非线性柱形涂层复合介质有效的直流-交流电响应

利用摄动展开方法, 研究了由圆柱形带涂层杂质随机嵌入基质所形成的非线性复合介质在外加 的带有不同频率和振幅的混合电场E₀ + E₁ sinωt+E₃ sin3ωt作用下有效的直流-交流电响应, 分别推导了复合介质在杂质核、涂层及基质区域的电势分布, 并在低杂质浓度下给出了复合介质有效的非线性响应及它们之间的关系. 关键词： 非线性柱形涂层复合介质 有效的非线性响应 外加交直流电场     

Effective response in nonlinear spherical coated composites under external AC and DC electric fields

By using the perturbation method,effective nonlinear direct current(DC) and alternating current(AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of an external electric field E a = E 0 + E 1 sin ωt + E 3 sin 3ωt with different amplitudes and frequencies.The local potentials of composites at all harmonics are given in the inclusion particles and the host regions.All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

Effective response in nonlinear spherical coated composites under external AC and DC electric field

By using the perturbation method, effective nonlinear direct current (DC) and alternating current (AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of external electric field E_a =E₀ +E₁ sin ωt+E₃ sin 3ωt with different amplitudes and frequencies. The local potentials of composites at all harmonics are given in the inclusion particles and the host regions. All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

Effective response of nonlinear cylindrical coated composites under external AC and DC electric field

This paper uses the perturbation method to study effective response of nonlinear cylindrical coated composites. Under the external AC and DC electric field E_a(1 + sinωt), the local potentials of composites at all harmonic frequencies are induced. An effective nonlinear response to composite is given for the cylindrical coated inclusions in the dilute limit.     

球形粒子复合介质非线性有效电导交流响应

利用摄动方法，研究了在外加交流电场作用下，含球形杂质的非线性复合介质有效电导的交流响应问题。在一类形如E1sinωt +E3sin3ωt的正弦电场作用下，分别导出了非线性复合介质中杂质粒子及基质所在区域的局部电势。在杂质浓度较低时，进一步得到了复合介质非线性有效电导在基频和三阶谐波下的响应，并讨论了二者之间的关系。     

Effective AC Response of Nonlinear Spherical Coated Composites

Under alternating current electric field, effective response of granular nonlinear composites with spherical coated inclusions is investigated in the dilute limit by using the perturbation approach. For an external sinusoidal applied field with finite frequency ω, the local fields and potentials of composites in general consist of components at all harmonics for cubic nonlinear constitutive relationships. We derive the local potentials of spherical coated composites at harmonics. Moreover, we give the formulae of the nonlinear effective AC susceptibility at the third harmonic frequency.     

金属/电介质颗粒复合介质的非线性交流响应

推广T矩阵法来研究二组分颗粒复合介质的非线性交流响应，解析推导出基频、三次及五次谐波频率下的有效线性介电常数及三阶和五阶非线性极化率的解析表达式.当组分颗粒的介电常数为实数时，表达式同以前微扰理论完全一致.进一步数值计算了金属-电介质复合介质的有效非线性交流响应，数值结果表明，体系的三阶、五阶非线性极化率在表面等离子共振频率附近有明显增强，而且，随着体积分数提高，共振峰增强且伴随着共振频率红移现象.还进一步讨论了维度效应对体系非线性交流响应的影响. 关键词： T矩阵方法 复合介质 非线性交流响应     

梯度圆柱颗粒复合介质的有效非线性响应

应用非线性微分有效偶极近似方法,导出了关于非线性梯度圆柱颗粒的等效线性介电常数和三阶非线性极化率的微分式,研究了稀释极限下,圆柱形梯度颗粒无规置入线性介质中组成的复合介质的有效线性介电常数和三阶非线性极化率.作为应用,数值计算了具有幂指数梯度分布的介电常数的颗粒复合介质的有效非线性响应,及梯度金属电介质颗粒复合介质的表面plasmon共振效应.     

Effective AC response of a nonlinear spherical coated composite

An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field,E a=E 1 sin(ωt) + E 3 sin(3ωt),is investigated using a perturbation method.The local potentials of the composite at higher harmonics are given both in the region of local inclusion particles and in the local host region under the external AC electric field.All effective nonlinear responses of the composite and the relationship between the effective nonlinear responses at the fundamental frequency and third harmonics are also studied for spherical coated inclusion in a dilute limit.     

Effective Response of Nonlinear Composite under External AC and DC Electric Field

A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα = εαE xα|E|2E. Under the external AC and DC electric field Eapp = Eα(1 sinwt), the effective nonlinear responses and local potentials are induced by the cubic nonlinearity of Kerr materials at all harmonics. As an example in three dimensions, we have investigated this kind of nonlinear composites with spherical inclusions embedded in a host. At all harmonic frequencies, the potentials in inclusion and host regions are derived. Furthermore, the formulae of the effective linear and nonlinear responses are given in the dilute limit.     

