652 publications from this institution
At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.
In this paper, a coupling method of a homotopy technique and a perturbation technique is proposed to solve non-linear problems. In contrast to the traditional perturbation methods, the proposed method does not require a small parameter in the equation. In this method, according to the homotopy technique, a homotopy with an imbedding parameter p∈[0,1] is constructed, and the imbedding parameter is considered as a “small parameter”. So the proposed method can take full advantage of the traditional perturbation methods. Some examples are given. The results reveal that the new method is very effective and simple.
A good initial guess and an appropriate homotopy equation are two main factors in applications of the homotopy perturbation method. For a nonlinear oscillator, a cosine function is used in an initial guess. This article recommends a general approach to construction of the initial guess and the homotopy equation. Duffing oscillator is adopted as an example to elucidate the effectiveness of the method.
This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estimation. We also take advantage of the discrete stochastic arithmetic (DSA) to find the optimal iteration, optimal error and optimal approximation of the HPM. The comparative graphs between exact and approximate solutions show the accuracy and efficiency of the method.
Via the semi-inverse method, a family of various variational principles is established for thermopiezoelectricity, including a Hamilton principle and a minimum complementary energy principle.
A brief introduction to the development of electrospinning is given, and various apparatus to fabricate nanofibres or nanoporous materials are systematically reviewed with emphasis on the vibration electrospinning and melt electrospinning for enlarging electrospinability, siro-electrospinning for mimicking the spinning procedure of a spider, magneto-electrospinning for controlling the instability arising in the electrospinning process and bubble electrospinning for mass production of nanofibres. Electrospinning for producing nanoporous materials and the nano-effect for improving the properties of nanofibres are also introduced.
A same phenomenon can lead to debating laws when observed on different scales, two-scale observation is needed for a discontinuous problem, the large scale matches with the continuum assumption, while the smaller one is to reveal the discontinuous properties. The basic properties of two-scale fractal are discussed in a layman way.
A linear dynamic model is established for two-strand or Sirospun yarn processing. Approximate oscillating frequencies in the vertical and horizontal directions are obtained. By suitable choice of certain processing parameters, the mixture construction after the convergence point can be optimally matched.
The Kubelka–Munk equation is solved approximately for paint films with finite thickness, an inequality is induced in the solution process, and a minimal Kubelka–Munk absorption coefficient is obtained.
Here, various variational iteration algorithms are compared. An auxiliary parameter can be introduced in the iteration procedure, and can be identified optimally, which results in Turkyilmazoglu’s optimal variational iteration method. Some unknown auxiliary parameters can be also included in the initial solution, and can be optimally determined, that is Herişanu and Marinca’s optimal variational iteration method.
Decreasing friction force between a swimming suit and water is the key factor to design swimming suits. Water continuum mechanics forbids discontinuous fluids, but in angstrom scale water is indeed discontinuous. Swimming suit is smooth on large scale, but it is discontinuous when the scale becomes smaller. If fractal dimensions of swimming suit and water are the same, a minimum of friction force is predicted, which means fractal harmonization. In the paper, fractal harmonic law is introduced to design a swimsuit whose surface fractal dimensions on a macroscopic scale should be equal to or closed to the water's fractal dimensions on an Angstrom scale. Various possible microstructures of fabric are analyzed and a method to obtain perfect fractal structure of fabric is proposed by spraying nanofibers to its surface. The fractal harmonic law can be used to design a moving surface with a minimal friction.
We propose a novel variational approach for limit cycles of a kind of nonlinear oscillators. Some examples are given to illustrate the effectiveness and convenience of the method. The obtained results are valid for the whole solution domain with high accuracy.
In this short survey, we give a complete list of the most important results obtained by El Naschie’s E-infinity Cantorian space-time theory in the realm of quantum physics and cosmology. Special attention is paid to his recent result on dark energy and revising Einstein’s famous formula .
No abstract is provided for this article.
Variational principles for generalized Korteweg–de Vries equation and nonlinear Schrödinger’s equation are obtained by the semi-inverse method. The most interesting features of the proposed method are its extreme simplicity and concise forms of variational functionals for a wide range of nonlinear problems. Comparison with the results obtained by the Noether’s theorem is made, revealing the present theorem is a straightforward and attracting mathematical tool.
In this paper, the author proposes a new perturbation technique coupling with iteration method, yielding a powerful mathematical tool for an analytical solution of nonlinear equations. The obtained results are valid not only for weakly nonlinear problems but also for strongly nonlinear ones. Furthermore, the approximate solutions are valid for the whole solution domain, and even the first-step iteration leads to high accuracy Some examples are given to illustrate its effectiveness.
Frictional force is a vitally important factor in the application of engineering either in macroscopic contacts or in micro/nanoscale contacts. Understanding of the influencing factors about frictional force is essential for the design of miniaturized devices and the use of minimal friction force. In the paper, dimensional analysis is used to analysis factors relative to frictional force. We show that the frictional force scales with where A is the contact area and N is the normal contact force. An experiment is carried out to verify the new friction law.
ADvANcES IN cALcuLuS OF vARIATIONS publishes high quality original research focusing on that part of calculus of variation and related applications which combines tools and methods from partial differential equations with geometrical techniques.In particular the journal will include the following topics: existence and regularity for minimizers and critical points; variational methods for partial differential equations; geometrical aspects of calculus of variation: minimal surfaces, harmonic mappings, geometrically motivated flows, curvature equations, quasi-conformal mappings; applications of variational methods to non-linear elasticity, free boundary problems, general relativity; geometric measure theory.
No abstract is provided for this article.
Is the world really more than four dimensional or for instance an eleven dimensional M-theory as proposed by Witten? The present Letter suggests that it is an eleven dimensional fractal. Based on this assumption it is shown that the probability of quantum entanglement is exactly equal to that predicted by L. Hardy’s well known criteria. It is further argued that this is an indirect but strong indication for the reality of the Cantorian fractal nature of micro spacetime.
