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 piece...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.展开更多
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 overwhelm...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.展开更多
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 followin...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.展开更多
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 LeFloc...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.展开更多
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 ( A...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.展开更多
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. Sinestra...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.展开更多
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 curva...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展开更多
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 ine...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.展开更多
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...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.展开更多
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 arbitr...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.展开更多
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 energ...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.展开更多
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 th...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.展开更多
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 soluti...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.展开更多
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 10...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.展开更多
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...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.展开更多
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...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.展开更多
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 ...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.展开更多
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 o...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.展开更多
基金supported in part by the NSFC(11801496,11926352)the Fok Ying-Tung Education Foundation(China)the Hubei Key Laboratory of Applied Mathematics(Hubei University).
文摘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.
基金Research Project No.[75-09-01] on medium-range numerical weather forecasts.
文摘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.
基金Kong and Wang was supported in part by the NSF of China (10671124)the NCET of China (NCET-05-0390)the work of Liu was supported in part by the NSF of China
文摘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.
基金supported in part by a grant from China Scholarship Councilthe National Natural Science Foundation of China(11301006)the Anhui Provincial Natural Science Foundation(1408085MA01)
文摘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.
基金Supported by the National Natural Science Foundation of China(10902050)the China Postdoctoral Science Foundation Funded Project(20100481138)the Aeronautical Science Foundation of China(20101452017)
文摘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.
基金supported partially by the National Natural Science Foundation of China (10871171)the Chinese-Hungarian Sci. and Tech. cooperation (for 2007-2009)
文摘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.
基金supported by the NSFC(11101267,11271132)the Innovation Program of Shanghai Municipal Education Commission(13YZ087)the Science and Technology Program of Shanghai Maritime University(20120061)
文摘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
文摘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.
文摘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.
基金supported by National Engineering School of Tunis (No.13039.1)
文摘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.
基金This work is supported by National Natural Science Foundation of China.
文摘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.
基金Supported by the Natural Science Foundation of Shanxi(202103021224068).
文摘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.
基金Supported by Natural Science Foundation of China (10631020, 10871061)the Grant for Ph.D Program of Ministry of Education of Chinasupported by Innovation Propject for the Development of Science and Technology (IHLB) (201098)
文摘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.
基金This research is supported by Natural Science Foundation of China(Contract No.40437017 and 40225015).
文摘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.
基金The project supported by the National Natural Science Foundation of China (59805001,10332010) and Key Science and Technology Research Project of Ministry of Education of China (No.104060)
文摘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.
基金Item Sponsored by Hi-Tech Research Development Programof China(863)(2004AA33G050)
文摘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.
基金This project is supported by National Natural Science Foundation of China(No.598005001, No.10332010) and Key Science and Technology Research Project of Ministry of Education (No.104060).
文摘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.
基金Item Sponsored by National Natural Science Foundation of China (50504007 ,50474086 ,50334010)
文摘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.