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We use finite element analysis method to optimize and design a new curve half-ring conductance sensor for gas-liquid two-phase flow system. Then we carry out gas-liquid two-phase flow experiment in multiphase flow loop facility, and use the designed sensor to measure multivariate time series corresponding to different flow patterns. According to the measured signals, we construct complex networks from multivariate time series for different flow patterns by a network inference method. Through investigating the community structures of the constructed networks, we find that different communities correspond to different flow patterns and the network statistics in community can be used to effectively characterize the dynamic behavior of different flow patterns. In this regard, our method can be a powerful tool for identifying flow patterns and uncovering the nonlinear dynamics governing the evolution of different flow patterns.
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Keywords:
- gas-liquid two-phase flow /
- complex network /
- community structure /
- fluid dynamics
[1] Lawkins W F, Daw C S, Downing D J, Jr Clapp N E 1993 Phys. Rev. E 47 2520
[2] Daw C S, Finney C E A, Vasudevan M, vanGoor N A, Nguyen K, Bruns D D, Kostelich E J, Grebogi C, Ott E, Yorke J A 1995 Phys. Rev. Lett. 75 2308
[3] Gao Z K, Jin N D 2009 Phy. Rev. E 79 066303
[4] Watts D J, Strogatz S H 1998 Nature 393 440
[5] Strogatz S H 2001 Nature 410 268
[6] Albert R, Barab′asi A L 2002 Rev. Mod. Phys. 74 47
[7] Wang W X, Wang B H, Hu B, Yan G, Ou Q 2005 Phys. Rev. Lett. 94 188702
[8] Pan Z F, Li X, Wang X F 2006 Phys. Rev. E 73 056109
[9] Huang L, Park K, Lai Y C, Yang L, Yang K Q 2006 Phys. Rev. Lett. 97 164101
[10] Huang L, Park K, Lai Y C 2006 Phys. Rev. E 73 035103(R)
[11] Li X G, Gao Z Y, Li K P, Zhao X M 2007 Phys. Rev. E 76 016110
[12] Pei W D, Chen Z Q, Yuan Z Z 2008 Chin. Phys. B 17 0373
[13] Zhou J, Lu J A, Lu J H 2008 Automatica 44 996
[14] Yang R, Wang W X, Lai Y C, Chen G R 2009 Phys. Rev. E 79 026112
[15] Lu X B, Wang X F, Fang J Q 2010 Physica D 239 341
[16] Zhou T, Kuscsik Z, Liu J G, Medo M, Wakeling J R, Zhang Y C 2010 Proc. Natl. Acad. Sci. USA 107 4511
[17] Wang W X, Yang R, Lai Y C, Kovanis V, Grebogi C 2011 Phys. Rev. Lett. 106 154101
[18] Liu F,Wang H O, Guan Z H 2012 Nonlinear Analysis: Real World Applications 13 1466
[19] Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[20] Zhou C S, Zemanov L, Zamora G, Hilgetag C C, Kurths J 2006 Phys. Rev. Lett. 97 238103
[21] Zhang J, Sun J F, Luo S D, Zhang K, Nakamura T, Small M 2008 Physica D 237 2856
[22] Yang Y, Yang H J 2008 Physica A 387 1381
[23] Lacasa L, Luque B, Ballesteros F, Luque J, Nuno J C 2008 Proc. Natl. Acad. Sci. USA 105 4972
[24] Xu X, Zhang J, Small M 2008 Proc. Natl. Acad. Sci. USA 105 19601
[25] Gao Z K, Jin N D 2009 Chaos 19 033137
[26] Gao Z K, Jin N D 2012 Nonlinear Analysis: Real World Applications 13 947
[27] Fang X L, Jiang Z L 2007 Acta Phys. Sin. 56 7330 (in Chinese) [方小玲, 姜宗来 2007 56 7330]
[28] Dong Z, Li X 2010 Acta Phys. Sin. 59 1600 (in Chinese)[董昭, 李翔 2010 59 1600]
[29] Zhou L, Gong Z Q, Zhi R, Feng G L 2009 Acta Phys. Sin. 58 7351[周磊, 龚志强, 支蓉, 封国林 2009 58 7351]
[30] Kramer M A, Eden U T, Cash S S, Kolaczyk E D 2009 Phys. Rev. E 79 061916
[31] Zhang J, Zhang K, Feng J F, Small M 2010 PLoS Comput. Biol. 6 e1001033
[32] Liu C, Zhou W, Yuan W 2010 Physica A 389 2675
[33] Shao Z G 2010 Appl. Phys. Lett. 96 073703
[34] Donner R V, Heitzig J, Donges J F, Zou Y, Marwan N, Kurths J 2011 Eur. Phys. J. B 84 653
[35] Xie W J, Zhou W X 2011 Physica A 390 3592
[36] Gong Z Q, Zhi R, Hou W, Wang X J, Feng G L 2012 Acta phys. Sin. 61 029202 (in Chinese)[龚志强, 支蓉, 侯威, 王晓娟, 封国林 2012 61 029202]
[37] Xiang R X, Zhang J, Xu X K, Small M 2012 Chaos 22 013107
