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Surface excitations, shape deformation and the long-time behavior in a stirred Bose-Einstein condensate
The surface excitations, shape deformation and the formation of persistent
current for a Gaussian obstacle potential rotating in an highly oblate
Bose-Einstein condensate(BEC)are investigated. Vortex dipole can be produced
and trapped in the center of the stirrer even for slow motion of the stirring
beam. When the barrier angular velocity is above some critical value, the
condensate shape can be deformed remarkably according to the rotation frequency
due to the existence of plenty of surface wave excitations. After a long enough
time, a few vortices are found to be left either trapped in the condensate or
pinned by the obstacle, a vortex dipole or several vortices can be trapped at
the beam center, which enables the possibility of vortex manipulation.Comment: 5 pages, 4 figure
Complete bounded -hypersurfaces in the weighted volume-preserving mean curvature flow
In this paper, we study the complete bounded -hypersurfaces in
weighted volume-preserving mean curvature flow. Firstly, we investigate the
volume comparison theorem of complete bounded -hypersurfaces with
and get some applications of the volume comparison theorem.
Secondly, we consider the relation among , extrinsic radius ,
intrinsic diameter , and dimension of the complete
-hypersurface, and we obtain some estimates for the intrinsic diameter
and the extrinsic radius. At last, we get some topological properties of the
bounded -hypersurface with some natural and general restrictions
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