Publications

Hierarchy of wool fibers and its interpretation using E-infinity theory

Why do wool fibers show excellent advantages in warmth-retaining and many other practical properties? The paper concludes that their hierarchical structure is the key. Using E-infinity theory, its Hausdorff dimension is estimated to be about 4.2325, very close to El Naschie’s E-infinity dimension, 4.2360, revealing an optimal structure for wool fibers.

Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method

In this paper, the Exp-function method is used for seeking solitary solutions, periodic solutions, and compacton-like solutions of nonlinear differential equations. The combined KdV–MKdV equation and the Liouville equation are chosen to illustrate the effectiveness and convenience of the proposed method.

Generalized equilibrium equations for shell derived from a generalized variational principle

In this paper, the general equations of equilibrium for axisymmetrical deformation including the torsional deformation of shells with general forms are derived as stationary conditions of a generalized variational principle, which is established by the semi-inverse method. It shows that they are different from the results obtained by Chien (1990) in case of revolutional shell, therefore Chien’s results can be further improved.

Vibrorheological effect on electrospun polyacrylonitrile (PAN) nanofibers

A facile strategy for preparing electrospun nanofibers by vibration technology is suggested. Under the influence of the vibration, the vibrorheological effects appear in dramatic reduction in viscosity, as a result moderate voltage is needed to produce fine nanofibers that is commonly observed during conventional electrospinning procedure at elevated voltage. The novel strategy produces finer nanofibers than those obtained without vibration.

Homotopy perturbation method for Fangzhu oscillator

No abstract is provided for this article.

Allometric Scaling and Instability in Electrospinning

Article Allometric Scaling and Instability in Electrospinning was published on September 1, 2004 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 5, issue 3).

Negative thermal coefficient of nanoporous biomaterials

Materials change their sizes when subjected to a temperature change. Generally the coefficient of thermal expansion is positive, however, a negative coefficient in nanoporous biomaterials from enteromorpha is observed.

Variational Iteration Method for Prediction of the Pull-In Instability Condition of Micro/Nanoelectromechanical Systems

No abstract is provided for this article.

A remark on “A nonlinear mathematical model of the corneal shape”

An analytical method using Taylor series is proposed to solve a nonlinear two-point boundary problem arising in corneal shape. The solution process makes it extremely easy to obtain a relatively accurate solution. The pencil-and-paper solution procedure can be extended to other boundary value problems.

BioMimic fabrication of electrospun nanofibers with high-throughput

Spider-spun fiber is of extraordinary strength and toughness comparable to those of electrospun fiber, the later needs a very high voltage (from several thousands voltage to several ten thousands voltages) applied to water-soluble protein “soup” that was produced by a spider, furthermore, its mechanical strength dramatically decreases comparable to spider silk. A possible mechanism in spider-spinning process is given, the distinct character in spider-spinning is that its spinneret consists of millions of nano scale tubes, and a bubble can be produced at the apex of each nano-tube. The surface tension of each bubble is extremely small such that it can be spun into nanofibers with an awfully small force, either by the spider’s body weight or tension created by the rear legs. We mimic the spider-spinning in electrospinning using an aerated solution, which leads to various small bubbles on surface with very small surface tension, as a result the bubble can be easily electrospun into nanofibers with low applied voltage. This fabrication process possesses features of high productivity, versatility, in addition, the minimum diameter of nanofibers produced by this process can reach as small as 50nm.

Frequency-Amplitude Relationship in Nonlinear Oscillators with Irrational Nonlinearities

This study investigates the frequency-amplitude relationship in nonlinear oscillators with irrational nonlinearities, which pose significant challenges to traditional analytical methods such as the homotopy perturbation method and variational iteration method. By employing a simplified frequency formulation, we analyze the impact of irrational nonlinearities on oscillation dynamics and derive a frequency-amplitude relationship in a single-step calculation. For small amplitudes, our results are consistent with those obtained by the homotopy perturbation method, validating the proposed approach. This research provides new insights into the complex dynamics of nonlinear oscillators and offers practical implications for fields such as physics, engineering, and applied mathematics. Additionally, it contributes to the design and optimization of MEMS systems and suggests future research directions, including the incorporation of damping and external forces for a more comprehensive understanding of system behavior.

The Maximal Wrinkle Angle During the Bubble Collapse and Its Application to the Bubble Electrospinning

Polymer bubbles are ubiquitously used for the fabrication of nanofibers by the bubble electrospinning. When a bubble is broken, the fragments tend to be wrinkled. The wrinkle angle plays an important in controlling the fiber morphology during the bubble electrospinning. This paper shows the maximal angle is about 49°, which is close to the experimental value of 50°. This maximal angle can be used for the optimal design of the nozzle in the bubble electrospinning for the fabrication of non-smooth nanofibers.

An Invitation to El Naschie’s Theory of Cantorian Space-Time and Dark Energy

The paper is a condensed but accurate account of El Naschie’s theory of Cantorian space-time which was used by him to clarify some major problems in theoretical physics and cosmology. In particular El Naschie’s revision and completion of relativity theory and demystification of dark energy are destined to be two milestones in the history of theoretical physics.

Analytical methods for nonlinear oscillators and solitary waves

Physics is mathematical, new physical phenomena require new mathematical tools. This Research Topic is an attractive introduction of some new mathematical concepts, e.g., the two-scale fractal geometry, the fractal-fractional models, the homotopy perturbation method and the frequency formulation appliable to physics. The new findings of physical phenomena using the new mathematical tools have excited physicists with their potential to reveal secrets in physics and have triggered new research frontiers in physics. Here is an overview of the Research Topic.

On He Map (River Map)and the Oldest Scientific Management Method

No abstract is provided for this article.

From Micro to Nano and from Science to Technology: Nano Age Makes the Impossible Possible

Homotopy perturbation method: a new nonlinear analytical technique

In this paper, a new perturbation method is proposed. In contrast to the traditional perturbation methods, this technique does not require a small parameter in an equation. In this method, according to the homotopy technique, a homotopy with an imbedding parameter p∈[0,1] is constructed, and the imbedding parameter is considered as a “small parameter”, so the method is called the homotopy perturbation method, which can take the full advantages of the traditional perturbation methods and homotopy techniques. To illustrate its effectiveness and its convenience, a Duffing equation with high order of nonlinearity is used; the result reveals that its first order of approximation obtained by the proposed method is valid uniformly even for very large parameter, and is more accurate than the perturbation solutions.

Exp-function method to solve the nonlinear dispersive K(m,n) equations

Article Exp-function method to solve the nonlinear dispersive K(m,n) equations was published on September 1, 2008 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 9, issue 3).