[38] Gao Z K, Jin N D 2009 Chin. Phys. B 18 5249
[39] Gao Z K, Jin N D, Wang W X, Lai Y C 2010 Phy. Rev. E 82 016210
[40] Gao Z K, Jin N D 2011 Chem. Eng. Sci. 66 2660
[41] Gao Z K, Jin N D 2012 Physica A 391 3005
[42] Benjamini Y, Yekutieli D 2001 Ann. Statist. 29 1165
[43] Kamada T, Kawai S 1989 Inform. Process. Lett. 31 7
[44] Borgatti S P, EverettMG, Freeman L C 2002 Ucinet forWindows: Software for social network analysis, Harvard Analytic Technologies
[45] Gao Z K, Jin N D, Wang W X, Lai Y C 2010 Phys. Lett. A 374 4014
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[1] Lawkins W F, Daw C S, Downing D J, Jr Clapp N E 1993 Phys. Rev. E 47 2520
[2] Daw C S, Finney C E A, Vasudevan M, vanGoor N A, Nguyen K, Bruns D D, Kostelich E J, Grebogi C, Ott E, Yorke J A 1995 Phys. Rev. Lett. 75 2308
[3] Gao Z K, Jin N D 2009 Phy. Rev. E 79 066303
[4] Watts D J, Strogatz S H 1998 Nature 393 440
[5] Strogatz S H 2001 Nature 410 268
[6] Albert R, Barab′asi A L 2002 Rev. Mod. Phys. 74 47
[7] Wang W X, Wang B H, Hu B, Yan G, Ou Q 2005 Phys. Rev. Lett. 94 188702
[8] Pan Z F, Li X, Wang X F 2006 Phys. Rev. E 73 056109
[9] Huang L, Park K, Lai Y C, Yang L, Yang K Q 2006 Phys. Rev. Lett. 97 164101
[10] Huang L, Park K, Lai Y C 2006 Phys. Rev. E 73 035103(R)
[11] Li X G, Gao Z Y, Li K P, Zhao X M 2007 Phys. Rev. E 76 016110
[12] Pei W D, Chen Z Q, Yuan Z Z 2008 Chin. Phys. B 17 0373
[13] Zhou J, Lu J A, Lu J H 2008 Automatica 44 996
[14] Yang R, Wang W X, Lai Y C, Chen G R 2009 Phys. Rev. E 79 026112
[15] Lu X B, Wang X F, Fang J Q 2010 Physica D 239 341
[16] Zhou T, Kuscsik Z, Liu J G, Medo M, Wakeling J R, Zhang Y C 2010 Proc. Natl. Acad. Sci. USA 107 4511
[17] Wang W X, Yang R, Lai Y C, Kovanis V, Grebogi C 2011 Phys. Rev. Lett. 106 154101
[18] Liu F,Wang H O, Guan Z H 2012 Nonlinear Analysis: Real World Applications 13 1466
[19] Zhang J, Small M 2006 Phys. Rev. Lett. 96 238701
[20] Zhou C S, Zemanov L, Zamora G, Hilgetag C C, Kurths J 2006 Phys. Rev. Lett. 97 238103
[21] Zhang J, Sun J F, Luo S D, Zhang K, Nakamura T, Small M 2008 Physica D 237 2856
[22] Yang Y, Yang H J 2008 Physica A 387 1381
[23] Lacasa L, Luque B, Ballesteros F, Luque J, Nuno J C 2008 Proc. Natl. Acad. Sci. USA 105 4972
[24] Xu X, Zhang J, Small M 2008 Proc. Natl. Acad. Sci. USA 105 19601
[25] Gao Z K, Jin N D 2009 Chaos 19 033137
[26] Gao Z K, Jin N D 2012 Nonlinear Analysis: Real World Applications 13 947
[27] Fang X L, Jiang Z L 2007 Acta Phys. Sin. 56 7330 (in Chinese) [方小玲, 姜宗来 2007 56 7330]
[28] Dong Z, Li X 2010 Acta Phys. Sin. 59 1600 (in Chinese)[董昭, 李翔 2010 59 1600]
[29] Zhou L, Gong Z Q, Zhi R, Feng G L 2009 Acta Phys. Sin. 58 7351[周磊, 龚志强, 支蓉, 封国林 2009 58 7351]
[30] Kramer M A, Eden U T, Cash S S, Kolaczyk E D 2009 Phys. Rev. E 79 061916
[31] Zhang J, Zhang K, Feng J F, Small M 2010 PLoS Comput. Biol. 6 e1001033
[32] Liu C, Zhou W, Yuan W 2010 Physica A 389 2675
[33] Shao Z G 2010 Appl. Phys. Lett. 96 073703
[34] Donner R V, Heitzig J, Donges J F, Zou Y, Marwan N, Kurths J 2011 Eur. Phys. J. B 84 653
[35] Xie W J, Zhou W X 2011 Physica A 390 3592
[36] Gong Z Q, Zhi R, Hou W, Wang X J, Feng G L 2012 Acta phys. Sin. 61 029202 (in Chinese)[龚志强, 支蓉, 侯威, 王晓娟, 封国林 2012 61 029202]
[37] Xiang R X, Zhang J, Xu X K, Small M 2012 Chaos 22 013107
[38] Gao Z K, Jin N D 2009 Chin. Phys. B 18 5249
[39] Gao Z K, Jin N D, Wang W X, Lai Y C 2010 Phy. Rev. E 82 016210
[40] Gao Z K, Jin N D 2011 Chem. Eng. Sci. 66 2660
[41] Gao Z K, Jin N D 2012 Physica A 391 3005
[42] Benjamini Y, Yekutieli D 2001 Ann. Statist. 29 1165
[43] Kamada T, Kawai S 1989 Inform. Process. Lett. 31 7
[44] Borgatti S P, EverettMG, Freeman L C 2002 Ucinet forWindows: Software for social network analysis, Harvard Analytic Technologies
[45] Gao Z K, Jin N D, Wang W X, Lai Y C 2010 Phys. Lett. A 374 4014
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