A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

Non-Acceleration Theorem in a Primitive Equation System: I. Acceleration of Zonal Mean Flow

Non-acceleration theorem in a primitive equation system is developed to investigate the influences of waves on the mean flow variation against external forcing. Numerical results show that mechanical forcing overwhelms thermal forcing in maintaining the mean flow in which the internal mechanical forcing associated with horizontal eddy flux of momentum plays the most important roles. Both internal forcing and external forcing are shown to be active and at the first place for the mean flow variations, whereas the forcing-induced mean meridional circulation is passive and secondary. It is also shown that the effects on mean flow of external mechanical forcing are concentrated in the lower troposphere, whereas those due to wave-mean flow interaction are more important in the upper troposphere. These act together and result in the vertically easterly shear in low latitudes and westerly shear in mid-latitudes. This vertical shear of mean flow is to some extent weakened by thermal forcing.

HYPERBOLIC MEAN CURVATURE FLOW:EVOLUTION OF PLANE CURVES

In this paper we investigate the one-dimensional hyperbolic mean curvatureflow for closed plane curves. More precisely, we consider a family of closed curves F ： S1 × [0, T ） → R^2 which satisfies the following evolution equation δ^2F /δt^2 （u, t） = k（u, t）N（u, t）-▽ρ（u, t）, ∨（u, t） ∈ S^1 × [0, T ） with the initial data F （u, 0） = F0（u） and δF/δt （u, 0） = f（u）N0, where k is the mean curvature and N is the unit inner normal vector of the plane curve F （u, t）, f（u） and N0 are the initial velocity and the unit inner normal vector of the initial convex closed curve F0, respectively, and ▽ρ is given by ▽ρ Δ=（δ^2F /δsδt ,δF/δt） T , in which T stands for the unit tangent vector. The above problem is an initial value problem for a system of partial differential equations for F , it can be completely reduced to an initial value problem for a single partial differential equation for its support function. The latter equation is a hyperbolic Monge-Ampere equation. Based on this, we show that there exists a class of initial velocities such that the solution of the above initial value problem exists only at a finite time interval [0, Tmax） and when t goes to Tmax, either the solution convergesto a point or shocks and other propagating discontinuities are generated. Furthermore, we also consider the hyperbolic mean curvature flow with the dissipative terms and obtain the similar equations about the support functions and the curvature of the curve. In the end, we discuss the close relationship between the hyperbolic mean curvature flow and the equations for the evolving relativistic string in the Minkowski space-time R^1,1.

SELF-SIMILAR SOLUTIONS TO THE HYPERBOLIC MEAN CURVATURE FLOW

This article concerns the self-similar solutions to the hyperbolic mean curvature flow （HMCF） for plane curves, which is proposed by Kong, Liu, and Wang and relates to an earlier proposal for general flows by LeFloch and Smoczyk. We prove that all curves immersed in the plane which move in a self-similar manner under the HMCF are straight lines and circles. Moreover, it is found that a circle can either expand to a larger one and then converge to a point, or shrink directly and converge to a point, where the curvature approaches to infinity.

ACOUSTIC PROPAGATION IN SHEARED MEAN FLOW USING COMPUTATIONAL AEROACOUSTICS

Acoustic propagation problems in the sheared mean flow are numerically investigated using different acoustic propagation equations , including linearized Euler equations ( LEE ) and acoustic perturbation equations ( APE ) .The resulted acoustic pressure is compared for the cases of uniform mean flow and sheared mean flow using both APE and LEE.Numerical results show that interactions between acoustics and mean flow should be properly considered to better understand noise propagation problems , and the suitable option of the different acoustic equations is indicated by the present comparisons.Moreover , the ability of APE to predict acoustic propagation is validated.APE can replace LEE when the 3-D flow-induced noise problem is solved , thus computational cost can decrease.

A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

Under the hypothesis of mean curvature flows of hypersurfaces, we prove that the limit of the smooth rescaling of the singularity is weakly convex. It is a generalization of the result due to G.Huisken and C. Sinestrari in. These apriori bounds are satisfied for mean convex hypersurfaces in locally symmetric Riemannian manifolds with nonnegative sectional curvature.

SOME EXTENSIONS OF THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

Given a family of smooth immersions of closed hypersurfaces in a locally symmetric Riemannian manifold with bounded geometry, moving by mean curvature flow, we show that at the first finite singular time of mean curvature flow, certain subcritical quantities concerning the second fundamental form blow up. This result not only generalizes a result of Le-Sesum and Xu-Ye-Zhao, but also extends the latest work of Le in the Euclidean case

The Propagation of Inertia-Gravity Waves and Their Influence on Zonal Mean Flow Part Two:Wave Breaking and Critical Levels

The gravity wave breaking is crucial to the large-scale circulation of middle atmosphere. In this paper, we follow Lindzen (1981) to draw out the parameterization of two-dimensional gravity wave breaking including inertial effect. Also we present some properties of critical levels and inertial critical levels.

