The validity of nonlinear geometric optics for weak solutions of conservation laws

The method of weakly nonlinear geometric optics is one of the main formal perturbation techniques used in analyzing nonlinear wave motion for hyperbolic systems. The tacit assumption in using such perturbation methods is that the corresponding solutions of the hyperbolic system remain smooth; since shock waves typically form in such solutions, these assumptions are rarely satisfied in practice. Nevertheless, in a variety of applied contexts, these methods give qualitatively reliable answers for discontinuous weak solutions. Here we give a rigorous proof for the validity of nonlinear geometric optics for general weak solutions of systems of hyperbolic conservation laws in a single space variable. The methods of proof do not mimic the formal construction of weakly nonlinear asymptotics but instead rely on structural symmetries of the approximating equations, stability estimates for intermediate asymptotic times, and the rapid decay in variation of weak solutions for large asymptotic times.Partially supported by NSF Grant No. DMS-8301135Partially supported by NSF Grant No. MCS-81-02360 and ARO Grant No. 483964-25530     

On affine scaling and semi-infinite programming

We consider an extension of the affine scaling algorithm for linear programming problems with free variables to problems having infinitely many constraints, and explore the relationship between this algorithm and the finite affine scaling method applied to a discretization of the problem.This material is based on research supported by Air Force Office of Scientific Research Grant AFOSR 89-0410.     

Asymptotic Correction of More Sturm–Liouville Eigenvalue Estimates

The asymptotic correction technique of Paine, de Hoog and Anderssen can dramatically improve the accuracy of finite difference or finite element eigenvalues at negligible extra cost if closed form expressions are available for the errors in a simpler related problem. This paper gives closed form expressions for the errors in the eigenvalues of certain Sturm–Liouville problems obtained by various methods, thereby increasing the range of problems for which asymptotic correction can achieve maximum efficiency. It also investigates implementation of the method for more general problems.     

Large Scale Linear Programs and Heuristics for the Design of Survivable Telecommunication Networks

We consider the problem of providing a minimum cost multi-service network subject to one link failure scenarios. We assume our network is fully meshed and demand is satisfied by using direct or two hop-paths. We provide a large scale linear programming formulation and propose and test two effective heuristics.     

Loops and the Lagrange Property

Let $\cal F$ be a family of finite loops closed under subloops and factor loops. Then every loop in $\cal F$ has the strong Lagrange property if and only if every simple loop in $\cal F$ has the weak Lagrange property. We exhibit several such families, and indicate how the Lagrange property enters into the problem of existence of finite simple loops.     

QCD correction to the leptonic decay rate ofD-wave vector mesons

We show that the first order QCD correction to the leptonic decay rate of heavy quark-antiquark³ D ₁ bound state is identical to that for a³ S ₁ state. Some phenomenological implications of this suppression are also discussed.     

Experiences in Expert Systems

This paper describes some work carried out in the Scientific Research and Development Branch (SRDB) of the Home Office, intended to contribute to an overall aim of building up internal expertise in the field of expert systems. This was done by carrying out a number of pilot and demonstrator projects, two of which are described in some detail. The plan, which proved successful, was to build as far as possible on the relevant skills already possessed by an OR group in the branch. The lessons learned from these are summarized in the hope that they will be of use to other groups who wish to become involved in this important area.     

内爆驱动式超高速发射技术的初步研究

为获得10 km/s左右的超高速发射能力,以内爆发射器为研究对象,利用AUTODYN 2D软件对口径为8 mm的内爆发射器进行有限元仿真分析,获得了典型状态下的弹丸发射速度。研制了口径为8 mm的内爆发射器,并在压缩管中填充5 MPa氦气进行实验,分别获得了0.55 g铝合金弹丸7.95 km/s和0.37 g镁合金弹丸10.28 km/s的发射速度,与有限元仿真计算结果的速度偏差分别为15.3%和3.7%。结果表明,设计的内爆发射器具备10 km/s发射能力,满足空间碎片撞击和防护研究的超高速发射需求。