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.
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.
No abstract is provided for this article.
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).
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 sugeests a method for fabrication of polyvinyl alcohol-honey nanofibers by electrospinning. Polyvinyl alcohol and honey are all biocompatible and environmentally friendly materials. This combination will lead to wide potential applications in various engineering fields.
No abstract is provided for this article.
In the paper, the homotopy perturbation method is applied to the nonlinear oscillators with discontinuities. Only one iteration leads to high accuracy of the solutions.
Nanoscale flows appear widely in nanofiber fabrication especially in electro-spinning, where a nanoscale jet is a multi-phase fluid including solvents and additives. This paper shows that the fiber morphology can be effectively controlled by adjusting the density of the multi-phase jet. TiO2 is used as an additive to produce polyacrylonitrile nanofibers by electrospinning; the results elucidate that uniform nanofiber can be obtained, and this phenomenon is explained theoretically.
The initial value problem used for modeling a magnetic actuator arising from the design of a magnetic Micro-Electro-Mechanical Structure (magMEMS) with current-carrying filaments is derived using the concept of mutual inductance. The resulting model differential equation is nonlinear since it contains a term corresponding to the magnetic force between two filaments of finite length. The dynamic pull-in which occurs in the magMEMS model with one fixed and one moving filament is analyzed. The closed form approximate conditions for the dynamic pull-in are established in terms of model parameters. Approximate periodic solutions are derived analytically and numerical simulations are used for verification. These results are useful for understanding the modeling and operation of single-degree-of-freedom magMEMS.
The electrohydrodynamics (EHD) instability of two separate overlapping viscous particle fluids moving in a porous medium is the subject of this paper. The incompressible packaging contains microscopic, uniformly sized fine dust particles. The system is influenced by a tangential electric field that remains constant. The abbreviated formulation of Hsieh is employed to account for the impact of mass and heat transfer (MHT). The problem solution follows the viscous potential theory (VPT) because of the problem complexity in mathematics. The significance of fluid-particle mixing in several applications of practical physics and engineering operates as the guiding force behind this investigation. The standard normal modes methodology is used to examine the standard fundamental equations of motion. The essential mechanisms of the nonlinear technique are the formulations of the linear controlling fundamental formulae and the application of the appropriate nonlinear boundary criteria. A number of nondimensional characteristic parameters are produced by the technique. The nonlinear stability results in a nonlinear Landau–Ginzburg equation. By giving the physical parameter numerical values, the stability designs have been graphically represented. Therefore, both linear and nonlinear approaches are depicted to illustrate the impacts of different physical quantities. Using the homotopy perturbation approach and the idea of extended frequency, a uniform approximate solution for a nonlinear interface displacement is provided. He’s frequency approach yields another nonperturbative solution of the surface displacement solution, which is validated using the Runge–Kutta method.
No abstract is provided for this article.
The Blasius' equation, with boundary conditions, is studied in this paper. An approximate analytical solution is obtained via the variational iteration method. The comparison with Howarth's numerical solution reveals that the proposed method is of high accuracy.
Purpose It is extremely difficult to establish a variational principle for plasma. Kalaawy obtained a variational principle by using the semi-inverse method in 2016, and Li and He suggested a modification in 2017. This paper aims to search for a generalized variational formulation with a free parameter. Design/methodology/approach The semi-inverse method is used by suitable construction of a trial functional with some free parameters. Findings A modification of Li-He’s variational principle with a free parameter is obtained. Originality/value This paper suggests a new approach to construction of a trial-functional with some free parameters.
