This note concerns the motion of relativistic strings in the Minkowski space R^(1+n).We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is differen...This note concerns the motion of relativistic strings in the Minkowski space R^(1+n).We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is different completelyfrom others.展开更多
Heat transfer and hydrodynamics of two phase closed thermosyphon （TPCT） is studied using finite difference method of Stream function and vorticity. The mathematical model is formed for both vapor phase and liquid fi...Heat transfer and hydrodynamics of two phase closed thermosyphon （TPCT） is studied using finite difference method of Stream function and vorticity. The mathematical model is formed for both vapor phase and liquid film in a non-dimensional form. The momentum and energy equations as parabolic equations have been solved by means of the locally one-dimensional scheme of A.A. Samarskii. The Poisson equation for the stream function has been approximated on the basis of the discrete scheme ＂cross＂. The obtained system of algebraic equations has been solved by the successive over relaxation method. The effect of the Rayleigh number on the velocity and temperature fields in the domain of interest and on the average Nusselt number at the solid-fluid interfaces is investigated. It was found that increase in the Rayleigh number leads to the increment of both the average Nusselt number and the stream function in the vapor zone.展开更多
An accurate closed form solution is proposed to estimate camera pose by several mirrored reference object images acquired via a planar mirror under different unknown poses. Compared with state-of-the-art methods, our ...An accurate closed form solution is proposed to estimate camera pose by several mirrored reference object images acquired via a planar mirror under different unknown poses. Compared with state-of-the-art methods, our method is more accurate when there are more than three images and has explicit geometric meanings. This method also properly handles cases in which some of the mirror poses are parallel. The central idea is to minimize an error metric based on all reflections of rotation, which enables the camera rotation to be estimated directly by SVD of sum of mirrored camera rotations. After that, the camera translation is computed by solving a large system of linear equations to minimize object space collinearity error. Both synthesized data and real data experiments show the advantages of our approach.展开更多
It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves,which have been not reported for other mainstream models of shallow water waves.In this letter,the closed-form solutions of peak...It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves,which have been not reported for other mainstream models of shallow water waves.In this letter,the closed-form solutions of peaked solitary waves of the KdV equation,the BBM equation and the Boussinesq equation are given for the first time.All of them have either a peakon or an anti-peakon.Each of them exactly satisfies the corresponding Rankine-Hogoniot jump condition and could be understood as weak solution.Therefore,the peaked solitary waves might be common for most of shallow water wave models,no matter whether or not they are integrable and/or admit breaking-wave solutions.展开更多
基金Supported in part by the NSF of China under Grant No.10671124the NCET of China under Grant No.-05-0390
文摘This note concerns the motion of relativistic strings in the Minkowski space R^(1+n).We rederive the generalsolution formula in closed form for the equation for the motion of relativistic string.Our method is different completelyfrom others.
文摘Heat transfer and hydrodynamics of two phase closed thermosyphon （TPCT） is studied using finite difference method of Stream function and vorticity. The mathematical model is formed for both vapor phase and liquid film in a non-dimensional form. The momentum and energy equations as parabolic equations have been solved by means of the locally one-dimensional scheme of A.A. Samarskii. The Poisson equation for the stream function has been approximated on the basis of the discrete scheme ＂cross＂. The obtained system of algebraic equations has been solved by the successive over relaxation method. The effect of the Rayleigh number on the velocity and temperature fields in the domain of interest and on the average Nusselt number at the solid-fluid interfaces is investigated. It was found that increase in the Rayleigh number leads to the increment of both the average Nusselt number and the stream function in the vapor zone.
基金supported by the National Natural Science Foundation of China(Grant No.11072263)
文摘An accurate closed form solution is proposed to estimate camera pose by several mirrored reference object images acquired via a planar mirror under different unknown poses. Compared with state-of-the-art methods, our method is more accurate when there are more than three images and has explicit geometric meanings. This method also properly handles cases in which some of the mirror poses are parallel. The central idea is to minimize an error metric based on all reflections of rotation, which enables the camera rotation to be estimated directly by SVD of sum of mirrored camera rotations. After that, the camera translation is computed by solving a large system of linear equations to minimize object space collinearity error. Both synthesized data and real data experiments show the advantages of our approach.
基金supported by the State Key Lab of Ocean Engineering(Grant No.GKZD010056-6)the National Natural Science Foundation of China(Grant Nos.10872129 and 11272209
文摘It is well-known that the celebrated Camassa-Holm equation has the peaked solitary waves,which have been not reported for other mainstream models of shallow water waves.In this letter,the closed-form solutions of peaked solitary waves of the KdV equation,the BBM equation and the Boussinesq equation are given for the first time.All of them have either a peakon or an anti-peakon.Each of them exactly satisfies the corresponding Rankine-Hogoniot jump condition and could be understood as weak solution.Therefore,the peaked solitary waves might be common for most of shallow water wave models,no matter whether or not they are integrable and/or admit breaking-wave solutions.
