A unified analysis of a micro-beam,droplet and CNT ring adhered on a substrate:Calculation of variation with movable boundaries

In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube （CNT） ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thor- oughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materi- als, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.

A Generalized Variational Principle for 2-D Piezoelectricity with Surface Electrodes

It is difficult to establish a classical variational model for piezoelectricity. Following the semi inverse method of establishing generalized variational principles, an energy like trial functional with a certain unknown function is constructed. The unknown function is easily identified step by step. A family of variational principles for the static behavior of the elastic and electric variables in the vicinity of a surface electrode attached to a piezoelectric ceramic is established directly from its field equations and boundary conditions.

A UNIVERSAL VARIATIONAL FORMULATION FOR TWO DIMENSIONAL FLUID MECHANICS

A universal variational formulation for two dimensional fluid mechanics is obtained. which is subject to the so-called parameter-constrained equations (the relationship between parameters in two governing equations). By eliminating the constraints the generalized variational principle (GVPs) can be readily derived from the formulation The formulation can be applied to any conditions in case the governing equations can be converted into conservative forms. Some illustrative examples are given to testify the effectiveness and simplicity of the method.

Theoretical Study on Mechanism and Kinetics of Reaction of O（^3p） with Propane

The reaction of C3H8＋O（^3p）→C3HT＋OH is investigated using ab initio calculation and dynamical methods. Electronic structure calculations for all stationary points are obtained using a dual-level strategy. The geometry optimization is performed using the unrestricted second-order Moller-Plesset perturbation method and the single-point energy is computed us- ing the coupled-cluster singles and doubles augmented by a perturbative treatment of triple excitations method. Results indicate that the main reaction channel is C3Hs＋O（^3p）→i- C3HT＋OH. Based upon the ab initio data, thermal rate constants are calculated using the variational transition state theory method with the temperature ranging from 298 K to 1000 K. These calculated rate constants are in better agreement with experiments than those reported in previous theoretical studies, and the branching ratios of the reaction are also calculated in the present work. Furthermore, the isotope effects of the title reaction are calculated and discussed. The present work reveals the reaction mechanism of hydrogenabstraction from propane involving reaction channel competitions is helpful for the understanding of propane combustion.

Review of Feynman’s Path Integral in Quantum Statistics:from the Molecular Schrödinger Equation to Kleinert’s Variational Perturbation Theory

Feynman’s path integral reformulates the quantum Schrödinger differential equation to be an integral equation.It has been being widely used to compute internuclear quantum-statistical effects on many-body molecular systems.In this Review,the molecular Schrödinger equation will first be introduced,together with the BornOppenheimer approximation that decouples electronic and internuclear motions.Some effective semiclassical potentials,e.g.,centroid potential,which are all formulated in terms of Feynman’s path integral,will be discussed and compared.These semiclassical potentials can be used to directly calculate the quantum canonical partition function without individual Schrödinger’s energy eigenvalues.As a result,path integrations are conventionally performed with Monte Carlo and molecular dynamics sampling techniques.To complement these techniques,we will examine how Kleinert’s variational perturbation(KP)theory can provide a complete theoretical foundation for developing non-sampling/non-stochastic methods to systematically calculate centroid potential.To enable the powerful KP theory to be practical for many-body molecular systems,we have proposed a new path-integral method:automated integrationfree path-integral(AIF-PI)method.Due to the integration-free and computationally inexpensive characteristics of our AIF-PI method,we have used it to perform ab initio path-integral calculations of kinetic isotope effects on proton-transfer and RNA-related phosphoryl-transfer chemical reactions.The computational procedure of using our AIF-PI method,along with the features of our new centroid path-integral theory at the minimum of the absolute-zero energy(AMAZE),are also highlighted in this review.

