In this paper, I give out an algorithm of the witten' s invariants of the 3-manifolds obtained by surgery on the links whose corresponding graphs may be no longer trees.
We study the equivalence of tripartite mixed states under local unitary transformations. The nonlocal properties for a class of tripartite quantum states in C^K× CM ^M×C^N composite systems are investigated ...We study the equivalence of tripartite mixed states under local unitary transformations. The nonlocal properties for a class of tripartite quantum states in C^K× CM ^M×C^N composite systems are investigated and a complete set of invariants under local unitary transformations for these states is presented. It is shown that two of these states are locally equivalent if and only if all these invariants have the same values.展开更多
The state of clean sand was mainly dependent on its void ratio(density)and confining stress that greatly influenced the mechanical behavior(compression,dilatancy and liquefaction)of clean sand.Confirming whether the c...The state of clean sand was mainly dependent on its void ratio(density)and confining stress that greatly influenced the mechanical behavior(compression,dilatancy and liquefaction)of clean sand.Confirming whether the confining stress was a state variable of sand required precise element tests at different confining stress,especially the tests under very low confining stress whose test data were very limited.In this study,static-dynamic characteristics of clean sand was comprehensively investigated by a unified test program under low and normal confining stress ranging from 5 to 98 kPa,under monotonic/cyclic and drained/undrained conditions,together with the literature available data under confining stress of 1.0 to 3.0 MPa.For monotonic loading tests,the contraction/dilation phase transition was observed for loose sand at low confining stress,and dilatancy angles were stress-dependent.In addition,the liquefaction resistance was observed to increase with reducing of confining stress,and the axial strain varied from compressive to dilative when confining stress increased.Special attention was also paid to the enhancement effect of membrane,and it was observed that its influence on the test results was limited.In addition,the experimental results were proved reliable by reproducibility.展开更多
Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical...Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical state theory of soil mechanics.Based on experimental data on different types of clay,a simple double-surface model was developed considering explicitly the location of critical state by incorporating the density state into constitutive equations.The model was then used to simulate undrained triaxial compression tests performed on isotropically and anisotropically consolidated samples with different stress ratios.The predictions were compared with experimental results.All simulations demonstrate that the proposed approach is capable of describing the drained and undrained compression behaviors following isotropic and anisotropic consolidations.展开更多
A system of nonlinear diffusion equations with three components is studied via the potential symmetry method. It is shown that the system admits the potential symmetries for certain diffusion terms. The invariant solu...A system of nonlinear diffusion equations with three components is studied via the potential symmetry method. It is shown that the system admits the potential symmetries for certain diffusion terms. The invariant solutions assoeiated with the potential symmetries are obtained.展开更多
In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the fir...In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the first-level search procedure is performed under the conditions of the initial time of escape manifold trajectory of the Sun-Earth halo orbit and the terminal time of capture manifold of the target planet fixed,by solving the optimal two-impulsive heliocentric trajectory to connect the two manifold trajectories.The contour map,helpful to the understanding of the global characteristics of the transfer opportunities,taking the initial time of escape manifold and the terminal time of capture manifold as variables,the optimal velocity increment of the first-level search as objective function,is used for the second-level search.Finally,taking the Earth-Mars and Earth-Venus halo to halo transfers for example,the transfer opportunities in 2015-2017 are searched.The results show the effectiveness of the proposed method and reveal the property of quasi-period of transfer opportunities between interplanetary halo orbits.展开更多
The space block search technology is used to determine a connected three-dimensional fracture network in polygonal shapes,i.e.,seepage paths.After triangulation on these polygons,a finite element mesh for 3D fracture ...The space block search technology is used to determine a connected three-dimensional fracture network in polygonal shapes,i.e.,seepage paths.After triangulation on these polygons,a finite element mesh for 3D fracture network seepage is obtained.Through introduction of the generalized Darcy's law,conservative equations for both fracture surface and fracture interactions are established.Combined with the boundary condition of Signorini's type,a partial differential equation(PDE) formulation is presented for the whole domain concerned.To solve this problem efficiently,an equivalent variational inequality(VI) formulation is given.With the penalized Heaviside function,a finite element procedure for unconfined seepage problem in 3D fracture network is developed.Through an example in a homogeneous rectangular dam,validity of the algorithm is verified.The analysis of an unconfined seepage problem in a complex fracture network shows that the proposed algorithm is very applicable to complex three-dimensional problems,and is effective in describing some interesting phenomenon usually encountered in practice,such as "preferential flow".展开更多
文摘In this paper, I give out an algorithm of the witten' s invariants of the 3-manifolds obtained by surgery on the links whose corresponding graphs may be no longer trees.
