652 publications from this institution
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In this paper, a modified Lindstedt–Poincare method is proposed. In this technique, we introduce a new transformation of the independent variable. This transformation will also allow us to avoid the occurrence of secular terms in the perturbation series solution. Some examples are given here to illustrate its effectiveness and convenience. The results show that the obtained approximate solutions are uniformly valid on the whole solution domain, and they are suitable not only for weakly non-linear systems, but also for strongly non-linear systems.
No abstract is provided for this article.
Fangzhu, which has been lost for thousands of years, is an ancient device for water collection from air; its mechanism is unknown yet. Here we elucidate its possible surface‐geometric and related physical properties by the oldest the Yin‐Yang contradiction. In view of modern nanotechnology, we reveal that Fangzhu's water‐harvesting ability is obtained through a hydrophilic‐hydrophobic hierarchy of the surface, mimicking spider web's water collection, lotus, or desert beetle's water intake. The convex‐concave hierarchy of Fangzhu's textured surface enables it to have low wettability (high geometric potential) to attract water molecules from air through the nanoscale convex surface and transfer the attracted water along the concave surface to the collector. A mathematical model is established to reveal three main factors affecting its effectiveness, i.e., the air velocity, the surface temperature, and surface structure. The lost technology can play an extremely important role in modern architecture, ocean engineering, transportation, and others to catch water from air for everyday use.
No abstract is provided for this article.
This paper shows that the half-integer spin is the first level of the quantized golden mean, and the electron magnetic momentum can be exactly calculated using the classic quantum mechanics without the spin-1/2 theory, where the g-factor was introduced to predict the magnetic momentum. The golden mean predicts an exact value of 2 for the g-factor, and other quantized numbers of the golden mean lead the g-factor to deviation from 2. Our results demonstrate that quantized golden mean evokes a new and challenging branch of physics. We anticipate the quantized golden mean to be a starting point to solve puzzle and paradox in physics and to revitalize a more sophisticated physics based on the golden mean.
Article Α Short Remark on Scaling Relationship between the Fetal and Placental Weights was published on December 1, 2010 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 11, issue 12).
Electrospun nanofiber technology bridges the gap between deterministic laws (Newton mechanics) and probabilistic laws (quantum mechanics). Our research reveals that fascinating phenomena arise when the diameter of the electrospun nanofibers is less than 100nm. The nano-effect has been demonstrated for unusual strength, high surface energy, surface reactivity, high thermal and electric conductivity. Dragline silk is made of many nano-fibers with diameter of about 20nm, thus it can make full use of nano-effects. It is a challenge to developing technologies capable of preparing for nanofibers within 100nm. Vibration-melt-electrospinning is uniquely qualified to address this challenge. The flexibility and adaptation provided by the method have made the method a strong candidate for producing nanofibers on such a scale. The application of Sirofil technology to strengthen nanofibers is also addressed, E-infinity theory is emphasized as a challenging theory for nano-scale technology and science.
A generalized KdV equation with fractal derivatives is suggested, and a special function is introduced to establish a fractal variational principle. A detailed derivation is elucidated step by step by the semi-inverse method, and some special cases are discussed.
Nonlinear science has had quite a triumph in all conceivable applications in science and technology, especially in high energy physics and nanotechnology. COBE, which was awarded the physics Nobel Prize in 2006, might be probably more related to nonlinear science than the Big Bang theory. Five categories of nonlinear subjects in research frontier are pointed out.
A mathematical model for a vehicle moving along a soft porous mat is established using aerodynamics and lubrication theories, and numerical analysis is given, showing the possibility of greatly enhancing its velocity and remarkably decreasing the fuel consumption and CO2 emission.
The nano/microelectromechanical systems (N/MEMS) have caught much attention in the past few decades for their attractive properties such as small size (low mass), high reliability (high thermal conductivity and high Young's modulus), batch fabrication, and low power consumption. The dynamic oscillatory behavior of these systems is very complex due to strong nonlinearities in these systems. The basic aim of this manuscript is to investigate the nonlinear vibration property of N/MEMS oscillators arising in nanotube‐based N/MEMS and resonators by the homotopy perturbation method coupled with Laplace transform (also called as He‐Laplace method in literature). A generalized N/MEMS oscillator is systematically studied, and a fairly accurate analytic solution is obtained. Three special cases for electrically actuated MEMS, multi‐walled carbon nanotubes‐based MEMS, and MEMS subjected to van der Waals attraction are considered for comparison, and a good agreement with exact solutions is observed.
As remarked by Nobel Laureate Gerardus ‘t Hooft discrete space–time may be the most radical but logical viewpoint of reality. All the same, string theory is formulated on a continuous smooth space–time. In the present note we show that an effective Lagrangian can be established in a discontinuous space–time. The work which was guided by E-infinity theory seems to confirm this viewpoint.
This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.
The combined electronic structure calculations and non-adiabatic surface-hopping dynamics simulations were performed to illuminate the excited-state relaxation mechanism of ExPh molecule.
This paper shows the special functions are a mathematical tool to solving nonlinear equations. The gamma function is used as an example to show the one-step solution process for a special nonlinear oscillator. Comparison with the exact solution and the approximate solution obtained by the homotopy perturbation method reveals the gamma function method is extremely simple and remarkably accurate.
