Localization effects and measure source terms in numerical schemes for balance laws

This paper investigates the behavior of numerical schemes for nonlinear conservation laws with source terms. We concentrate on two significant examples: relaxation approximations and genuinely nonhomogeneous scalar laws. The main tool in our analysis is the extensive use of weak limits and nonconservative products which allow us to describe accurately the operations achieved in practice when using Riemann-based numerical schemes. Some illustrative and relevant computational results are provided.

     

基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

Dicyclopentadienyl complexes of titanium,niobium, and tungsten in the controlled synthesis of poly(methyl methacrylate)

Organometallic compounds Cp₂TiCl₂, (EtC₅H₄)₂NbCl₂, and (PrⁱC₅H₄)₂WCl₂ were assessed as additives that control polymer chain growth in the polymerization of methyl methacrylate. In the presence of compounds mentioned in amounts comparable with that of the initiator, a uniform process with no gel-effect occured and respective linear increase in the molecular weight of the polymer up to high degrees of the monomer conversion was observed.     

Upper Bounds of the Pursuer Control Based on a Linear-Quadratic Differential Game

Differential game formulations provide an adequate basis for a guidance law synthesis against highly maneuvering targets. This paper deals with a guidance law based on a linear-quadratic differential game formulation. This guidance law has many attractive properties: it is continuous, linear with respect to the state variables, and its gain coefficients can be precalculated offline. Nevertheless, due to the lack of hard control constraints in the formulation, the magnitude of the control can exceed the admissible level imposed by the nature of the problem. In this paper, the upper bound of the interceptor control is obtained depending on the system parameters and the penalty coefficients of the game performance index. It is shown that the interceptor can guarantee an arbitrarily small miss distance without exceeding the control constraints if it has sufficient maneuverability and if the penalty coefficients are chosen properly. By manipulating the penalty coefficients, it is possible to reduce significantly the maneuverability requirements compared to the case of zero interceptor penalty coefficient.     

初-边值问题驻波解的渐近稳定性

本文考虑一带有人工粘性的二维定常等熵无旋平面流方程组的初-边值问题. 在一定的假设下,我们证明其驻波解是渐近稳定的.     

On rank-perfect subclasses of near-bipartite graphs

Shepherd95 proved that the stable set polytopes of near-bipartite graphs are given by constraints associated with the complete join of antiwebs only. For antiwebs, the facet set reduces to rank constraints associated with single antiwebs by Wagler2004. We extend this result to a larger graph class, the complements of fuzzy circular interval graphs, recently introduced in ChudnovskySeymour2004. Received: November 2004 / Revised version: June 2005     

Sigma Models and Minimal Surfaces

Correspondence is established between sigma models, minimal surfaces and the Monge–Ampére equation. The Lax pairs of the minimality condition of the minimal surfaces and the Monge–Ampére equations are given. Existence of infinitely many nonlocal conservation laws is shown and some Bäcklund transformations are also given.     

Approximate symmetries and conservation laws for Itô and Stratonovich dynamical systems

A new definition for the approximate symmetries of Itô dynamical system is given. Determining systems of approximate symmetries for Itô and Stratonovich dynamical systems have been obtained. It has been shown that approximate conservation laws can be found from the approximate symmetries of stochastic dynamical systems which do not arise from a Hamiltonian. The results have been applied to an example.     

On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics

In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem.     

Pseudo-Anosov foliations on periodic surfaces

We study lifts of the stable foliation of a pseudo-Anosov diffeomorphism to abelian covers. Under certain conditions, we show that it is ergodic but not uniquely ergodic and describe the ergodic measures.