The Propagation of Inertia-Gravity Waves and Their Influence on Mean Zonal Flow, Part One: the Propagation of Inertia-Gravity Waves

Inertia-gravity waves play an increasingly important role in the middle atmosphere dynamics. As a result, more attention has been paid to the study of inertia-gravity waves, especially to the middle atmosphere gravity waves. This paper presents some aspects of inertia-gravity waves with emphasis on the propagation. Two methods are used here, namely, geometric optical method and physical optical method. We can see from the study that inertia-gravity waves are similar to planetary waves in some respects and they are different from planetary waves in others.

A simplified two-dimensional boundary element method with arbitrary uniform mean flow

To reduce computational costs, an improved form of the frequency domain boundary element method（BEM） is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation（BIE） representation solves the two-dimensional convected Helmholtz equation（CHE） and its fundamental solution, which must satisfy a new Sommerfeld radiation condition（SRC） in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Green＇s kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole,dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation.

Quasi-40-Day Oscillation and Its Teleconnection Structure together with the Possible Dependence on Conversion of Barotropic Unstable Energy of Temporal Mean Flow

A study is made of the distribution of the diagnostic quantity vector E and the teleconnection structure of 30-50 (quasi-40) day oscillation, together with the dependence on the conversion of barotropic unstable energy of mean flow in terms of ECWMF daily 500 hPa grid data in winter, indicating that the energy transportation is closely associated with the westerly jet position, with zonal (meridional) propagation in the strong (weak) wind region, that considerable conversion of barotropic energy occurs at the jet exit region where low-frequency oscillation gains energy from the mean flow, leading to maximum kinetic energy for the oscillation observed there, which is marked by evident barotropy in striking contrast to the baroclinicity at low latitudes and that the teleconnection core is related to the center of action in the atmosphere and bound up with the pattern of the west wind.

Symmetries and conservation laws associated with a hyperbolic mean curvature flow

Under investigation in this paper is a hyperbolic mean curvature flow for convex evolving curves.Firstly,in view of Lie group analysis,infinitesimal generators,symmetry groups and an optimal system of symmetries of the considered hyperbolic mean curvature flow are presented.At the same time,some group invariant solutions are computed through reduced equations.In particular,we construct explicit solutions by applying the power series method.Furthermore,the convergence of the solutions of power series is certificated.Finally,conservation laws of the hyperbolic mean curvature flow are established via Ibragimov's approach.

SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS

First, we review the authors＇ recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric solutions. Then we study the sufficient condition for which the translating solution is rotationally symmetric. We will use a moving plane method to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition.

沉浸其中就可以了吗?——沉浸体验和意义体验对旅游演艺游客满意度影响研究

旅游演艺迭代升级中,具身体验设计被产业界视为制胜法宝,但学术界对其如何影响游客满意度缺乏深入解读。该研究基于叙事传输理论和精细加工可能性模型,深入研究影响旅游演艺游客满意度的沉浸体验与意义体验,分析基于认知评价的中心路径和基于情感反应的边缘路径对游客满意度产生的加成效应和削弱效应,并进一步分析边缘路径对中心路径产生的偏见效应。研究发现,沉浸体验主要通过诱发情感反应进而影响满意度,意义体验则主要通过引致认知评价进而影响满意度,且意义体验通过认知评价对游客满意度的间接效应强于沉浸体验通过情感反应对游客满意度的间接效应。此外,旅游演艺游客体验中游客对旅游演艺的理性思考与评价会受到其情感反应的影响。文章深化了旅游演艺游客体验相关理论,为旅游演艺的创意策划和开发设计提供了方法指导和决策参考。

Evaluation of Mid-Depth Currents of NCEP Reanalysis Data in the Tropical Pacific Using ARGO Float Position Information

The global project of the Array for Real-time Geostrophic Oceanography （ARGO） provides a unique opportunity to observe the absolute velocity in mid-depths of the world oceans. A total of 1597 velocity vectors at 1000 （2000） db in the tropical Pacific derived from the ARGO float position information during the period November 2001 to October 2004 are used to evaluate the intermediate currents of the National Centers for Environmental Prediction reanalysis. To derive reliable velocity information from ARGO float trajectory points, a rigorous quality control scheme is applied, and by virtue of a correction method for reducing the drift error on the surface in obtaining the velocity vectors, their relative errors are less than 25%. Based on the comparisons from the quantitative velocity vectors and from the space-time average currents, some substantial discrepancies are revealed. The first is that the velocities of the reanalysis at mid-depths except near the equator are underestimated relative to the observed velocities by the floats. The average speed difference between NCEP and ARGO values ranges from about -2.3cm s^-1 to -1.8 cm s^-1. The second is that the velocity difference between the ocean model and the observations at 2000 dB seems smaller than that at 1000 dB. The third is that the zonal flow in the reanalysis is too dominant so that some eddies could not be simulated, such as the cyclonic eddy to the east of 160°E between 20°N and 30°N at 2000 dB. In addition, it is noticeable that many floats parking at 1000 dB cannot acquire credible mid-depth velocities due to the time information of their end of ascent （start of descent） on the surface in the trajectory files. Thus, relying on default times of parking, descent and ascent in the metadata files gravely confines their application to measuring mid-depth currents.

