A Theorem on Discrete,Torsion Free Subgroups of Isom H <Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

Let H ⁿ be the hyperbolic n-space with n⩾ 2. Suppose that Γ H ⁿ is a discrete, torsion free subgroup and a is a point in the domain of discontinuity Ω (Γ). Let p be the projection map from H ⁿ to the quotient manifold M=H ⁿ/Γ. In this paper we prove that there exists an open neighborhood U of a in H ⁿ∪ Ω (Γ) such that p is an isometry on U∩ H ⁿ.Mathematics Subject Classification (2000). primary: 51M10; secondary: 22E40, 57M50.     

Interaction of evaporation fronts with a formation interface in a porous medium

The evolutionarity and structure of water-vapor phase discontinuities formed in a geothermal reservoir on the interface between permeable formations with different properties are considered. In the short-wave approximation a graphic method is proposed for solving the problem of breakdown of an arbitrary discontinuity in a geothermal reservoir consisting of two formations with different properties.     

Grazing Bifurcation of a Cantilever Vibrating System with One-sided Impact

与光滑动力系统不同,擦边分岔是非光滑动力系统中的一种特殊分岔行为. 局部不连续映射 是研究非光滑动力系统擦边分岔的一种有力工具. 对一类单侧弹性碰撞悬臂振动系统进行了擦边分岔分析. 首先建立了系统对应的局部不连 续映射(ZDM)和全局Poincar\'{e}映射,进而在其他参数固定,碰撞间隙$g$为分 岔参数时利用数值仿真的方法分别对原系统和对应的Poincar\'{e} 映射进行擦边分岔分析,得到了该系统的两种不同类型的擦边分岔行为：周期1到周期2运 动和周期1到混沌,这两种擦边分岔与刚性碰撞系统的情况是不相同的. 由分析可知,对 于含高阶非线性项的非光滑动力系统的擦边分岔,同样可以利用局部不连续映射的方法进行 研究.     

一种强健的守恒型间断跟踪法在一维Euler方程组上的实现

文[8,9]研究设计了一种守恒型的间断跟踪法,其主要特点是以解的守恒性作为跟踪的机制而不是像传统的间断跟踪法利用Rankine-Hugoniot条件,将该跟踪法对一维Euler方程组进行实现.对一维单个守恒律凸流的实现见文[7].由于Euler方程组有3类特征线,信息沿每类特征线传播并相互穿透.如果仍然象单个守恒律那样间断两侧的数值解的计算只用到来自间断同侧的信息,则间断一侧的信息就不能传到间断的另一侧,而会堆积在间断附近.设计了一种几乎是二阶的按特征方式分离信息的方法,将堆积在间断附近的信息分离.而且按此思想可做成高阶方法.该方法中不仅用到了精确Riemann分解,还用到了Roe^[12]的近似Riemann分解及各种插值和重构技巧.数值实验表明这样的处理是有效的.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated.The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wav...     

DEALING WITH MOVINGS AND COLLISIONS OF ARBITRARY MANY DISCONTINUITIES IN CONSERVATIVE FRONT-TRACKING METHOD

An approach to deal with movings and collisions of arbitrary many discontinuities in the conservative front tracking method is developed. Using this approach one may develop an "all-purposed and robust" front-tracking algorithm. The algorithm with this approach may have some inconsistency and thus will have O(1) magnitude errors in some grid cells at sometimes. Nevertheless, these errors will be eliminated by the conservation-preserving property of the front-tracking method in the following computation. Numerical examples are presented to illustrate the efficiency of the approach.     

Finite difference methods for modeling porous media flows

The purpose of this study is to determine what finite-difference algorithms are best used in numerical simulation of two-dimensional single-phase saturated porous media flows when the models have a nondiagonal symmetric tensor for the mobility (or hydraulic conductivity) that has nontrivial jump discontinuities along lines that are not aligned with the coordinate axes. Such problems arise naturally in many modeling situations and, in addition, when simpler problems are studied using adaptive grids.The answer is surprising, the simplest finite-difference method, called the MAC Scheme with Linear Averaging, performs nearly as well as most other algorithms over a wide range of problems. A new algorithm, called the Full Harmonic Averaged Scheme, is significantly more costly to use, but does perform better than the simplest scheme in certain interesting cases. The simplest finite-difference method is compared to some finite-element simulations taken from the literature; the finite-difference algorithm performs better.Many of the conclusions of the paper rest on testing the algorithms on a new class of problems with analytic solutions. The problems have a nondiagonal mobility tensor and can have a jump discontinuity of arbitrary height.The research on which this report is based was financed in part by the U.S. Department of Energy through the New Mexico Waste-management Education and Research Consortium (WERC) and Sandia National Laboratories and the Department of Energy under Contract DE-AC04-76DP00789, Dr. M. G. Marietta, Technical Monitor, and the Schlumberger Foundation.     

Weak discontinuities in a chemically reacting atmosphere

Summary The growth and decay of a weak discontinuity headed by a singular surface of arbitrary shape in three dimensions is investigated in a chemically reacting atmosphere, in the absence of dissipative mechanisms such as viscosity, diffusion and heat conduction. The combined effects of the disequilibrium due to the chemical reaction and a wave front curvature on the propagation of discontinuities have been examined and discussed. It has been observed that the chemical disequilibrium, with its Arrhenius rate dependence, causes the compression wave to steepen more swiftly that it does in an inert atmosphere. The critical values of the initial discontinuity, and time for shock formation, in cases of diverging and converging waves, have been determined.     

On the Hochstadt–Lieberman Theorem for Discontinuous Boundary-valued Problems

In this paper, we discuss the half inverse problem for Sturm–Liouville equations with boundary conditions dependent on the spectral parameter and a finite number of discontinuities inside the interval and prove the Hochstadt–Liberman type theorem for the above boundary-valued problem.     

血液动力学中血管流激波与驻波的相互作用

血液动力学问题是生物力学心血管系统中的重要研究课题.血管内斑块处,血管截面和血管壁的材质发生变化,对血液流动产生重要影响.血液流动中基本波及其相互作用对探究血液流动的规律、生理学意义及与疾病的关系有着重要的意义.本文研究血液动力学血液流动简化数学模型的基本波的相互作用.血管流模型是3×3非严格双曲型方程组.构造性地得到了初值为三段常状态时,血管流问题的解,即解决了激波与驻波的相互作用问题.特别地,给出四种后前激波与驻波的相互作用的结果.