Ji-Huan He

articles in International journal of nonlinear sciences and numerical simulation

Ji-Huan He — Fri, 12 Aug 2011 18:59:59 PDT

papers published in IJNSNS

Application of the Fractional Complex Transform to Fractional Differential Equations

Zheng-Biao Li et al. — Fri, 12 Aug 2011 18:42:57 PDT

The fractional complex transform is used to analytically deal with fractional differential equations. Two examples are given to elucidate the solution procedure, showing it is extremely accessible to nonmathematicians

The 3rd International Symposium on Nonlinear Dynamics

Ji-Huan He — Sat, 13 Mar 2010 23:22:48 PST

The 3rd International Symposium on Nonlinear Dynamics will be held on Sept. 25-28, 2010,Shanghai , China www.isnd2010.com.cn (under construction) Our Symposium will be held during the Shanghai Expo 2010, of which the theme is "Better City, Better Life" . About 70 million visitors are estimated to visit World Expositions according to its official web : http://en.expo2010.cn/ . We warmly invite you to submit a paper to the Symposium and attend the symposium, feeling the dynamics of Shanghai's development and touching the world at the Sanghai Expo 2010. All submissions relative to nonlinear phenomena, nonlinear equations, and nonlinear analyses are welcome. Please send your papers to the symposium secretary, Dr. Lan Xu, by email isnd2010@yahoo.cn. Please prepare your paper using the word template, which can be downloaded from http://www.nonlinearscience.com/template.doc.

Fractional Calculus of Variations in Fractal Spacetime

Guo-Cheng Wu et al. — Sat, 13 Mar 2010 23:18:26 PST

A physical law in continuous space-time is, in general, expressible by a variational principle. Physical phenomena in a fractal spacetime, however, are describable by the fractional calculus. The natural question then arises: does a system of fractional differential equations admit a variational principle? This paper asserts that fractional variational principles can be established using Jumarie’s modified Riemann-Liouville derivative, which reveals fractional actions in a fractal spacetime. See: http://www.nonlinearscience.com/

The Variational Iteration Method Which Should Be Followed

Ji-Huan He et al. — Sat, 28 Nov 2009 22:14:15 PST

This paper proposes three standard variational iteration algorithms for solving differential equations, integro-differential equations, fractional differential equations, fractal differential equations, differential-difference equations and fractional/fractal differential-difference equations. The physical interpretations of the fractional calculus and the fractal derivative are given and an application to discrete lattice equations is discussed. The paper then examines the acceleration of some iteration formulae with particular emphasis being placed on the exponential Padé approximant that is suggested for solitary solutions and the sinusoidal Padé approximant that is usually used for periodic and compacton solutions. The paper points out that there may not be any physical meaning to the exact solutions of many nonlinear equations and stresses the importance of searching for approximate solutions that satisfy both the equations and the appropriate initial/boundary conditions. The variational iteration method is particularly suitable for solving this kind of problems. Approximate initial/boundary conditions and point boundary initial/conditions are also discussed, with the variational iteration method being capable of recovering the correct initial/boundary conditions and finding the solutions simultaneously. =============================================== Contents 1. Introduction 2. Variational Iteration Algorithm-I 3. Variational Iteration Algorithm-II 4. Variational Iteration Algorithm-III 5. Variational Iteration Algorithms for Ordinary Differential Equations and Partial Differential Equations 6. Variational Iteration Algorithms for Fractional Differential Equations 7. Physical Understanding of Fractional Calculus 8. Variational Iteration Algorithms for Fractal Differential Equations 9. Physical Understanding of Fractal Differential Equations 10. Variational Iteration Algorithms for Differential-difference Equations 11. Physical Understanding of Differential-difference Equations 12. Variational Iteration Algorithms for Fractal-difference Equations and Fractional-difference Equations 13. Series Solutions, Exponential Padé Approximant and Sinusoidal Padé Approximant 14. Approximate Solutions vs Exact Solutions 15. Approximate Initial/Boundary Conditions and Point Boundary Conditions 16. Conclusions http://www.nonlinearscience.com/

