Deflections and curvatures of a film-substrate structure with the presence of gradient stress in MEMS applications

The close form solutions of deflections and curvatures for a film-substrate composite structure with the presence of gradient stress are derived. With the definition of more precise kinematic assumption, the effect of axial loading due to residual gradient stress is incorporated in the governing equation. The curvature of film-substrate with the presence of gradient stress is shown to be nonuniform when the axial loading is nonzero. When the axial loading is zero, the curvature expressions of some structures derived in this paper recover the previous ones which assume the uniform curvature. Because residual gradient stress results in both moment and axial loading inside the film-substrate composite structure, measuring both the deflection and curvature is proposed as a safe way to uniquely determine the residual stress state inside a film-substrate composite structure with the presence of gradient stress.

Quantum phase transitions in the S=1/2 distorted diamond chain

By means of the second derivative of the ground-state and first-excited energy, the quantum phase transitions (QPTs) for the distorted diamond chain (DDC) with ferromagnetic and antiferromagnetic frustrated interactions and the trimerized case are investigated, respectively. Our results show the plentiful quantum phases owing to the spin interaction competitions in the model. Meanwhile, by using the transfer-matrix renormalization-group technique, we study the two-site thermal entanglement of the DDC model in the thermodynamic limit for a further understanding of the QPTs.

Generalized Viscoplastic Modeling of Debris Flow

Various concepts have been proposed or used in the development of rheological models for debris flow. The earliest model developed by Bagnold was based on the concept of the “dispersive” pressure generated by grain collisions. Bagnold’s concept appears to be theoretically sound, but his empirical model has been found to be inconsistent with most theoretical models developed from non-Newtonian fluid mechanics. Although the generality of Bagnold’s model is still at issue, debris-flow modelers in Japan have generally accepted Takahashi’s formulas derived from Bagnold’s model. Some efforts have recently been made by theoreticians in non-Newtonian fluid mechanics to modify or improve Bagnold’s concept or model. A viable rheological model should consist both of a rate-independent part and a rate-dependent part. A generalized viscoplastic fluid (GVF) model that has both parts as well as two major rheological properties (i.e., the normal stress effect and soil yield criterion) is shown to be sufficiently accurate, yet practical, for general use in debris-flow modeling. In fact, Bagnold’s model is found to be only a particular case of the GVF model. Analytical solutions for (steady) uniform debris flows in wide channels are obtained from the GVF model based on Bagnold’s simplified assumption of constant grain concentration.

带参并发系统的模型检测

带参并发系统 实际包含一族并发系统实例，其中以一个（或多个）参数表示每个系统实例的规模，比如实例系统中 并发执行的进程个数或数据域的大小。带参模型检测的任务是验证 对任意的参数数值，所有的系统实例都满足所期望的性质。本文研究带参并发系统的模型检测方法和技术。 一般来说， 带参系统的参数不仅代表进程个数，也可以是通信缓冲区容量、数据域大小、数据通路宽度等。然而迄今为止，该领域的绝大多数研究都 针对前者类型的参数，而往往忽视数据方面的参数。本文中，我们提出基于带符号迁移图的复合型带参网络协议建模框架。 系统表示为顺序结构的“结点进程”的并发复合，彼此通过“信道进程”进行通讯；性质以一种嵌套谓词等式系形式的一阶$\mu$ 演算表达；进而相应扩展由实验室自主开发的传值进程模型检测工具，对于数据带参的并发系统给出有效的验证方法， 并且对于一些典型的带参系统作出实例研究。 出乎意料的是，在GERMAN2004 协议的缓存一致性已经被其他研究者证明正确的情况下，我们却发现了它在于数据一致性方面的一个严重错误，并予以更正。 进一步，应用我们检测工具中所实现的“数据无关”技术，我们有效推广了研究结论，证明了对于任意大小的数据域， 修改后的GERMAN协议仍然保证满足数据一致性要求。 环境抽象的方法将计数抽象的思想借鉴到谓词抽象的技术中，对于控制带参的并发系统给出一般性验证框架。然而该方法具有相当 高的复杂度；对于很多实际应用的系统而言，所构造的抽象系统规模仍然超出常用模型检测工具所能处理的范围。为了克服这个困难， 我们提出了{\em 状态聚类}方法，在 局部可达性分析的基础上，通过对系统表达式的分析把全部可达的局部状态分组成为少数几个状态簇。在进行 状态聚类的启发式算法中，我们采用了先分裂后聚合的策略，即在识别出不同类的具有代表性的状态配置后，再将类似的状态尽可能 合并到同一个状态簇。这样局部状态被相应划分成为若干等价类，每个类以一个单元状态为代表。然后我们在系统描述的层次上， 通过程序重写的方式直接构造生成对应的抽象系统。 实例研究显示，状态聚类方法通常能够将抽象节点的大小缩减约3个数量级。 参数抽象作为带参系统的安全性性质验证的另外一个有效方法，其最困难之处在于找到合适的辅助不变量，用以进行卫加强 以精化抽象模型。针对这个问题，我们提出一种启发式的方法，通过在参考模型中计算自动产生辅助不变量。 利用这一技术，我们将参数截断的思想应用于 处理环境抽象中依赖于参数类型的复杂变量，使得环境抽象在状态聚类后得到进一步优化。我们有效结合了参数抽象与环境抽象技术， 显著降低了抽象系统状态空间规模，从而极大节省了模型检测的内存开销；并且由于抽象中的每个 步骤都以现行的模型检测工具辅助计算，整个验证过程可以机械化完成，不需要过多的人工介入。作为示范，对于 工业应用的复杂的缓存一致性协议FLASH，我们在保留了其中最为著名的“三跳”事务处理的情况下，验证了缓存一致性和数据一致性。 据我们所知，这是首次这样工业实用的复杂协议能够同时在控制方面和数据方面在如此的精度上得到成功验证。

Magnetic frustration induced quantum phase transitions in the S=1/2 vertically asymmetric diamond chain

This work was supported by the National Basic Research Program of China (973 Program) grant No. G2009CB929300 and the National Natural Science Foundation of China under Grant Nos. 60521001 and 60776061.

