652 publications from this institution
No abstract is provided for this article.
Variational theory is the theoretical basis for various numerical methods. A minimum variational principle plays an important role in guaranteeing the convergence of the numerical algorithm, and the Weierstrass theorem is used to judge the minimum. This paper suggests a fractal modification of Weierstrass function for fractal variational principles, and a strong minimum condition is given. The Hamilton least-action principle for the Duffing oscillator in a fractal space is used as an example to show the correctness of the suggested strong minimum condition.
Electrospinning is a simple but powerful method for making nanofibers that can then be collected to create porous mats. We expand the range of this technique by making nanofibers from macromolecules with a molecular weight of 3,000,000, namely poly(ethylene oxide) (PEO). Gelation of PEO blocks its spinning by traditional electrospinning. PEO was mixed with pure alcohol, and in specific concentration 10 wt % and under vibration condition, the mixed solution behaves like polymers for electrospinning, the average diameter of the obtained nanofibers is about 100 nm. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3840–3843, 2007
Recently, Wazwaz [Appl. Math. Comput. 118 (2001) 311–325] applied the Adomian’s decomposition method to solve analytically the solution of sixth-order boundary value problems. The same problem is discussed via the variational principle, which reveals to be much more simpler and much more efficient.
Nonlinear vibration arises in engineering and physics, and the periodic motion of these nonlinear oscillatory systems have rich dynamics. An estimation of amplitude-frequency relationship of a nonlinear oscillator is much needed, therefore, well-known homotopy perturbation method is employed for this purpose. In this paper, two last modifications of the homotopy perturbation method are briefly reviewed, which couples with either the parameter-expansion technology or the enhanced perturbation method. Both modifications are extremely effective for nonlinear oscillators, and the cubic-quintic-septic Duffing oscillator is used as an example to elucidate the solution processes.
Homotopy perturbation method is applied to nonlinear boundary value problems. Comparison of the result obtained by the present method with that obtained by Adomian method [A.M. Wazwaz, Found. Phys. Lett. 13 (2000) 493] reveals that the present method is very effective and convenient.
Purpose The purpose of this paper is to suggest a general numerical algorithm for nonlinear problems by the variational iteration method (VIM). Design/methodology/approach Firstly, the Laplace transform technique is used to reconstruct the variational iteration algorithm-II. Secondly, its convergence is strictly proved. Thirdly, the numerical steps for the algorithm is given. Finally, some examples are given to show the solution process and the effectiveness of the method. Findings No variational theory is needed to construct the numerical algorithm, and the incorporation of the Laplace method into the VIM makes the solution process much simpler. Originality/value A universal iteration formulation is suggested for nonlinear problems. The VIM cleans up the numerical road to differential equations.
The Blasius' equation f″′ + ff″ 2 =0, with boundary conditions f(0) = f′(0)0, f′(+∞)=1 is studied in this paper. An approximate analytical solution is obtained via the variational iteration method. The comparison with Howarth's numerical solution reveals that the proposed method is of high accuracy.
Via the semi-inverse method proposed by He, a generalized variational principle of classical type (not Curtin-type & not involving convolutions) for the entitled problem of linear anisotropic materials has been obtained directly from the field equations & boundary conditions.
<abstract><p>This paper presents the Elzaki homotopy perturbation transform scheme ($ {\bf{E}} $HPTS) to analyze the approximate solution of the multi-dimensional fractional diffusion equation. The Atangana-Baleanu derivative is considered in the Caputo sense. First, we apply Elzaki transform ($ {\bf{E}} $T) to obtain a recurrence relation without any assumption or restrictive variable. Then, this relation becomes very easy to handle for the implementation of the homotopy perturbation scheme (HPS). We observe that HPS produces the iterations in the form of convergence series that approaches the precise solution. We provide the graphical representation in 2D plot distribution and 3D surface solution. The error analysis shows that the solution derived by $ {\bf{E}} $HPTS is very close to the exact solution. The obtained series shows that $ {\bf{E}} $HPTS is a very simple, straightforward, and efficient tool for other problems of fractional derivatives.</p></abstract>
The resistance to tearing is an important characteristic of warp knitted fabrics. In this paper, tongue tear tests were performed on warp knitted fabrics with three different sizes of hexagonal meshes, and a mathematical model is established to outline the basic tearing behavior, the geometrical and mechanical effects on tearing properties are elucidated. The theoretical model is verified with tearing experiments of various samples which validated the efficiency and accuracy of the mathematical model. This model can be extended to benefit for the design and manufacture of textile products.
A mathematical model describing the resistance of conductive polymer is proposed, which is naturally different from that for metal conductors. An allometric scaling law between the resistance and the section area is obtained. In the derivation, He Chengtian's interpolation, which has millennia history, is applied.
Article Bubble-electrospinning for Fabrication of Nanofibers with Diameter of about 20nm was published on December 1, 2010 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 11, issue Supplement).
This paper considers the movement of an incompressible non-Newtonian Walters’ B liquid within a rotating annulus. The flow lies within porous media and is magnetized by a uniform normal magnetic field. Mass transmission is included in the arrangements of homogeneous and heterogeneous chemical reactions (HHCR) with a thermal diffusion effect. Heat diffusion is exposed with a temperature- dependent heat source (THS) and an exponential radial-dependent heat source (ERHS), besides Joule heating and viscous dissipations. The mathematical construction is shown by momentum, energy and concentration of chemical materials equations along with time-periodic boundary conditions. The innovation of this study stems from considering mass transfer utilizing HHCR, with thermal diffusion effects in the flow within a rotating annulus, trying to understand the effect of these reactions on the flow and related applications. The principal regulating the structure of nonlinear partial differential equations is transferred by ordinary ones utilizing appropriate similarity analysis. These equations are analyzed by the homotopy perturbation method. Subsequently, the analytical solutions of the main profiles are obtained, and a graphical construction is established to clarify the effects of the relevant physical elements. It is observed that the velocity waves decrease with annulus width enlargement and increase with the wave phase amplitude. With an increase in all significant parameters, heat transmission gets better. Furthermore, as the strength of HHCR is increased, the concentration of molecules decreases. These outcomes are significant in several applications like cancer therapy, biochemical manufacturing purposes through reactors, where biochemical interactions can be regulated by accurate control of various parameters.
In engineering, a fast estimation of the periodic property of a nonlinear oscillator is much needed. This paper reviews some simplest methods for nonlinear oscillators, including He’s frequency formulation, the max-min approach and the homotopy perturbation method. A mathematical insight into He’s frequency formulation is given, and the weighted average is introduced to further improve the estimated accuracy of the frequency. Fractional oscillators are also discussed.
Electrospun nanofibers have a wide range of potential applications such as photonic structures, microfluid channels (nanofluidics), catalysis, sensors, medicine, pharmacy, drug delivery, invisibility devices (e.g. stealth planes, stealth clothes), radioprotection, tissue engineering, and nanometer-sized semiconductor devices. A hierarchy of motion in electrospinning process is identified, and the E-infinity theory is applied to explain the phenomenon. These materials with hierarchical geometrical structures always display quantum-like properties and have many fascinating nano-effects, such as a remarkable increase in strength, high surface energy and surface reactivity, excellent thermal and electric conductivity. Here we also show that nanotechnology could be seen as a link between the deterministic classic mechanics and the indeterministic quantum mechanics, and E-infinity theory could help in understanding various nano effects. We also predict that the Hausdorff dimension for the hierarchy of motion should be close to the average Hausdorff dimension of E-infinity spacetime, and the characteristics of electrospun nanofibers depend mainly upon the Hausdorff-fractal dimension. An experiment is performed to verify our predictions.