Electrospun Nanofibres and Their Applications

Ji-Huan He et al. — Fri, 31 Jul 2009 04:48:16 PDT

This Update covers all aspects of electrospinning as used to produce Nanofibres. It contains an array of colour diagrams, mathematical models, equations and detailed references. It will be invaluable to anyone who is interested in using this technique and also to those interested in finding out more about the subject. Electrospinning is the cheapest and the most straightforward way to produce nanomaterials. Electrospun Nanofibres are very important for the scientific and economic revival of developing countries. Electrospinning was developed from electrostatic spraying and now represents an attractive approach for polymer biomaterials processing, with the opportunity for control over morphology, porosity and composition using simple equipment. Because electrospinning is one of the few techniques to prepare long fibres of nano- to micrometre diameter, great progress has been made in recent years. It is now possible to produce a low-cost, high-value, high-strength fibre from a biodegradable and renewable waste product for easing environmental concerns. For example, electrospun nanofibres can be used in wound dressings, filtration applications, bone tissue engineering, catalyst supports, non-woven fabrics, reinforced fibres, support for enzymes, drug delivery systems, fuel cells, conducting polymers and composites, photonics, medicine, pharmacy, fibre mats serving as reinforcing component in composite systems, and fibre templates for the preparation of functional nanotubes. If you have an ongoing interest in this area then why not consider also purchasing the Electrospinning and Nanofibres Bulletin? This current awareness service from the Polymer Library provides you with regular updates containing abstracts of new research from journals, conference proceedings, books and reports. It lets you know about all of the latest developments on both Electrospinning and Nanofibres, so you don't have to waste time, effort and money finding it all yourself. Combined with the 'Electrospun Nanofibres and Their Applications' Update, you'll have the complete package to introduce you to the topic, then keep you up-to-date with new developments. Add both products to your cart and you will save £100! Table of Contents 1. Introduction 1.1 What is nanotechnology 1.2 What is electrospinning 1.3 What affects electrospinning 1.4 Applications 1.5 Global Interest in the field of Electrospinning 2. Mathematical Models for Electrospinning Process 2.1 One-dimensional Model 2.2 Spivak-Dzenis model 2.3 Wan-Guo-Pan Model 2.4 Modified One-Dimensional Model 2.5 Modified Conservation of Charge 2.6 Renekers model 2.7 E-Infinity theory 3. Allometric Scaling in Electrospinning 3.1 Allometric Scaling in Nature 3.2 Allometrical Scaling Laws in Electrospinning 3.2.1 Relationship between radius r of jet and the axial distance z 3.2.2 Allometric scaling relationship between current and voltage 3.2.3 Allometric scaling relation between solution flow rate and current 3.2.4 Effect of concentration on electrospun polyacrylonitrile (PAN) nanofibres 3.2.5 Allometric Scaling Law between Average Polymer Molecular Weight and Electrospun Nanofibre Diameter 3.2.6 Effect of voltage on morphology and diameter of electrospun nanofibres 3.2.7 Enlarging Electrospinability by Nonionic Surfactants 3.3 Allometric Scaling Law for Static Fiction of Fibrous Materials 3.4 Allometric scaling in Biology 4. Application of Vibration Technology to Electrospinning 4.1 Effect of viscosity on diameter of electrospun fibre 4.2 Effect of Vibration on Viscosity 4.3 Application of vibration technology to polymer electrospinning 4.4 Effect of solution viscosity on mechanical characters of Electrospun Fibres 4.5 Carbon Nanotube Reinforced Polyacrylonitrile Nanofibres by Vibration-Electrospinning 5. Megnetio-electrospinning: Control of the instability 5.1 Critical Length of Straight Jet in Electrospinning 5.2 Controlling Stability by Magnetic Field 5.3 Controlling Stability by Temperature 5.4 Siro-electrospinning 6. BioMimic Fabrication of Electrospun Nanofibres with High-throughput 6.1 Spider-spinning 6.2 Electrospinning of silk fibroin nanofibres 6.3 Mystery in spider-spinning process 6.4 Bubble-electrospinning 7. Controlling Numbers and Sizes of Beads in Electrospun nanofibres 7.1 Experiment Observation 7.2 Effects of different solvents 7.3 Effect of the polymer concentration 7.4 Effect of salt additive 8. Electrospun Nanoporous Microspheres for Nanotechnology 8.1 Electrospun nanoporous spheres with Chinese drug 8.2 Electrospinning-dilation 8.3 Single Nanoporous Fibre by Electrospinning 8.4 Micro sphere with nano-porosity 8.5 Micro-composite fibres by electrospinning 9. Super-carbon Nanotubes: An E-infinity Approach 9.1 E-infinity Nanotechnology 9.2 Application of E-Infinity to Electrospinning 9.3 Super-carbon Nanotubes: An E-infinity Approach 10. Mechanics in Nano-textile Science 10.1 Jet-vortex spinning and Cyclone model 10.2 Two-phase flow of Yarn Motion in High Speed Air and Micropolar Model 10.3 Mathematical Model for Yarn motion in Tube 10.4 Nano-hydrodynamics 10.5 A New Resistance Formulation for Carbon Nanotubes and Nerve Fibres 10.6 Differential-difference Model for Nanotechnology 11. Nonlinear Dynamics in Sirofil/Sirospun Yarn Spinning 11.1 Convergent point 11.2 Linear Dynamical Model 11.3 Nonlinear Dynamical Model 11.4 Stable Working Condition for Three-strand Yarn Spinning 11.5 Nano-sirospinning

