Publications

Modeling and numerical analysis for an MEMS graphene resonator

This paper delves into the static and dynamic behavior of graphene cantilever beam resonators under electrostatic actuation at their free tips. A rigorous analysis of the system’s response is performed. The constitutive nonlinear equation of the system is derived using the energy method and Hamilton’s principle. An analytical solution to the nonlinear static problem is obtained. The generalized stiffness coefficient for the lumped model of the cantilever graphene beam under load at its tip is calculated, enabling a comprehensive analysis of its dynamic behavior. A key focus is on investigating the dynamic pull-in conditions of the system under both constant and harmonic excitation. Analytical predictions are validated through numerical simulations. The system exhibits periodic solutions when the excitation parameters are below a certain threshold described by a separatrix curve, leading to sustained oscillations. On the other hand, if the excitation parameters exceed this threshold, the system experiences pull-in instability, causing the beam to touch down. Furthermore, we explore the impact of excitation frequency on the dynamic response of the graphene cantilever beam under harmonic load. The simulations reveal that choosing the excitation frequency near the beam’s resonance frequency can lead to structural collapse under certain parameter conditions.

The number of elementary particles in a fractal M-theory of 11.2360667977 dimensions

It is generally accepted that there are 60 experimentally found particles. The standard model strongly predicts two more hypothetical particles, the Higgs and the graviton. This paper reveals other possible scenario for predicting 69 particles at different energy scales in 11+ ϕ 3 fractal dimensions of a fractal M theory, where ϕ = ( 5 - 1 ) / 2 . A modified Newton’s law is suggested to experimentally verify our predictions at extremely small quantum scales. The modified Newton’s law is in harmony with Heisenberg’s uncertainty principle.

Mysterious Pi and a Possible Link to DNA Sequencing

No abstract is provided for this article.

THE FRACTIONAL COMPLEX TRANSFORM: A NOVEL APPROACH TO THE TIME-FRACTIONAL SCHRÖDINGER EQUATION

This paper presents a thorough study of a time-dependent nonlinear Schrödinger (NLS) differential equation with a time-fractional derivative. The fractional time complex transform is used to convert the problem into its differential partner, and its nonlinear part is then discretized using He’s polynomials so that the homotopy perturbation method (HPM) can be applied powerfully. The two-scale concept is used to explain the substantial meaning of the fractional time complex transform and the solution.

Homotopy perturbation method for nonlinear oscillators with coordinate-dependent mass

Nonlinear oscillators with no linear term or negative linear term are difficult to be solved analytically. This paper shows that the homotopy perturbation method can be effectively applied to such kinds of nonlinear oscillator by the parameter expansion technology. A nonlinear oscillator with coordinate-dependent mass is used as an example to elucidate the effectiveness and convenience of the method. The condition for periodic solution is obtained.

THE ENHANCED HOMOTOPY PERTURBATION METHOD FOR AXIAL VIBRATION OF STRINGS

A governing equation is established for string axial vibrations with temporal and spatial damping forces by the Hamilton principle. It is an extension of the well-known Klein-Gordon equation. The classical homotopy perturbation method (HPM) fails to analyze this equation, and a modification with an exponential decay parameter is suggested. The analysis shows that the amplitude behaves as an exponential decay by the damping parameter. Furthermore, the frequency equation is established and the stability condition is performed. The modified homotopy perturbation method yields a more effective result for the nonlinear oscillators and helps to overcome the shortcoming of the classical approach. The comparison between the analytical solution and the numerical solution shows an excellent agreement.

From Leibniz’s Notation for Derivative to the Fractal Derivative, Fractional Derivative and Application in Mongolian Yurt

No abstract is provided for this article.

Generalized Hellinger-Reissner Principle

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]

Construction of solitary solution and compacton-like solution by variational iteration method

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.

Preparation of PLGA/MWCNT Composite Nanofibers by Airflow Bubble-Spinning and Their Characterization

Poly(lactic-co-glycolic acid) (PLGA)/multi-walled carbon nanotube (MWCNT) composite nanofibers have been successfully fabricated via airflow bubble-spinning. In this work, a systematic study of the effects of solution concentration, relative humidity (RH), and composition on the morphology of PLGA nanofibers is reported. By comparing the distribution of fiber diameter, we found that the spinning effect was the best when the temperature was kept at 25 °C, the collecting distance 18 cm, the concentration 8 wt %, and the relative humidity 65%. MWCNTs used as added nanoparticles were incorporated into the PLGA nanofibers. The volatile solvents were used to achieve the purpose of producing nanoporous fibers. Besides, the rheological properties of solutions were studied and the PLGA or PLGA/MWCNT composite nanofibers with a nanoporous structure were also completely characterized using scanning electron microscope (SEM), a thermogravimetric analyzer(TGA), X-ray diffraction(XRD) and Fourier-transform infrared (FTIR) spectroscopy. In addition, we compared the mechanical properties of the fibers. It was found that the addition of MWCNTs significantly enhanced the tensile strength and elasticity of composite nanofibers without compromising the nanoporous morphology. The results showed that the breaking strength of the composite fiber bundle was three times as strong as the pure one, and the elongation at the break was twice as great. This work provided a novel technique successfully not only to get rid of the potential safety hazards caused by unexpected static but also prepare oriented nanoporous fibers, which would demonstrate an impressive prospect for the fields of adsorption and filtration.

