Application of the Energy Conservation Law in the Cold Plasma Model

Computational Mathematics and Mathematical Physics - For the two-fluid hydrodynamic cold plasma model, differential relations characterizing the energy conservation law are derived. The case when...     

Mixing Closures for Conservation Laws in Stratified Flows

A closure for shocks involving the mixing of the fluids in two-layer stratified flows is proposed. The closure maximizes the rate of mixing, treating the dynamical hydraulic equations and entropy conditions as constraints. This closure may also be viewed as yielding an upper bound on the mixing rate by internal shocks. It is shown that the maximal mixing rate is accomplished by a shock moving at the fastest allowable speed against the upstream flow. Depending on whether the active constraint limiting this speed is the Lax entropy condition or the positive dissipation of energy, we distinguish precisely between internal hydraulic jumps and bores. Maximizing entrainment is shown to be equivalent to maximizing a suitable entropy associated to mixing. By using the latter, one can describe the flow globally by an optimization procedure, without treating the shocks separately. A general mathematical framework is formulated that can be applied whenever an insufficient number of conservation laws is supplemented by a maximization principle.     

Pressure Stabilization Method for Steady Viscous Flows in a System of Pipes

This paper deals with a singular perturbation of the stationary Stokes and Navier-Stokes systems. The term ε²Δp is added to the continuity equation, where ε is a small parameter. For a domain with cylindrical outlets to infinity and exponentially decaying data, existence and uniqueness of solutions under flux conditions at infinity are established for the linear problem and also for the nonlinear problem in the case of small data. Asymptotically exact estimates are proved for ε tending to zero. For sufficiently regular data, these estimates imply the convergence in H _loc ^5/2−δ for the velocity parts and in H _loc ^3/2−δ for the pressure parts, respectively. Bibliography: 17 titles.Dedicated to V. A. Solonnikov on the occasion of his 70th birthday__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 306, 2003, pp. 107–133.     

Exact Boundary Observability of Unsteady Supercritical Flows in a Tree-Like Network of Open Canals

The author establishes the exact boundary observability of unsteady supercritical flows in a tree-like network of open canals with general topology. An implicit duality between the exact boundary controllability and the exact boundary observability is also given for unsteady supercritical flows.     

二阶非Четаев型非完整系统的守恒律

研究二阶非ЧｅＴａｅＢ型完整系统的守恒律,引入Ｊｏｕｒｄａｉｎ生成元,给出无限小变换下Ｊｏｕｒ－ｄａｉｎ原理的不变性条件,在一定条件下得到系统的守恒律,并举例说明结果的应用。     

广义相对论之守恒定律与重力波辐射

本文证明爱因斯坦之广义相对论运动方程能演变成为物质守恒定律。虽然获得的重力场能量动量张量相等于Ｌａｎｄａｕ－Ｌｉｆｓｈｉｔｚ所得的．但演变过程之物理概念是不同的。除此之外，本文分别从物体运动方程和测地线方程着手，提供了两个寻找重力波辐射的方法。     

Energy Conservation with Non-Symplectic Methods: Examples and Counter-Examples

Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented. AMS subject classification (2000) 65L06, 65P10, 37J99.Submitted June 2004. Accepted October 2004. Communicated by Syvert Nørsett.     

J积分在多层介质中的守恒性和其应用

首先证明和讨论了当裂纹平行于多层介质界面时,其裂纹尖端J积分的守恒性;然后建立了具有界面裂纹的由4种介质构成的材料分析模型,根据J积分在多层介质中的守恒性原理,提出了该模型的I型断裂能量释放率守恒假设,并经过了数值实验的验证,通过能量分析和量纲分析,用渐近分析方法得到了计算该模型结构界面裂纹尖端能量释放率和复应力强度因子的分析公式,并且进行了讨论。     

未确知测度模型在建筑节能方案评价中的应用

建筑节能方案评价是一个涉及多因素的系统工程,目前常用的单一指标评价并不能对节能方案的推广起至应有作用,根据我国能源政策设计了一套多指标综合评价体系.给出了一种定量化描述建筑节能方案评价指标的方法,建立了基于未确知测度的评价模型,并通过信息熵确立指标的分类权重,明显优于过去常用的AHP确定权重的主观判断方法,具有更高的科学性和实际应用价值,有利于优秀节能技术的扩散.     

The Global Solutions of the Scalar Nonconvex Conservation Law with Boundary Condition

Using the polygonal approximations method, we construct the global approximate solution of the initial boundary value problem (1.1)-(1.3) for the scalar nonconvex conservation law, and prove its convergence. The crux of this work is to clarify the behavior of the approximations on the boundary x = 0.     

