The evolution of traveling waves in a simple isothermal chemical system modeling quadratic autocatalysis with strong decay

In this paper, we study a reaction–diffusion system for an isothermal chemical reaction scheme governed by a quadratic autocatalytic step A+B→2B$A+B\to 2B$ and a decay step B→C$B\to C$, where A, B, and C are the reactant, the autocatalyst, and the inner product, respectively. Previous numerical studies and experimental evidences demonstrate that if the autocatalyst is introduced locally into this autocatalytic reaction system where the reactant A initially distributes uniformly in the whole space, then a pair of waves will be generated and will propagate outwards from the initial reaction zone. One crucial feature of this phenomenon is that for the strong decay case, the formation of waves is independent of the amount of the autocatalyst B introduced into the system. It is this phenomenon of KPP-type which we would like to address in this paper. To study the propagation of reactant and autocatalyst analytically, we first use the tail behavior of waves to construct a pair of generalized super-/sub-solutions for the approximate system of the autocatalytic reaction system. Note that the autocatalytic reaction system does not enjoy comparison principle. Together with a family of truncated problems, we can establish the existence of a family of traveling waves with the minimal speed. Second, we use this pair of generalized super-/sub-solutions to show that the propagation of waves is fully determined by the rate of decay of the initial data at infinity in the sense of Aronson–Weinberger formulation, which in turn confirms the aforementioned numerical and experimental results.     

具有阶段结构和非线性种群内制约关系竞争系统的行波解

构造并研究一类具有非局部时滞和非线性种内制约关系的竞争系统的反应扩散模型.利用Wang,Li和Ruan建立的非局部时滞反应扩散方程组波前解存在性的理论,证明了连接两个边界平衡解的行波解的存在性.     

毫米波行波管电子光学系统的设计

 利用基于虚边界元法的VBGUN程序和基于边界元法的MOM程序，对一折叠波导毫米波行波管的电子光学系统进行了设计。设计过程中使用计算相关性系数的方法调节参数，通过计算敏感性系数以考察加工误差带来的影响。设计过程显示：低导流系数、小束腰、高压缩比的毫米波电子枪的层流性与电极尺寸相关性很大，易受到加工误差的影响；聚束系统的设计难点在于轴上峰值磁感应强度要受到漂移管半径的限制，这一点可以通过提高工作电压和降低电流来平衡，因此它的设计必须与慢波结构的设计同时进行。     

Genetic algorithms for the traveling salesman problem

This paper is a survey of genetic algorithms for the traveling salesman problem. Genetic algorithms are randomized search techniques that simulate some of the processes observed in natural evolution. In this paper, a simple genetic algorithm is introduced, and various extensions are presented to solve the traveling salesman problem. Computational results are also reported for both random and classical problems taken from the operations research literature.     

模拟退火算法的改进及其应用

模拟退火算法是随机优化近似算法。本文首先介绍其物理背景和一般形式，然后通过对算法增加记忆和返回两个功能以及在算法之后链接一个局部搜索过程，改善了算法性能，接着将改进算法应用于解旅游商问题，最后对该算法作简要的性能评论。     

An efficient genetic algorithm for the traveling salesman problem with precedence constraints

The traveling salesman problem with precedence constraints (TSPPC) is one of the most difficult combinatorial optimization problems. In this paper, an efficient genetic algorithm (GA) to solve the TSPPC is presented. The key concept of the proposed GA is a topological sort (TS), which is defined as an ordering of vertices in a directed graph. Also, a new crossover operation is developed for the proposed GA. The results of numerical experiments show that the proposed GA produces an optimal solution and shows superior performance compared to the traditional algorithms.     

Radiation Losses of Bent Planar Waveguides

Bent planar waveguides are conformally mapped into straight figures with equivalent index profile. Airy functions of traveling-wave form are introduced to express the radiation mode in the outer cladding region. Calculation results of radiation loss are confirmed to give excellent accuracy.     

Identification of non-optimal arcs for the travelling salesman problem

Conditions are presented for the identification of (directed) arcs for the traveling salesman problem, that can be eliminated with at least one optimal solution remaining. The conditions are not based on lower or upper bounds; the presence of an identified arc in a solution implies that the solution is not 3-optimal. An example illustrates how to use the conditions.     

Transmission line based struck string model

The analogy of a vibrating string to an electrical transmission line with the correspondences of the displacement to the voltage and the rigid end to the short circuit and the calculations for the hammer–string force in the well known finite difference form of the wave equation for a struck string are applied to build a transmission line based struck string model. The proposed model is validated by showing that the displacements and the forces exerted on the string at the contact with a hammer from the proposed model are consistent with those from the finite difference form.