二维气体动力学中压差方程的特征分解和简单波

利用直接的方法讨论了在自相似平面上气体动力学中二维压差方程的特征分解理论,得到了压强P和特征值A±的特征分解.进一步地,若流动来自常状态,还可得到速度（u,v）的特征分解.由此,可以得到与常状态流动相邻的流动是简单波,并说明了简单波的流动区域是被一族直线所覆盖,且沿着每条直线, （P,u,v）为常数.     

多孔介质中可压溶混流动的Galerkin方法

在多孔介质中,考虑单相的、一种可压流体被另一种流体所溶混驱替的流动.设诸集层Ω是单位厚度且视其为R~2中的有界区域,忽略重力项,混合流体的Darcy速度可表为 u=-K(x)/μ(c)?p,其中p为压力,K(x)为介质的渗透率,μ为与浓度c有关的粘度.设dρ_i/ρ_i=z_idp,其     

Fokas方程的显示孤立尖波解和周期尖波解

利用一个独立变换和动力系统方法对Fokas方程:u_(tx)=(1+v(?)■_x~2)sin(u),x∈R,t0进行研究.在对该方程所对应的平面动力系统进行定性分析的基础上,得到了该方程所有可能的显式孤立尖波解和周期尖波解.     

无粘定常超音平面流动中同类激波的相追

§1.引言 标题中的流动,由以下守恒律组所描述: (ρu)_x (ρv)_y=0(质量守恒), (1) [ρ_u(h ((u~2 v~2)/2))]_x [ρ_v(h ((u~2 v~2)/2))]_v=0 (能量守恒),(4)其中ρ——密度、p——压强、(u,v)——速度、h——焓,本文研究多方气体,h=rp/(r-1)ρ,r>1。所谓超音流动,即指     

一类变式Boussinesq系统的行波解

本文研究—类变式Boussinesq系统ηt+((1+αη)w)x-β/6wxxx=0, wt+αwwx+ηx-β/2wxxt=0,其中α和β都是正常数.许多逼近模型都能从此系统中被推导出,比如Boussinesq系统和两分量Camassa-Holm系统等.本文利用平面动力系统方法研究它的行波解及相图,得到了孤立波解,广义扭波解,广义反扭波解,紧孤立波解和周期波解,并给出了这些解的数值模拟.     

关于两个复变数的全纯函数的一个Schwarz引理

设 p(u,v)为实变数 u,v 的一个齐次多项式,其次数 m(p)及系数均大于零.另一方面,设 Q 为空间 C~2中含有点(0,0)的一个开集,g(z_1,z_2)为定义于 C~2的一个复函数,使对于 C~2中每一点,它有一个相应的有穷值或∞值,W=(?)(w)为在圆|w|<1内之一单叶全纯函数,使(?)(0)=0,并将此圆变换为一区域△,以 w=ψ(W)表示其定义于△的反函数.     

一类非线性双曲-抛物耦合问题的A.D.I.Galerkin方法

1　引　言考虑三维非线性双曲 -抛物耦合初边值问题 :utt- . (a1 (X,t,u) u) +b1 (X,t,u,v) . u　　　　 +α1 e. v =f(X,t,u,v) ,X∈Ω,t∈ J.vt-a2 Δv +b2 (X,t,u,v) . v　　　　 +α2 e. ut=g(X,t,u,v) ,X∈Ω,t∈ J.u(X,t) =v(X,t) =0 , X∈ Ω ,t∈ J.u(X,0 ) =u0 (X) ,ut(X,0 ) =ut0 (X) ,v(X,0 ) =v0 (X) ,X∈Ω.(1 .1 )其中 ,X=(x1 ,x2 ,x3) ,Ω=(c1 ,d1 )× (c2 ,d2 )× (c3,d3)为 R3中矩形区域 ,边界 Ω . J=[0 ,T] ,T>0为一正常数 .b1 ,b2 ,f,g均为已知光滑函数 (其中 b1 ,b2 为向量函数 ) ,且关于 u,v满足 L…     

