Analysis of film strain and stress in a film-substrate cantilever system

The bending problem of a magnetic film-nonmagnetic substrate cantilever system is studied by using the principle of energy minimization. Emphasis is placed on the analysis of geometrical and physical parameter dependence of the neutral plane, internal film stress and strain of the cantilever system, and then the influence of such a parameter on the bending characteristic is presented. The results indicate, owing to the anisotropic expanding feature of the magnetostriction, that the neutral plane is generally anisotropic, and moves downwards rapidly with the increasing thickness ratio. Meanwhile, the bounding rigidity of substrate on the film will decrease with the increasing thickness ratio, and thus release the film stress, i.e., it decreases, but the film strain increases. The effect of Poisson’s ratio of the materials on the film strain, the stress and the neutral plane in the direction transverse to the magnetization is prominent. For the strain and the stress in the magnetization, however, the role of Poisson’s ratio is inconspicuous. This property is due to the initiative elongating (or contracting) feature of the magnetic film along its magnetization. Supported by the National Natural Science Foundation of China (Grant No. 10762001), the Key Project of the Chinese Ministry of Education (Grant No. 206024), and the Program for New Century Excellent Talents in University of China (Grant No. NCET-2005-0272)     

Classical Limits of Euclidean Gibbs States for Quantum Lattice Models

Models of quantum and classical particles on a lattice ^d are considered. The classical model is obtained from the corresponding quantum model when the reduced mass of the particle m = / #x210F;² tends to infinity. For these models, the convergence of the Euclidean Gibbs states, when m + , is described in terms of the weak convergence of local Gibbs specifications, determined by conditional Gibbs measures. In fact, it is shown that all conditional Gibbs measures of the quantum model weakly converge to the conditional Gibbs measures of the classical model. A similar convergence of the periodic Gibbs measures and, as a result, of the order parameters, for such models with pair interactions possessing the translation invariance, has also been shown.     

Transfer Operators and State Spaces for Discrete Multidimensional Linear Systems

This paper treats multidimensional discrete input-output systems from the constructive point of view. We adapt and improve recursive algorithms, derived earlier by E. Zerz and the second author from standard Gröbner basis algorithms, for the solution of the canonical Cauchy problem for linear systems of partial difference equations with constant coefficients on the lattices N = ^r1 × ^r2. These recursive algorithms, in turn, furnish four other solution methods for the initial value problem, namely by transfer operators, by canonical Kalman global state equations, by parametrizations of controllable systems and, for systems with proper transfer matrix and left bounded input signals, by convolution with the transfer matrix. In the 2D-case N = ² the last method was studied by S. Zampieri. Minimally embedded systems are studied and give rise to especially simple Kalman equations. The latter also imply a useful characterization of the characteristic or polar variety of the system by eigenvalue spectra. For N = ^r we define reachability of a system and prove that controllability implies reachability, but not conversely. Moreover we solve, in full generality, the modelling problem which was introduced and partially solved by F. Pauer and S. Zampieri. Various algorithms have been implemented by the first author in axiom, and examples are demonstrated by means of computer generated pictures. Related work on state space representations has been done by the Padovian and Groningian system theory schools.     

用雷诺应力模型计算旋风分离器中气-固两相流动

针对分离器内部的复杂的三维强旋转、气-固两相湍流运动,采用雷诺应力模型(SSG),利用贴体网格技术,模拟计算了分离器内部流动,并将计算结果与实验数据进行分析、比较。分离器内的固体颗粒运动采用涉及湍流扩散影响的随机轨道模型和确定轨道模型,在流场计算的基础上,模拟了不同直径的颗粒在分离器内的运动规律及颗粒分离效率,并同理论和实验得到的数据进行了比较。     

A characterization for mixtures of semi-Markov processes

Mixtures of recurrent semi-Markov processes are characterized through a partial exchangeability condition of the array of successor states and holding times. A stronger invariance condition on the joint law of successor states and holding times leads to mixtures of Markov laws.     

Caged H atom and H2 molecule in relation to Monte Carlo study of molecular dissociation at constant volume

Summary Analytic results for electronic kinetic energy are first presented for a hydrogen atom in a spherical cage for two radii near to the corresponding densities employed in the path-integral Monte Carlo study of isochoric molecular dissociation in dense hydrogen by Magroet al. (Magro W. R., Ceperley D. M., Pierleoni C. andBernu B.,Phys. Rev. Lett.,76 (1996) 1240). The relevance of the ?cage? results to the behaviour of dense atomic hydrogen is pointed out. Attention is then shifted to the molecular regime, and the variation with density of electronic kinetic energy for a H₂ molecule in a rigid spheroidal cage is compared and contrasted with the Monte Carlo findings. The rigid-cage model mimics this, as well as bond length contraction, under compression.     

Small-Mass Behavior of Quantum Gibbs States for Lattice Models with Unbounded Spins

We construct the distribution of the infinite-dimensional Markov process associated with a finite-temperature Gibbs state for a quantum mechanical anharmonic crystal. The corresponding state is constructed via a cluster expansion technique for an arbitrary fixed temperature and, correspondingly, small enough masses of particles.     

CuO在高压下的状态方程、电学性质与相变

 在活塞－圆筒式高压装置上研究了CuO在4.5 GPa内的p-V关系，给出了它的状态方程、格临爱森参数γ₀、体积模量B₀以及B₀的压力导数B₀'。在金刚石压砧装置上，采用我们建立的电阻、电容测量方法研究了CuO在22 GPa内电阻、电容与压力的关系。实验结果表明，CuO的电阻和电容在一些压力下都发生了突然的变化。这些变化可能与CuO内部的电子结构和晶界处的结构状态变化有关。     

An algorithmic approach for a special class of Markov chains

In this paper, we develop an algorithmic method for the evaluation of the steady state probability vector of a special class of finite state Markov chains. For the class of Markov chains considered here, it is assumed that the matrix associated with the set of linear equations for the steady state probabilities possess a special structure, such that it can be rearranged and decomposed as a sum of two matrices, one lower triangular with nonzero diagonal elements, and the other an upper triangular matrix with only very few nonzero columns. Almost all Markov chain models of queueing systems with finite source and/or finite capacity and first-come-first-served or head of the line nonpreemptive priority service discipline belongs to this special class.