Methods to study the ionic conductivity of polymeric electrolytes using a.c. impedance spectroscopy

Composite polymeric electrolytes of PEO-LiClO4-Al2O3 and PEO-LiClO4-EC were prepared and the ionic conductivity by a.c. impedance was calculated using four different methods, and three kinds of representations of a.c. impedance spectra were adopted. The first is based on the Nyquist impedance plot of the imaginary part (Z") versus the real part (Z') of the complex impedance. The second and the third correspond to the plots of imaginary impedance Z" as a function of frequency (f), and the absolute value (\Z\) and phase angle (theta) as a function of f, respectively. It was found that the values of the ionic conductivity calculated using the three representations of a.c. impedance spectra are basically identical.

A meso elastoplastic constitutive model for polycrystalline metals based on equivalent slip systems with latent hardening

A meso material model for polycrystalline metals is proposed, in which the tiny slip systems distributing randomly between crystal slices in micro-grains or on grain boundaries are replaced by macro equivalent slip systems determined by the work-conjugate principle. The elastoplastic constitutive equation of this model is formulated for the active hardening, latent hardening and Bauschinger effect to predict macro elastoplastic stress-strain responses of polycrystalline metals under complex loading conditions. The influence of the material property parameters on size and shape of the subsequent yield surfaces is numerically investigated to demonstrate the fundamental features of the proposed material model. The derived constitutive equation is proved accurate and efficient in numerical analysis. Compared with the self-consistent theories with crystal grains as their basic components, the present theory is much simpler in mathematical treatment.

Time-Frequency Analysis of Nonlinear Systems: The Skeleton Linear Model and the Skeleton Curves

The joint time-frequency analysis method is adopted to study the nonlinear behavior varying with the instantaneous response for a class of S.D.O.F nonlinear system. A time-frequency masking operator, together with the conception of effective time-frequency region of the asymptotic signal are defined here. Based on these mathematical foundations, a so-called skeleton linear model (SLM) is constructed which has similar nonlinear characteristics with the nonlinear system. Two skeleton curves are deduced which can indicate the stiffness and damping in the nonlinear system. The relationship between the SLM and the nonlinear system, both parameters and solutions, is clarified. Based on this work a new identification technique of nonlinear systems using the nonstationary vibration data will be proposed through time-frequency filtering technique and wavelet transform in the following paper.

2-DELTA-FUNCTION GENERALIZED PLASMA POLE MODEL FOR 1ST PRINCIPLE CALCULATIONS OF QUASI-PARTICLE ENERGIES IN MANY-ELECTRON SYSTEMS

To evaluate the dynamical effects of the screened interaction in the calculations of quasiparticle energies in many-electron systems a two-delta-function generalized plasma pole model (GPP) is introduced to simulate the dynamical dielectric function. The usual single delta-function GPP model has the drawback of over simplifications and for the crystals without the center of symmetry is inappropriate to describe the finite frequency behavior for dielectric function matrices. The discrete frequency summation method requires too much computation to achieve converged results since ab initio calculations of dielectric function matrices are to be carried out for many different frequencies. The two-delta GPP model is an optimization of the two approaches. We analyze the two-delta GPP model and propose a method to determine from the first principle calculations the amplitudes and effective frequencies of these delta-functions. Analytical solutions are found for the second order equations for the parameter matrices entering the model. This enables realistic applications of the method to the first principle quasiparticle calculations and makes the calculations truly adjustable parameter free.

Refinement of edge-to-edge matching model and its application in the Mg17Al12/alpha-Mg and alpha-Y/alpha-Mg systems

A refined version of the edge-to-edge matching model is described here. In the original model, the matching directions were obtained from the planes with all the atomic centers that were exactly in the plane, or the distance from the atomic center to the plane which was less than the atomic radius. The direction-matching pairs were the match of straight rows-straight rows and zigzag rows-zigzag rows. In the refined model, the matching directions were obtained from the planes with all the atomic centers that were exactly in the plane.

Statistical thermodynamics of polydisperse polymer systems in the framework of lattice fluid model: Effect of molecular weight and its distribution on the spinodal in polymer solution

With the aid of thermodynamics of Gibbs, the expression of the spinodal was derived for the polydisperse polymer-solvent system in the framework of Sanchez-Lacombe Lattice Fluid Theory (SLLFT). For convenience, we considered that a model polydisperse polymer contains three sub-components. According to our calculation, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights of the polydisperse polymer, but the z-average molecular weight ((M) over bar (z)) dependence on the spinodal is invisible. The dependence of free volume on composition, temperature, molecular weight, and its distribution results in the effect of (M) over bar (n) on the spinodal. Moreover, it has been found that the effect of changing (M) over bar (w) on the spinodal is much bigger than that of changing (M) over bar (n) and the extrema of the spinodal increases with the rise of the weight-average molecular weight of the polymer in the solutions with upper critical solution temperature (UCST). However, the effect of polydispersity on the spinodal can be neglected for the polymer with a considerably high weight-average molecular weight. A more simple expression of the spinodal for the polydisperse polymer solution in the framework of SLLFT was also derived under the assumption of upsilon(*)=upsilon(1)(*)=upsilon(2)(*) and (1/r(1)(0))-(1/r(2i)(0))-->(1/r(1)(0)).