Publications

A new fractional derivative is defined through the variational iteration method, and its application in explaining the excellent thermal protection of polar bear hairs is elucidated. The fractal porosity of its inner structure makes a polar bear mathematically adapted for living in a harsh Arctic region.

The semi-inverse method is adopted to establish a family of fractal variational principles of the one-dimensional compressible flow under the microgravity condition, and Cauchy–Lagrange integral is successfully derived from the obtained variational formulation. A suitable application of the Lagrange multiplier method is also elucidated.

Many nature materials have hierarchical structure, and its last cascade is always on a molecule scale, e. g., double-stranded DNA, making the hierarchy effective with minimal building blocks. Now artificial hierarchy can begin with a nanoscale level to embody the material with remarkable and fascinating properties which can be never achieved using non-hierarchical structure. A strong desire to fabricate some biomimicking hierarchies from a molecule level has been stimulating scientists. Herein we show that molecular structure can be easily controlled by a long and narrow tube, and self-assembly of macromolecules can be achieved to improve its crystallinity with plenty of excellent properties. We anticipate this paper to be a starting point for more sophisticated fabrication of fibers with self-assembly of macromolecules.

Article A Variational Model for Micropolar Fluids in Lubrication Journal Bearing was published on June 1, 2000 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 1, issue 2).

The article is concerned with Electrohydrodynamics (EHD) instability of an incompressible dielectric viscous fluid in a vertical cylinder that surrounds a dielectric viscous/inviscid gas. The incompressible packing has microscopic fine dust particles of a consistent size. An unchanged tangential electric field influences the system which is saturated in porous media. Given their importance in the stability picture, the fundamental equations that regulate the particle mixture are constructed. The linear stability approach is employed to analyze the system. The motivation for tackling this problem lies in the growing interest in a variety of practical physics and engineering disciplines. The profiles of velocity fields and pressure are evaluated by the conventional normalized approach. A transcendental dispersion relationship connects the rate of growth and the wave number of the wave propagation. The procedure produces several numbers of non-dimensional characteristics of the problem at hand. Appropriate findings have been yielded that match the existing results in the available literature.

Bubbfil spinning is to use polymers' or melts' bubbles or membranes for fabrication of nanomaterials including smooth nanofibers and discontinuous nanofibers by using electrostatic force, blowing air or mechanical force to overcome the surface tension, it mainly includes the bubble-electrospinning, blown bubble spinning and membrane spinning. The initial ejecting velocity of the Bubbfil spinning process is as high as 100 meters per second. A history of the development of Bubbfil spinning is briefly elucidated, its main properties are emphasized, some effective modifications are discussed for different applications including single bubble electrospinning, blown bubble spinning, air-jet assisted bubble electrospinning, electrostatic-field-assisted blown bubble spinning, and vibration bubble electrospinning which is suitable for melts or high-concentration solutions. Morphology properties are also discussed for different applications.

This work demonstrates the 3D motion of 6-DOF rigid body around the main inertial axes relative to a fixed point. The novelty of this work is to examine the influence of the gyrostatic moment vector and the magnetic field on the gyrostatic motion besides the action of the Newtonian field in accordance with the Bobylev-Steklov conditions. This motion is characterized by the possibility of placing an acceptable constraint on the governing system of motion in the form of imposing a large value of the projection of the angular velocity around the axial axis of the body. The importance of this restriction is that the governing system in addition to the first-integrals can be reduced to an appropriate system of two semi-linear differential equations from second-order and one first integral. The new analytic approximate solutions of the governing equations are achieved using the small parameter technique of Poincaré. Euler's angles are determined to evaluate the motion at any instance. The realized solutions are represented graphically for different values ​​of the gyrostatic moment and the point charge causing the magnetic field to estimate the impact of these values ​​on the rotational motion. Moreover, the phase plane plots which illustrate the stability behavior of the body are portrayed. The significance of this work goes back to its several applications in practical life and in engineering application like satellites, submarines, and aircraft.

No abstract is provided for this article.

A generalized Boltzmann transform is introduced to convert the Richards’ equation into an ordinary differential equation, and an approximate solution for the moving wetted front of water transport in unsaturated soils is obtained. The developed theory is also valid for water transport in porous fabrics.

This paper elucidates the significance of partial slips and temperature jumps on the heat and mass transfer of a boundary layer nanofluid flowing through a stretched or shrinking surface. Considerable consideration is given to the dynamic properties of the nanofluid process, including Brownian motion and thermophoresis. A similarity transform is introduced to obtain a physical model of nonlinear ordinary differential equations, and the Chebyshev method of collocation is used to numerically analyze the influences of parameters of physical flow such as slip, temperature jump, Brownian motion, thermophoresis, suction (or injection) parameters, and Lewis and Prandtl numbers. The numerical results for temperature and concentration profiles, and heat and mass transfer rates, are graphically represented, and insights into the effects of slips and temperature jumps are revealed. In the case of a stretched sheet, the slip parameter enhances the temperature field and increases the thermal boundary layer thickness as well as the concentration function’s boundary layer thickness. When the slip parameter is raised in the case of the shrinking sheet, the dual solutions for temperature and concentration functions are reduced. For the first solution, both the temperature and concentration functions drop as the slip parameter increases, but for the second solution, both the temperature and concentration functions rise as the slip parameter increases. The discoveries have applications in a number of disciplines, including heat transfer in a solar energy collector. Glass blowing, annealing, and copper wire thinning are just a few of the technical and oilfield applications for the current problem. In high-temperature industrial applications, radiation heat transfer research is critical.

Bubble electrospinning with aqueous solvent is used to fabricate nanofibers within 100nm. The effect of applied voltage on the diameters of nanofibers is experimentally studied, revealing that the higher voltage favors the smaller diameter. Polyvinyl Alcohol (PVA) with water as solvent is used to produce environmentally benign nanofibers, and the minimal diameter reaches as small as 46.8nm.

Modern advances in pure mathematics and particularly in transfinite set theory have introduced into the fundamentals of theoretical physics many novel concepts and devices such as fractal quasi manifolds with non-integer (Hausdorff) dimension for its geometry as well as infinite dimensional wild topology and non classical fuzzy logic. In the present work transfinite fractal sets and fuzzy logic are combined to enable the introduction of a new theory termed fractal logic to the foundation of high energy particle physics. This leads naturally to a new look at quantum gravity. In particular we will show that to understand and develop quantum gravity we have to bring various fields together, particularly fractals and nonlinear dynamics as well as sphere packing, fuzzy set theory, number theory and quantum entanglement and irrationally q-deformed algebra.

In this paper, we re-study an ancient Chinese algorithm, the Ying Buzu Shu, in about second century BC, known as the rule of double false position in West after 1202 AD. The method can powerfully applied to solve nonlinear equations. Some examples are given.

No abstract is provided for this article.

No abstract is provided for this article.

Bubbfil spinning is a generalized bubble electrospinning, including bubble spinning, blown-bubble spinning, and membrane spinning, for mass production of nanofiber. This paper shows small bubbles in liquid membrane are the best candidate for uniform nanofibers.