Article Application of Parameter-expanding Method to Strongly Nonlinear Oscillators was published on March 1, 2007 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 8, issue 1).
Newton’s iteration method is widely used in numerical methods, but its convergence is low. Though a higher order iteration algorithm leads to a fast convergence, it is always complex. An optimal iteration formulation is much needed for both fast convergence and simple calculation. Here, we develop a two-step optimal fourth-order iterative method based on linear combination of two iterative schemes for nonlinear equations, and we explore the convergence criteria of the proposed method and also demonstrate its validity and efficiency by considering some test problems. We present both numerical as well as graphical comparisons. Further, the dynamical behavior of the proposed method is revealed.
Background: There are many patents on design of a material surface with special wetting property, however, theoretical methods are lacked. The wetting property of a nanofiber member has attracted much attention. A material with different sizes or with different structures possesses different wetting properties. No theory can explain the phenomenon. Methods: The contact angle, fiber fineness, pore size and layer of the nanofiber membrane were tested. The contact angles were measured for membranes with different thicknesses. The geometrical potential is used to explain the experimental phenomenon. Results: The wetting property of a nanofiber membrane mainly depends on fiber diameter and thickness. Conclusion: Wetting property of a PVA nanofiber membrane depends upon not only the hydrophilic groups, but also the geometrical structure of its surface, the latter prevails when the porous size of the membrane tends to a nanoscale, and the wetting property can be inverted from hydrophilicity to hydrophobicity.
This paper suggests a simple method to construct a needed Lagrangian using the semi-inverse by introducing a simple auxiliary function, the presented method is simpler than Zhang's method to construct a Lagrangian.
An allometric scaling law is established for explaining sleep time per day which scales with brain mass. The theoretical prediction agrees well with Savage and West’s experimental data.
The bubble electrospinning is used to produce nanoparticles from several nano-meters to several hundred nanometers in diameter. Silk fibroin aqueous solution with low concentration is used in the experiment. The spinning process can be well controlled by temperature.
This paper finds that a polymer liquid membrane can be effectively used for nanomaterials fabrication using a blowing air and an electronic force. Polyvinyl alcohol solution is used to produce membrane on a rotating ring, which passes through periodically the solution, the membrane is deformed into a bubble by the blowing air under the presence of an electrostatic field. The experimental data show that the receptor distance affects the fiber size greatly.
A variational formulation of a chemical problem can be very useful because special solution methods can be used, and it gives a deeper insight into the structure, for example, of diffusion reaction. In this study, a variational theory is established for coupled diffusion and n th‐order reaction in a spherical catalyst pellet. Various variational approaches can be applied to obtain both analytical and numerical solutions.
In this Letter a simple but effective iteration method is proposed to search for limit cycles or bifurcation curves of delay-differential equations. An example is given to illustrate its convenience and effectiveness.
E2H2 (E = As, Sb, Bi) structures involving multiple bonds have attracted much attention recently. The E2H3+ cations (protonated E2H2) are predicted to be viable with substantial proton affinities (>180 kcal/mol). Herein, the bonding characters and energetics of a number of E2H3+ isomers are explored through CCSD(T) and DFT methods. For the As2H3+ system, the CCSD(T)/cc-pVQZ-PP method predicts that the vinylidene-like structure lies lowest in energy, with the trans and cis isomers higher by 6.7 and 9.3 kcal/mol, respectively. However, for Sb2H3+ and Bi2H3+ systems, the trans isomer is the global minimum, while the energies of the cis and vinylidene-like structures are higher, respectively, by 2.0 and 2.4 kcal/mol for Sb2H3+ and 1.6 and 15.0 kcal/mol for Bi2H3+. Thus, the vinyledene-like structure is the lowest energy for the arsenic system but only a transition state of the bismuth system. With permanent dipole moments, all minima may be observable in microwave experiments. Besides, we have also obtained transition states and planar-cis structures with higher energies. The current results should provide new insights into the various isomers and provide a number of predictions for future experiments.
No abstract is provided for this article.
The equation of a ball-bearing oscillator shows nonlinear behaviour without a possible small parameter. In order to apply the perturbation technique, we use cosine trial function with the assumption of exact period (though it can be identified only approximately), as a result the residual must be relatively small, so we can obtain its perturbation solution.
Diameter of sea-silk based nanofibers prepared by electrospinning is closely related to the concentrations of sea-silk solution. A mathematical model is established according the mass conservation law in fluid mechanics to predict the diameter of fibers, and the MATLsoftware is used to fit the experiment value. The results show that the fitted equation is quite accurate and efficient for estimating the diameter of fibers with different concentrations.
The recorded physiological periods in Huangdi Neijing is re-built using allometric scaling laws. Physiological periods are multiples of 7 years for females while 8 years for males. The oldest findings can be used for modern health policy, education and labor agreement considering sexual difference. Key words: Allometric scaling, ancient Chinese medicine, ancient Chinese mathematics.
A general allometric model between metabolic rate and body size has been derived for early plant ontogeny. The scaling exponent is ( 2 + N / 6 ) / 3 , where N is the cell’s degree of freedom of motion. For early plant ontogeny N = 2 , our prediction agrees well with Sack et al.’s observation [Sack, L., Maranon, T., Grubb, P.J., 2002. Science 295, 1923].
A nonlinear oscillator arising in the microelectromechanical system is complex and it is difficult to obtain a variational principle. This paper begins with a wrong variational formulation and uses the semi-inverse method to obtain a genuine variational principle. Additionally, this paper gives simple formula for the fast frequency estimation of the nonlinear oscillator. Only simple calculation is needed to have a relatively high accuracy results when compared with the other methods.
Similar to Casimir force, nanofibers have a potential that attracts water molecules, while the porosity of the nanofiber mat produces a repelling force. Wetting property of a nanofiber mat is a result of combination of the forces and gravity. A new concept, the geometric potential or the boundary-induced force, is introduced to elucidate the basic property of wetting. Various nanofiber mats with different fiber morphologies are fabricated by the bubble electrospinning. The pa-per concludes that superhydrophobic properties of nanofiber mat depends upon mainly fiber morphology and porous structure of the mat, hydrophilic properties of ZnO nanorods will not affect the water contact angle much.
The homotopy perturbation method is applied to the search for traveling wave solutions of nonlinear wave equations. Some examples are given to illustrate the determination of the periodic solutions or the bifurcation curves of the nonlinear wave equations.
