In this paper we use Poincaré’s equations in group variables to de- scribe the motion of a holonomic mechanical system and to determine Jacobi's mul- tiplier for the equations of motion.
The author proves the Poincar′e lemma on some(n + 1)-dimensional corank1 sub-Riemannian structures, formulating the(n-1)n(n^2+3 -2)/8 necessarily and sufficient y "curl-vanishing" compatibility conditions. ...The author proves the Poincar′e lemma on some(n + 1)-dimensional corank1 sub-Riemannian structures, formulating the(n-1)n(n^2+3 -2)/8 necessarily and sufficient y "curl-vanishing" compatibility conditions. In particular, this result solves partially an open problem formulated by Calin and Chang. The proof in this paper is based on a Poincar′e lemma stated on Riemannian manifolds and a suitable Ces`aro-Volterra path integral formula established in local coordinates. As a byproduct, a Saint-Venant lemma is also provided on generic Riemannian manifolds. Some examples are presented on the hyperbolic space and Carnot/Heisenberg groups.展开更多
The inverse Faraday effect(IFE),which usually refers to the phenomenon in which a quasi-static axial magnetic field is self-generated when a circularly polarized beam propagates in a plasma,has rarely been studied for...The inverse Faraday effect(IFE),which usually refers to the phenomenon in which a quasi-static axial magnetic field is self-generated when a circularly polarized beam propagates in a plasma,has rarely been studied for lasers with unconventional polarization states.In this paper,IFE is reconsidered for weakly relativistic full Poincarébeams,which can contain all possible laser polarization states.Starting from cold electron fluid equations and the conservation of generalized vorticity,a self-consistent theoretical model combining the nonlinear azimuthal current and diamagnetic current is presented.The theoretical results show that when such a laser propagates in a plasma,an azimuthally varying quasi-static axial magnetic field can be generated,which is quite different from the circularly polarized case.These results are qualitatively and quantitatively verified by three-dimensional particle-in-cell simulations.Our work extends the theoretical understanding of the IFE and provides a new degree of freedom in the design of magnetized plasma devices.展开更多
文摘In this paper we use Poincaré’s equations in group variables to de- scribe the motion of a holonomic mechanical system and to determine Jacobi's mul- tiplier for the equations of motion.
文摘The author proves the Poincar′e lemma on some(n + 1)-dimensional corank1 sub-Riemannian structures, formulating the(n-1)n(n^2+3 -2)/8 necessarily and sufficient y "curl-vanishing" compatibility conditions. In particular, this result solves partially an open problem formulated by Calin and Chang. The proof in this paper is based on a Poincar′e lemma stated on Riemannian manifolds and a suitable Ces`aro-Volterra path integral formula established in local coordinates. As a byproduct, a Saint-Venant lemma is also provided on generic Riemannian manifolds. Some examples are presented on the hyperbolic space and Carnot/Heisenberg groups.
基金supported by the National Natural Science Foundation of China(NSFC)under Grant No.11975014the Strategic Priority Research Program of Chinese Academy of Sciences under Grant Nos.XDA25050400 and XDA25010200.
文摘The inverse Faraday effect(IFE),which usually refers to the phenomenon in which a quasi-static axial magnetic field is self-generated when a circularly polarized beam propagates in a plasma,has rarely been studied for lasers with unconventional polarization states.In this paper,IFE is reconsidered for weakly relativistic full Poincarébeams,which can contain all possible laser polarization states.Starting from cold electron fluid equations and the conservation of generalized vorticity,a self-consistent theoretical model combining the nonlinear azimuthal current and diamagnetic current is presented.The theoretical results show that when such a laser propagates in a plasma,an azimuthally varying quasi-static axial magnetic field can be generated,which is quite different from the circularly polarized case.These results are qualitatively and quantitatively verified by three-dimensional particle-in-cell simulations.Our work extends the theoretical understanding of the IFE and provides a new degree of freedom in the design of magnetized plasma devices.
基金Supported by the National Natural Science Foundation of China(1146103211401267)+2 种基金the Foundation of Jiangxi University of Science and Technology(NSFJ2015-G25)the Youth Foundation of Jiangxi Provincial Education Department of China(GJJ150646GJJ151356)