The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were...The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were derived. Furthermore, whether these curves lie on a curvature line or not was investigated and some applications were given.展开更多
The indirect boundary element method （IBEM） is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave fiel...The indirect boundary element method （IBEM） is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and effi- ciently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.展开更多
In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to ...In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G3.展开更多
Let M be a n-dimensional compact irreducible complex space with a line bundle L. It is shown that if M is completely intersected with respect to L and dimH0(M, L) = n + 1, then M is biholomorphic to a complex projecti...Let M be a n-dimensional compact irreducible complex space with a line bundle L. It is shown that if M is completely intersected with respect to L and dimH0(M, L) = n + 1, then M is biholomorphic to a complex projective space Pn of dimension n.展开更多
The discovery of the momentum space crystal based on the alkaline-earth atom ^(88)Sr in narrow-line cooling has paved the way to explore this novel physical phenomenon in other cold atom systems. In this paper, a mome...The discovery of the momentum space crystal based on the alkaline-earth atom ^(88)Sr in narrow-line cooling has paved the way to explore this novel physical phenomenon in other cold atom systems. In this paper, a momentum space crystal based on the fermions ^(87)Sr in narrow-line cooling of transition^1S_0–~3P_1 is demonstrated. We theoretically analyze and compare the formation principle of the narrow-line with that of broad-line cooling, and achieve the momentum space crystal in experiment. Beyond that we present a series of numerical calculations of those important parameters which influence the distribution and size of the momentum space crystal. Correspondingly, we vary the values of these parameters in experiment to observe the momentum space crystal evolution and distribution. The experimental results are in conformity with the results of the theoretically numerical calculations. These results and analyses provide a detailed supplementary study on the formation and evolution of momentum space crystal. In addition, this work could also give a guideline on atomic manipulation by narrow-line cooling.展开更多
Half-space Green's function due to a spatially harmonic line load has been expressed as a sum of the full-space Green's functions and a 2-D integral representation of the reflected waves by the free surface of...Half-space Green's function due to a spatially harmonic line load has been expressed as a sum of the full-space Green's functions and a 2-D integral representation of the reflected waves by the free surface of the half-space.By using the obtained half-space Green's function,an integral rep- resentation of the scattered waves by a cylindrical obstacle is then derived.Finally,by analyzing the far-zone behavior of the integrands of the integral representation.the far-field pattern of the scattered waves in a half-space obtained.展开更多
This paper proposed an optimal algorithm using the sun line-of-sight vector to improve the probe attitude estimation accuracy in deep-space mission.Firstly,the elaborate analysis of the attitude estimation error from ...This paper proposed an optimal algorithm using the sun line-of-sight vector to improve the probe attitude estimation accuracy in deep-space mission.Firstly,the elaborate analysis of the attitude estimation error from vector observations was done to demonstrate that the geometric relation between the reference vectors is an important factor which influences the accuracy of attitude estimation.Then,with introduction of the sun line-of-sight vector,the attitude quaternion obtained from the star-sensor was converted into a pair of mutually perpendicular reference vectors perpendicular to the sun vector.The normalized weights were calculated according to the accuracy of the sensors.Furthermore,the optimal attitude estimation in the least squares sense was achieved with the quaternion estimation method.Finally,the results of simulation demonstrated the validity of the proposed optimal algorithm based on the practical data of the Deep Impact mission.展开更多
文摘The relaxed elastic line of second kind on an oriented surface in the Minkowski space was defined and for the relaxed elastic line of second kind which is lying on an oriented surface the Euler-Lagrange equations were derived. Furthermore, whether these curves lie on a curvature line or not was investigated and some applications were given.
基金National Natural Science Foundation of China under Grants (51278327)the Tianjin Research Program of Application Foundation and Advanced Technology (14JCYBJC21900)
文摘The indirect boundary element method （IBEM） is developed to solve the scattering of plane SH-waves by a lined tunnel in elastic wedge space. According to the theory of single-layer potential, the scattered-wave field can be constructed by applying virtual uniform loads on the surface of lined tunnel and the nearby wedge surface. The densities of virtual loads can be solved by establishing equations through the continuity conditions on the interface and zero-traction conditions on free surfaces. The total wave field is obtained by the superposition of free field and scattered-wave field in elastic wedge space. Numerical results indicate that the IBEM can solve the diffraction of elastic wave in elastic wedge space accurately and effi- ciently. The wave motion feature strongly depends on the wedge angle, the angle of incidence, incident frequency, the location of lined tunnel, and material parameters. The waves interference and amplification effect around the tunnel in wedge space is more significant, causing the dynamic stress concentration factor on rigid tunnel and the displacement amplitude of flexible tunnel up to 50.0 and 17.0, respectively, more than double that of the case of half-space. Hence, considerable attention should be paid to seismic resistant or anti-explosion design of the tunnel built on a slope or hillside.
文摘In this article, we derive the intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean 3-dimensional space G3. These equations will give direct and more geometric approach to questions concerning about generalized relaxed elastic lines on an oriented surface in G3.
文摘Let M be a n-dimensional compact irreducible complex space with a line bundle L. It is shown that if M is completely intersected with respect to L and dimH0(M, L) = n + 1, then M is biholomorphic to a complex projective space Pn of dimension n.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11474282 and 61775220)the Key Research Project of Frontier Science of the Chinese Academy of Sciences(Grant No.QYZDB-SSW-JSC004)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB21030100)
文摘The discovery of the momentum space crystal based on the alkaline-earth atom ^(88)Sr in narrow-line cooling has paved the way to explore this novel physical phenomenon in other cold atom systems. In this paper, a momentum space crystal based on the fermions ^(87)Sr in narrow-line cooling of transition^1S_0–~3P_1 is demonstrated. We theoretically analyze and compare the formation principle of the narrow-line with that of broad-line cooling, and achieve the momentum space crystal in experiment. Beyond that we present a series of numerical calculations of those important parameters which influence the distribution and size of the momentum space crystal. Correspondingly, we vary the values of these parameters in experiment to observe the momentum space crystal evolution and distribution. The experimental results are in conformity with the results of the theoretically numerical calculations. These results and analyses provide a detailed supplementary study on the formation and evolution of momentum space crystal. In addition, this work could also give a guideline on atomic manipulation by narrow-line cooling.
文摘Half-space Green's function due to a spatially harmonic line load has been expressed as a sum of the full-space Green's functions and a 2-D integral representation of the reflected waves by the free surface of the half-space.By using the obtained half-space Green's function,an integral rep- resentation of the scattered waves by a cylindrical obstacle is then derived.Finally,by analyzing the far-zone behavior of the integrands of the integral representation.the far-field pattern of the scattered waves in a half-space obtained.
文摘This paper proposed an optimal algorithm using the sun line-of-sight vector to improve the probe attitude estimation accuracy in deep-space mission.Firstly,the elaborate analysis of the attitude estimation error from vector observations was done to demonstrate that the geometric relation between the reference vectors is an important factor which influences the accuracy of attitude estimation.Then,with introduction of the sun line-of-sight vector,the attitude quaternion obtained from the star-sensor was converted into a pair of mutually perpendicular reference vectors perpendicular to the sun vector.The normalized weights were calculated according to the accuracy of the sensors.Furthermore,the optimal attitude estimation in the least squares sense was achieved with the quaternion estimation method.Finally,the results of simulation demonstrated the validity of the proposed optimal algorithm based on the practical data of the Deep Impact mission.