Solitons and Compactons

Ji-Huan He et al. — Fri, 31 Jul 2009 04:38:02 PDT

Article Outline Glossary Definition of the Subject Introduction Solitons Compactons Generalized Solitons and Compacton-like Solutions Future Directions Cross References Bibliography Glossary Soliton A soliton is a stable pulse-like wave that can exist in some nonlinear systems. The soliton, after a collision with another soliton, eventually emerges unscathed. Compacton A compacton is a special solitary traveling wave that, unlike a soliton, does not have exponential tails. Generalized soliton A generalized soliton is a soliton with some free parameters. Generally a generalized soliton can be expressed by exponential functions. 8458 S Solitons and Compactons Compacton-like solution A compcton-like solution is a special wave solution which can be expressed by the squares of sinusoidal or cosinoidal functions. Definition of the Subject Soliton and compacton are two kinds of nonlinear waves. They play an indispensable and vital role in all ramifications of science and technology, and are used as constructive elements to formulate the complex dynamical behavior of wave systems throughout science: from hydrodynamics to nonlinear optics, from plasmas to shock waves, from tornados to theGreat Red Spot of Jupiter, from traffic flow to Internet, from Tsunamis to turbulence. More recently, soliton and compacton are of key importance in the quantum fields and nanotechnology especially in nanohydrodynamics.

Soliton Perturbation

Ji-Huan He — Fri, 31 Jul 2009 04:29:26 PDT

Glossary Soliton A soliton is a nonlinear pulse-like wave that can exist in some nonlinear systems. The isolated wave can propagate without dispersing its energy over a large region of space; collision of two solitons leads to unchanged forms, solitons also exhibit particlelike properties. Soliton perturbation theory The soliton perturbation theory is used to study the solitons that are governed by the various nonlinear equations in presence of the perturbation terms. Homotopy perturbation method The homotopy perturbationmethod is a useful tool to the search for solitons without the requirement of presence of small perturbations. In this method, a homotopy is constructed with a homotopy parameter, p. When p D 0, it becomes a nonlinear wave equation such as a KdV equation with a known soliton solution; when p D 1, it turns out to be the original nonlinear equation. To change p from zero to unity, one must only change from a trial soliton to the solved soliton. Variational iteration method The variational iteration method is a new method for obtaining soliton-type solutions of various nonlinear wave equations. The method begins with a soliton-type solution with some unknown parameters which can be determined after few iterations. The iteration formulation is constructed by a general Lagrange multiplier which can be identified optimally via variational theory. Exp-function method The exp-function method is a new method for searching for both soliton-type solutions and periodic solutions of nonlinear systems. The method assumes that the solutions can be expressed in arbitrary forms of the exp-function. Definition of the Subject The soliton is a kind of nonlinear wave. There are many equations ofmathematical physics which have solutions of the soliton type. The first observation of this kind of wave was made in 1834 by John Scott Russell [1]. In 1895, the famous KdV equation, which possesses soliton solutions, was obtained by D. J. Korteweg and H. de Vries [2], who established a mathematical basis for the study of various solitary phenomena. From a modern perspective, the soliton is used as a constructive element to formulate the complex dynamical behavior of wave systems throughout science: from hydrodynamics to nonlinear optics, from plasmas to shock waves, from tornados to the Great Red Spot of Jupiter, from traffic flow to the Internet, from Tsunamis to turbulence [3]. More recently, solitary waves are of key importance in the quantum fields: on extremely small scales and at very high observational resolution equivalent to a very high energy, space–time resembles a stormy ocean and particles and their interactions have soliton-type solutions [4].

