外加直流电场作用下高阶弱非线性复合介质的电势分布

赵庆凯; 陈小刚; 崔继峰

doi:10.7498/aps.62.107201

摘要

利用同伦分析方法, 研究了一类由柱形杂质随机嵌入基质所形成的、电场和电流密度满足J = σ E + χ |E|2E + η|E|4E 形式本构关系的高阶弱非线性复合介质在外加直流电场作用下的电势分布问题. 首先利用模函数展开法, 将本构方程及边界条件化成了一系列非线性常微分方程的边值问题; 再利用同伦分析方法进行求解, 给出了电势在基质和杂质区域的渐近解析解.

关键词:

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.

Keywords:

high-order weakly nonlinear composites /
mode function expansion method /
homotopy analysis method /
electrostatic potential distribution

作者及机构信息

1.
内蒙古工业大学理学院, 呼和浩特 010051;

2.
上海交通大学船舶海洋与建筑工程学院, 上海 200240

基金项目: 内蒙古自然科学基金(批准号: 2011MS0113) 和内蒙古人才基金(2010)资助的课题.

Authors and contacts

1.
College of Science, Inner Mongolia University of Technology, Hohhot 010051, China;

2.
School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiaotong University, Shanghai 200240, China

Funds: Project supported by the Natural Science Foundation of Inner Mongolia, China (Grant No. 2011MS0113) and the Talent Foundation of Inner Mongolia (2010).

参考文献

[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]

施引文献

[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]

[1]	于家成, 仲佳勇, 安维明, 平永利. 短脉冲强激光驱动磁重联过程的靶后电势分布特征. , 2021, 70(6): 065201. doi: 10.7498/aps.70.20201339
[2]	吴钦宽. 输电线非线性振动问题的同伦映射近似解. , 2011, 60(6): 068802. doi: 10.7498/aps.60.068802
[3]	叶望川, 李彪, 王佳. Sinh-Gordon方程的同伦近似解. , 2011, 60(3): 030207. doi: 10.7498/aps.60.030207
[4]	李帮庆, 马玉兰, 徐美萍. （G'/G）展开法与高维非线性物理方程的新分形结构. , 2010, 59(3): 1409-1415. doi: 10.7498/aps.59.1409
[5]	那仁满都拉, 韩元春. 非均匀圆柱壳中非线性波传播模型的同伦分析解法. , 2010, 59(5): 2942-2947. doi: 10.7498/aps.59.2942
[6]	石兰芳, 莫嘉琪. 一类扰动非线性发展方程的类孤子同伦近似解析解. , 2009, 58(12): 8123-8126. doi: 10.7498/aps.58.8123
[7]	马玉兰, 李帮庆, 孙践知. (G′/G)展开法在高维非线性物理方程中的新应用. , 2009, 58(11): 7402-7409. doi: 10.7498/aps.58.7402
[8]	张志锋, 张鹤鸣, 胡辉勇, 宣荣喜, 宋建军. 应变Si沟道nMOSFET阈值电压模型. , 2009, 58(7): 4948-4952. doi: 10.7498/aps.58.4948
[9]	莫嘉琪, 张伟江, 陈贤峰. 强非线性发展方程孤波同伦解法. , 2007, 56(11): 6169-6172. doi: 10.7498/aps.56.6169
[10]	杨红娟, 石玉仁, 段文山, 吕克璞. 非线性演化方程孤立波的同伦分析法求解. , 2007, 56(6): 3064-3069. doi: 10.7498/aps.56.3064
[11]	石玉仁, 汪映海, 杨红娟, 段文山. 高维非线性演化方程孤立波的同伦分析法求解. , 2007, 56(12): 6791-6796. doi: 10.7498/aps.56.6791
[12]	张政伟, 樊养余, 曾黎. 一种精确检测未知弱复合周期信号频率的非线性融合方法. , 2006, 55(10): 5115-5121. doi: 10.7498/aps.55.5115
[13]	石玉仁, 许新建, 吴枝喜, 汪映海, 杨红娟, 段文山, 吕克璞. 同伦分析法在求解非线性演化方程中的应用. , 2006, 55(4): 1555-1560. doi: 10.7498/aps.55.1555
[14]	吴平, 吕百达, 陈天禄. 光束分数傅里叶变换的Wigner分布函数分析方法. , 2005, 54(2): 658-664. doi: 10.7498/aps.54.658
[15]	顾利萍, 高雷. 弱非线性复合体中的高阶非线性响应. , 2005, 54(2): 987-992. doi: 10.7498/aps.54.987
[16]	徐伟, 孙中奎, 杨晓丽. 基于参数展开的同伦分析法在强非线性随机动力系统中的应用. , 2005, 54(11): 5069-5076. doi: 10.7498/aps.54.5069
[17]	石玉仁, 郭　鹏, 吕克璞, 段文山. 修正Jacobi椭圆函数展开法及其应用. , 2004, 53(10): 3265-3269. doi: 10.7498/aps.53.3265
[18]	张善卿, 李志斌. Jacobi 椭圆函数展开法的新应用. , 2003, 52(5): 1066-1070. doi: 10.7498/aps.52.1066
[19]	刘式适, 傅遵涛, 刘式达, 赵强. Jacobi椭圆函数展开法及其在求解非线性波动方程中的应用. , 2001, 50(11): 2068-2073. doi: 10.7498/aps.50.2068
[20]	李向亭, 马红孺. 用Bergman方法计算复合介质的电势分布. , 1999, 48(3): 461-467. doi: 10.7498/aps.48.461

计量

文章访问数: 6251
PDF下载量: 433
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板