事件空间中二阶非Четаев型非完整系统的守恒律

研究事件空间中二阶非чeTaeB型非完整系统的守恒律。提出事件空间中的Jourdain原理，引入事件空间中的Jorudain生成元，给出无限小变换下的Jourdain原理的不变性条件。在一定条件下得到事件空间中系统的守恒律。并举例说明结果的应用。     

Energy Dissipated Across Shocks in Weak Solutions of Conservation Laws

Manipulation of conservation laws through multiplication by mappings of the unknown function result in singular terms that are densities supported on the discontinuity locus. We derive an expression for these singular terms which have been interpreted as the energy dissipated at the shocks. As an application, the expression for these singular terms is obtained from the transport equation governing the propagation of small amplitude high frequency waves in hyperbolic conservation laws. Analogous formulas are obtained for rich systems in several space dimensions.     

能源价格变化对我国宏观经济及节能减排的影响研究——基于联立方程模型的分析

基于供给需求理论构建了能源——经济联立方程模型,定量研究各类能源价格变化对我国宏观经济的影响.结果发现,能源价格上涨可以降低能源消耗,通过供给渠道对潜在生产能力和GDP产生紧缩作用,对通货膨胀产生向上压力.石油价格上涨对主要经济指标的影响略小,煤炭价格与电力价格上涨对经济的影响较大,煤、电价格联合上涨对经济的影响最大.这与目前我国能源消费结构吻合.各种能源价格的持续上涨冲击对潜在产出、能源消费、能源强度和碳排放强度的负向影响有继续增强的趋势.     

The Algebra of Flows in Graphs

We define a contravariant functorKfrom the category of finite graphs and graph morphisms to the category of finitely generated graded abelian groups and homomorphisms. For a graphX, an abelian groupB, and a nonnegative integerj, an element of Hom(K^j(X), B) is a coherent family ofB-valued flows on the set of all graphs obtained by contracting some (j − 1)-set of edges ofX; in particular, Hom(K¹(X), ) is the familiar (real) “cycle-space” ofX. We show thatK ^· (X) is torsion-free and that its Poincaré polynomial is the specializationt^{n − k}T_X(1/t, 1 + t) of the Tutte polynomial ofX(hereXhasnvertices andkcomponents). Functoriality ofK ^· induces a functorial coalgebra structure onK ^· (X); dualizing, for any ringBwe obtain a functorialB-algebra structure on Hom(K ^· (X), B). WhenBis commutative we present this algebra as a quotient of a divided power algebra, leading to some interesting inequalities on the coefficients of the above Poincaré polynomial. We also provide a formula for the theta function of the lattice of integer-valued flows inX, and conclude with 10 open problems.     

Analysis of a Compressed Thin Film Bonded to a Compliant Substrate: The Energy Scaling Law

We consider the deformation of a thin elastic film bonded to a thick compliant substrate, when the (compressive) misfit is far beyond critical. We take a variational viewpoint—focusing on the total elastic energy, i.e. the membrane and bending energy of the film plus the elastic energy of the substrate—viewing the buckling of the film as a problem of energy-driven pattern formation. We identify the scaling law of the minimum energy with respect to the physical parameters of the problem, and we prove that a herringbone pattern achieves the optimal scaling. These results complement previous numerical studies, which have shown that an optimized herringbone pattern has lower energy than a number of other patterns. Our results are different, because (i) we make the scaling law achieved by the herringbone pattern explicit, and (ii) we give an elementary, ansatz-free proof that no pattern can achieve a better law.     

一维单个守恒型方程的二阶熵耗散格式

本文考虑一维单个守恒律方程，对其设计了一种非线性守恒型差分格式，此格式为二阶Godunov型的，用的是分片线性重构，重构函数的斜率是根据熵耗散得到的，格式满足熵条件，且数值实验表明格式具有非线性稳定性，在此格式中一个所谓的熵耗散函数起了很重要的作用，它在每个网格的计算中耗散熵，在文中我们给出了熵耗散函数应满足的条件，并给出了一种具体的构造形式，最后给出了一些数值算例，从中可看出熵耗散函数是如何抑制非物理振荡的，及格式对计算的有效性。     

The Global Solution of the Scalar Nonconvex Conservation Law with Boundary Condition (continuation)

Using the Kruskov's method [1], we show the uniqueness for the global weak solution of the initial-boundary value problem (1.1)-(1.3) (in the class of bounded and measurable functions).