In this paper, the cubic and quintic diffusion equation under stochastic non homogeneity is solved using Wiener- Hermite expansion and perturbation (WHEP) technique, Homotopy perturbation method (HPM) and Pickard appr...In this paper, the cubic and quintic diffusion equation under stochastic non homogeneity is solved using Wiener- Hermite expansion and perturbation (WHEP) technique, Homotopy perturbation method (HPM) and Pickard approximation technique. The analytic solution of the linear case is obtained using Eigenfunction expansion .The Picard approximation method is used to introduce the first and second order approximate solution for the non linear case. The WHEP technique is also used to obtain approximate solution under different orders and different corrections. The Homotopy perturbation method (HPM) is also used to obtain some approximation orders for mean and variance. Using mathematica-5, the methods of solution are illustrated through figures, comparisons among different methods and some parametric studies.展开更多
使用由微波接收天线、衰减器、二极管检波器和波形记录等单元组成的测量系统测量高功率微波(high power microwave,HPM)功率是一种常用方法。在外场(尤其冬季),室外环境温度与室内温度相差较大(通常可达30~40℃),必然导致二极管检波器...使用由微波接收天线、衰减器、二极管检波器和波形记录等单元组成的测量系统测量高功率微波(high power microwave,HPM)功率是一种常用方法。在外场(尤其冬季),室外环境温度与室内温度相差较大(通常可达30~40℃),必然导致二极管检波器特性变化。如何有效抑制温度变化引起的二极管检波器特性变化对脉冲微波功率测量结果的影响,是提高此类系统在外场测量HPM功率精度的关键。本文论述了比较法测量脉冲微波功率的原理,理论分析得出,在二极管检波器工作于电压-功率线性区时,比较法测量脉冲微波功率的精度不受检波器温度特性的影响。实验研究了二极管检波器在不同温度条件下,直接检波法和比较法测量微波源输出相同脉冲微波功率的相对偏差变化,直接检波法的偏差为14%,比较法的偏差为−5.3%,测量结果表明运用比较法可以有效减小二极管检波器温度特性变化对测量脉冲微波功率的影响。展开更多
In this paper, comparison of homotopy perturbation method (HPM) and homotopy perturbation transform method (HPTM) is made, revealing that homotopy perturbation transform method is very fast convergent to the solution ...In this paper, comparison of homotopy perturbation method (HPM) and homotopy perturbation transform method (HPTM) is made, revealing that homotopy perturbation transform method is very fast convergent to the solution of the partial differential equation. For illustration and more explanation of the idea, some examples are provided.展开更多
In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example...In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.展开更多
In this research work, Homotopy perturbation method (HPM) is applied to find the approximate solution of the Van der Pol Differential equation (VDPDE), which is a well-known nonlinear ODE. Firstly, the approximate sol...In this research work, Homotopy perturbation method (HPM) is applied to find the approximate solution of the Van der Pol Differential equation (VDPDE), which is a well-known nonlinear ODE. Firstly, the approximate solution of Van Der Pol equation is developed using Dirichlet boundary conditions. Then a comparison between the present results and previously published results is presented and a good agreement is observed. Finally, HPM method is applied to find the approximate solution of VDPDE with Robin and Neumann boundary conditions.展开更多
This study investigates the flow and heat transfer of dusty Williamson (MHD) Nanofluid flow over a stretching permeable cylinder in a porous medium. Dusty Williamson Nanofluid was considered due to its thermal propert...This study investigates the flow and heat transfer of dusty Williamson (MHD) Nanofluid flow over a stretching permeable cylinder in a porous medium. Dusty Williamson Nanofluid was considered due to its thermal properties and potential benefits of increasing the heat transfer rate. Firstly, partial differential equations are transformed into coupled non-linear ordinary differential equations through a similarity variables transformation. The resulting set of dimensionless equations is solved analytically by using the Homogony Perturbation Method (HPM). The effects of the emerging parameters on the velocity and temperature profiles as well as skin-friction coefficient and Nusselt number are publicized through tables and graphs with appropriate discussions. The present result has been compared with published papers and found to be in agreement. To the best of author’s knowledge, there has been sparse research work in the literature that considers the effect of dust with Williamson Nanofluid and also solving the problem analytically. Therefore to the best of author’s knowledge, this is the first time analytical solution has been established for the problem. The results revealed that the fluid velocity of both the fluid and dust phases decreases as the Williamson parameter increases. Motivated by the above limitations and the gaps in past works, therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science, industry and engineering.展开更多
首先分析了检波器现有标定方法存在的问题,并且进行了实验研究。研究结果表明信号源输出功率未实时监测和检波器驻波比引起的反射是检波器灵敏度存在差异的主要原因。在此基础上提出了改进后的检波器标定方法,并且实验验证了改进后标定...首先分析了检波器现有标定方法存在的问题,并且进行了实验研究。研究结果表明信号源输出功率未实时监测和检波器驻波比引起的反射是检波器灵敏度存在差异的主要原因。在此基础上提出了改进后的检波器标定方法,并且实验验证了改进后标定方法的正确性。分别采用Agilent信号源和Agilent矢量网络分析仪研究了HPM常用测量器件窄脉冲和连续波下的衰减量差异。研究结果表明:测量器件衰减环节窄脉冲下衰减量可采用矢网连续波测试结果,二者最大差别约0.3 d B。展开更多
文摘In this paper, the cubic and quintic diffusion equation under stochastic non homogeneity is solved using Wiener- Hermite expansion and perturbation (WHEP) technique, Homotopy perturbation method (HPM) and Pickard approximation technique. The analytic solution of the linear case is obtained using Eigenfunction expansion .The Picard approximation method is used to introduce the first and second order approximate solution for the non linear case. The WHEP technique is also used to obtain approximate solution under different orders and different corrections. The Homotopy perturbation method (HPM) is also used to obtain some approximation orders for mean and variance. Using mathematica-5, the methods of solution are illustrated through figures, comparisons among different methods and some parametric studies.
