Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites

丁霞^{1},贾艳霞^{2},魏恩泊^{3}

1. College of Mathematics and Physics, Qingdao University of Science & Technology, Qingdao 266061, China;
2. Hisense Trans-Tech Company Limited, Qingdao 266071, China;
3. Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China

Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites

Ding Xia^{a},Jia Yan-Xia^{b},Wei En-Bo^{c}

1. College of Mathematics and Physics, Qingdao University of Science & Technology, Qingdao 266061, China;
2. Hisense Trans-Tech Company Limited, Qingdao 266071, China;
3. Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China

摘要 The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current (AC) and direct-current (DC) electric field E_{app} = E_{0} (1+sin ωt). The dielectric profile of the cylindrical inclusions is modeled by function ε_{i} (r) = C_{k} r^{k} (r ≤ a), where r is the radius of the cylindrical inclusion, and C_{k}, k, a are parameters. In the dilute limit, the local potentials and the effective nonlinear responses at all harmonics are derived. Meanwhile, the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field. It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field. Moreover, the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable, and the maximum of the electric field inside the cylinder is at its center.

Abstract：The perturbation method is used to study the localization of electric field distribution and the effective nonlinear response of graded composites under an external alternating-current (AC) and direct-current (DC) electric field E_{app} = E_{0} (1+sin ωt). The dielectric profile of the cylindrical inclusions is modeled by function ε_{i} (r) = C_{k} r^{k} (r ≤ a), where r is the radius of the cylindrical inclusion, and C_{k}, k, a are parameters. In the dilute limit, the local potentials and the effective nonlinear responses at all harmonics are derived. Meanwhile, the general effective nonlinear responses are also derived and compared with the effective nonlinear responses at harmonics under the AC and DC external field. It is found that the effective nonlinear AC and DC responses at harmonics can be calculated by those of the general effective nonlinear of the graded composites under the external DC electric field. Moreover, the obtained local electrical fields show that the electrical field distribution in the cylindrical inclusions is controllable, and the maximum of the electric field inside the cylinder is at its center.

(Electrostatics; Poisson and Laplace equations, boundary-value problems)

基金资助:Project supported by the National Natural Science Foundation of China (Grant Nos. 40876094 and JQ10974106), the National High Technology Research and Development Program of China (Grant Nos. 2009AA09Z102 and 2008AA09A403), the Excellent Youth Fundation of Shandong Scientific Committee, China (Grant No. JQ201018), and the Natural Science Foundation of Shandong Province, China (Grant No. ZR2009AZ002).

引用本文:

丁霞,贾艳霞,魏恩泊. Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites[J]. 中国物理B, 2012, 21(5): 57202-057202.
Ding Xia,Jia Yan-Xia,Wei En-Bo. Electric field distribution and effective nonlinear AC and DC responses of graded cylindrical composites. Chin. Phys. B, 2012, 21(5): 57202-057202.