Rebuild of King Fang 40 BC musical scales

No abstract is provided for this article.

Permeability of PTFE flat-type membrane for absorption chiller.

Applying the hydrophobic membrane into the absorber and generator of the absorption chiller can significantly downsize the absorption system. In this study, the permeability of the hydrophobic membrane is evaluated using CO2 prior to the system test. The PTFE flat-type membrane with three nominal pope sizes of 0.1, 0.45 and 1 micron were tested for both flow directions. Results show that the permeability decreases with imposed pressure when the pressure is relatively small, and then tends to be constant. The mass transport mechanism differs for the membrane samples, and higher permeability was obtained with larger pore sizes. The variation of the permeability can be qualitatively explained with the pore size distribution.

Fractional Calculus of Variations in Fractal Spacetime

Difference equation vs differential equation on different scales

Purpose The purpose of this paper is to demonstrate that the numerical method is not everything for nonlinear equations. Some properties cannot be revealed numerically; an example is used to elucidate the fact. Design/methodology/approach A variational principle is established for the generalized KdV – Burgers equation by the semi-inverse method, and the equation is solved analytically by the exp-function method, and some exact solutions are obtained, including blowup solutions and discontinuous solutions. The solution morphologies are studied by illustrations using different scales. Findings Solitary solution is the basic property of nonlinear wave equations. This paper finds some new properties of the KdV–Burgers equation, which have not been reported in open literature and cannot be effectively elucidated by numerical methods. When the solitary solution or the blowup solution is observed on a much small scale, their discontinuous property is first found. Originality/value The variational principle can explain the blowup and discontinuous properties of a nonlinear wave equation, and the exp-function method is a good candidate to reveal the solution properties.

Nonlinear dynamic analysis of vibratory behavior of a graphene nano/microelectromechanical system

The nano/microelectromechanical systems (N/MEMS) have gained considerable attention in the past few decades for their attractive properties such as small size, high reliability, batch fabrication, and low power consumption. Carbon‐based nanostructures such as one‐dimensional carbon nanotubes (CNTs) and two‐dimensional graphene are the key materials in many N/MEMS and very attractive due to their unique properties and ultra‐small dimensions especially the large surface area‐to‐volume ratio make them prime candidates for sensing applications in N/MEMS. Therefore, the main objective of this manuscript is to analyze the dynamic behavior of a graphene N/MEMS. The mathematical model of this system uses constitutive stress–strain law and the electrostatic Coulomb force for the restoring force of the spring and the driving force of the mass attached to the spring, respectively. The modeled system is then solved by employing the variational iteration method (VIM) accompanied by the techniques of the Laplace transform. This coupling of VIM and Laplace transform (Laplace‐based variational iteration method [LVIM]) not only suggests an easier approach to determine the Lagrange multiplier used in the VIM but also provides approximate nonlinear frequency and approximate solution of graphene N/MEMS in an efficient way. Moreover, the LVIM also approximates the pull‐in threshold, a critical phenomenon associated with N/MEMS, in terms of model parameters. Finally, to verify the obtained findings, the results are compared with those achieved numerically as well.

Mathematical models for thermal science

nema

High temperature resistant nanofiber by bubbfil-spinning

Heat-resisting nanofibers have many potential applications in various industries, and the bubbfil spinning is the best candidate for mass-production of such materials. Polyether sulfone/zirconia solution with a bi-solvent system is used in the experiment. Experimental result reveals that polyether sulfone/zirconia nanofibers have higher resistance to high temperature than pure polyether sulfone fibers, and can be used as high-temperature-resistant filtration materials.

Enhanced piezoelectric performance of PVDF nanofibers by biomimicking the Spider’s long liquid transport

Scientists have been fascinated by the spider's spinning process, which enables its silk to be incredibly strong. This paper explores the use of a long needle in the electrospinning process to control the inner structure of a PVDF nanofiber. The results show that a longer needle can significantly enhance the nanofiber's piezoelectric performance. The mechanism behind this enhancement is elucidated using the laminar flow theory.