Monte Carlo Hamiltonian: Linear Potentials

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.     

Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations

In this paper, we review briefly some methods for minimizing a functionF(x), which proceed by follwoing the solution curve of a system of ordinary differential equations. Such methods have often been thought to be unacceptably expensive; but we show, by means of extensive numerical tests, using a variety of algorithms, that the ODE approach can in fact be implemented in such a way as to be more than competitive with currently available conventional techniques.This work was supported by a SERC research studentship for the first author. Both authors are indebted to Dr. J. J. McKeown and Dr. K. D. Patel of SCICON Ltd, the collaborating establishment, for their advice and encouragement.     

Combinatorial computational chemistry approach of tight-binding quantum chemical molecular dynamics method to the design of the automotive catalysts

Recently, we have developed a new tight-binding quantum chemical molecular dynamics program “Colors” for combinatorial computational chemistry approach. This methodology is based on our original tight-binding approximation and realized over 5000 times acceleration compared to the conventional first-principles molecular dynamics method. In the present study, we applied our new program to the simulations on various realistic large-scale models of the automotive three-way catalysts, ultrafine Pt particle/CeO₂(111) support. Significant electron transfer from the Pt particle to the CeO₂(111) surface was observed and it was found to strongly depend on the size of the Pt particle. Furthermore, our simulation results suggest that the reduction of the Ce atom due to the electron transfer from the Pt particle to the CeO₂ surface is a main reason for the strong interaction of the Pt particle and CeO₂(111) support.     

Decay of confined,two-dimensional,spatially periodic arrays of vortices: A numerical investigation

The disarrangement of a perturbed lattice of vortices was studied numerically. The basic state is an exponentially decaying, exact solution of the Navier-Stokes equations. Square arrays of vortices with even numbers of vortex cells along each side were perturbed and their evolution was investigated. Whether the energy in the perturbation grows somewhat before it decays or decays monotonically depends on the initial strength of the vortices of the basic state, the extent of lateral confinement and the structure of the perturbation. The critical condition for temporally local instability, i.e. the critical amplitude of the basic state that must be exceeded to allow energy transfer from the basic state to the perturbation, is discussed. In the strongly confined case of a square lattice of four vortices the appearance of enchancement of global rotation is the result of energy transfer from the basic state to a temporally local unstable mode. Energy is transferred from the basic state to larger-scaled structures (inverse cascade) only if the scales of the larger structures are inherently contained in the initial structure of the perturbation. The initial structure of the double array of vortices is not maintained except for a very special form of perturbation. The facts that large scales decay more slowly than small scales and that, when non-linearities are sufficiently strong, energy is transferred from one scale to another explain the differences in the disarrangement process for different initial strengths of the vortices of the basic state. The stronger vortices, i.e. the vortices perturbed in a manner that increases their strength, tend to dominate the weaker vortices. The pairing and subsequent merging (or capture) of vortices of like sense into larger-scale vortices are described in terms of peaks in the evolution of the square root of the palinstrophy divided by the enstrophy.     

无原子布氏代数理论的计算复杂性

研究无原子布氏代数的计算复杂性 .得到了下面的新定理 :定理 1　无原子布氏代数理论Δ具有完全的量词消去法 ,也就是说每一个式子都Δ等价于一个开式子 .定理 2　无原子布氏代数的初等型Γ (x1,… ,xn)是由型内的不含量词的全体开式子所唯一决定 .定理 3　无原子布氏代数的一个长度为 n的语句的判断过程所消耗的 Turing时间和空间都是属于 2 2 cn指数级 .     

强激光远场焦斑重构算法研究

 通过CCD图像采集单元结合传统的列阵相机测量高功率固体激光器的远场焦斑分布，采用图像处理技术的边缘算子提取焦斑的几何中心，提出通过几何中心对心的焦斑嵌套重构算法，解决了光斑饱和时的对心难题，实现了快捷准确测量激光焦斑，为激光器的实时控制提供参考数据。     

Petrographic/geochemical studies of primary and alteration–weathering minerals in garnetiferous ultramafic xenoliths–basanite, Tartous Province, NW Syria

Kimberlitic–pyropic peridotite–xenolites, probably of Jurassic–Cretaceous age, were found mixed with a younger Upper Tertiary basanitic diabase, as flow texture of plagioclase laths and ilmenite rods around those xenoliths indicated. Mafic–ultramafic rocks were crushed, sheared, and cropped along a creek about 15–18 km NE of the town of Dreikeesh, NW Syria. ⁴⁰K–⁴⁰Ar isotopic dating of a pure fresh black cpx sample, collected from the peridotite xenoliths, yielded an age of about 70 Ma. This age is concurrent to the time when Africa, Eurasia, and America were part of the super continent Pangaea. It also suggests that kimberlite–pyropic peridotitic rocks were located within a cratonic pipe prior to their 2000-km eastward journey (starting from the Mid-Atlantic Rift). Sampled outcrops were located within a ring of about 40 km diameter, considered to be a dome consisting of one or more clusters of kimberlitic pipes. The dome structure, mostly covered with Upper Jurassic–Cretaceous carbonate beds, was tilted westward, and rifted and sheared along its eastern edge. Tilting and crushing were accomplished after the opening of the Red Sea in the Miocene, and the counterclockwise movements of the Arabian plate, which folded the carbonate beds to form the N–S-trending Alawite mountain range along the Syrian coast. Olivine, cpx, and pyrope were the major phases in peridotite. Pyrope, including its Cr–Ni-contents, was found to be the best indicator to decipher the temperature–pressure (T–P) conditions for the system. The inferred temperature was found to be about 1460 °C, at a pressure of 62 kb (around 207 km-depth). Petrographic studies revealed many zoned, resorbed, octahedral and non-metasomatized tiny grains, associated with partly to wholly metasomatized and iddingsitized olivines.     

Structure and defects at Y2BaCuO5 interfaces in melt-textured YBa2Cu3Ox superconductors

Y₂BaCuO₅ (211) inclusions are prominent microstructural features found in melt-textured YBa₂Cu₃O_x (123) superconductors. These particles are of interest because the 123/211 interfaces and the interface-associated defects have been proposed to be flux pinning centers. In addition, the 211 particles are believed to be heterogeneous nucleation centers of dislocation which can increase the critical current density of 123. Unfortunately, only limited studies have been performed on these particles to ascertain their roles in flux pinning. In this investigation, 211 particles, the interfacial structure and defects in undeformed and mechanically deformed melt-textured 123 have been studied by transmission electron microscopy. It was found that there appears to be a preferred orientation between large oblong 211 particles and the 123 matrix. In addition, while the 123/211 interfaces in undeformed 123 are sharp and relatively undistorted, the interfaces in deformed 123 samples are much thicker. Also, the distribution of strained regions and dislocations around oblong 211 particles in undeformed 123 is nonuniform; the interfaces of low surface curvature are relatively free of defects while the surfaces of high curvature are abundant in dislocations. In contrast, the 123/211 interfaces in deformed 123 samples contain high density of dislocations regardless of interface curvature.     

The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

Pulsed gas lenses

The concept of a pulsed gas lens is proposed. Potential applications are envisaged and preliminary experiments with pulsed ray refraction are reported.