A LEVEL SET METHOD FOR STRUCTURAL TOPOLOGY OPTIMIZATION WITH MULTI-CONSTRAINTS AND MULTI-MATERIALS

Combining the vector level set model,the shape sensitivity analysis theory with the gradient projection technique,a level set method for topology optimization with multi-constraints and multi-materials is presented in this paper.The method implicitly describes structural material in- terfaces by the vector level set and achieves the optimal shape and topology through the continuous evolution of the material interfaces in the structure.In order to increase computational efficiency for a fast convergence,an appropriate nonlinear speed mapping is established in the tangential space of the active constraints.Meanwhile,in order to overcome the numerical instability of general topology opti- mization problems,the regularization with the mean curvature flow is utilized to maintain the interface smoothness during the optimization process.The numerical examples demonstrate that the approach possesses a good flexibility in handling topological changes and gives an interface representation in a high fidelity,compared with other methods based on explicit boundary variations in the literature.

Numerical Simulation of Austenite Recrystallization in CSP Hot Rolled C-Mn Steel Strip

An integrated mathematical model is developed to predict the microstructure evolution of C-Mn steel during multipass hot rolling on the CSP production line, and the thermal evolution, the temperature distribution, the deformation, and the austenite recrystallization are simulated. The characteristics of austenite recrystallization of hot rolled C-Mn steel in the CSP process are also discussed. The simulation of the microstructure evolution of C-Mn steel ZJ510L during CSP multipass hot rolling indicates that dynamic recrystallization and metadynamic recrystallization may easily occur in the first few passes, where nonuniform recrystallization and inhomogeneous grain size microstructure may readily occur; during the last few passes, static recrystallization may occur dominantly, and the microstructure will become more homogeneous and partial recrystallization may occur at relatively low temperature.

LEVEL SET METHOD FOR TOPOLOGICAL OPTIMIZATION APPLYING TO STRUCTURE, MECHANISM AND MATERIAL DESIGNS

Based on a level set model, a topology optimization method has been suggestedrecently. It uses a level set to express the moving structural boundary, which can flexibly handlecomplex topological changes. By combining vector level set models with gradient projectiontechnology, the level set method for topological optimization is extended to a topologicaloptimization problem with multi-constraints, multi-materials and multi-load cases. Meanwhile, anappropriate nonlinear speed, mapping is established in the tangential space of the activeconstraints for a fast convergence. Then the method is applied to structure designs, mechanism andmaterial designs by a number of benchmark examples. Finally, in order to further improvecomputational efficiency and overcome the difficulty that the level set method cannot generate newmaterial interfaces during the optimization process, the topological derivative analysis isincorporated into the level set method for topological optimization, and a topological derivativeand level set algorithm for topological optimization is proposed.

中国古代舞蹈审美层面论

情与志的密不可分、合二而一是中国舞蹈审美在内容层面上的独有特征;拧、倾、曲、圆的形态特征,轻盈流动的舞姿,精彩绝伦的旋转形象共同构成古代舞蹈审美形式层面上"圆润流转"的美学风格;在艺术思想层面上,中国古代舞蹈审美直接指向意境,从圆润流转的舞蹈艺术形式中流溢出空灵流动的生命情调和神韵,在舞蹈艺术表演中又蕴涵着以实带虚、虚实相生的思想,而这些恰恰是其它一切古典艺术样式的最高美学追求。

Prediction of Rolling Load, Recrystallization Kinetics, and Microstructure During Hot Strip Rolling

The recrystallization kinetics and grain size models were developed for the C Mn and niobium containing steels to describe the metallurgical phenomenon such as softening, grain growth, and strain accumulation. Based on the recrystallization kinetics equations, the mean flow stress and the rolling load of each pass were predicted and the optimum rolling schedule was proposed for hot strip rolling. The austenite grain refinement is associated with the addition of niobium, the decrease of starting temperature of finish rolling, and the reduction of finished thickness. The mean flow stress curve with a continuous rising characteristic can be usually observed in the finish rolling of niobium containing steel, which is formed as a result of the heavy incomplete softening and strain accumulation. The predic ted rolling loads are in good agreement with the measured ones.