文摘使用由微波接收天线、衰减器、二极管检波器和波形记录等单元组成的测量系统测量高功率微波(high power microwave,HPM)功率是一种常用方法。在外场(尤其冬季),室外环境温度与室内温度相差较大(通常可达30~40℃),必然导致二极管检波器特性变化。如何有效抑制温度变化引起的二极管检波器特性变化对脉冲微波功率测量结果的影响,是提高此类系统在外场测量HPM功率精度的关键。本文论述了比较法测量脉冲微波功率的原理,理论分析得出,在二极管检波器工作于电压-功率线性区时,比较法测量脉冲微波功率的精度不受检波器温度特性的影响。实验研究了二极管检波器在不同温度条件下,直接检波法和比较法测量微波源输出相同脉冲微波功率的相对偏差变化,直接检波法的偏差为14%,比较法的偏差为−5.3%,测量结果表明运用比较法可以有效减小二极管检波器温度特性变化对测量脉冲微波功率的影响。
文摘In this paper, comparison of homotopy perturbation method (HPM) and homotopy perturbation transform method (HPTM) is made, revealing that homotopy perturbation transform method is very fast convergent to the solution of the partial differential equation. For illustration and more explanation of the idea, some examples are provided.
文摘In this article,the main objective is to employ the homotopy perturbation method(HPM)as an alternative to classical perturbation methods for solving nonlinear equations having periodic coefficients.As a simple example,the nonlinear damping Mathieu equation has been investigated.In this investigation,two nonlinear solvability conditions are imposed.One of them was imposed in the first-order homotopy perturbation and used to study the stability behavior at resonance and non-resonance cases.The next level of the perturbation approaches another solvability condition and is applied to obtain the unknowns become clear in the solution for the firstorder solvability condition.The approach assumed here is so significant for solving many parametric nonlinear equations that arise within the engineering and nonlinear science.
文摘In this research work, Homotopy perturbation method (HPM) is applied to find the approximate solution of the Van der Pol Differential equation (VDPDE), which is a well-known nonlinear ODE. Firstly, the approximate solution of Van Der Pol equation is developed using Dirichlet boundary conditions. Then a comparison between the present results and previously published results is presented and a good agreement is observed. Finally, HPM method is applied to find the approximate solution of VDPDE with Robin and Neumann boundary conditions.
文摘This study investigates the flow and heat transfer of dusty Williamson (MHD) Nanofluid flow over a stretching permeable cylinder in a porous medium. Dusty Williamson Nanofluid was considered due to its thermal properties and potential benefits of increasing the heat transfer rate. Firstly, partial differential equations are transformed into coupled non-linear ordinary differential equations through a similarity variables transformation. The resulting set of dimensionless equations is solved analytically by using the Homogony Perturbation Method (HPM). The effects of the emerging parameters on the velocity and temperature profiles as well as skin-friction coefficient and Nusselt number are publicized through tables and graphs with appropriate discussions. The present result has been compared with published papers and found to be in agreement. To the best of author’s knowledge, there has been sparse research work in the literature that considers the effect of dust with Williamson Nanofluid and also solving the problem analytically. Therefore to the best of author’s knowledge, this is the first time analytical solution has been established for the problem. The results revealed that the fluid velocity of both the fluid and dust phases decreases as the Williamson parameter increases. Motivated by the above limitations and the gaps in past works, therefore, it is hoped that the present work will assist in providing accurate solutions to many practical problems in science, industry and engineering.
文摘首先分析了检波器现有标定方法存在的问题,并且进行了实验研究。研究结果表明信号源输出功率未实时监测和检波器驻波比引起的反射是检波器灵敏度存在差异的主要原因。在此基础上提出了改进后的检波器标定方法,并且实验验证了改进后标定方法的正确性。分别采用Agilent信号源和Agilent矢量网络分析仪研究了HPM常用测量器件窄脉冲和连续波下的衰减量差异。研究结果表明:测量器件衰减环节窄脉冲下衰减量可采用矢网连续波测试结果,二者最大差别约0.3 d B。
