A dual ascent approach for steiner tree problems on a directed graph

The Steiner tree problem on a directed graph (STDG) is to find a directed subtree that connects a root node to every node in a designated node setV. We give a dual ascent procedure for obtaining lower bounds to the optimal solution value. The ascent information is also used in a heuristic procedure for obtaining feasible solutions to the STDG. Computational results indicate that the two procedures are very effective in solving a class of STDG's containing up to 60 nodes and 240 directed/120 undirected arcs. The directed spanning tree and uncapacitated plant location problems are special cases of the STDG. Using these relationships, we show that our ascent procedure can be viewed as a generalization ofboth the Chu-Liu-Edmonds directed spanning tree algorithm and the Bilde-Krarup-Erlenkotter ascent algorithm for the plant location problem. The former comparison yields a dual ascent interpretation of the steps of the directed spanning tree algorithm.     

Computing a longest common subsequence for a set of strings

The known 2-string LCS problem is generalized to finding a Longest Common Subsequence (LCS) for a set of strings. A new, general approach that systematically enumerates common subsequences is proposed for the solution. Assuming a finite symbol set, it is shown that the presented scheme requires a preprocessing time that grows linearly with the total length of the input strings and a processing time that grows linearly with (K), the number of strings, and () the number of matches among them. The only previous algorithm for the generalized LCS problem takesO(K·|S ₁|·|S ₂|·...|S _k |) execution time, where |S _i | denotes the length of the stringS _i . Since typically is a very small percentage of |S ₁|·|S ₂|·...·|S _k |, the proposed method may be considered to be much more efficient than the straightforward dynamic programming approach.     

岩体结构识别的三角多项式函数模式图方法

通过构造工程岩体结构分类的三角多项式函数,基于实际工程的各种岩体结构的典型特征,建立数学模型,并利用其数学特征所展示的韵律进行岩体结构类型的划分和识别。应用这种方法对长江三峡工程坝基块状岩体及清江高坝洲层状坝基岩体典型岩体结构建立三角模式图,作为各种类型岩体结构的标准模式图。岩体结构识别的三角多项式函数模式图方法为工程岩体结构类型的定量划分提供了一种有效的方法。     

Simulation of elastic wave propagation using cellular automata and peridynamics,and comparison with experiments

Peridynamics is a non-local continuum mechanics formulation that can handle spatial discontinuities as the governing equations are integro-differential equations which do not involve gradients such as strains and deformation rates. This paper employs bond-based peridynamics. Cellular Automata is a local computational method which, in its rectangular variant on interior domains, is mathematically equivalent to the central difference finite difference method. However, cellular automata does not require the derivation of the governing partial differential equations and provides for common boundary conditions based on physical reasoning. Both methodologies are used to solve a half-space subjected to a normal load, known as Lamb’s Problem. The results are compared with theoretical solution from classical elasticity and experimental results. This paper is used to validate our implementation of these methods.     

红石河堰塞湖漫顶溃坝风险评估

四川省青川县红石河堰塞湖是2008年5月12日汶川大地震形成的34座大型堰塞湖之一,是由东河口滑坡堵塞红石河形成的。该堰塞体高度约50 m、宽度约250 m、顺河向长度约500 m、形成的最大库容约400万m3。本文作者对红石河堰塞体做了较详尽的现场试验,包括土的冲蚀试验、土的基本物性试验等。基于现场试验数据,对土的冲蚀性和漫顶溃坝风险做了详细的分析。结果显示,从土的抗冲蚀性角度考虑,只要有水溢出就会有土体被冲蚀,这说明红石河堰塞体的漫顶溃决可能性较高。本文还提出经验公式来预测红石河堰塞体漫顶的溃决时间,大约为4.5d,如果考虑到大石块对抗冲蚀稳定性的有利影响,这一数值会增大。此外,还研究了溃决深度随时间的变化规律。     

四川某水库右坝肩滑坡成因机制及稳定性分析

拟建水库右坝肩处于由砖红色砂岩夹薄层或透镜状泥岩、粉砂质泥岩构成的斜向V形河谷中,无明显断层构造,雨水充沛且存在一古滑坡,经过调查,滑坡主要由滑坡堆积体和滑动面以及其下方的扰动带组成,滑坡区发育的纵向和横向结构面以及岩层面构成一楔形槽。认为滑坡的成因是暴雨下楔形槽内控制的滑移-拉裂破坏。经过定性分析,古滑坡天然状态是稳定的。采用极限平衡法计算古滑坡在天然状态、地震作用以及暴雨等工况下的稳定系数分别为1.45、1.39及1.27,由此可知滑坡在天然状态下是稳定的,地震作用对其稳定性影响不大,但暴雨作用下滑坡的稳定性有所降低。最后通过数值模拟再现了现阶段古滑坡的应力应变场和变形破坏特征。     

Development of a fully Lagrangian MPS-based coupled method for simulation of fluid–structure interaction problems

A fully Lagrangian particle-based method is developed for simulating the FSI (Fluid–Structure Interaction) problems corresponding to incompressible fluid flows and elastic structures. First, the developed elastic structure model is verified by static and dynamic tests corresponding to a simple cantilever beam. The simulation results are compared with analytical and other researchers׳ numerical solutions. Then, the structure model is carefully coupled with a fluid model comprising of the so-called PNU-MPS (Pusan-National-University-modified Moving Particle Simulation) method and several recently developed enhanced schemes. The coupled fluid–structure method is applied to a dam break with an elastic gate and a violent sloshing flow with a hanging rubber baffle. The results of simulations are compared with those of the experiments by Antoci et al. (2007) and Idelsohn et al. (2008).     

Bipartite 2‐Factorizations of Complete Multipartite Graphs

It is shown that if K is any regular complete multipartite graph of even degree, and F is any bipartite 2‐factor of K, then there exists a factorization of K into F; except that there is no factorization of K_{6, 6} into F when F is the union of two disjoint 6‐cycles.     

On the stochastic versions of Neumann and oblique derivative problems

In some areas, for instance geodesy, one finds the need of suitably defining the solution of certain boundary value problems (BVPs), for instance, the Laplace equation, where boundary data are very irregular and can be described as fields of random variables, with suitable regularity constraints (Rummel and Sansò, Lecture Notes on Earth Sciences, Vol. 65, 1997). This item has been attacked in the literature, although mainly for the case of the Dirichlet problem while much less material is available, for instance, for the Neumann and the Oblique Derivative Problem. In studying these stochastic problems in detail, the authors have found fairly general criteria which provide an automatic translation of a deterministic result into the corresponding stochastic one.     

STEFAN PROBLEMS WITH KINETIC CONDITIONS AT THE FREE BOUNDARY

In this paper,we prove the existence theorems of locbal or global classical solutions to Stefan problems with various kinetic conditions at the free boundary.