652 publications from this institution
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.
Lotus effect is the superhydrophobicity property, and widely used for self-cleaning in modern textile engineering. This paper reveals that the lotus effect is a kind of nanoeffect or size effect in nanotechnology, the surface morphology, solution?s molecule weight, and temperature are three main factors affecting the lotus effect. Solutions? pH values or ionic liquids are also discussed in this paper. A series of experiments are carried out to measure contact angles for different solutions/liquids on the lotus surface at different temperature.
A brief introduction to the development of the homotopy perturbation method is given, and the main milestones are elucidated with more than 90 references. This paper further improves the method by constructing a homotopy equation with one or more auxiliary parameters embedding in the linear term with a clear advantage in accelerating and controlling the approximation convergence speed. Moreover, a revision of a recent amplitude-period approximation formula is presented providing an answer to an open problem related to the optimal approximation along with a new universal formula. Duffing equation is used as an example to illustrate the solution process for the homotopy perturbation method, and only one or few iterations are needed in practical applications, making the method much attractive. From the side of amplitude-period formulation, the nonlinear pendulum, the Duffing equation and an oscillator with discontinuity are analyzed providing an asymptotic exact equivalence for bigger parameter values in the case of Duffing’s system. This mini review gives a tutorial guideline for practical applications of the homotopy perturbation method, the references are not exhaustive.
A nonlinear vibration system, over a span of convincing periodic motion, might break out abruptly a catastrophic instability, but the lack of a theoretical tool has obscured the prediction of the outbreak. This paper deploys the amplitude-frequency formulation for nonlinear oscillators to reveal the critically important mechanism of the pseudo-periodic motion, and finds the quadratic nonlinear force contributes to the pull-down phenomenon in each cycle of the periodic motion, when the force reaches a threshold value, the pull-down instability occurs. A criterion for prediction of the pull-down instability is proposed and verified numerically.
In this paper, a new kind of analytical technique for a non-linear problem called the variational iteration method is described and used to give approximate solutions for some well-known non-linear problems. In this method, the problems are initially approximated with possible unknowns. Then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory. Being different from the other non-linear analytical methods, such as perturbation methods, this method does not depend on small parameters, such that it can find wide application in non-linear problems without linearization or small perturbations. Comparison with Adomian’s decomposition method reveals that the approximate solutions obtained by the proposed method converge to its exact solution faster than those of Adomian’s method.
No abstract is provided for this article.
Tulachan et al. found that silk cocoon membrane can generate electrical current due to ionic conduction. We argue that the current is produced by osmosis as that in a commercial osmotic plant.
This paper examines the periodic motion of the micro-electro-mechanical system (MEMS), which is governed by a singularity that makes it challenging to find an exact solution and to understand its dynamical properties. This paper applies the frequency formulation to gain insight into the frequency-amplitude relationship of the system. It is found that when the amplitude reaches a threshold value, the periodic motion becomes pull-in instability. This finding simplifies the warning system for the system’s unsafe operating conditions, and the frequency-amplitude relationship can be used for optimal design of the system with high accuracy and high reliability.
It is generally accepted that there are 60 experimentally found particles. The standard model strongly predicts two more hypothetical particles, the Higgs and the graviton. This paper reveals other possible scenario for predicting 69 particles at different energy scales in 11+ ϕ 3 fractal dimensions of a fractal M theory, where ϕ = ( 5 - 1 ) / 2 . A modified Newton’s law is suggested to experimentally verify our predictions at extremely small quantum scales. The modified Newton’s law is in harmony with Heisenberg’s uncertainty principle.
Applying the hydrophobic membrane into the absorber and generator of the absorption chiller can significantly downsize the absorption system. In this study, the permeability of the hydrophobic membrane is evaluated using CO2 prior to the system test. The PTFE flat-type membrane with three nominal pope sizes of 0.1, 0.45 and 1 micron were tested for both flow directions. Results show that the permeability decreases with imposed pressure when the pressure is relatively small, and then tends to be constant. The mass transport mechanism differs for the membrane samples, and higher permeability was obtained with larger pore sizes. The variation of the permeability can be qualitatively explained with the pore size distribution.
Heat-resisting nanofibers have many potential applications in various industries, and the bubbfil spinning is the best candidate for mass-production of such materials. Polyether sulfone/zirconia solution with a bi-solvent system is used in the experiment. Experimental result reveals that polyether sulfone/zirconia nanofibers have higher resistance to high temperature than pure polyether sulfone fibers, and can be used as high-temperature-resistant filtration materials.
In this paper we investigate the transport equations in fractal porous media by using the fractional complex transform method. The local fractional linear and nonlinear transport equations with local fractional time and space fractional derivatives are obtained. The proposed models adequately describe the fractal transport processes.
A governing equation is established for string axial vibrations with temporal and spatial damping forces by the Hamilton principle. It is an extension of the well-known Klein-Gordon equation. The classical homotopy perturbation method (HPM) fails to analyze this equation, and a modification with an exponential decay parameter is suggested. The analysis shows that the amplitude behaves as an exponential decay by the damping parameter. Furthermore, the frequency equation is established and the stability condition is performed. The modified homotopy perturbation method yields a more effective result for the nonlinear oscillators and helps to overcome the shortcoming of the classical approach. The comparison between the analytical solution and the numerical solution shows an excellent agreement.
This paper focuses on studying the dynamical response of a vibrating three degrees-of-freedom (DOF)auto-parametric system near resonance. The structure of this system is composed of an attached damped oscillator with a damped spring pendulum. The governing equations of motion are derived using Lagrange's equations of second kind. They are asymptotically solved using the multiple scales approach to obtain the analytic solutions up to the third approximations as new and accurate results. The resonance cases are classified and the effect of the different parameters of considered system is analysed. The stability and instability regions are examined in which the behavior of the system is found to be stable for a wide range of parameters. The achieved results reveal that we can use the pendulum as a dynamic absorber. The significance impact of this work is due to its great engineering applications in the high towers, buildings and bridges.
The two most important steps in application of the homotopy perturbation method are to construct a suitable homotopy equation and to choose a suitable initial guess. The homotopy equation should be such constructed that when the homotopy parameter is zero, it can approximately describe the solution property, and the initial solution can be chosen with an unknown parameter, which is determined after one or two iterations. This paper suggests an alternative approach to construction of the homotopy equation with an auxiliary term; Dufing equation is used as an example to illustrate the solution procedure.
Taylor cone can be easily observed in the electrospinning process, and its height can be used to control the fiber diameter. This paper gives a theoretical analysis of the relationship between the cone height and fiber diameter.