一维绝热流动中初等波的相互作用

<正> 一维绝热流动的守恒律组(在拉格朗日座标下)为其中u——速度、p——压强、v——比容、E=e+u~2/2,而在多方气体的情形e=pv/(γ-1),绝热指数γ为常数,γ>1.人们称它的某些特解为初等波,其中包括前、后向激波S、S;前、后向中心疏散波R、R和上、下跳接触间断T、T.它们的相互作用一方面在     

带有Logistic源的吸引-排斥趋化性系统的整体有界性和渐近行为北大核心CSCD

该文研究了有界区域ΩR^N(N≥1)中,齐次Neumann边值条件下带有Logistic源的吸引-排斥趋化性系统u_t=Δu-▽·(u▽v)+μ_1u(1-u),0=Δv+w-v,w_t=Δw+▽·(w▽z)+μ_2w(1-w),0=△z-z+u,其中μ_1,μ_2>0.证明了对任何非负初值u_0(x),w_0(x)∈C(Ω),解(u(·,t),v(·,t),w(·,t),z(·,t))整体有界.此外,如果μ_1,μ_2>1/16,那么当t→∞时,解(u(·,t),u(·,t),w(·,t),z(·,t))在L~∞模意义下渐近收敛于常数平衡解(1,1,1,1).     

多孔介质可混溶流动问题的混合元与区域分裂特征差分格式

1 引 言 用区域分裂方法求微分方程的数值解,是近年来计算数学领域的—个新方法。这种方法通过分裂区域来减少所处理问题的规模,并实现并行计算,因此,特别适用于大范围的工程技术问题和数学物理问题。本文用这种方法处理平面可混溶不可压缩流动问题其中J=[0.T].u为Darcy速度,p为压力,c为浓度,k为渗透率,μ（c)为流体粘性,c为注入井给定浓度,q为外界源汇项,q~+=max{q,0}.φ为孔隙度。D为扩散矩阵,本文D与u无关。即仅考虑分子扩散,边条件可取为第一或第二类边条件。本文考虑第一类初边值问题     

Three-Dimensional Nonlinear Dispersive Waves on Shear Flows

The Green–Naghdi equations describing three-dimensional water waves are considered. Assuming that transverse variations of the flow occur at a much shorter lengthscale than variations along the wave propagation direction, we derive simplified asymptotic equations from the Green–Naghdi model. For steady flows, we show that the approximate model reduces to a one-dimensional Hamiltonian system along each stream line. Exact solutions describing a wide class of free-boundary flows depending on several arbitrary functions of one argument are found. The numerical results showing different patterns of steady three-dimensional waves are presented.     

二维拟定常可压流Euler方程组的简单波

简单波是这样的流动,它在像空间中的像是一条曲线．“简单波理论是除基本流动结构以外构造流动问题的解的基础”,见Courant和Friedrichs的经典著作《超声速流与冲击波》．该文主要研究二维拟定常可压流Euler方程组的简单波的几何结构.根据这些几何诠释,还构造了绕一拟流线弯曲部的疏散和压缩的简单波流动结构．这种流动结构将作为一个局部流动结构出现在4个接触间断的Riemann问题的整体解中．     

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.     

Paralinearization of the Dirichlet to Neumann Operator,and Regularity of Three-Dimensional Water Waves

This paper is concerned with a priori C ^∞ regularity for three-dimensional doubly periodic travelling gravity waves whose fundamental domain is a symmetric diamond. The existence of such waves was a long standing open problem solved recently by Iooss and Plotnikov. The main difficulty is that, unlike conventional free boundary problems, the reduced boundary system is not elliptic for three-dimensional pure gravity waves, which leads to small divisors problems. Our main result asserts that sufficiently smooth diamond waves which satisfy a Diophantine condition are automatically C ^∞. In particular, we prove that the solutions defined by Iooss and Plotnikov are C ^∞. Two notable technical aspects are that (i) no smallness condition is required and (ii) we obtain an exact paralinearization formula for the Dirichlet to Neumann operator.     

