In this paper the well-known Chauchy's inequality is applied to prediction of critical length of the straight jet in electrospinning. A critical relationship between radius r of jet and the axial distance z from nozzle is obtained for the straight jet. Critical length number and critical radius number are defined, which might be found potential applications in experiment and apparatus design.
No abstract is provided for this article.
By a general Lagrange multiplier, an iteration approach is proposed to solve the generalized normalized diode equation, by suitable choice of the initial trial-function, one-step iteration leads to a high accurate solution, which is valid for the whole solution domain. Copyright © 2004 John Wiley & Sons, Ltd.
No abstract is provided for this article.
Using the semi‐inverse method proposed by the present author, a family of variational principle for direct problem of S2‐flow in mixed‐flow turbomachinery is obtained; then, applying the functional variation with variable domain, two families of variational principles are established for the hybrid problems of determining the unknown shape of bladings, where pressure or velocity is over‐specified. The present variational models are well posed for redundant data at boundaries. The theory provides both rational ways for best contouring the hub/casing walls to meet various practical design requirements and a theoretical basis for introducing the finite element method into computational aerodynamics of turbomachinery.
A mathematical model describing the resistance in cell membrane and nerve fiber is proposed, which is naturally different from that for metal conductors. An allometric scaling law between the resistance and the section area is obtained. In the derivation, He Chengtian's interpolation, which has millennia history, is applied. Most famous models, such as the Hodgkin–Huxley model, FitzHugh–Nagumo models, should be, therefore, revised.
The convergence point of two-strand yarn spinning was determined by the densities and velocities of two strands and the spun yarn, independent of their mechanical properties.
The adsorption process has a fractional property, and a fractional model is suggested to study a transport model of direct textile industry wastewater. An approximate solution of the concentration is obtained by the variational iteration method.
This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this field in China so the references, therefore, are not exhaustive.
There exists NO classical variational principle for continuum dynamics so far. The well-known Hamilton’s principle is valid only for the conditions prescribed at the beginning and at the end of the motion and is therefore useless to deal with the usual initial-boundary condition problems. In this paper an exact classical variational theory is established, all initial conditions are converted into natural ones, furthermore, all natural final conditions automatically meet the physical requirements, leading to a vital innovation of Hamilton’s principle.
Article Frontier of Modern Textile Engineering and Short Remarks on Some Topics in Physics was published on July 1, 2010 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 11, issue 7).
A fabric?s moisture/air permeability is a main factor for the fabric design for advanced applications, and no theoretical model was available in literature for an optimal permeability. In this paper, we use the capillary-like effect to elucidate the permeability property, and the effect of nano/micro particles on the fabric?s surface on the permeability is studied by the geometric potential theory. Our theoretical analysis shows that an unclean surface gives a negative impact on the permeability. A superhydrophobic surface is needed to design a good and lasting moisture/air permeability.
We give the exact geometrical shape and study the combinatorial properties of higher dimensional polytopes for the dimensions from n =4 to n =12 as well n =26 relevant to Heterotic, M and F superstring theories. Connections to E-infinity theory and the holographic principles are also discussed.
A family of generalized variational principles of piezoelectricity can be obtained straightforwardly from the field equations and boundary conditions via the semi-inverse method of establishing variational principles proposed by He without using Lagrange multipliers. The present theory provides a quite straightforward tool to search for various variational principles for physical problems. 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.
The Kundu–Mukherjee–Naskar equation (KMN) can model the data transmission in birefringent fibers through molecules or pulses in a few Femto-seconds. A fractional modification with Riemann-Liouville time-fractional derivative is suggested to take into account the discontinuous period, and the wave-train description is used to reduce the equation to a fractional nonlinear Schrödinger equation, which is further converted to a damping Duffing equation. Effective modification of the homotopy perturbation method is suggested to deal with the damping term.
Nanofibers with high orientation are of significant applications. This paper demonstrates a method to fabricate high orientation ordered nanofibers by electrospinning. The distribution of the electric field is simulated by using computational fluid dynamics software ANSYS14.0 to illustrate its mechanism.
