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By using the homotopy analysis method (HAM), the electrostatic potential distribution problems of a type of high-order weakly nonlinear composite with a cylindrical inclusion randomly embedded in a host medium, which obeyes a current-field constitutive relation of J = σ E + χ |E|2E + η|E|4E, are investigated under the action of an external direct current electric field. With the mode expansion method, the current-field constitutive relation and their boundary conditions are transformed into a series of boundary value problems of nonlinear ordinary differential equations. Then the HAM is used to solve the boundary value problems of nonlinear ordinary differential equations and the asymptotic analytical solutions of electrostatic potential distribution in the inclusion and the host regions are given.
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Keywords:
- high-order weakly nonlinear composites /
- mode function expansion method /
- homotopy analysis method /
- electrostatic potential distribution
[1] Yin Z W 2003 Dielectric Physics (2nd Ed.) (Beijing: Science Press) pp1-27 (in Chinese) [殷之文 2003 电介质物理学 (第二版) (北京: 科学出版社) 第1–27页]
[2] Xie B C, Gao L 2000 Acta Phys. Sin. 49 365 (in Chinese) [谢秉川, 高雷 2000 49 365]
[3] Gao L, Hong G 2003 Acta Phys. Sin. 52 575 (in Chinese) [高雷, 洪刚 2003 52 575]
[4] Ma H R, Xiao R F, Sheng P 1998 J. Opt. Soc. Am. B 15 1022
[5] Li X T, Ma H R 1999 Acta Phys. Sin. 48 461 (in Chinese) [李向亭, 马红孺 1999 48 461]
[6] Gao L 2001 J. Phys.: Condens. Matter 13 7271
[7] Gao L 2003 Phys. Status Solidi B 236 182
[8] Gao L 2004 Phys. Lett. A 322 250
[9] Yuen K P, Law M F, Yu K W, Sheng P 1997 Phys. Rev. E 56 1322
[10] Wu Y M, Chen G Q 2006 Acta Phys. Sin. 55 5242 (in Chinese) [吴亚敏, 陈国庆 2006 55 5242]
[11] Gu G Q, Yu K W 1991 Acta Phys. Sin. 40 709 (in Chinese) [顾国庆, 余建华 1991 40 709]
[12] Gu G Q, Yu J H 1992 Phys. Rev. B 46 4502
[13] Yu K W, Wang Y C, Hui P M 1993 Phys. Rev. B 47 1782
[14] Levy O, Bergman D J, Stroud D G 1995 Phys. Rev. E 52 3184
[15] Wei E B, Gu G Q 2001 Chin. Phys. Lett. 18 960
[16] Hui P M, Cheung P, Stroud D 1998 J. Appl. Phys. 84 3451
[17] Hui P M, Cheung P 2000 Physica B 279 45
[18] Gu G Q, Hui P M, Yu K W 2000 Physica B 279 62
[19] Wei E B, Gu G Q 2001 Commun. Theor. Phys. 35 501
[20] Wei E B, Song J B, Gu G Q 2002 Physica B 324 322
[21] Chen X G, Liang F C, Wei E B 2005 Chin. Phys. 14 1217
[22] Wei E B, Tian J W, Song J B 2003 J. Phys. Condens. Matter 15 8907
[23] Wei E B, Tian J W, Song J B 2004 Chin. Phys. 13 388
[24] Chen X G, Wei E B, Song J B 2004 Commun. Theor. Phys. 41 771
[25] Wei E B, Yang Z D, Gu G Q 2004 J. Phys. D: Appl. Phys. 37 107
[26] Wei E B, Song J B, Tian J W, Gu G Q 2003 Phys. Lett. A 309 160
[27] Li Z, Wei E B, Zhang H D, Tian J W 2005 Chin. Phys. Lett. 22 2360
[28] Ding X, Jia Y X, Wang X 2008 Phys. Lett. A 372 4247
[29] Hao Y H, Chen X G, Hou R, Wang R 2010 Chin. Phys. B 19 067202
[30] Potisook C, Natenapit M 2012 Physica B 407 598
[31] Liu Y, Liang F C, Shen H L 2005 Commun. Theor. Phys. 44 731
[32] Wei E B, Song J B, Gu G Q 2004 J. Appl. Phys. 95 1377
[33] Natenapit M, Thongboonrithi C, Potisook C 2008 Physica B 403 4314
