Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus th...Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus the information extracted from each electrode represents the local phase distribution and fraction change at that location. The multivariate maximum Lyapunov exponent(MMLE) is extracted from the 16-dimension time-series to demonstrate the change of flow pattern versus the superficial velocity ratio of oil to water. The correlation dimension of the multivariate time-series is further introduced to jointly characterize and finally separate the flow patterns with MMLE. The change of flow patterns with superficial oil velocity at different water superficial velocities is studied with MMLE and correlation dimension, respectively, and the flow pattern transition can also be characterized with these two features. The proposed MMLE and correlation dimension map could effectively separate the flow patterns, thus is an effective tool for flow pattern identification and transition analysis.展开更多
In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y...In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y, z）, z）, which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung＇s Theorem.展开更多
If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching s...If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching some crossings with the linking number：lk（L）=∑i=1^mεiC（EiL）＋n展开更多
基金Projects(61227006,61473206) supported by the National Natural Science Foundation of ChinaProject(13TXSYJC40200) supported by Science and Technology Innovation of Tianjin,China
文摘Oil–water two-phase flow patterns in a horizontal pipe are analyzed with a 16-electrode electrical resistance tomography(ERT) system. The measurement data of the ERT are treated as a multivariate time-series, thus the information extracted from each electrode represents the local phase distribution and fraction change at that location. The multivariate maximum Lyapunov exponent(MMLE) is extracted from the 16-dimension time-series to demonstrate the change of flow pattern versus the superficial velocity ratio of oil to water. The correlation dimension of the multivariate time-series is further introduced to jointly characterize and finally separate the flow patterns with MMLE. The change of flow patterns with superficial oil velocity at different water superficial velocities is studied with MMLE and correlation dimension, respectively, and the flow pattern transition can also be characterized with these two features. The proposed MMLE and correlation dimension map could effectively separate the flow patterns, thus is an effective tool for flow pattern identification and transition analysis.
文摘In this paper, we introduce a polynomial sequence in K[x], in which two neighbor polynomials satisfy a wonderful property. Using that,we give partial answer of an open problem： ifφ（x, y, z） = （f（x, y）, g（x, y, z）, z）, which sends every linear coordinate to a coordinate, then φ is an automorphism of K[x, y, z]. As a byproduct, we give an easy proof of the well-known Jung＇s Theorem.
文摘If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching some crossings with the linking number：lk（L）=∑i=1^mεiC（EiL）＋n
