652 publications from this institution
Article Modified Lindsted-Poincare Methods For Some Strongly Nonlinear Oscillations Part III : Double Series Expansion was published on December 1, 2001 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 2, issue 4).
The homotopy perturbation method is extremely accessible to non-mathematicians and engineers. The method decomposes a complex problem under study into 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 paid to constructing a suitable homotopy equation.
No abstract is provided for this article.
Nanoporous structures are potentially of great technological interest for the development of electronic, catalytic and hydrogen-storage systems, invisibility device (e.g. stealth plane) and others. Here we describe a general strategy for the synthesis of micro sphere with nanoporosity by electrospinning, the porous sizes having uniform but tunable diameters can be controlled by voltage applied in the electrospinning process.
By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.
A solitary wavenumber-frequency formulation is suggested using an ancient Chinese arithmetic. The nonlinear Schrödinger equation is used as an example to show the effectiveness of the formulation.
No abstract is provided for this article.
When Cavalieri found his theory in 1635, Chinese mathematicians had used the theory for more than one millennium.
Mathematics serves as the fundamental basis for innovation, propelling technological advancement. In the forthcoming decade, the convergence of differential equations and control processes is poised to redefine the frontiers of scientific exploration. The integration of artificial intelligence and machine learning with differential equations is set to inaugurate a new era of problem-solving, enabling the extraction of latent physical insights and accelerating solution discovery. Multi-scale modeling, with its capacity to span disparate physical domains, has the potential to resolve long-standing puzzles in fields such as fluid mechanics and nanoscience. Furthermore, the integration of fractal geometry with differential equations holds the promise of novel perspectives for understanding and optimizing complex systems, ranging from urban landscapes to turbulent flows. The integration of artificial intelligence (AI) with control innovations is poised to play a pivotal role in the development of next-generation technologies, with the potential to transform diverse sectors such as medicine, communication, and autonomous systems. This paper explores these developments, highlighting their potential impacts and emphasizing the necessity for interdisciplinary collaboration to leverage their full potential.
Traditional preparation of ZnO nanocrystal requires heating zinc acetate to a temperature over 350 °C, whereas in this work, zinc acetate was first electrospun with PVDF to form a nanofiber, followed by thermal treatment at only 140 °C to give nanocrystalline ZnO. The much lower temperature required in thermal treatment is attributed to the high reactivity of zinc acetate at nano dimension. The as-prepared ZnO-doped PVDF nanofiber mat shows excellent effect in the photocatalytic degradation of Rhodamine B, comparable to ZnO particle thermally treated at 600 °C. Highly-oriented ZnO nanorods were obtained by further hydrothermal synthesis of the electrospun nanofiber mat, giving nanostructured ZnO of different morphologies well-aligned on the surface of organic nanofiber. Notably, the hydrothermal synthesis of the successful preparation of these nanostructured ZnO requires a processing temperature below 100 °C at atmospheric pressure, showing great potential to be scaled up for vast manufacturing.
The identification of the Lagrange multiplier plays an import rule in the variational iteration method, and the variational theory is widely used for this purpose. This paper suggests an easier approach by the Laplace transform to determining the multiplier, making the method accessible to researchers facing various nonlinear problems. A nonlinear oscillator is adopted as an example to elucidate the identification process and the solution process, only one iteration leads to an ideal result.
Lagrange multipliers are a commonly employed method for the elimination of constraints in both variational theory and optimal control. However, it should be noted that the validity of this approach may be compromised when the identified multiplier is equal to zero. The paper elucidates the phenomenon of a zero multiplier and its hidden mechanism, and it proffers two methodologies for surmounting the associated challenges.
The morphology of a shallow-water wave is affected by the unsmooth boundary, while its peak is rarely changed. This phenomenon cannot be explained by a differential model. This paper adopts a fractal modification of the Boussinesq equation, and its traveling solitary solution is studied through its fractal variational principle, the results reveal the basic properties of solitary waves in fractal space.
The homotopy perturbation method proposed by the present author is further improved in this paper, which is proved to be effective and convenient to solving nonlinear equations.
Purpose – Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus. Design/methodology/approach – This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional differential equations, e.g. the variational iteration method, the homotopy perturbation method and the fractional complex transform, are outlined and the main solution processes are given. Findings – Heat conduction in silk cocoon and ground water flow are modeled by the local fractional calculus, the solutions can explain well experimental observations. Originality/value – Particular attention is paid throughout the paper to giving an intuitive grasp for fractional calculus. Most cited references are within last five years, catching the most frontier of the research. Some ideas on this review paper are first appeared.
Polyvinyl alcohol (PVA) with a degree of 1750±50 was successfully fabricated into nanofibers via the traditional electrospinning process. Daughter charged jets and combined fibers were observed. A combined fiber might be simple combination of two separate fibers without mass transfer, or it is a daughter cascade caused in hierarchical motion of a charged jet with mass/energy transfer. Minimal fiber reaches as small as 5nm (50 angstroms) in diameter, this might be the smallest artificial fiber, which might have excellent properties due to nanoeffect.
