线性耦合微分方程组的精确解析解

提出了利用耦合的Riccati方程组的某些特解构造非线性微分方程组精确解析解的一种方法.应用这种方法研究了两个耦合的常微分方程组,系统地获得了它们的一些精确解.给出了非线性浅水波近似方程组和非线性Schr?dinger-KdV方程组若干新的孤波解. 关键词： 非线性耦合方程组 Riccati方程组 符号计算 孤波     

经典物理理论中电磁波的传播规律

为了处理波传播的相关问题,引用了麦克斯韦经典理论中波的传播规律.基于麦克斯韦方程组和伽利略变换,利用微分方程来计算不同参考系下同-电磁波的传播.由于介质的运动对波动有重要的影响,所以在多普勒效应中介质的运动也被考虑进来.同时,根据该经典物理理论中的波的传播规律从不同的角度来解释迈克尔逊-莫雷实验的结果.经典物理理论中电...     

基于龙格-库塔的弹道微分方程解算的FPGA实现

针对火控计算中求解弹道微分方程组的速度、精确度以及资源配置间的冲突,设计了一种在FPGA硬件平台上实现、基于龙格-库塔的微分方程组求解器。通过在方程组之间以及方程内的计算步骤中采用多通道二级并行的方式实现算法硬件加速。实验结果表明,对于精度要求高、计算复杂度大的微分方程组,FPGA硬件实现的运算性能较传统的软件实现方式加速性能明显。     

一类非线性发展方程的复合型双孤子新解

通过下列步骤,构造了一类非线性发展方程的无穷序列复合型双孤子新解: 步骤一, 给出两种函数变换,把一类非线性发展方程化为二阶非线性常微分方程; 步骤二, 再通过函数变换, 二阶非线性常微分方程转化为一阶非线性常微分方程组,并获得了该方程组的首次积分; 步骤三, 利用首次积分与两种椭圆方程的新解与Bäcklund 变换, 构造了一类非线性发展方程的无穷序列复合型双孤子新解.     

基于Voronoi图盲区的无线传感器网络覆盖控制部署策略

针对无线传感器网络在二维平面应用场景中的覆盖控制问题, 提出了一种基于泰森盲区多边形形心的覆盖控制部署策略(blind-zone centroid-based scheme, BCBS). BCBS先对监测区域做Voronoi图划分以得到被每个传感器节点覆盖的泰森多边形, 而后根据泰森多边形顶点的覆盖情况分析得出泰森多边形内的盲区, 并构造与盲区形状相近的多边形, 最后以该多边形的几何中心作为传感器节点移动的候选目标位置, 从而达到提高网络覆盖率的目的. 仿真实验结果表明, BCBS在覆盖率、节点分布均匀性与节点覆盖效率等方面相比CBS有明显优势. 关键词： 无线传感器网络 节点覆盖 Voronoi图 多边形形心     

Balanced differential phase-shift keying detector performance: an analytical study

A simple explanation of the observed approximately 3 dB advantage of differential phase-shift keying (DPSK) balanced detection over the intensity-modulated directly detected (IM-DD) type detection that can be easily used for system engineering purposes is presented. A Gaussian approximation is used to describe the tails of the detected noisy random signals leading to an analytical explanation of the observed approximately 3 dB advantage of DPSK balanced detection over the IM-DD type detection.     

周期激励微分方程中超次谐周期轨道的不存在性

证明了在一类周期激励微分动力系统中如果存在周期解则只可能是次谐周期解，超次谐周期解不可能存在，并进一步证明了在一类平面问题中所定义的旋转（R）型超次谐周期解同样不可能存在.作为该结论的一个应用，通过考察几个典型的算例，指出平面扰动系统是否存在超次谐周期轨道不能通过现有的二阶Melnikov方法作出判断，并作出了几何上的解释.     

人工免疫危险理论中的平衡机制研究及应用

危险理论作为人工免疫学的新兴研究方向,其主要思想是通过危险信号的发现和融合来检测异常,危险信号的自适应感知是人工免疫危险理论需要解决的首要问题。从生物免疫系统保障机体生理平衡这一机理出发,将免疫系统中的平衡思想引入危险理论中,通过寻找导致信息系统失衡的变化因素,来实现危险行为的自适应发现。从机体免疫平衡理论出发,借鉴数学中的微分方法对信息系统各种行为发生时资源的占用特征进行形式化描述;从信息系统资源指标占用特征入手,实现对信息系统中各种平衡的描述,通过对失衡状态的判定来进行危险的发现,并对其实现方法和步骤做出了解释;最后以僵尸程序（SpyBot）为实验对象验证了所提出的利用免疫平衡理论检测危险方法的有效性。     