Effective Response of Nonlinear Composite under External AC and DC Electric Field

A perturbation method is used to study effective response of nonlinear Kerr composites, which are subject to the constitutive relation of electric displacement and electric field, Dα=εαE＋xα｜E｜^2E. Under the external AG and DC electric field Eapp = Eα（1 ＋ sinωt）, the effective nonlinear responses and local potentials are induced by the cubic nonlinearity of Kerr materials at all harmonics. As an example in three dimensions, we have investigated this kind of nonlinear composites with spherical inclusions embedded in a host. At all harmonic frequencies, the potentials in inclusion and host regions are derived. Furthermore, the formulae of the effective linear and nonlinear responses are given in the dilute Iimit.     

A theory of nonlinear AC response in coated composites

A method for determining effective dielectric responses of Kerr-like coated nonlinear composites under the alternating current (AC) electric field is proposed by using perturbation approach. As an example, we have investigated the composite with coated cylindrical inclusions randomly embedded in a host under an external sinusoidal field with finite frequency ω. The local field and potential of composites in general consists of components with all harmonic frequencies. The effective nonlinear AC responses at all harmonics are induced by the coated nonlinear composites because of the nonlinear constitutive relation. Moreover, we have derived the formulae of effective nonlinear AC responses at the fundamental frequency and the third harmonic in the dilute limit.     

Effective AC and DC Responses of Nonlinear Composites at Higher Concentration

For higher concentration of inclusions, an effective medium approximation （EMA） method is used to investigate the bulk effective response of weakly nonlinear composites, which are subject to the constitutive relation of electric displacement and electric field, Dα = εαE ＋Xα｜E｜^2 E. As an example of three dimensions, under the external AC and DC electric fields Eapp = Eα（1 ＋ sinωt）, we have derived the general effective nonh＇near response of composites by the EMA method for higher concentration of spherical inclusions. Furthermore, the effective nonlinear responses at harmonics are predicted.     

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

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 = E₀ (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.     

The Effective AC Response of Nonlinear Composites

A perturbative approach is used to study the AC response of nonlinear compostie media,which obey a current-field relation of the form J=σE χ|E|^2E with comp[onents having nonlinear response at finite frequencies.For a sinusoidal applied field,we extend the local potential in terms of sinusoidal components at fundamental frequency and high-order harmonic frequencies to treat the nonlinear comosites.For nonlinear composite media with a low concentrations of spherical inclusions,we give the formulae of the nonlinear effective AC susceptibility χ3ω at the third harmonic frequency.     

具有各向异性的梯度颗粒复合材料的有效介电响应

本文研究了具有梯度壳层椭球颗粒复合体系的有效介电响应，在稀释条件下用准静态近似方法, 推导了颗粒壳层具有任意介电梯度形式的椭球颗粒复合体系的有效介电常数和部分共振条件的一般表达式。并以壳层的介电常数为主轴的幂函数形式为例，得出了通过调节壳层的介电梯度形式、颗粒的结构和形状,可以提高该体系的有效介电常数和实现部分共振的结论。     

Effective Response of Nonlinear Spherical Coated Composites Under External AC and DC Electric Field

Under the external AC and DC electric field, the effective response of nonlinear spherical coated composites, which obey the constitutive relation of electric displacement and electric field, is investigated in the dilute limit by using the perturbation method. The local potentials in inclusion and host regions are derived at all harmonics. Moreover, the formulae of the effective linear and nonlinear responses are given in the dilute limit.     

Effective medium approximation for strongly nonlinear media

The effective medium approximation is one of the most popular approximations used for calculating the effective coefficients of linear composite media. When the same approach is applied to the case of power-law nonlinear composite media the obtained expression contains a function whose values are unknown. In order to determine the form of this function and to calculate some coefficients related to it, we calculate the electric field for the case of a single inclusion. The numerical solution is based on the relaxation method for solving differential equations, but involves some modifications due to the nonlinearity. After the solution of the differential equation the function and the coefficients are calculated and examined. The results differ considerably from those obtained earlier by simple approximations. An erratum to this article is available at .     

Effective responses of nonlinear elliptic cylindrical composites

The higher-order dielectric responses of composites composed of weakly nonlinear elliptic cylindrical inclusions randomly embedded in linear media are investigated. The general formulae for effective DC coefficients are newly derived by the average field method up to the ninth order and then applied to analyze the effects of inclusion shapes on the effective response. The results are directly transformed to the quasi-static AC response of the composites under the sinusoidal external electric field with fundamental and third harmonic frequencies. The more general relationships between the effective DC and AC coefficients are established up to the seventh order and third harmonic, which are applicable to all weakly nonlinear isotropic composites.     

Effective nonlinear AC response to graded cylindrical composites

The perturbation method is used to study the effective nonlinear response of graded cylindrical composites with power-law gradient inclusions under a sinusoidal alternating current (AC) external field of finite frequency ω. In dilute limit, the local potentials and the formulae of effective nonlinear AC responses are derived at the fundamental frequency and the third harmonics. Furthermore, the general effective nonlinear responses are given and compared with the effective nonlinear AC responses of fundamental frequency and the third harmonics, and the relationships between the nonlinear effective AC response and the general effective nonlinear response are also determined.