652 publications from this institution
A variational principle is established for the differential–difference system arising in stratified hydrostatic flows by the semi-inverse method. An insight into its physical understanding is given.
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.
The Chen–Lee–Liu equation is a modified Schrödinger equation to describe a solitary wave of ultrashort pulses in optics, which lead to a discontinuous time, so a fractal modification is suggested and a fractal variational principle is established by the semi-inverse method.
Polyvinyl alcohol (PVA) with a degree of 1750±50 was successfully fabricated into nanofibers via the traditional electrospinning process. Daughter charged jets and combined fibers were observed. A combined fiber might be simple combination of two separate fibers without mass transfer, or it is a daughter cascade caused in hierarchical motion of a charged jet with mass/energy transfer. Minimal fiber reaches as small as 5nm (50 angstroms) in diameter, this might be the smallest artificial fiber, which might have excellent properties due to nanoeffect.
Complex mechanical systems usually include nonlinear interactions between their components which can be modeled by nonlinear equations describing the sophisticated motion of the system. In order to interpret the nonlinear dynamics of these systems, it is necessary to compute more precisely their nonlinear frequencies. The nonlinear vibration process of a conservative oscillator always follows the law of energy conservation. A variational formulation is constructed and its Hamiltonian invariant is obtained. This paper suggests a Hamiltonian-based formulation to quickly determine the frequency property of the nonlinear oscillator. An example is given to explicate the solution process.
Via He’s semi-inverse method, a family of generalized variational principles of micromorphic elasticity is established directly from the field equations and boundary conditions. This paper aims at providing a more complete theoretical basis for the finite element applications and other direct variational methods such as Ritz’s, Trefftz’s and Kantorovitch’s methods.
This paper provides another approach to the establishment of Reynolds-type equation in lubrication theory by variational theory. By the semi-inverse method, a minimum energy functional is established for one dimensional non-Newtonian lubrication, where the Rabinowitsch constitutive relation is adopted.
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.
The homotopy perturbation method proposed by the present author is further improved in this paper, which is proved to be effective and convenient to solving nonlinear equations.
Purpose – Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus. Design/methodology/approach – This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional differential equations, e.g. the variational iteration method, the homotopy perturbation method and the fractional complex transform, are outlined and the main solution processes are given. Findings – Heat conduction in silk cocoon and ground water flow are modeled by the local fractional calculus, the solutions can explain well experimental observations. Originality/value – Particular attention is paid throughout the paper to giving an intuitive grasp for fractional calculus. Most cited references are within last five years, catching the most frontier of the research. Some ideas on this review paper are first appeared.
Article Application of Vibration Technology to Polymer Electrospinning was published on September 1, 2004 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 5, issue 3).
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.
No abstract is provided for this article.
A new special function is introduced, and a variational formulation is established for two-dimensional incompressible inviscid flow, which might find potential applications in numerical simulation and various inverse problems.
We establish a variational model for one-dimensional tube flow with a more general form of pressure-density relation. Applying the semi-inverse method proposed by He, a family of variational principle for the discussed problem is systematically derived directly from the field equations and boundary / initial conditions.
This paper gives the simplest approach to the cubic-quintic Duffing equation (M.S.H. Chowdhury et al., Results in Physics 7(2017): 3962–3967), providing an extremely fast and relatively accurate estimation of the frequency of a nonlinear conservative oscillator.
No abstract is provided for this article.
