652 publications from this institution
The parameter-expansion method is applied to a nonlinear oscillator with discontinuity. One iteration is sufficient to obtain a highly accurate solution, which is valid for the whole solution domain. Comparison of the obtained solution with the exact one shows that the method is very effective and convenient.
In this paper a simple but effective iteration method is proposed to search for limit cycles or bifurcation curves of nonlinear equations. Some examples are given to illustrate its convenience and effectiveness.
Laplace and Fourier transforms are widely used independently in engineering for linear differential equations including fractional differential equations. Here we introduce a generalized integral transform, which is a generalization of the Fourier transform, Laplace transform, and other transforms, e.g., Sumudu transform, Aboodh transform, Pourreza transform, and Mohand transform, making the new transform much attractive and promising. Its basic properties are elucidated, and its applications to initial value problems and integral equations are illustrated, when coupled with the homotopy perturbation, it can be used for various non-linear problems, opening a new window for non-linear science.
By a general Lagrange multiplier, an iteration approach is proposed to solve the generalized normalized diode equation, by suitable choice of the initial trial‐function, one‐step iteration leads to a high accurate solution, which is valid for the whole solution domain. Copyright © 2004 John Wiley & Sons, Ltd.
Geng and Cai suggested a modified He's frequency–amplitude formulation for nonlinear oscillators (Geng and Cai 2007 Eur. J. Phys. 28 923–31). We point out the accuracy of both the original one and the modified version depends upon the chosen location point, and so far we have no general rule for the location choice. The method of weighted residuals is suggested to overcome the shortcoming.
The Exp-function method is used to obtain generalized solitonary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics using symbolic computation. The method is straightforward and concise, and its applications are promising.
BACKGROUND: Electrospinning is widely used to produce nanofibers; however, not every polymer can be electrospun into nanofibers. To enhance electrospinability, much effort has been made in designing new apparatus, such as vibration‐electrospinning, magneto‐electrospinning and bubble‐electrospinning. RESULTS: A representative non‐ionic surfactant, TritonR X‐100, is used to enhance electrospinability. The surfactant is added to an electrospun poly(vinyl pyrrolidone) polymer solution, and a dramatic reduction in surface tension is observed. As a result, a moderate voltage is needed to produce fine nanofibers, which are commonly observed during the conventional electrospinning procedure only at elevated voltage. CONCLUSION: The novel strategy produces smaller nanofibers than those obtained without surfactants, and the minimum threshold voltage is much decreased. Copyright © 2008 Society of Chemical Industry
No abstract is provided for this article.
A new perturbation technique called linearized perturbation method is proposed. Contrary to the traditional perturbation techniques, the unperturbed equation is obtained by linearizing the original nonlinear equation, not by setting ε = 0. The obtained results are valid not only for small parameters, but also for very large values of ε. The period for the Duffing equation with 5th order nonlinearity is of very high accuracy, the maximal relative error in the total region 0 ≤ ε < ∞ is less than 0.08%.
A nonlinear dynamic model is established for two-strand spun or Sirospun yarns. The homotopy perturbation method proposed in our earlier work is used to calculated the approximate oscillating periods in the vertical and horizontal directions. The study reveals that the optimal convergence angle of the two strands in equilibrium is 90°, while when the convergence angle is near 127°, resonance occurs.
A nonlinear vibration system in a fractal space can be effectively modeled using the fractal derivatives, and the homotopy perturbation method is employed to solve fractal Duffing oscillator with arbitrary initial conditions. A detailed solving process is given, and it can be easily followed for applications to other nonlinear vibration problems.
No abstract is provided for this article.
Macromolecules are the foundation stone to construct a nanofiber in the electro-spinning. Their distribution and orientation greatly affect the product?s properties. In this paper, a rotary blowing air is used to control the radial topological structure of a nanofiber, and a macromolecule-scale inner structure can be designed. The influence of the flow properties on nanofibers? mechanical properties is studied experimentally.
Khuri (A new approach to Bratu's problem, Applied Mathematics and Computation, 147(2004), 131-136) applied Adomian decomposition method to study the problem, the procedure is tedious though the expression is a lovely closed-form, furthermore the procedure can only locate one branch of the solutions. The problem, however, can be solved with easy to find the two branch solutions and identify the bifurcation point by the variational method.
When an oscillator vibrates in a porous medium or along an unsmooth surface, a fractal model can be adopted using the two-scale fractal derivative. This paper elucidates a simple but effective method for fast and exclusive insight into the asymptotically periodic property at the initial stage and the extremely low frequency property when time tends to infinity. Some examples are illustrated to show the one-step solution process and the accurate results.