Variational transition state theory study of the reactions Li+HF and Li+HCl on the BO potential energy surfaces

Variational transition state theory is used to study the kinetics of the reactions Li+HF and Li+HCl on the BO potential energy surfaces, fitted to ab initio values by Lagana et al. The saddle point, the location of generalized transition state and other kinetic features on the bottleneck of the po- tential energy surface are obtained. We point out that the location of generalized transition state tends to the direction in which the two atoms with larger reduced mass separate off. It can be determined whether a potential energy surface is accurate or not by a fine analysis of its bottleneck region and a comparison of kinetic calculation with experimental result. This is helpful for building a more accurate potential energy surface.

Whither East-West Comparative Literature? One Recent Answer from China

Comparative literature,as a discipline,has been in selfdoubt and crisis since its birth.Various scholars give different answers to its tendency and future.With the growth of East-West comparative literature research in East Asia,Chinese School of Comparative Literature proposed its own answer to it.In response to James St.André’s review essay'Whither East-West Comparative Literature?Two Recent Answers from the U.S.',this paper focuses on a new answer from Cao Shunqing’s work The Variation Theory of Comparative Literature,aiming to explore the two focuses of this new platform:one is the heterogeneity,and the other is the variation,which are different from French comparatism based on influences and American part based on analogies.On this basis this article tries to have a dialogue with imagology study of variation theory and sinicization of Western literary theory in Cao’s works.By highlighting the heterogeneity and variation,Chinese scholars seek to promote crosscivilization communication based on maintaining and developing the uniqueness of different literatures and civilizations,thus building a harmonious world without uniformity.

Comparative Literature Studies in China:From Seeking Homogeneity to Heterogeneity

Variation theory is one of the very few ideas put forward by a Chinese comparatist.It indicates that comparative literature,especially Chinese-Western comparative literature studies no longer merely seeks homogeneity.It is also characterized by seeking heterogeneity,for Chinese literature and Western literature belong to two entirely different cultural backgrounds.In this sense,homogeneity is only relative,while heterogeneity is absolute.In this way,the variation theory will point to a new orientation for current international comparative literature studies which is viewed as being in a crisis.

Mechanics analysis of thin-walled box continuous girder with variable cross-sections in considering effect of large deflection and shear lag

In order to study the mechanics behavior of a thin-walled box continuous girder with variable crosssections,using potential variation theories,considering the effect of shear lag of flange’s stress and the nonlinear geometry of vertical displacement,and evolving five generalized displacements with the spline function,the large deflection problem of the thin-walled box continuous girder with variable cross-section was transformed to a nonlinear algebraic equation,which was solved using the Newton-Raphon iterative method.The results of the calculation show that different shear lag warp functions to the cantilever,top and bottom plate should be taken to analyze the mechanics behavior of the thin-walled box continuous girder reliably.The thin-walled box continuous girder with variable cross-sections has more reasonable stress state and is more adaptable for the longitudinal change of internal forces than that with equal crosssections.The effect of large deflection on the stress and displacement of the thin-walled box continuous girder with variable cross-sections depends on the values of the load.

Mechanistic study and kinetic properties of the CF_3CHO+Cl reaction

Theoretical investigations have been carried out on the mechanism and kinetics for the reaction of CF 3 CHO + Cl using duallevel direct dynamics method. The potential energy surface information was obtained at the MCQCISD/3//MP2/cc-pVDZ level and the kinetic calculations were done using variational transition state theory with interpolated single-point energy (VTST-ISPE) approach. The calculated results show that the reaction proceeds primarily via the H-abstraction channel, while the Cl-addition channel is unfavorable due to the higher barriers. The improved canonical variational transition-state theory (ICVT) with the small-curvature tunneling correction (SCT) was used to calculate the rate constants. The theoretical rate constants at room temperature are in general agreement with the experimental values. A three-parameter rate constant expression was fitted over a wide temperature range of 200-2000 K.

The Moduli Space in the Gauged Linear Sigma Model

This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper the authors focus on the description of the moduli.