具无穷时滞中立型泛函微分方程的解的存在性、唯一性及连续相依性

本文研究了无穷时滞中立型泛函微分方程的解的局部理论.为了便于应用,得到了具无穷时滞中立型泛函微分方程的解的存在性、唯一性及关于初值的连续相依性.     

Bayesian statistical data assimilation for ecosystem models using Markov Chain Monte Carlo

This study considers advanced statistical approaches for sequential data assimilation. These are explored in the context of nowcasting and forecasting using nonlinear differential equation based marine ecosystem models assimilating sparse and noisy non-Gaussian multivariate observations. The statistical framework uses a state space model with the goal of estimating the time evolving probability distribution of the ecosystem state. Assimilation of observations relies on stochastic dynamic prediction and Bayesian principles. In this study, a new sequential data assimilation approach is introduced based on Markov Chain Monte Carlo (MCMC). The ecosystem state is represented by an ensemble, or sample, from which distributional properties, or summary statistical measures, can be derived. The Metropolis-Hastings based MCMC approach is compared and contrasted with two other sequential data assimilation approaches: sequential importance resampling, and the (approximate) ensemble Kalman filter (including computational comparisons). A simple illustrative application is provided based on a 0-D nonlinear plankton ecosystem model with multivariate non-Gaussian observations of the ecosystem state from a coastal ocean observatory. The MCMC approach is shown to be straightforward to implement and to effectively characterize the non-Gaussian ecosystem state in both nowcast and forecast experiments. Results are reported which illustrate how non-Gaussian information originates, and how it can be used to characterize ecosystem properties.     

基于N-S方程的航行船舶辐射问题数值模拟

基于N-S(Navier-Stokes)方程,进行了航行船舶辐射问题的数值模拟,包括强制垂荡和强制纵摇的模拟.计算了船舶垂荡和纵摇的附加质量和阻尼.数值模拟中,控制方程--BANS(Reynolds Averaged Navier-Stokes)方程和连续性方程使用有限体积法离散,非线性自由面采用VOF方法处理.文中给出了以不同航速前进的船舶强制垂荡和纵摇的力与力矩,以及船舶垂荡和纵摇的附加质量系数和阻尼系数,并与DUT(Delft University of Technology)的试验数据进行了比较,二者吻合良好.     

关于连续正整数Diophantine方程的正整数解

连续正整数Diophantine方程xn+(x+1)n+…+(x+h)n=(x+h+1)n的正整数解问题,是一个迄今为止尚未彻底解决的数论难题。目前已知的结果是:①当6≤n≤33时;②当n>3且为奇数时;③当34≤n≤200且为偶数时,该方程均无正整数解。采用多种素数模筛法证明了:当200相似文献   

扰动微分方程在优化约束问题中的应用

研究了扰动微分方程在优化约束问题中的应用，指出对某些类型的奇解扰动后不存在部分变量收敛到优化约束问题的可行点。     

Residential location,vehicle ownership and travel in Asia: a comparative analysis of Kei-Han-Shin and Kuala Lumpur metropolitan areas

The study examines the relationships between residential location, vehicle ownership and mobility in two metropolitan areas of Asia, Kei-Han-Shin area of Japan and Kuala Lumpur area of Malaysia. It shows that, behind apparent similarities of household auto ownership and travel time expenditure per household member, there are many causal relationships that are distinct between the areas. The similarities and differences between the two areas point to the conjecture that the evolution of a metropolitan area may be unique and path dependent, being heavily influenced by the history and culture of the locale, spatial and geographical constraints, and historical progression in infrastructure development.

不同时空格式在求解Boussinesq水波模型中的应用

为了解不同时间空间差分格式在常用的二阶或四阶Boussinesq模型中的应用,针对4组近似到0（旷）阶完全非线性的二阶或四阶色散性的高阶Boussinesq水波方程,在非交错网格下,利用Crank-Nicolson格式、蛙跳格式、混合四阶Adams-Bashforth-Moulton格式,建立不同的数学模型。利用这些数值模型模拟波浪在潜堤上的传播变形,通过数值结果与试验结果的比较．考察时间格式及空间格式对模型的影响。结果表明：对同一方程,混合四阶Adams-Bashforth-Mouhon格式和Crank-Nicolson格式均能取得较好模拟效果,蛙跳格式的模拟效果最差;二阶Boussinesq模型采用追赶法求解已能满足要求;对四阶Boussineq模型,二阶空间导数色散项亦采用四阶精度,其数值效果会更好。     

M—C屈服准则的应力场及其唯一性

基于三维问题的库仑屈服函数f,证明了max{f}=0就是M—C屈服准则,并获得了M—C屈服准则相应的应力分量表达式。得出了简化M—C屈服准则对应的应力分量表达式,这是表述岩土极限状态的一套完备的数学方程;和平衡方程一起构成极限分析问题的一套完备的基本方程。基于文中应力分量表达式与基于库仑屈服准则的极限分析是一致的,相应的应力场是唯一的。     

弧形防浪墙的迎浪面波压力数值模拟

以Navier-Stokes方程为控制方程,使用VOF方法追踪自由液面,对FLUENT进行二次开发,将各功能区的源项表达式添加到动量方程中,从而实现动量源造波和消波。模拟二阶Stokes波作用下不同断面形式防浪墙的流场和波压力,并将计算结果与物理模型试验数据进行对比,结果吻合较好。比较直立式和弧形防浪墙波浪压力数值计算结果可以发现,在相同水位和波浪要素情况下,作用在圆弧墙上的最大点压强明显大于直立墙,而且最大压强发生在圆弧部分,工程中应该对圆弧部分进行加固处理。     

A porous cell method for the simulation of fluid-solid interactions

There are many ways of describing a solid,porous or fluid region of the computational domain when solving the Navier-Stokes equations(NSE)for flow motions.Amongst these the porous cell method is one of the most flexible approaches.In this method,a parameter is defined as a ratio of the volume open to water and air in a calculation cell to its cell volume.In the calculation,the same numerical procedure is applied to every cell and no explicit boundary conditions are needed at solid boundaries.The method is used to simulate flow through porous media,around solid bodies and over a moving seabed.The results compare well with experimental data and other numerical results.In our future work the porous cell method will be applied to more complex fluid-solid interaction situations.