This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natura...This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.展开更多
In the light of Robinson and Wilczek's new idea,and motivated by Banerjee and Kulkarni's simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole,we generally extend ...In the light of Robinson and Wilczek's new idea,and motivated by Banerjee and Kulkarni's simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole,we generally extend the work to Kerr-Newman black hole in dragging coordinates frame.It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame,which supports and extends Robinson and Wilczek's opinion.展开更多
The geocentric coordinates of three mobile sites including Fangshan in Beijing, Urumqi in the Xinjiang Uy-gur Autonomous Region and Lhasa in Tibet are determinedin the ITRF2000 frame by means of both the global SLRdat...The geocentric coordinates of three mobile sites including Fangshan in Beijing, Urumqi in the Xinjiang Uy-gur Autonomous Region and Lhasa in Tibet are determinedin the ITRF2000 frame by means of both the global SLRdata and the mobile (SLR) data obtained by a mobile satel-lite laser ranging (SLR) apparatus from Aug. 2000 to Dec.2001. The results showed that the geometrical performance of Chinese SLR network has been significantly improved.展开更多
文摘This paper discusses the relationship between natural coordinates in fluid mechanics and orthogonal curvilinear coordinates. Since orthogonal curvilinear coordinates have some excellent mathematical properties, natural coordinates can be applied more widely if they can be transformed to orthogonal curvilinear coordinates. Frenet formulas which describe the differential properties of natural coordinates were compared with the derivative formulas of orthogonal curvilinear coordinates to show that natural coordinates are not generally orthogonal curvilinear coordinates. A method was introduced to transform natural coordinormal planes of the natural coordinates about the streamlines. The transformation is true as long as the natural coordinates satisfy several equations. Vorticity decomposition in the natural coordinates is used to show that these conditional equations are satisfied only if the streamlines are perpendicular to the vortexlines on every given point in the flow field. These equations apply in both planar flows and axisymmetric flows without a circumferential velocity component, but do not apply in some 3-D flows such as Beltrami flow.
基金supported by National Natural Science Foundation of China under Grant No.10773008
文摘In the light of Robinson and Wilczek's new idea,and motivated by Banerjee and Kulkarni's simplified method of using only the covariant anomaly to derive Hawking radiation from a black hole,we generally extend the work to Kerr-Newman black hole in dragging coordinates frame.It is shown that the flows introduced to cancel the anomaly at the event horizon are equal to the corresponding Hawking radiation in dragging coordinates frame,which supports and extends Robinson and Wilczek's opinion.
基金supported by the Chinese Academy of Sciences(Grant No.KJCX2-SW-T1)the National Natural Science Foundation of China(Grant No.40174008).
文摘The geocentric coordinates of three mobile sites including Fangshan in Beijing, Urumqi in the Xinjiang Uy-gur Autonomous Region and Lhasa in Tibet are determinedin the ITRF2000 frame by means of both the global SLRdata and the mobile (SLR) data obtained by a mobile satel-lite laser ranging (SLR) apparatus from Aug. 2000 to Dec.2001. The results showed that the geometrical performance of Chinese SLR network has been significantly improved.
