652 publications from this institution
This paper explores the performance of a flying vehicle on a soft porous blanket at a high speed. The flying vehicle employs the basic principle of lubrication theory. An airplane can fly in air, because air is strong enough to support the airplane. The flying vehicle can also fly on the soft porous blanket if the moving body pushes air in the soft compressible porous mat. A model is established.
This paper recommends a simple and excusive approach to a strongly nonlinear oscillator. Its frequency property can be immediately obtained by the simplest calculation. The results show that the method leads to an approximate solution with relatively high accuracy. Considering the simplest solution process, this paper provides a highly efficient tool for fast determination of the amplitude-frequency relationship of a nonlinear oscillator. The large amplitude vibration of a string is used as an example to illustrate the solution process.
In this work, He Chengtian’s interpolation, which has millennial history, is applied to the Bethe equation. The result shows that the present technology is very convenient and effective.
No abstract is provided for this article.
Variational iteration method is used to construct solitary solutions and compacton-like solutions for nonlinear dispersive equations. The chosen initial solution (trial function) can be in compacton form or in soliton form with some unknown parameters which can be determined in the solution procedure. The compacton-like solution can be converted to solitary solution by suitable choice of a parameter, and vice versa.
Graphene hydrogels hold great potential for the disinfection of bacteria-contaminated water. However, the intrinsic antibacterial activity of graphene hydrogels is not satisfactory, and the incorporation of other antibacterial agents often results in their unwanted releases. Here, we present a new strategy to improve the antibacterial activities of graphene hydrogels. We first synthesized a new pi-conjugated molecule containing five aromatic rings and two side-linked quaternary ammonium (QA) groups, denoted as piQA. Next, we fabricated composite gravity filters by assembling piQA with reduced graphene oxide (rGO) hydrogel. The rGO hydrogel helps to form a sponge-like physical sieve, contributes to the overall antibacterial activity, and provides abundant pi-rich surfaces. The large aromatic cores of piQA allow the formation of collectively strong pi-pi interactions with rGO, resulting in a high piQA mass loading of ∼31 wt%. Due to the sieving effect of rGO hydrogel and the synergistic antibacterial activity of rGO and piQA, the filters prepared based on piQA-rGO assemblies can remove over 99.5% of Gram-negative Escherichia coli (E. coli) and Gram-positive Staphylococcus aureus (S. aureus) cells with a high-water treatment capacity of 10 L g−1. Furthermore, the piQA-rGO assemblies show low toxicity towards two different mammalian cell lines (L929 and macrophages), and the release of piQA is also negligible. Overall, the new piQA-rGO assembly demonstrates high potential for water disinfection applications.
Electrospinning is now commercially used for the fabrication of nano/micro fibers. Compared with spider dragline silk, artificial fibers have poor mechanical properties. Unlike natural silk, which has a hierarchical structure with an approximate 3-fold symmetry, the molecular structure of spun fiber has neither folding nor orientation. To date, it is almost impossible to control molecule orientation during the spinning process. Here, we show that macromolecule orientation can be easily controlled using the laminar flow of fluid mechanics. A lasting laminar flow in a long needle can order macromolecules. We find that the orientation of macromolecules can greatly affect the morphology and mechanical properties of fibers. We expect our technology to be helpful for more sophisticated fabrication of fibers with ordered macromolecules and DNA-like twists.
By the semi-inverse method of establishing variational principles, the Hellinger-Reissner principle can be obtained straightforwardly from energy trial-functionals without using Lagrange multipliers, and a family of generalized Hellinger-Reissner principles with an arbitrary constant are also obtained, some of which are unknown to us at the present time. The present theory provides a straightforward tool to search for various variational principles directly from governing equations and boundary conditions. [S0021-8936(00)00702-9]
Article An Improved Amplitude-frequency Formulation for Nonlinear Oscillators was published on June 1, 2008 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 9, issue 2).
This paper elucidates the possibility of applying soft compressive porous material to improving transportation in a more environmentally friendly way with less carbon emission. A completely theoretical interpretation on its principle is given.
Wu and Liu (2012) presented some results for the existence and uniqueness of the periodic solutions for the hematopoiesis model. This paper gives a simple approach to find an approximate period of the model.
No abstract is provided for this article.
<abstract> This paper argues that any economic phenomena should be observed by two different scales, and any economic laws are scale-dependent. A one-scale law arising in either macroeconomics or microeconomics might be mathematically correct and economically relevant, however, sparking debates might arise for a different scale. This paper re-analyzes the basic assumptions of the Evans model for dynamic economics, and it concludes that they are quite reasonable on a large time-scale, but the assumptions become totally invalid on a smaller scale, and a fractal modification has to be adopted. A two-scale price dynamics is suggested and a fractal variational theory is established to maximize the profit at a given period. Furthermore Evans 1924 variational principle for the maximal profit is easy to be solved for a quadratic cost function using the Lagrange multiplier method. Here a quadratic-cubic cost function and a nonlinear demand function are used, and the stationary condition of the variational formulation is derived step by step, and a more complex dynamic system is obtained. The present derivation process can be extended to a more complex cost function and a more complex demand function, and the paper sheds a promising light on mathematics treatment of complex economic problems. </abstract>
A way to obtain approximate periodic solutions to nonlinear oscillators arising in a microelectromechanical system (MEMS) is presented for the case of zero initial conditions and magnetostatic excitation. The frequency–amplitude relationship is derived by adopting He′s frequency formulation. The obtained analytical results are illustrated graphically. The proposed simple approach gives the fast insight into the dynamics of the singular oscillator and can be useful for design of MEMS devices.
This paper is an elementary introduction to the concepts of variational iteration method. First, the main concepts in variational iteration method, such as general Lagrange multiplier, restricted variation, correction functional, are explained heuristically. Subsequently, the solution procedure is systematically addressed, in particular, for nonlinear oscillators. Particular attention is paid throughout the paper to give an intuitive grasp for the method. The main motivation is to put things together in a convenient form for later reference and systematic use.
We have demonstrated herein the ability to fabricate continuous and uniform nanofibers by electrospinning using an aerated polymer solution, which led to various small bubbles on the surface with small surface tension; as a result, bubbles could be easily electrospun into nanofibers. According to bubble dynamics, we discussed the principle of this electrospinning process, and found it was deceptively simple and it was primarily based on small surface tension of the produced bubble. The experimental results were in keeping with the analysis with the aid of a high-speed digital camera. Additionally, the transient motion of a jet was captured in our experiment, which was similar to that of an ordinary electrospinning process.
The spider dragline is of intelligent character, different from that of traditional smart materials. A constitutive relation is established by taking into account the effect of vibration on the stress and electric field. The effect of oscillation frequency on its mechanical property is illustrated.
This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-infinity theory in high energy physics, Kleiber's 3/4 law in biology, possible mechanism in spider-spinning process and fractal approach to carbon nanotube are briefly introduced. Bubble-electrospinning for mass production of nanofibers is illustrated. There are in total more than 280 references.