AC Conductance Through a Vibrating Molecular Dot in Kondo Regime

In the present paper, by applying the Lang-Firsov canonical transformation and the so-called non-crossing approximation technique, we investigate the joint effects of the electron-phonon interaction and an external alternating gate voltage on the transport of a quantum dot system in the Kondo regime. We find that, while the satellite Kondo resonant peaks appear in both the averaged local density of states and the differential conductance, the main Kondo peak at the Fermi energy is greatly suppressed. These results confirm the previous ones derived by other methods, such as the equation of motion solution. Furthermore, based on the picture of virtual transition between quasi-eigenstates in the system, we also give a slightly different explanation on these phenomena.     

Oscillators with chaotic behavior: An illustration of a theorem by Shil'nikov

Using an explicit one-parameter family of differential equations describing oscillators with feedback effects, we prove the existence of values of the parameters such that there exist infinitely many unstable periodic orbits of saddle type. The proof relies on a theorem by Shil'nikov which we propose as an explanation for the origin and structure of the chaotic behavior displayed by many well-known third-order differential systems.     

时间非对称外力驱动分数阶布朗马达的定向输运

本文研究了周期对称势中时间非对称外力驱动的布朗粒子输运现象, 建立了分数阶布朗马达输运模型. 其中外力是零均值的, 而分数阶阶数则刻画了客观环境的非均匀性程度. 通过将模型离散化进行数值模拟, 讨论了分数阶阶数、系统参量和外部参量与定向流之间的依赖关系. 研究表明, 即使没有倾斜势场的作用, 时间非对称外力也可以诱导系统产生定向输运; 输运速度随分数阶阶数的增大而单调递增; 当阶数固定时, 系统的输运速度会随着势垒高度、噪声强度非单调变化, 表现出广义随机共振现象. 分析指出, 分数阶郎之万方程所刻画的输运现象是在整数阶模型基础上的一个推广, 进而为输运现象提供了一个可能更为真实的模型.     

Anomalous increase of thermopower in epitaxial graphene

Thermoelectric effect in epitaxial graphene formed on the surface of a semiconductor is considered in the context of the Davydov model. The approach based on the Kubo formula for the conductivity and differential thermopower is used. It is shown that near the edges of the semiconductor bandgap, the thermopower of epitaxial graphene increases by more than four times as compared to the thermopower near the Dirac point. A possible explanation of this effect is given.     

Analysis of long crack lines in paper webs

A differential cluster variation method (DCVM) is proposed for analysis of spinoidal decomposition in alloys. In this method, lattice symmetry operations in the presence of an infinitesimal composition gradient are utilized to deduce the connection equations for the correlation functions and to reduce the number of independent variables in the cluster variation analysis. Application of the method is made to calculate the gradient energy coefficient in the Cahn-Hilliard free energy function and the fastest growing wavelength for spinodal decomposition in Al-Li alloys. It is shown that the gradient coefficient of congruently ordered Al-Li alloys is much larger than that of the disordered system. In such an alloy system, the calculated fastest growing wavelength is approximately 10 nm, which is an order of magnitude larger than the experimentally observed domain size. This may provide a theoretical explanation why spinodal decomposition after a congruent ordering is dominated by the antiphase boundaries.Received: 17 November 2003, Published online: 2 April 2004PACS: 64.75. + g Solubility, segregation, and mixing; phase separation - 81.30.-t Phase diagrams and microstructures developed by solidification and solid-solid phase transformations - 05.70.Ln Nonequilibrium and irreversible thermodynamics     

等离子体驱动碎片加速器中脉冲充气电磁阀

在等离子体碎片加速器中设计和安装了脉冲充气电磁阀,气体脉冲的上升时间小于0.1ms,脉宽为0.2～2ms之间,一次脉冲进气量是1021～1022个气体分子.阀头的运动可用一组偏微分方程来描述,计算结果可以合理解释充气参数与工作电压关系中的跳变的出现.     

Oscillations appearing during sorption of amino acids on ion-exchanger grains on the basis of mathematical simulation

Oscillations in concentration and grain size could occur in the process of amino acid sorption on ion-exchanger grains. This phenomenon has been observed in several experimental works. The theoretical explanation of the phenomenon was given earlier by means of an elementary model. In this work the process was studied using a physically more sophisticated model represented by partial differential equations as the result of mathematical simulation. The structure of oscillations inside the grain could not be determined experimentally and also is studied in this work.