This paper studies the effective polytropic index in the central plasma sheet （CPS） by using the method of Kartalev et al. （2006）, which adopts the denoising technique of Haar wavelet to identify the homogeneous M...This paper studies the effective polytropic index in the central plasma sheet （CPS） by using the method of Kartalev et al. （2006）, which adopts the denoising technique of Haar wavelet to identify the homogeneous MHD Bernoulli integral （MBI） and has been frequently used to study the polytropic relation in the solar wind. We chose the quiet CPS crossing by Cluster C1 during the interval 08：51：00-09：19：00 UT on 03 August 2001. In the central plasma sheet, thermal pressure energy per unit mass is the most important part in MBI, and kinetic energy of fluid motion and electromagnetic energy per unit mass are less important. In the MBI, there are many peaks, which correspond to isothermal or near isothermal processes. The interval lengths of homogenous MBI regions are generally less than 1 min. The polytropic indexes are calculated by linearly fitting the data of lnp and Inn within a 16 s window, which is shifted forward by 8 s step length. Those polytropic indexes with IRI ≥0.8 （R is the correlation coefficient between lnp and inn） and p-value≤0.1 in the homogeneous regions are almost all in the range of [0, 1]. The mean and median effective polytropic indexes with high R and low p-value in homogeneous regions are 0.34 and 0.32 respectively, which are much different from the polytropic index obtained by traditional method （αtrad=-0.15）. This result indicates that the CPS is not uniform even during quiet time and the blanket applications of polytropic law to plasma sheet may return misleading value of polytropic index. The polytropic indexes in homogeneous regions with a high correlation coefficient basically have good regression significance and are thus credible. These results are very important to understand the energy transport in magnetotail in the MHD frame.展开更多
The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}i=1^∞, if {C^＊（Xi）}i=1...The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}i=1^∞, if {C^＊（Xi）}i=1^∞ are equi-nuclear and under some proper gluing conditions, it is proved that C＊（X） is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C^＊ （X） is not nuclear.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.41431071,41174141,41474124)the National Basic Research Program of China(Grant No.2011CB811404)
文摘This paper studies the effective polytropic index in the central plasma sheet （CPS） by using the method of Kartalev et al. （2006）, which adopts the denoising technique of Haar wavelet to identify the homogeneous MHD Bernoulli integral （MBI） and has been frequently used to study the polytropic relation in the solar wind. We chose the quiet CPS crossing by Cluster C1 during the interval 08：51：00-09：19：00 UT on 03 August 2001. In the central plasma sheet, thermal pressure energy per unit mass is the most important part in MBI, and kinetic energy of fluid motion and electromagnetic energy per unit mass are less important. In the MBI, there are many peaks, which correspond to isothermal or near isothermal processes. The interval lengths of homogenous MBI regions are generally less than 1 min. The polytropic indexes are calculated by linearly fitting the data of lnp and Inn within a 16 s window, which is shifted forward by 8 s step length. Those polytropic indexes with IRI ≥0.8 （R is the correlation coefficient between lnp and inn） and p-value≤0.1 in the homogeneous regions are almost all in the range of [0, 1]. The mean and median effective polytropic indexes with high R and low p-value in homogeneous regions are 0.34 and 0.32 respectively, which are much different from the polytropic index obtained by traditional method （αtrad=-0.15）. This result indicates that the CPS is not uniform even during quiet time and the blanket applications of polytropic law to plasma sheet may return misleading value of polytropic index. The polytropic indexes in homogeneous regions with a high correlation coefficient basically have good regression significance and are thus credible. These results are very important to understand the energy transport in magnetotail in the MHD frame.
基金supported by the National Natural Science Foundation of China(Nos.10731020,10971023)the Shu Guang Project of Shanghai Municipal Education Commission and Shanghai Education DepartmentFoundation(No.07SG38)the Foundation of the Ministry of Education of China
文摘The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}i=1^∞, if {C^＊（Xi）}i=1^∞ are equi-nuclear and under some proper gluing conditions, it is proved that C＊（X） is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C^＊ （X） is not nuclear.
