652 publications from this institution
Article A Mathematical Model for Preparation by AC-Electrospinning Process was published on September 1, 2005 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 6, issue 3).
This paper shows that the Toda oscillator can be converted to a new Helmholtz-Fangzhu equation, which is solved by the homotopy perturbation method with three expansions. The solution, the negative frequency and the damping rate are expanded into power forms in the homotopy parameter, the solution process is given step by step, and the results are of high accuracy. This paper gives a general approach to damp vibrations with singular terms,especially to the Helmholtz-Fangzhu oscillator.
This paper reveals the effectiveness of the homotopy perturbation method for strongly nonlinear oscillators. A generalized Duffing oscillator is adopted to elucidate the solving process step by step, and a nonlinear frequency–amplitude relationship is obtained with a relative error of 0.91% when the amplitude tends to infinity, the solution morphology is also discussed, and the zero-th approximate solution is enough for conservative nonlinear oscillators, while the accuracy of the frequency can be improved if the iteration continues.
Kundu–Mukherjee–Naskar equation admits many attractive solitary wave solutions as discussed by Biswas et al. (Results in Physics, Volume16, 2020, 102850). This paper shows that a variational formulation can be established by the semi-inverse method, and its periodic solution is elucidated. This short note sheds a light on new research frontiers of solitary wave theory.
In this paper, a tutorial introduction to the two-scale fractal calculus is given. The two-scale fractal derivative is conformable with the traditional differential derivatives. When the fractal dimensions tend to an integer value, its basic properties are discussed, and the fractal Zhiber–Shabat oscillator is used as an example to reveal the basic properties of a fractal differential equation. The two-scale transform is used to convert the nonlinear Zhiber–Shabat oscillator with the fractal derivatives to the traditional model. The homotopy perturbation method has been demonstrated under a suitable transformation of the system containing several exponential nonlinear terms to the famous Helmholtz–Duffing oscillator. Stability behavior is discussed. Several numerical illustrations are also provided to exhibit the integrity of the introduced formulation. It is demonstrated that the proposed formulation is accurate enough for highly nonlinear differential equations containing large nonlinear terms.
A variational model is established for ( 2 + 1 ) -dimensional Broer–Kaup equations by the semi-inverse method [Int. J. Turbo Jet-Engines 14 (1) (1997) 23].
Resistance of tear is an important characteristic of textile materials, especially for fabrics used for personal protective equipment. In this study, a constant force is applied to tear the fabric specimens to obtain the del-zone theoretically. The strain-stress curve for a single yarn is obtained from experiment, and the del-zone is determined by an ancient Chinese algorithm. This combination of ancient Chinese algorithm and actual tearing behavior of woven fabrics provides a noval analysis approach of tearing performance of textile product theoretically.
A fuzzy model for dye removal is suggested to study a transport model of the direct textile industry wastewater, and the variational iteration method is adopted to obtain its analytical solutions. The concentration depends upon not only the parameters in the governing equation, but also the pair of the initial condition.
El-Naschie’s E-infinity theory is applied to turbulence. The Hausdorff-fractal dimension for turbulent flow is defined, the critical values for laminar flow (D =3.98) and turbulent flow (D =4.23) are obtained, and the fractal dimension for fully developed turbulent flow is D >6.8. It is also shown that the Navier–Stokes equations are invalid for an exact model of turbulent flow and that two-dimensional planar turbulence does not exist in nature.
He Chengtian’s inequality is used to re-build the King Fang’s musical scales 41/24 and 53/31 in 40 BC. The technology, which might be little known to the West, has been used for millennia by ancient Chinese, and can be powerfully applied to nonlinear problems.
An innovative approach to finding limit cycles is proposed and illustrated on the van der Pol equation. The technique developed in this Letter is similar to the Ritz's method in variational theory. The present theory can be applied to not only weakly nonlinear equations, but also strongly nonlinear ones, and the obtained results are valid for the whole solution domain.
No abstract is provided for this article.
It is well-known that the boundary conditions will greatly affect the wave shape of a nonlinear wave equation. This paper reveals that the peak of a solitary wave is weakly affected by the unsmooth boundary. A fractal Korteweg-de Vries (KdV) equation is used as an example to show the solution properties of a solitary wave travelling along an unsmooth boundary. A fractal variational principle is established in a fractal space and its solitary wave solution is obtained, and its wave shape is discussed for different fractal dimensions of the boundary.
A modified equation for charge conservation in electrospinning is suggested, and a nonlinear relation between the electric current of charged jet and the solution flow rate is obtained.
The fractal Toda oscillator with an exponentially nonlinear term is extremely difficult to solve; Elias-Zuniga et al. (2020) suggested the equivalent power-form method. In this paper, first, the fractal variational theory is used to show the basic property of the fractal oscillator, and a new form of the Toda oscillator is obtained free of the exponential nonlinear term, which is similar to the form of the Jerk oscillator. The homotopy perturbation method is used to solve the fractal Toda oscillator, and the analytical solution is examined using the numerical solution which shows excellent agreement. Furthermore, the effect of the order of the fractal derivative on the vibration property is elucidated graphically.
This paper applies the variational approach to the relativistic oscillator. In order to effectively deal with the irrational term, an ancient Chinese mathematics is introduced. Comparison of the obtained result with the numerical one elucidates the efficiency of the present treatment.
Retraction: He, J–H, Jin, X. ‘A short review on analytical methods for the capillary oscillator in a nanoscale deformable tube’ Math Meth Appl Sci. 2020; 1–8. doi: 10.1002/mma.6321 The above article, published online on 05 March 2020 in Wiley Online Library wileyonlinelibrary.com , has been retracted by agreement between, the journal Editor in Chief, Wolfgang Sprößig, and John Wiley and Sons Ltd. The retraction has been agreed following an investigation based on concerns raised by a third party. During re‐evaluation of this manuscript by an independent expert in this field, a major overlap with a previously published article from the same group of authors was found. The authors did not agree with the decision to retract this article.
The laws governing life should be as simple as possible; however, theoretical investigations into allometric laws have become increasingly complex, with the long-standing debate over the scaling exponent in allometric laws persisting. This paper re-examines the same biological phenomenon using two different scales. On a macroscopic scale, a cell surface appears smooth, but on a smaller scale, it exhibits a fractal-like porous structure. To elaborate, a few examples are given. Employing the two-scale fractal theory, we theoretically predict and experimentally verify the scaling exponent values for basal, active, and maximal metabolic rates. This paper concludes that Rubner’s 2/3 law and Kleiber’s 3/4 law are two facets of the same truth, manifested across different scale approximations.
