Maslov-type index and brake orbits in nonlinear Hamiltonian systems

In this paper, we study the Maslov-type index theory for linear Hamiltonian systems with brake orbits boundary value conditions and its applications to the existence of multiple brake orbits of nonlinear Hamiltonian systems.     

基于矩阵初等变换的n元函数极值的快速判别法

给出了 n元函数极值的一个充分条件 ,并结合矩阵的初等变换建立了 n元函数极值的一种快速判别法 ,最后给出了一个例子     

Solution of the hyperbolic mild‐slope equation using the finite volume method

A finite volume solver for the 2D depth‐integrated harmonic hyperbolic formulation of the mild‐slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov‐type second‐order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild‐slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality‐free. Copyright © 2003 John Wiley & Sons, Ltd.     

一类三参数混沌动力学系统模型及其在经济增长研究中的应用

从非线性自回归模型Xt+1=-αXtλ+1+βXt+γ出发,通过变量替换Xt=aYt,推出三参数混沌动力学系统模型Yt+1=kYt(1-Ytλ)+c;采用线性回归与非线性回归相结合的改进的混合法,对模型参数作了估计;实际研究表明,该模型可以用于对国内生产总值GDP增长的研究.     

郑开大道顶进箱涵临时支撑结构设计

下穿京港澳高速公路顶推箱涵是郑开大道的关键控制性工程,顶进过程中箱涵的裂缝控制是该顶推工程成功与否的重要因素。经实践结果表明,临时支撑结构达到了预期的目的,值得应用推广。     

基于爆轰波原理声源定位方法初探

基于弹丸发射时所发出的爆轰波,利用传感器接收时差信息,从而确定声源位置。本文建立了该声源定位反问题的物理和数学模型,并依据该模型寻求适当的数值解法,最后针对延拓-广义逆法声源定位问题进行了演算和简要分析。     

Implementation of some higher-order convection schemes on non-uniform grids

A generalized formulation is applied to implement the quadratic upstream interpolation (QUICK) scheme, the second-order upwind (SOU) scheme and the second-order hybrid scheme (SHYBRID) on non-uniform grids. The implementation method is simple. The accuracy and efficiency of these higher-order schemes on non-uniform grids are assessed. Three well-known bench mark convection-diffusion problems and a fluid flow problem are revisited using non-uniform grids. These are: (1) transport of a scalar tracer by a uniform velocity field; (2) heat transport in a recirculating flow; (3) two-dimensional non-linear Burgers equations; and (4) a two-dimensional incompressible Navier-Stokes flow which is similar to the classical lid-driven cavity flow. The known exact solutions of the last three problems make it possible to thoroughly evaluate accuracies of various uniform and non-uniform grids. Higher accuracy is obtained for fewer grid points on non-uniform grids. The order of accuracy of the examined schemes is maintained for some tested problems if the distribution of non-uniform grid points is properly chosen.     

Improved experimental tracking techniques for validating discrete element method simulations of tumbling mills

We report on further developments in the three-dimensional tracking of a particle deep within the tumbling ball charge of an experimental mill. The experimental X-ray program employing the use of bi-planar X-ray angiography now includes the tracking of a typical 6 mm bulk charge particle in three dimensions with a spatial resolution that is accurate to within 0.15 mm. The improved experimental tracking techniques presented were developed for the purpose of generating accurate three-dimensional particle trajectory data against which to validate a numerical method for the simulation of discrete media, namely the discrete element method (DEM). These improvements are complimented with techniques for comparing charge profiles between numerical DEM simulations and three-dimensional experimental trajectory data.     

Solving large-scale semidefinite programs in parallel

We describe an approach to the parallel and distributed solution of large-scale, block structured semidefinite programs using the spectral bundle method. Various elements of this approach (such as data distribution, an implicitly restarted Lanczos method tailored to handle block diagonal structure, a mixed polyhedral-semidefinite subdifferential model, and other aspects related to parallelism) are combined in an implementation called LAMBDA, which delivers faster solution times than previously possible, and acceptable parallel scalability on sufficiently large problems. This work was supported in part by NSF grants DMS-0215373 and DMS-0238008.     

New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values

New variants of the generalized level method for minimization of convex Lipschitz functions on a compact set with a nonempty interior are proposed. These variants include the well-known generalized and classical level methods. For the new variants, an estimate of the convergence rate is found, including the variants in which the auxiliary problems are solved approximately.