Fatalness of virus depends upon its cell fractal geometry

Ji-Huan He — Tue, 21 Jul 2009 00:28:56 PDT

Why do more complex viruses (e.g., HIV, AIDS-virus and SARS coronavirus) tend to be more fatal? The paper concludes that the cell fractal geometry of viruses is the key. This paper also suggests two possible new approaches using nanotechnology and temperature to cure or prevent virus infection

An elementary introduction to the homotopy perturbation method

Ji-Huan He — Tue, 21 Jul 2009 00:21:59 PDT

This paper is an elementary introduction to the concepts of the homotopy perturbation method. Particular attention is paid to giving an intuitive grasp for the solution procedure throughout the paper.

AN ELEMENTARY INTRODUCTION TO RECENTLY DEVELOPED ASYMPTOTIC METHODS AND NANOMECHANICS IN TEXTILE ENGINEERING

Ji-Huan He — Sun, 07 Sep 2008 20:40:35 PDT

This review is an elementary introduction to the concepts of the recently developed asymptotic methods and new developments. Particular attention is paid throughout the paper to giving an intuitive grasp for Lagrange multiplier, calculus of variations, optimization, variational iteration method, parameter-expansion method, exp-function method, homotopy perturbation method, and ancient Chinese mathematics as well. Subsequently, nanomechanics in textile engineering and E-infinity theory in high energy physics, Kleiber's 3/4 law in biology, possible mechanism in spider-spinning process and fractal approach to carbon nanotube are briefly introduced. Bubble-electrospinning for mass production of nanofibers is illustrated. There are in total more than 280 references

Electrospinning: The big world of small fibers

Ji-Huan He — Sat, 16 Aug 2008 18:47:36 PDT

Similar to the nuclear age, the so-called nanoage is coming, the growing gap between nano haves and nano have-nots, however, will remain, as has global competition, particularly from the electrospinning technology.

Non-ionic surfactants for enhancing electrospinability and for the preparation of electrospun nanofibers

Shu-Qiang Wang et al. — Sun, 10 Aug 2008 22:33:13 PDT

Abstract BACKGROUND: Electrospinning is widely used to produce nanofibers; however, not every polymer can be electrospun into nanofibers. To enhance electrospinability, much effort has been made in designing new apparatus, such as vibration-electrospinning, magneto-electrospinning and bubble-electrospinning. RESULTS: A representative non-ionic surfactant, TritonR X-100, is used to enhance electrospinability. The surfactant is added to an electrospun poly(vinyl pyrrolidone) polymer solution, and a dramatic reduction in surface tension is observed. As a result, a moderate voltage is needed to produce fine nanofibers, which are commonly observed during the conventional electrospinning procedure only at elevated voltage. CONCLUSION: The novel strategy produces smaller nanofibers than those obtained without surfactants, and the minimum threshold voltage is much decreased. Copyright © 2008 Society of Chemical Industry

Twenty-six dimensional polytope and high energy spacetime physics

Ji-Huan He et al. — Tue, 29 Jul 2008 18:09:16 PDT

We give the exact geometrical shape and study the combinatorial properties of higher dimensional polytopes for the dimensions from n = 4 to n = 12 as well n = 26 relevant to Heterotic, M and F superstring theories. Connections to E-infinity theory and the holographic principles are also discussed

Exp-function method to solve the nonlinear dispersive K(m,n) equations

Xin-Wei Zhou et al. — Thu, 17 Jul 2008 00:07:44 PDT

Some new exact solutions are obtained for the nonlinear dispersive K(m, n) equations using the exp-function method. The results show that the method is straightforward and concise and its applications are promising.