[34] Shen Y Y, Chen X G, Li Q Q, Cui W, Hao Y H 2009 Commun. Theor. Phys. 51 743
[35] Shen Y Y, Chen X G, Cui W, Hao Y H, Li Q Q 2009 Chin .Phys. B 18 757
[36] Ding X, Jia Y X, Wei E B 2012 Chin. Phys. B 21 057202-8
[37] Wei E B, Gu G Q 2000 Chin. Phys. 9 464
[38] Liao S J (Translated by Chen C, Xu H) 2006 Beyond Perturbation: Introduction to the Homotopy Analysis Method (1st Ed.) (Beijing: Science Press) pp1-57 (in Chinese) [廖世俊著(陈晨, 徐航译) 2006 超越摄动–-同伦分析方法导论 (北京: 科学出版社) 第1–57页]
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[1] Yin Z W 2003 Dielectric Physics (2nd Ed.) (Beijing: Science Press) pp1-27 (in Chinese) [殷之文 2003 电介质物理学 (第二版) (北京: 科学出版社) 第1–27页]
[2] Xie B C, Gao L 2000 Acta Phys. Sin. 49 365 (in Chinese) [谢秉川, 高雷 2000 49 365]
[3] Gao L, Hong G 2003 Acta Phys. Sin. 52 575 (in Chinese) [高雷, 洪刚 2003 52 575]
[4] Ma H R, Xiao R F, Sheng P 1998 J. Opt. Soc. Am. B 15 1022
[5] Li X T, Ma H R 1999 Acta Phys. Sin. 48 461 (in Chinese) [李向亭, 马红孺 1999 48 461]
[6] Gao L 2001 J. Phys.: Condens. Matter 13 7271
[7] Gao L 2003 Phys. Status Solidi B 236 182
[8] Gao L 2004 Phys. Lett. A 322 250
[9] Yuen K P, Law M F, Yu K W, Sheng P 1997 Phys. Rev. E 56 1322
[10] Wu Y M, Chen G Q 2006 Acta Phys. Sin. 55 5242 (in Chinese) [吴亚敏, 陈国庆 2006 55 5242]
[11] Gu G Q, Yu K W 1991 Acta Phys. Sin. 40 709 (in Chinese) [顾国庆, 余建华 1991 40 709]
[12] Gu G Q, Yu J H 1992 Phys. Rev. B 46 4502
[13] Yu K W, Wang Y C, Hui P M 1993 Phys. Rev. B 47 1782
[14] Levy O, Bergman D J, Stroud D G 1995 Phys. Rev. E 52 3184
[15] Wei E B, Gu G Q 2001 Chin. Phys. Lett. 18 960
[16] Hui P M, Cheung P, Stroud D 1998 J. Appl. Phys. 84 3451
[17] Hui P M, Cheung P 2000 Physica B 279 45
[18] Gu G Q, Hui P M, Yu K W 2000 Physica B 279 62
[19] Wei E B, Gu G Q 2001 Commun. Theor. Phys. 35 501
[20] Wei E B, Song J B, Gu G Q 2002 Physica B 324 322
[21] Chen X G, Liang F C, Wei E B 2005 Chin. Phys. 14 1217
[22] Wei E B, Tian J W, Song J B 2003 J. Phys. Condens. Matter 15 8907
[23] Wei E B, Tian J W, Song J B 2004 Chin. Phys. 13 388
[24] Chen X G, Wei E B, Song J B 2004 Commun. Theor. Phys. 41 771
[25] Wei E B, Yang Z D, Gu G Q 2004 J. Phys. D: Appl. Phys. 37 107
[26] Wei E B, Song J B, Tian J W, Gu G Q 2003 Phys. Lett. A 309 160
[27] Li Z, Wei E B, Zhang H D, Tian J W 2005 Chin. Phys. Lett. 22 2360
[28] Ding X, Jia Y X, Wang X 2008 Phys. Lett. A 372 4247
[29] Hao Y H, Chen X G, Hou R, Wang R 2010 Chin. Phys. B 19 067202
[30] Potisook C, Natenapit M 2012 Physica B 407 598
[31] Liu Y, Liang F C, Shen H L 2005 Commun. Theor. Phys. 44 731
[32] Wei E B, Song J B, Gu G Q 2004 J. Appl. Phys. 95 1377
[33] Natenapit M, Thongboonrithi C, Potisook C 2008 Physica B 403 4314
[34] Shen Y Y, Chen X G, Li Q Q, Cui W, Hao Y H 2009 Commun. Theor. Phys. 51 743
[35] Shen Y Y, Chen X G, Cui W, Hao Y H, Li Q Q 2009 Chin .Phys. B 18 757
[36] Ding X, Jia Y X, Wei E B 2012 Chin. Phys. B 21 057202-8
[37] Wei E B, Gu G Q 2000 Chin. Phys. 9 464
[38] Liao S J (Translated by Chen C, Xu H) 2006 Beyond Perturbation: Introduction to the Homotopy Analysis Method (1st Ed.) (Beijing: Science Press) pp1-57 (in Chinese) [廖世俊著(陈晨, 徐航译) 2006 超越摄动–-同伦分析方法导论 (北京: 科学出版社) 第1–57页]
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