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.     

NMR investigation of concentrated alumina and silica slurries

The longitudinal relaxation times (T₁) of water in concentrated silica and alumina slurries were measured as a function of solids content. It was shown that the results could be fit very well with a two-phase fast-exchange model between free and surface-bound water. As expected, values of T₁ for bound water were in the order of 20–2000 times lower than that for free water, indicating a higher effective viscosity of the surface-bound water. The strength of the interaction depended on the particular surface, and all of the aluminas examined interacted more strongly with water than the two silicas studied, which themselves differed considerably. The chemical mechanical polishing (CMP) removal rate of tantalum by silica slurries was shown to be directly correlated with the interaction parameters, derived from the NMR relation times rather than with total surface hydroxyl group concentration.     

因素空间理论与知识表示的数学框架(XⅢ)──描述架中概念的结构(2)

本文是［１，１２］的继续，研究描述架中概念的结构；本文讨论后半部分，内容涉及概念内涵与外延的转换，清晰关系的内投影与内变换，概念的结构＊以及有关问题的注记。     

逆（反）对策问题与“奇门遁甲”预测理论（术）

本文首先提出逆（反）对策这一新问题，给出了数学模型；探讨了“奇门遁甲”预测理论（术）中的数学问题；通过系统分析“专门遁甲”预测过程，可知它的预测过程隐含着一个特殊的逆（反）对策问题；最后指出逆（反）对策问题的广泛存在并给出案例分析．     

THERMAL AND THERMO-ELASTIC-PLASTIC RESPONSE OF CERAMIC-METAL FUNCTIONALLY GRADED MATERIALS—THERMAL SHOCK PROBLEM

The thermal and thermo-elastic-plastic response of newly developed ceramic-metalfunctionally graded materials under a thermal shock load is studied.The materials are heated at the ce-ramic surface with a sudden high-intensity heat flux input,and cooled at the metal surface with aflowing liquid nitrogen.Emphasis is placed on two aspects:(1)the influence of the graded composi-tion of the materials on the temperature and stress response;and(2)the optimum design of the gradedcomposition from a unified viewpoint of the heat insulation property and stress relaxation property.Moreover,a comparison between the thermoelastic stress and the thermo-elastic-plastic stress is alsomade to indicate the plasticity effect.     

Miscible blends of modified poly(aryl ether ketones) with aromatic polyimides

The phase behavior of binary blends of poly(ether ether ketone) (PEEK), sulfonated PEEK, and sulfamidated PEEK with aromatic polyimides is reported. PEEK was determined to be immiscible with a poly(amide imide) (TORLON 4000T). Blends of sulfonated and sulfamidated PEEK with this poly(amide imide), however, are reported here to be miscible in all proportions. Blends of sulfonated PEEK and a poly(ether imide) (ULTEM 1000) are also reported to be miscible. Spectroscopic investigations of the intermolecular interactions suggest that formation of electron donoracceptor complexes between the sulfonated/sulfamidated phenylene rings of the PEEKs and the n-phenylene units of the polyimides are responsible for this miscibility. © 1993 John Wiley & Sons, Inc.     

Chemical reactivity of hypervalent silicon compounds: The local hard and soft acids and bases principle viewpoint

The silicon atom may increase its coordination number to values greater than four, to form pentacoordinated compounds. It has been observed experimentally that, in general, pentacoordinated compounds show greater reactivity than tetracoordinated compounds. In this work, density functional theory is used to calculate the global softness and the condensed softness of the silicon atom for SiH _n F_4−n and SiH _n F _5−n ¹⁻ . The values obtained show that the global and condensed softness are greater in the pentacoordinated compounds than in the tetracoordinated compounds, a result that explains the enhanced reactivity. If the results are analysed through a local version of the hard and soft acids and bases principle, it is possible to suggest that in nucleophilic substitution reactions, soft nucleophiles preferably react with SiH _n F _5−n ¹⁻ , and hard nucleophiles with SiH _n F_4−n .     

Structure of norbornene-fused 3,1-oxazine double cycloadducts

Pentacyclic isoxazolines were obtained by the cycloaddition of benzonitrile oxide to norbornene-azetidinone-fused 3,1-oxazines. The constitutions of two of the isomers obtained, and the configurations and conformations of all products, were determined by means of ¹H and ¹³C NMR spectroscopy and DNOE experiments.     

Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.