Semiempirical calculation of the fine structure of the indium ion

The fine-structure parameters of a series of configurations of the first ion of indium and the gyromagnetic ratios in intermediate coupling are calculated by a semiempirical method in the single-configuration approximation.     

A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.     

Probability Inequalities and Limit Theorems for Generalized L-Statistics

We obtain exponential upper bounds for tails of distributions of generalized L-statistics based on a sample from an exponential distribution. We prove the asymptotic normality of generalized L-statistics based on a sample from the uniform distribution on [0,1] and of L-statistics with decomposed kernels (without any restrictions on the sample distribution type).     

Numerical Modeling of Interior Ballistics Processes in Light Gas Guns

An improved procedure for modeling the operation of a light-gas gun is proposed. The motion of working bodies in both the firing chamber and the light-gas chamber is studied within the framework of the mechanics of heterogeneous media. The problem of barrel heating taking into account its melting and removal of thermal ablation products into the medium inside the bore is solved in a coupled formulation. Heat and mass transfer and friction on the barrel surface are calculated using empirical dependences. The deformable piston is considered compressible and elastoviscoplastic. Allowance is made for the presence of a clearance between the lateral surface of the piston and the barrel bore walls and the associated gas flow between the firing and the light-gas chamber. Calculation results are given.     

Stationary entanglement between macroscopic mechanical oscillators

We show that the optomechanical coupling between an optical cavity mode and two movable cavity mirrors is able to entangle two different macroscopic oscillation modes of the mirrors. This continuous variable entanglement is maintained by the light bouncing between the mirrors and is robust against thermal noise. In fact, it could be experimentally demonstrated using present technology. Received 2 September 2002 / Received in final form 10 October 2002 Published online 7 January 2003     

放射性9C束流不同贯穿深度上的线能谱测量

为阐述放射性⁹C束流应用于治癌的物理基础, 运用一个球形生物组织等效正比计数器测量了⁹C束流不同贯穿深度上的线能谱, 得到了沿束流贯穿深度上的剂量平均线能分布. 将实验测量得到的线能谱转换成为不同传能线密度在吸收剂量中所占份额的分布, 得到了该⁹C束流在不同贯穿深度上的剂量平均传能线密度分布. 将生物组织等效正比计数器测量得到的与先前通过平行板正比计数器测量得到的该⁹C束流的剂量平均传能线密度分布进行比较, 发现: 在束流入射通道上, 两者测量数据符合很好, 而在束流Bragg峰附近⁹C离子的沉积区域, 由组织等效正比计数器测量得到的剂量平均传能线密度值大于由平行板正比计数器测量得到的值.     

A test problem for molecular dynamics integrators

We derive a test problem for evaluating the ability of time-steppingmethods to preserve the statistical properties of systems inmolecular dynamics. We consider a family of deterministic systemsconsisting of a finite number of particles interacting on acompact interval. The particles are given random initial conditionsand interact through instantaneous energy- and momentum-conservingcollisions. As the number of particles, the particle density,and the mean particle speed go to infinity, the trajectory ofa tracer particle is shown to converge to a stationary Gaussianstochastic process. We approximate this system by one describedby a system of ordinary differential equations and provide numericalevidence that it converges to the same stochastic process. Wesimulate the latter system with a variety of numerical integrators,including the symplectic Euler method, a fourth-order Runge-Kuttamethod, and an energyconserving step-and-project method. Weassess the methods' ability to recapture the system's limitingstatistics and observe that symplectic Euler performs significantlybetter than the others for comparable computational expense.     

Poincaré-Hopf inequalities

In this article the main theorem establishes the necessity and sufficiency of the Poincaré-Hopf inequalities in order for the Morse inequalities to hold. The convex hull of the collection of all Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data determines a Morse polytope defined on the nonnegative orthant. Using results from network flow theory, a scheme is provided for constructing all possible Betti number vectors which satisfy the Morse inequalities for a pre-assigned index data. Geometrical properties of this polytope are described.

     

Structuring Multi-attribute Value Hierarchies

The first stage in a multi-attribute value analysis is the development of a hierarchical structure of the attributes of the problem. This paper reports the process of developing such a structure for the problem of choosing a suitable mode of transport for radioactive waste. The initial hierarchy of attributes went through several stages of development as new insights emerged about the nature of the problem. Some of the reasons behind this restructuring are discussed, and several important questions about the structuring process are formulated.