Numerical Energy Conservation for Multi-Frequency Oscillatory Differential Equations

The long-time near-conservation of the total and oscillatory energies of numerical integrators for Hamiltonian systems with highly oscillatory solutions is studied in this paper. The numerical methods considered are symmetric trigonometric integrators and the St?rmer–Verlet method. Previously obtained results for systems with a single high frequency are extended to the multi-frequency case, and new insight into the long-time behaviour of numerical solutions is gained for resonant frequencies. The results are obtained using modulated multi-frequency Fourier expansions and the Hamiltonian-like structure of the modulation system. A brief discussion of conservation properties in the continuous problem is also included. AMS subject classification (2000) 65L05, 65P10     

带缓冲器的巴黎地铁定价策略

本在巴黎地铁定价(PMP(Paris Metro Pricing))的基础上研究了一种带有缓冲器的巴黎地铁定价策略。同样将网络分成几个逻辑上独立的不同部分，每一个部分制定不同的价格，各部分仅在价格上有区别。但是额外增加一个适合“中性消费”需求的缓冲器，使得“中性消费”可以先向缓冲器提交服务请求，而后由ISP网络提供商根据各部分的实际负载状况将其分配到合适的服务节点。最后通过仿真说明与巴黎地铁相比，带有缓冲器的巴黎地铁定价策略在网络拥塞控制与网络资源分配等方面有更高的效率。     

Error analysis of the numerical solution of split differential equations

The operator splitting method is a widely used approach for solving partial differential equations describing physical processes. Its application usually requires the use of certain numerical methods in order to solve the different split sub-problems. The error analysis of such a numerical approach is a complex task. In the present paper we show that an interaction error appears in the numerical solution when an operator splitting procedure is applied together with a lower-order numerical method. The effect of the interaction error is investigated by an analytical study and by numerical experiments made for a test problem.     

High accuracy time and space transform method for advection–diffusion equation in an unbounded domain

A new numerical method called high accuracy time and space transform method (TSTM) is introduced to solve the advection–diffusion equation in an unbounded domain. By a spatial transform, the advection–diffusion equation in the unbounded domain Rⁿ is converted to one on the bounded domain [?1, 1]ⁿ, and the Laplace transform is applied to eliminate time dependency. The consequent boundary value problem is solved by collocation on Chebyshev points. To face the well‐known computational challenge represented by the numerical inversion of the Laplace transform, Talbot's method is applied, consisting of numerically integrating the Bromwich integral on a special contour by means of trapezoidal or midpoint rules. Numerical experiments illustrate that TSTM has exponential rate in time and space. Copyright © 2008 John Wiley & Sons, Ltd.     

一个创新网络动态性的仿真模型

提出了一个关于创新网络动态性研究的仿真模型,模型较为全面地考察了网络的形成过程和不同的角色在创新和网络中的作用,研究结论指出:网络的形成是由于创新主体为适应创新的复杂性而寻求资源互补效应的动态相互作用的结果,中小型企业的个体在网络演化的早期和中期起了重要的作用,合作体的作用主要发挥在中后期.     

Numerical techniques for finding equilibrium in von Neumann’s model

Numerical methods for finding an equilibrium position in von Neumann’s multisector economy model are proposed. They can be implemented using computers with floating-point arithmetic. The proposed methods are based on reducing the problem to solving the corresponding matrix games.     

一类三阶牛顿变形方法

A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton's method,are given.Their convergence properties are proved.They are at least third order convergence near simple root and one order convergence near multiple roots.In the end,numerical tests are given and compared with other known Newton's methods.The results show that the proposed methods have some more advantages than others.They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.     

流量大小对混合流场特性等的影响

 在主、副气流各组份的流量比不变的情况下，改变输入氧碘化学激光器（COIL）光腔总气流流量，数值模拟给出了COIL拉伐尔喷管主、副气流混合状况和各物理量的分布等，通过对这些结果进行对比分析得出：输入COIL光腔总气流流量增加三倍，氧碘气流的混合状况稍稍变差，但Mach数和密度等的分布和变化规律基本不变。     

Quantum mechanical ab initio simulation of the electron screening effect in metal deuteride crystals

In antecedent experiments the electron screening energies of the d+d reactions in metallic environments have been determined to be enhanced by an order of magnitude in comparison to the case of gaseous deuterium targets. The analytical models describing averaged material properties have not been able to explain the experimental results so far. Therefore, a first effort has been undertaken to simulate the dynamics of reacting deuterons in a metallic lattice by means of an ab initio Hartree-Fock calculation of the total electrostatic force between the lattice and the successively approaching deuterons via path integration. The calculations have been performed for Li and Ta, clearly showing a migration of electrons from host metallic to the deuterium atoms. However, in order to avoid more of the necessary simplifications in the model the utilization of a massive parallel supercomputer would be required.     

Numerical simulation of tidal bore in Hangzhou Gulf and Qiantangjiang

In this paper, a new numerical model, based on a set of non‐linear shallow water equations is developed for the simulation of the formation and evolution of tidal bore in the Hangzhou Gulf and Qiantangjiang river of China. The numerical method and boundary conditions are described in detail. The method is validated against analytical solutions and experimental data. Simulation of the actual tidal bore in Hangzhou Gulf and its propagation in the Qiantangjiang river are performed. Numerical results show that this proposed method is effective for the prediction of tidal bore and current flow at the entrance of Qiantangjiang river. Copyright © 2001 John Wiley & Sons, Ltd.