scholarly journals Additional boundary condition for electric quadrupolar continua derived from Maxwell's differential equations

Radio Science ◽  
2016 ◽  
Vol 51 (8) ◽  
pp. 1312-1321 ◽  
Author(s):  
A. D. Yaghjian ◽  
M. G. Silveirinha
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Additional Boundary Condition

Postbuckling Analysis of a Nonlocal Nanorod Under Self-Weight

2020 ◽  
Vol 12 (04) ◽  
pp. 2050035
Author(s):  
Chinnawut Juntarasaid ◽  
Tawich Pulngern ◽  
Somchai Chucheepsakul
Keyword(s):  
Boundary Condition ◽  
Differential Equations ◽  
Nonlocal Elasticity ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Constraint Equation ◽  
Form Solution ◽  
Postbuckling Behavior ◽  
Euler Beam ◽  
Softening Behavior

This paper presents the postbuckled configurations of simply supported and clamped-pinned nanorods under self-weight based on elastica theory. Numerical solution is considered in this work since closed-form solution of postbuckling analysis under self-weight cannot be obtained. The set of nonlinear differential equations of a nanorod including the effect of nonlocal elasticity are investigated. The constraint equation at boundary condition technique is introduced for the solution of postbuckling analysis. In order to solve the set of nonlinear differential equations, the shooting method is utilized, where the set of these equations along with boundary conditions are integrated by the fourth-order Runge-Kutta algorithm. Numerical results are obtained and the highlighting influences of the nonlocal elasticity on postbuckling behavior of nanorods are discussed. The obtained results indicate that the rotation angle and the postbuckled configurations of nanorods are varied by changing the nonlocal elasticity parameter. The effect of nonlocal elasticity shows the softening behavior in comparison with the Euler beam. The present formulation together with constraint boundary condition technique is an effective solution for postbuckling analysis of a nanorod under self-weight including the effect of nonlocal elasticity.

scholarly journals On the Convergence of Solutions for SPDEs under Perturbation of the Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Zhongkai Guo ◽  
Jicheng Liu ◽  
Wenya Wang
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dirichlet Boundary Condition ◽  
Stochastic Partial Differential Equations ◽  
Dirichlet Boundary ◽  
Mild Solutions ◽  
Partial Differential ◽  
Domain Perturbation ◽  
Convergence Of Solutions

We investigate the effect of domain perturbation on the behavior of mild solutions for a class of semilinear stochastic partial differential equations subject to the Dirichlet boundary condition. Under some assumptions, we obtain an estimate for the mild solutions under changes of the domain.

scholarly journals MHD Slip Flow of Newtonian Fluid past a Stretching Sheet with Thermal Convective Boundary Condition, Radiation, and Chemical Reaction

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Reda G. Abdel-Rahman
Keyword(s):  
Mass Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Nonlinear Ordinary Differential Equations ◽  
Convective Boundary

An analysis is carried out to study the problem of heat and mass transfer flow over a moving permeable flat stretching sheet in the presence of convective boundary condition, slip, radiation, heat generation/absorption, and first-order chemical reaction. The viscosity of fluid is assumed to vary linearly with temperature. Also the diffusivity is assumed to vary linearly with concentration. The governing partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by using Lie group point of transformations. The system of transformed nonlinear ordinary differential equations is solved numerically using shooting techniques with fourth-order Runge-Kutta integration scheme. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The effects of the various interesting parameters on the flow, heat, and mass transfer are analyzed and discussed through graphs in detail. The values of the local Nusselt number, the local skin friction, and the local Sherwood number for different physical parameters are also tabulated.

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