652 publications from this institution
The Stanton number was originally proposed for describing heat transfer through a smooth surface. A modified one is suggested in this paper to take into account non-smooth surface or fractal surface. The emphasis is put on the heat transfer through fabrics.
No abstract is provided for this article.
Purpose The purpose of this paper is to find an approximate solution of a fractional differential equation. The fractional Newell–Whitehead–Segel equation (FNWSE) is used to elucidate the solution process, which is one of the nonlinear amplitude equation, and it enhances a significant role in the modeling of various physical phenomena arising in fluid mechanics, solid-state physics, optics, plasma physics, dispersion and convection systems. Design/methodology/approach In Part 1, the authors adopted Mohand transform to find the analytical solution of FNWSE. In this part, the authors apply the fractional complex transform (the two-scale transform) to convert the problem into its differential partner, and then they introduce the homotopy perturbation method (HPM) to bring down the nonlinear terms for the approximate solution. Findings The HPM makes numerical simulation for the fractional differential equations easy, and the two-scale transform is a strong tool for fractal models. Originality/value The HPM with the two-scale transform sheds a bright light on numerical approach to fractional calculus.
No abstract is provided for this article.
Newton’s iteration method is widely used in numerical methods, but its convergence is low. Though a higher order iteration algorithm leads to a fast convergence, it is always complex. An optimal iteration formulation is much needed for both fast convergence and simple calculation. Here, we develop a two-step optimal fourth-order iterative method based on linear combination of two iterative schemes for nonlinear equations, and we explore the convergence criteria of the proposed method and also demonstrate its validity and efficiency by considering some test problems. We present both numerical as well as graphical comparisons. Further, the dynamical behavior of the proposed method is revealed.
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.
No abstract is provided for this article.
Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily applied to fractional calculus. Two examples are given.
Rubner 1880 surface law reveals that the basal metabolic rate scales with body mass raised to the power of 2/3, which is geometrically correct and biologically relevant. However, Kleiber 1932 scaling law experimentally found that the scaling index was 3/4 instead of 2/3. There is no theory that can explain the Kleiber's data, explanations in Science in 1997 and later in Nature in 2002 for 3/4 scaling law for all life were apparently wrong. Here we show that Rubner's surface law was approximately correct, and it requires modification due to the fact that a cell is porous. Using fractal theory, the scaling index is about 0.7, 0.73, and 0.83, respectively, for inactive, active and motion statuses, and Kleiber's exponent can be fully explained by Rubner's law.
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.
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.
In this Letter, the variational iteration method is applied to solve integro-differential equations. Some examples are given to illustrate the effectiveness of the method, the results show that the method provides a straightforward and powerful mathematical tool for solving various integro-differential equations.
During electrospinning process, charged web jets solidify with solvent evaporation and form two-dimensional (2D) web-like nanofibers on the collecting plate. In this paper, Poly [(lactic acid)-co-(glycolic acid)] (PLGA) solutions are used to produce different 2D web-like nanofibers, which can mimic the physical features of natural extracellular matrix (ECM) at the nanoscale and improve fibroblast growth. According to mass conservation, the possible mechanisms for the web formation are investigated.
The textile with Steiner tree structure has good stability. This article studies the effect of the local destruction of the textile with Steiner tree structure on the whole textile stability.
The identification of the Lagrange multiplier plays an import rule in the variational iteration method, and the variational theory is widely used for this purpose. This paper suggests an easier approach by the Laplace transform to determining the multiplier, making the method accessible to researchers facing various nonlinear problems. A nonlinear oscillator is adopted as an example to elucidate the identification process and the solution process, only one iteration leads to an ideal result.
