No abstract is provided for this article.
A significant phenomenon associated with devices used in nano/microelectromechanical systems (N/MEMS) is the dynamic pull-in instability. The basic theme of this manuscript is to study the nonlinear oscillation and dynamic pull-in instability in an N/MEMS switch with a current carrying conductor due to magnetic force. The variational iteration method accompanied by the techniques of the Laplace transform is used to find the approximate nonlinear frequency and approximate analytic solution of the model problem. The critical condition for the pull-in threshold is successfully obtained, which is extremely useful for the optimal design of N/MEMS. The effects of parameters on the frequency and the solution are discussed as well. The present findings exceptionally agree with the numerical results obtained by the Runge-Kutta method of order four and also give better accuracy when compared to other methods.
Article Α Review on Some New Recently Developed Nonlinear Analytical Techniques was published on March 1, 2000 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 1, issue 1).
For the strongly nonlinear equations without small parameter, a transformation u = βv can be introduced for the nonlinear equation L(u) + N(u) = 0, where L and N are general linear and nonlinear differential operators respectively, β is sufficiently small. Therefore, a strongly non-linear system is transformed into a small parameter system with respect to the new introduced parameter β, thus various traditional perturbation techniques can be applied. By Lindstedt-Poincare method, a perturbation solution for Dufing equation with 5th order nonlinearity is obtained, which is valid not only for the small parameter ε in the equation, but also for very large values of ε.
In this paper, a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed, which has modified the well-known Darcy law and overcome the continuity assumption of seepage flow. A new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem. The results show that the proposed iteration method, requiring no linearization or small perturbation, is very effective and convenient.
A modified Morris–Lecar model is suggested taking into account the size effect of the interacting ionic channels.
Phase change materials for thermal energy storage have been widely applied to clothing insulation, electronic products of heat energy storage. The thermal storage potential of the nanofiber membranes was analyzed using the differential scanning calorimetry. Effect of microstructure of the membrane on energy storage was analyzed, and its applications to electronic devices were elucidated.
BACKGROUND: Electrospinning is a powerful and effective method to produce nanofibers. Beads have been observed widely in electrospun products, but effects of solvents, weight concentrations and salt additives on the number and morphology of beads in the electrospinning process have not been systematically studied. RESULTS: Both theoretical analysis and experimental results show that beads strongly depend upon solvents, weight concentrations and salt additives. Either a suitable weight concentration or a suitable salt additive can completely prevent the occurrence of beads in the electrospinning process; solvents can affect the number of beads and the morphology of electrospun fibers. CONCLUSION: Beads are mainly caused by lower surface tension. With a higher surface tension, the size and number of beads in electrospun products are smaller and fewer, respectively. Copyright © 2007 Society of Chemical Industry
No abstract is provided for this article.
No abstract is provided for this article.
In this paper, a new perturbation method is proposed. In contrast to the traditional perturbation methods, this technique does not require a small parameters in the equation. In this method, according to the homotopy technique, a homotopy with an imbedding parameter is constructed, and the imbedding parameter is considered as a “small parameter”, so the method is called homotopy perturbation method, which can take the full advantage of the traditional perturbation methods and the homotopy technique. To illustrate its effectiveness and its convenience, a few typical nonlinear equations are used. The results reveal their first-order approximations obtained by the proposed method are valid uniformly even for very large parameters, and are more accurate than the perturbation solutions.
The critical volume of wetting liquid, above which coalescence of aligned flexible fibers does not occur, is of great practical interest. By means of dimensional analysis, the formulation of the critical volume is obtained, which depends mainly on the geometrical and mechanical factors.
A fractional nonlinear wave equation is used as an example to elucidate how to solve fractional differential equations with local fractional derivatives via the fractional complex transform and the exp-function method.
Air permeability in hierarchic porous media does not obey Fick′s equation or its modification because fractal objects have well‐defined geometric properties, which are discrete and discontinuous. We propose a theoretical model dealing with, for the first time, a seemingly complex air permeability process using fractal derivative method. The fractal derivative model has been successfully applied to explain the novel air permeability phenomenon of cocoon. The theoretical analysis was in agreement with experimental results.
The variational iteration method is applied to the eighth-order initial-boundary value problems. Only one iteration is needed, and the obtained solutions are of remarkable accuracy.
Article Variational Theory for Linear Magneto-Electro-Elasticity was published on December 1, 2001 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 2, issue 4).
In this paper, via the semi-inverse method proposed previously by the present author, a family of variational principles of bending problems of plates is derived directly from their governing equations and boundary conditions, without using the Lagrange multiplier method. In this method, an energy-like trial functional is constructed with a certain unknown function, which can be identified step by step. A new generalized variational principle is obtained.