Stokes waves with constant vorticity: I. Numerical computation

Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via a conformal mapping as a nonlinear pseudodifferential equation, involving a periodic Hilbert transform for a strip, and solved by the Newton‐GMRES method. For strong positive vorticity, in the finite or infinite depth, overhanging profiles are found as the amplitude increases and tend to a touching wave, whose surface contacts itself at the trough line, enclosing an air bubble; numerical solutions become unphysical as the amplitude increases further and make a gap in the wave speed versus amplitude plane; another touching wave takes over and physical solutions follow along the fold in the wave speed versus amplitude plane until they ultimately tend to an extreme wave, which exhibits a corner at the crest. Touching waves connected to zero amplitude are found to approach the limiting Crapper wave as the strength of positive vorticity increases unboundedly, while touching waves connected to the extreme waves approach the rigid body rotation of a fluid disk.     

Minimax tests for convex cones

Let (P : R ^p ) be a simple shift family of distributions onR ^p , and letK R ^p be a convex cone. Within the class of nonrandomized tests ofK versusR ^p K, whose acceptance regionA satisfiesA=A+K, a test with minimal bias is constructed. This minimax test is compared to a likelihood ratio type test, which is optimal with respect to a different criterion. The minimax test is mimicked in the context of linear regression and one-sided tests for covariance matrices.     

On linear and nonlinear Rossby waves in an ocean

This paper deals with recent developments of linear and nonlinear Rossby waves in an ocean. Included are also linear Poincaré, Rossby, and Kelvin waves in an ocean. The dispersion diagrams for Poincaré, Kelvin and Rossby waves are presented. Special attention is given to the nonlinear Rossby waves on a β-plane ocean. Based on the perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies a modified nonlinear Schrödinger equation. The solution of this equation represents solitary waves in a dispersive medium. In other words, the envelope of the amplitude of the waves has a soliton structure and these envelope solitons propagate with the group velocity of the Rossby waves. Finally, a nonlinear analytical model is presented for long Rossby waves in a meridional channel with weak shear. A new nonlinear wave equation for the amplitude of large Rossby waves is derived in a region where fluid flows over the recirculation core. It is shown that the governing amplitude equations for the inner and outer zones are both KdV type, where weak nonlinearity is balanced by weak dispersion. In the inner zone, the nonlinear amplitude equation has a new term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude, and this term occurs to account for a nonlinearity due to the flow over the vortex core. The solution of the amplitude equations with the linear shear flow represents the solitary waves. The present study deals with the lowest mode (n=1) analysis. An extension of the higher modes (n?2) of this work will be made in a subsequent paper.     

Two-Way Interactions Between Equatorially-Trapped Waves and the Barotropic Flow

Lateral energy exchange between the tropics and the midlatitudes is a topic of great importance for understanding Earth＇s climate system. In this paper, the authors address this issue in an idealized set up through simple shallow water models for the interactions between equatorially trapped waves and the barotropic mode, which supports Rossby waves that propagate poleward and can excite midlatitude teleconnection patterns. It is found here that the interactions between a Kelvin wave and a fixed meridionai shear （mimicking the jet stream） generates a non-trivial meridional velocity and meridional convergence in phase with the upward motion that can attain a maximum of about 50%, which oscillates on frequencies ranging from one day to 10 days. When, on the other hand, the barotropic flow is forced by slowly propagating Kelvin waves a complex flow pattern emerges; it consists of a phase-locked barotropic response that is equatoriaily trapped and that propagates eastward with the forcing Kelvin wave and a certain number of planetary Rossby waves that propagate westward and toward the poles as seen in nature. It is suggested here that the poleward propagating waves are to some sort of multi-way resonant interaction with the phase locked response. Moreover, it is shown here that a numerical scheme with dispersion properties that depend on the direction perpendicular to the direction of propagation, namely the 2D central scheme of Nessyahu and Tadmor, can artificially alter significantly the topology of the wave fields and thus should be avoided in climate models.     

点度与图的上可嵌入性

本文证明了:(1) 设G是2-连通简单图,且不含K_3,若对任意一对距离为2的点u,u,有max{d(u),d(u)}>n/3-1,其中n=|V(G)|,则G是上可嵌入的,且条件中不等式的界"n/3-1"是不可达的;(2) 设G是3-连通简单图,若对任意依次相邻的三点u,u,W,有max{d(u),d(u),d(w)}≥n/6+1,其中n=|V(G)|,则G是上可嵌入的,且条件中不等式的界"n/6+1"是最好的.