基金The project supported by National Natural Science Foundation of China under Grant No. 10375038, the Fund of Beijing MEC under Grant No. KM200510028021 and NSF of Beijing under Grant No. 1042004
文摘We study the equivalence of tripartite mixed states under local unitary transformations. The nonlocal properties for a class of tripartite quantum states in C^K× CM ^M×C^N composite systems are investigated and a complete set of invariants under local unitary transformations for these states is presented. It is shown that two of these states are locally equivalent if and only if all these invariants have the same values.
基金Projects(51908288,41627801)supported by the National Natural Science Foundation of China。
文摘The state of clean sand was mainly dependent on its void ratio(density)and confining stress that greatly influenced the mechanical behavior(compression,dilatancy and liquefaction)of clean sand.Confirming whether the confining stress was a state variable of sand required precise element tests at different confining stress,especially the tests under very low confining stress whose test data were very limited.In this study,static-dynamic characteristics of clean sand was comprehensively investigated by a unified test program under low and normal confining stress ranging from 5 to 98 kPa,under monotonic/cyclic and drained/undrained conditions,together with the literature available data under confining stress of 1.0 to 3.0 MPa.For monotonic loading tests,the contraction/dilation phase transition was observed for loose sand at low confining stress,and dilatancy angles were stress-dependent.In addition,the liquefaction resistance was observed to increase with reducing of confining stress,and the axial strain varied from compressive to dilative when confining stress increased.Special attention was also paid to the enhancement effect of membrane,and it was observed that its influence on the test results was limited.In addition,the experimental results were proved reliable by reproducibility.
基金Project(SKLGP2011K013)supported by the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,ChinaProject(20110073120012)supported by the Research Fund for the Doctoral Program of Higher Education of China+1 种基金Project(11PJ1405700)supported by the the Shanghai Pujiang Talent Plan,ChinaProject(41002091)supported by the National Natural Science Foundation of China
文摘Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical state theory of soil mechanics.Based on experimental data on different types of clay,a simple double-surface model was developed considering explicitly the location of critical state by incorporating the density state into constitutive equations.The model was then used to simulate undrained triaxial compression tests performed on isotropically and anisotropically consolidated samples with different stress ratios.The predictions were compared with experimental results.All simulations demonstrate that the proposed approach is capable of describing the drained and undrained compression behaviors following isotropic and anisotropic consolidations.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10371098 and 10447007 and the Program for New Century Excellent Talents in Universities （NCET）
文摘A system of nonlinear diffusion equations with three components is studied via the potential symmetry method. It is shown that the system admits the potential symmetries for certain diffusion terms. The invariant solutions assoeiated with the potential symmetries are obtained.
基金supported by the National Basic Research Program of China ("973" Program) (Grant No. 2012CB720000)the National Natural Science Foundation of China (Grant Nos. 10832004 and 11102020)
文摘In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the first-level search procedure is performed under the conditions of the initial time of escape manifold trajectory of the Sun-Earth halo orbit and the terminal time of capture manifold of the target planet fixed,by solving the optimal two-impulsive heliocentric trajectory to connect the two manifold trajectories.The contour map,helpful to the understanding of the global characteristics of the transfer opportunities,taking the initial time of escape manifold and the terminal time of capture manifold as variables,the optimal velocity increment of the first-level search as objective function,is used for the second-level search.Finally,taking the Earth-Mars and Earth-Venus halo to halo transfers for example,the transfer opportunities in 2015-2017 are searched.The results show the effectiveness of the proposed method and reveal the property of quasi-period of transfer opportunities between interplanetary halo orbits.
基金supported by the National Natural Science Foundation of China(Grant No.51079110)the National Basic Research Program of China("973"Project)(Grant No.2011CB013506)
文摘The space block search technology is used to determine a connected three-dimensional fracture network in polygonal shapes,i.e.,seepage paths.After triangulation on these polygons,a finite element mesh for 3D fracture network seepage is obtained.Through introduction of the generalized Darcy's law,conservative equations for both fracture surface and fracture interactions are established.Combined with the boundary condition of Signorini's type,a partial differential equation(PDE) formulation is presented for the whole domain concerned.To solve this problem efficiently,an equivalent variational inequality(VI) formulation is given.With the penalized Heaviside function,a finite element procedure for unconfined seepage problem in 3D fracture network is developed.Through an example in a homogeneous rectangular dam,validity of the algorithm is verified.The analysis of an unconfined seepage problem in a complex fracture network shows that the proposed algorithm is very applicable to complex three-dimensional problems,and is effective in describing some interesting phenomenon usually encountered in practice,such as "preferential flow".
