We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compact- ification of Teichmfiller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured...We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compact- ification of Teichmfiller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured geodesic lamination converges to the Gardiner-Masur boundary. Using the embedding of flat metrics into the space of geodesic currents, we prove that a horocycle path in Teichmiiller space, which is induced by a quadratic differential whose vertical measured foliation is uniquely ergodic, converges to the Gardiner-Masur boundary and to the Thurston boundary.展开更多
We prove that in dimensions three and higher the Landau-Lifshitz-Gilbert equation with small initial data in the critical Besov space is globally well-posed in a uniform way with respect to the Gilbert damping paramet...We prove that in dimensions three and higher the Landau-Lifshitz-Gilbert equation with small initial data in the critical Besov space is globally well-posed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schr¨odinger maps in the natural space as the Gilbert damping term vanishes. The proof is based on some studies on the derivative Ginzburg-Landau equations.展开更多
For a low carbon steel tube with small wall factor D/t and bending radius R,the over-thinning induced localized necking is one dominant failure in tube numerical control(NC) bending process,which strongly restricts th...For a low carbon steel tube with small wall factor D/t and bending radius R,the over-thinning induced localized necking is one dominant failure in tube numerical control(NC) bending process,which strongly restricts the bendability limit of the tube.In addition,the deterioration of bendability of a tube is increased by the existence of the weak weld region.Therefore,an important issue is how to determinate and predict the welded tube bendability limit.In the present study,a finite element(FE) model with weld and subdivided heat affected zones under ABAQUS platform is employed to explore the deformation behaviors of welded tube NC bending.A localized necking criterion based on the critical thickness thinning is used to predict the critical principal strains,critical bending radius and burst location during the forming process.It is found that the failures always occur at the rigid supporting point of mandrel flexible balls near the tangent point at the outside of the bend,where the wall thickness of the tube is the lowest.The bending limit curves(BLCs) of the QSTE340 welded tube are obtained by shifting the standard shaped forming limit curve to the critical principal strains along the major strain axis.Comparison between the numerical and experimental results has shown that the BLC and critical bending radius predictions agree well with the experimental results.In addition,the effect of weld positions on BLC is discussed,the weld region shows an almost negligible effect on the forming limit at a non-critical location that is far away from the outside of the bend.However,when the weld is at the large tensile deformation region on the outside of the bend,a decrease of the forming limit strains is seen.展开更多
Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension o...Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension of the domain is two or more.展开更多
In this paper, a one-dimensional bipolar Euler-Poisson system (a hydrodynamic model) from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric f...In this paper, a one-dimensional bipolar Euler-Poisson system (a hydrodynamic model) from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations. The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented. Next, two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy's law time asymp- totically. Finally, as a by-product, the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L∞ entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the cor- responding one-dimensional compressible Euler equations with damping exponentially fast as t → +∞. As far as we know, this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary effects and a vacuum.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11271378 and 11201078)
文摘We study the convergence of earthquake paths and horocycle paths in the Gardiner-Masur compact- ification of Teichmfiller space. We show that an earthquake path directed by a uniquely ergodic or simple closed measured geodesic lamination converges to the Gardiner-Masur boundary. Using the embedding of flat metrics into the space of geodesic currents, we prove that a horocycle path in Teichmiiller space, which is induced by a quadratic differential whose vertical measured foliation is uniquely ergodic, converges to the Gardiner-Masur boundary and to the Thurston boundary.
基金supported by Australian Research Council Discovery Project (Grant No. DP170101060)National Natural Science Foundation of China (Grant No. 11201498)the China Scholarship Council (Grant No. 201606495010)
文摘We prove that in dimensions three and higher the Landau-Lifshitz-Gilbert equation with small initial data in the critical Besov space is globally well-posed in a uniform way with respect to the Gilbert damping parameter. Then we show that the global solution converges to that of the Schr¨odinger maps in the natural space as the Gilbert damping term vanishes. The proof is based on some studies on the derivative Ginzburg-Landau equations.
基金supported by the National Natural Science Foundation of China (Grant No. 50875216)111 Project (Grant No. B08040)
文摘For a low carbon steel tube with small wall factor D/t and bending radius R,the over-thinning induced localized necking is one dominant failure in tube numerical control(NC) bending process,which strongly restricts the bendability limit of the tube.In addition,the deterioration of bendability of a tube is increased by the existence of the weak weld region.Therefore,an important issue is how to determinate and predict the welded tube bendability limit.In the present study,a finite element(FE) model with weld and subdivided heat affected zones under ABAQUS platform is employed to explore the deformation behaviors of welded tube NC bending.A localized necking criterion based on the critical thickness thinning is used to predict the critical principal strains,critical bending radius and burst location during the forming process.It is found that the failures always occur at the rigid supporting point of mandrel flexible balls near the tangent point at the outside of the bend,where the wall thickness of the tube is the lowest.The bending limit curves(BLCs) of the QSTE340 welded tube are obtained by shifting the standard shaped forming limit curve to the critical principal strains along the major strain axis.Comparison between the numerical and experimental results has shown that the BLC and critical bending radius predictions agree well with the experimental results.In addition,the effect of weld positions on BLC is discussed,the weld region shows an almost negligible effect on the forming limit at a non-critical location that is far away from the outside of the bend.However,when the weld is at the large tensile deformation region on the outside of the bend,a decrease of the forming limit strains is seen.
基金NSF of Shandong Province (No.Y98A09012, No. Q99A05.)
文摘Abstract. In this paper, we discuss the limit behaviour of solutious to equivalued surfaceboundary value problem for parabolic equations when the equivalued surface boundaryshrinks to a point and the space dimension of the domain is two or more.
基金supported by the National Natural Science Foundation of China(No.11171223)the Innovation Program of Shanghai Municipal Education Commission(No.13ZZ109)
文摘In this paper, a one-dimensional bipolar Euler-Poisson system (a hydrodynamic model) from semiconductors or plasmas with boundary effects is considered. This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations. The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented. Next, two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy's law time asymp- totically. Finally, as a by-product, the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L∞ entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the cor- responding one-dimensional compressible Euler equations with damping exponentially fast as t → +∞. As far as we know, this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary effects and a vacuum.