物理学报
物理學報
물이학보
2013年
10期
360-366
,共7页
赵庆凯%陈小刚?%崔继峰
趙慶凱%陳小剛?%崔繼峰
조경개%진소강?%최계봉
高阶弱非线性复合介质%模函数展开法%同伦分析方法%电势分布
高階弱非線性複閤介質%模函數展開法%同倫分析方法%電勢分佈
고계약비선성복합개질%모함수전개법%동륜분석방법%전세분포
high-order weakly nonlinear composites%mode function expansion method%homotopy analysis method%electrostatic potential distribution
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 =σE+χ|E|2 E+η|E|4 E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.
利用同倫分析方法,研究瞭一類由柱形雜質隨機嵌入基質所形成的、電場和電流密度滿足 J =σE+χ|E|2 E+η|E|4 E形式本構關繫的高階弱非線性複閤介質在外加直流電場作用下的電勢分佈問題.首先利用模函數展開法,將本構方程及邊界條件化成瞭一繫列非線性常微分方程的邊值問題;再利用同倫分析方法進行求解,給齣瞭電勢在基質和雜質區域的漸近解析解.
이용동륜분석방법,연구료일류유주형잡질수궤감입기질소형성적、전장화전류밀도만족 J =σE+χ|E|2 E+η|E|4 E형식본구관계적고계약비선성복합개질재외가직류전장작용하적전세분포문제.수선이용모함수전개법,장본구방정급변계조건화성료일계렬비선성상미분방정적변치문제;재이용동륜분석방법진행구해,급출료전세재기질화잡질구역적점근해석해.
@@@@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 =σE+χ|E|2 E+η|E|4 E, 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.