Hierarchy of Wool Fibers and Fractal Dimensions

Jie Fan et al. — Thu, 17 Jul 2008 00:03:11 PDT

Wool fiber shows excellent advantages in warmth-retaining and many other practical properties possibly due to its hierarchical structure. Its fractal dimension of wool fiber is calculated which is very close to the Golden Mean, 1.618. The present study might provide a new interpretation for the reason why wool fiber has so many excellent properties

Recent development of the homotopy perturbation method

Ji-Huan He — Wed, 16 Jul 2008 23:46:08 PDT

The homotopy perturbation method is extremely accessible to non-mathematicians and engineers. The method decomposes a complex problem under study to a series of simple problems that are easy to be solved. This note gives an elementary introduction to the basic solution procedure of the homotopy perturbation method. Particular attention is oaid to constructing a suitable homotopy equation.

A New Resistance Formulation for Carbon Nanotubes

Ji-Huan He — Wed, 16 Jul 2008 20:02:11 PDT

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.

Mathematical models for continuous electrospun nanofibers and electrospun nanoporous microspheres

Ji-Huan He et al. — Thu, 03 Jul 2008 01:34:16 PDT

Abstract: A brief review of mathematical models of electrospinning is given. The nano-effect and electrospinning dilation are presented to explain how to prepare extremely high strength continuous nanotibers and nanoporous microspheres, respectively. According to the established models, vibration-electrospinning is introduced to improve electrospinability, Siro-electrospinning is suggested to mimic the spinning procedure of a spider and magneto-electrospinning is used to control the instability arising in the electrospinning process. A new theory linked to both classical mechanics and quantum mechanics should be developed to explain certain special phenomena in electrospinning. E-infinity theory is considered to be a potential theory to deal with quantum-like properties and nano-effect on the nanoscale. The emphasis of this brief review is upon the authors' recent work, and the references are not exhaustive. (c) 2007 Society of Chemical Industry. Document Type: Article Language: English Author Keywords: electrospinning; nanofiber; nanoporous microspheres; nano-effect; dragline silk; magneto-electrospinning; vibration-electrospinning; Sirofil; Siro-electrospinning; E-infinity theory KeyWords Plus: E-INFINITY THEORY; ELECTRICALLY FORCED JETS; BOMBYX-MORI SILK; SPIDER SILK; EXPERIMENTAL-VERIFICATION; NONLINEAR DYNAMICS; MAMMALIAN-CELLS; POLYMER MELTS; SCALING LAW; FIBERS Addresses: He, JH (reprint author), Donghua Univ, Modern Text Inst, Inst Phys Fibrous Soft Matter, 1882 Yan An Xilu Rd, Shanghai 200051, Peoples R China Donghua Univ, Modern Text Inst, Inst Phys Fibrous Soft Matter, Shanghai 200051, Peoples R China E-mail Addresses: jhhe@dhu.edu.cn Publisher: JOHN WILEY & SONS LTD, THE ATRIUM, SOUTHERN GATE, CHICHESTER PO19 8SQ, W SUSSEX, ENGLAND Subject Category: Polymer Science IDS Number: 221VF ISSN: 0959-8103 DOI: 10.1002/pi.2370

Approximate analytical solution for seepage flow with fractional derivatives in porous media

Ji-Huan He — Wed, 25 Jun 2008 15:04:50 PDT

In this paper, a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed, which has modified the well-known Darcy law and overcome the continuity assumption of seepage flow. A new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem. The results show that the proposed iteration method, requiring no linearization or small perturbation, is very effective and convenient.