652 publications from this institution
By the semi-inverse method, a variational principle is obtained for the Lane–Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.
No abstract is provided for this article.
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Copper/PA66 nanofibers are fabricated by the bubbfil spinning, and their thermal stability is studied by calcination treatment. It reveals that the addition of copper nanoparticles can greatly improve the thermal stability of nanofibers.
In recent decades, nano/microelectromechanical systems (N/MEMS) have garnered significant attention due to their appealing characteristics, such as compact size, batch fabrication capabilities, high reliability and low power consumption. However, these vibratory systems often present challenges, including zero conditions at the initial time, involving zero velocity and zero displacement, which complicates the solution process. Nonetheless, the theory of geometric potential offers insights into various phenomena in nanoscience and nanotechnology. In this paper, we implement the theory of geometric potential to develop an N/MEMS model. We then analyze the periodicity property of the nonlinear system using a novel method based on Sturm’s algorithm. Our analysis reveals that the model with zero initial conditions exhibits periodic solution under specific conditions on lumped parameter. Finally, we validate our findings by comparing them with numerically achieved results.
The seeds within a lotus seedpod are distributed in an orderly fashion and safeguarded within a secure packaging system. The distribution law is thus revealed, and the packaging mechanism can be emulated for contemporary applications. This paper presents a novel and ingenious method for optimizing fractal super-ropes, inspired by the captivating distribution patterns observed in lotus seeds. The distinctive configuration of the lotus seed represents a model of natural optimization, offering insights that can enhance the exceptional performance and multifaceted functionality of super-ropes utilized in the construction of formidable aircraft carriers, elegantly designed cable-stayed bridges, and stab, bulletproof fabrics. The lotus seedpod provides the fundamental structural framework upon which super-ropes with a sophisticated hierarchical configuration are meticulously constructed. The five super-ropes are presented for detailed examination, offering a promising avenue for further investigation. This paper presents a novel geometrical approach to the optimal design of super-ropes, thereby establishing a promising foundation for extensive future research.
No abstract is provided for this article.
In this paper, we propose the following modified Newton–Raphson iteration formulation: In case r =1, the obtained formulation reduces to the Newton–Raphson formulation. The present technique circumvent pitfalls of the Newton–Raphson iteration method. Some examples are illustrated. Copyright © 2004 John Wiley & Sons, Ltd.
No abstract is provided for this article.
Fractal calculus is very simple but extremely effective to deal with phenomena in hierarchical or porous media. Its operation is almost same with that by the advanced calculus, making it much accessible to all non-mathematicians. This paper begins with the basic concept of fractal gradient of temperature, i.e., the temperature change between two points in a fractal medium, to reveal the basic properties of fractal calculus. The fractal velocity and fractal material derivative are then introduced to deduce laws for fluid mechanics and heat conduction in fractal space. Conservation of mass in a fractal space is geometrically explained, and an approximate transform of a fractal space on a smaller scale into its continuous partner on a larger scale is illustrated by a nanofiber membrane, which is smooth on any observable scales, but its air permeability has to studied in a nano scale, under such a small scale, the nanofiber membrane becomes a porous one. Finally an example is given to explain cocoon's heat-proof property, which cannot be unveiled by advanced calculus.
The pull-in voltage is crucial in designing an optimal nano/micro-electromechanical system (N/MEMS). It is vital to have a simple formulation to calculate the pull-in voltage with relatively high accuracy. Two simple and effective methods are suggested for this purpose; one is an ancient Chinese algorithm and the other is an extension of He’s frequency formulation.
Purpose This paper aims to review some effective methods for fully fourth-order nonlinear integral boundary value problems with fractal derivatives. Design/methodology/approach Boundary value problems arise everywhere in engineering, hence two-scale thermodynamics and fractal calculus have been introduced. Some analytical methods are reviewed, mainly including the variational iteration method, the Ritz method, the homotopy perturbation method, the variational principle and the Taylor series method. An example is given to show the simple solution process and the high accuracy of the solution. Findings An elemental and heuristic explanation of fractal calculus is given, and the main solution process and merits of each reviewed method are elucidated. The fractal boundary value problem in a fractal space can be approximately converted into a classical one by the two-scale transform. Originality/value This paper can be served as a paradigm for various practical applications.
An extremely simple and elementary but rigorous derivation of maximal biomass of parasitic plants is given using an assumption that metabolic rate of the parasite should not be larger than that of its host organ
This paper is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential‐difference equations, and nonlinear fractional differential equations. Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter‐expansion method, the Yang‐Laplace transform, the Yang‐Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this paper are first appeared.
A dynamic model is established for two-strand yarn processing. The oscillating frequencies of Sirofil spinning in vertical and horizontal directions are approximately obtained. The stability and chaotic characters of Sirofil spinning are analysed analytically, and an optimal condition for the spinning system is suggested.
A new resistance formulation for carbon nanotubes is suggested using fractal approach. The new formulation is also valid for other nonmetal conductors including nerve fibers, conductive polymers, and molecular wires. Our theoretical prediction agrees well with experimental observation.
The Fractional Complex Transform is extended to solve exactly time-fractional differential equations with the modified Riemann-Liouville derivative. How to incorporate suitable boundary/initial conditions is also discussed.
Recently Liu applied the variational homotopy perturbation method for fractional initial boundary value problems. This note concludes that the method is a modified variational iteration method using He’s polynomials. A standard variational iteration algorithm for fractional differential equations is suggested.
This paper proposes a new type of soft matter, namely fibrous materials. The common characteristics of soft matter that are shared by fibrous materials, such as the multiphase composition, porous and highly deformable structures, and the non-negligible contributions of entropy to the material behavior are illustrated. More importantly, some unique problems, complex and interesting, yet more or less unrealized, or ignored in dealing with fibrous materials are highlighted. The study includes the packing geometry of fibers, macro—micro behavioral inconsistencies, friction and self-locking mechanisms, bi-modular behavior, and allometric or scaling problems. The fabric wrinkling or crumpling problem and its peculiar fracture behavior and failure criteria are discussed. This paper also elucidates the significance of treating fibrous materials as soft matter and the great potential of such study to materials in general and to biomaterials in particular.
