652 publications from this institution
This Letter compares the classical variational iteration method with the fractional variational iteration method. The fractional complex transform is introduced to convert a fractional differential equation to its differential partner, so that its variational iteration algorithm can be simply constructed.
No abstract is provided for this article.
No abstract is provided for this article.
Polyacrylonitrile(PAN) is used to study the effect of surface charge on electrospinning by adding LiCl. The theoretical analysis shows that the relationship between radius r of jet and the axial distance z from nozzle follows an allometric law in the form r∼z −0.5 in case of full surface charge, and the scaling exponent becomes larger for partly charged fibers in electrospinning.
The perturbation method is a prevalent approach for nonlinear oscillators; however, the outcomes are only applicable to situations with weak nonlinearity. Other analytical methods, such as the variational iteration method and the homotopy perturbation method, can yield a satisfactory approximate solution; however, each method necessitates the completion of multiple calculations. Hereby is recommended a one-step frequency formulation for nonlinear oscillators, and this part 1 focuses itself on odd nonlinearity.
Exp-function method is used to find a unified solution of a nonlinear wave equation. Variant Boussinesq equations are selected to illustrate the effectiveness and simplicity of the method. A generalized solitary solution with free parameters is obtained.
This paper proposes a new asymptotic approach to search for the periodic solutions of a kind of nonlinear oscillations. In this method the iteration technique is coupled with the traditional perturbation techniques, yielding a powerful mathematical tool for solving strongly nonlinear equations. Some examples are given to illustrate its effectiveness, convenience and accuracy. Generally, the first iteration leads to a highly accurate approximate solution which is uniformly valid for the whole solution domain. The new asymptotic approach is named the iteration-perturbation method.
An allometric scaling relationship between cortical white and gray volumes is derived from a general model that describes brain’s remarkable efficiency and prodigious communications between brain areas. The model assumes that (1) a cell’s metabolic rate depends upon cell’s surface; (2) the overall basal metabolic rates of brain areas depend upon their fractal structures; (3) differential brain areas have same basal metabolic rate at slow wave sleep. The obtained allometric exponent scaling white matter to gray matter is 1.2, which is very much close to Zhang and Sejnowski’s observation data.
The parameters such as the angle in “V” area in Sirofil spinning system, the tension and torque of the filament and roving with different feeding spacing are theoretically discussed. The optimal strand-spacing of different spinning materials is, thus, recommended. The configuration, strength and elongation, hairiness and evenness of the yarn were studied experimentally. The theoretical results agreed very well with experimental data.
Article A Variational Model for Compressible Rotational Blade-to-Blade Flow Using Liu-Type Potential Function was published on June 1, 2000 in the journal International Journal of Turbo & Jet-Engines (volume 17, issue 2).
Blossman-Myer and Burggren (Comp. Biochem. Phys. A, 155, 2010,259-263) found that the cocoon of the silkworm, Bombyx mori , while creating a tough barrier offering mechanical protection to the pupa, imposes no barrier to the diffusion of oxygen or water vapor. In view of its mechanical properties, silk cocoon is an "emperor's new clothes" for pupa. A theoretical analysis is given to explain the fascinating phenomenon by a fractal hydrodynamic model for discontinuous membrane composed of hierarchical silk cascade. The model reveals that when the fractal dimensions of the microstructure of the cocoon meet a special condition, air and water vapor can flow through the cocoon as if there were no cocoon. However, at extremes of weather, the cocoon is an excellent thermal protection for both high and cool temperatures. A better understanding of the cocoon mechanism could help the further design of bio-mimetic artificial clothes for special applications.
Adsorption of fine particles in air by a leaf is studied experimentally. It is found that each leaf can absorb only a kind of particles with almost same size, and it also exhibits high selectivity over other particles. The SEM study reveals that the size of nanopore on the epidermis is a main factor of the highly selective adsorption; the smaller nanopores can absorb larger nanoparticles in air. The morphology of a lotus leaf, which is waterproof and dustproof, has, on the other hand, many short nanofibrils instead of nanopores. It is concluded that the nanoscale geometrical structure of a surface affects its attraction/repulsion property. The experiment also shows that one square millimeter surface with nanopores in diameter of 18 nm can absorb 2 million nanoparticles of about 200 nm in diameter from air in 24 hours. A better understanding of the adsorption/repulsion mechanism could help the further design of bio-mimetic waterproof/dustproof artificial materials and artificial porous materials/fabrics/nonwovens for adsorption of nanoparticles in air.
Magnetic properties play an important role in electrocatalysis and electrodeposition. The current study is concerned with a novel mathematical approach to the Kelvin Helmholtz instability (KHI) saturated in porous media with heat and mass transfer. The system consists of two finite horizontal magnetic fluids, which is acted upon by a uniform tangential magnetic field. The field permits the presence of surface charges on the surface of separation. The rheological behavior of the visco-elastic fluid is characterized by Reiner-Rivlin model. Typically, the solutions of the governing equations of motion in accordance with the appropriate nonlinear boundary conditions resulted in a characteristic nonlinear second-order partial differential equation of a complex nature. This equation controls the behavior of the surface deflection and may be treated to yield the Helmholtz-Duffing equation. By means of He-Laplace method, an approximate bounded analytic solution is obtained and plotted. Additionally, the technique of the nonlinear expanded frequency is applied to attain the stability criteria. In the nonlinear stability approach, the numerical calculations reveal additional physical parameters in the stability configuration. The implication of the linear/nonlinear curves shows that stability is judged only by the linear curve.
This paper delves into the static and dynamic behavior of graphene cantilever beam resonators under electrostatic actuation at their free tips. A rigorous analysis of the system’s response is performed. The constitutive nonlinear equation of the system is derived using the energy method and Hamilton’s principle. An analytical solution to the nonlinear static problem is obtained. The generalized stiffness coefficient for the lumped model of the cantilever graphene beam under load at its tip is calculated, enabling a comprehensive analysis of its dynamic behavior. A key focus is on investigating the dynamic pull-in conditions of the system under both constant and harmonic excitation. Analytical predictions are validated through numerical simulations. The system exhibits periodic solutions when the excitation parameters are below a certain threshold described by a separatrix curve, leading to sustained oscillations. On the other hand, if the excitation parameters exceed this threshold, the system experiences pull-in instability, causing the beam to touch down. Furthermore, we explore the impact of excitation frequency on the dynamic response of the graphene cantilever beam under harmonic load. The simulations reveal that choosing the excitation frequency near the beam’s resonance frequency can lead to structural collapse under certain parameter conditions.
No abstract is provided for this article.
This paper presents a thorough study of a time-dependent nonlinear Schrödinger (NLS) differential equation with a time-fractional derivative. The fractional time complex transform is used to convert the problem into its differential partner, and its nonlinear part is then discretized using He’s polynomials so that the homotopy perturbation method (HPM) can be applied powerfully. The two-scale concept is used to explain the substantial meaning of the fractional time complex transform and the solution.
Nonlinear oscillators with no linear term or negative linear term are difficult to be solved analytically. This paper shows that the homotopy perturbation method can be effectively applied to such kinds of nonlinear oscillator by the parameter expansion technology. A nonlinear oscillator with coordinate-dependent mass is used as an example to elucidate the effectiveness and convenience of the method. The condition for periodic solution is obtained.
