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Liu H.-Y.,Zhongyuan University of Technology | He J.-H.,Soochow University of China | Li Z.-B.,Qujing Normal University
International Journal of Numerical Methods for Heat and Fluid Flow | Year: 2014

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. © Emerald Group Publishing Limited.

Mu G.,Qujing Normal University | Qin Z.,Fudan University
Nonlinear Analysis: Real World Applications | Year: 2014

By means of the Hirota bilinear method, explicit representations of general rogue waves for the Mel'nikov equation are explored in terms of determinants. As applications, it is found that this system admits bright- and dark-types rogue waves localized in two dimensional space. Furthermore, the superposition of such bright rogue waves are investigated graphically by different choices of the free parameters.© 2014 Elsevier Ltd. All rights reserved.

Mu G.,Qujing Normal University | Qin Z.,Fudan University | Qin Z.,University of Michigan
Journal of the Physical Society of Japan | Year: 2012

In this work, firstly it is shown that the coupled Schrödinger- Boussinesq equation, which governs the nonlinear propagation of coupled Langmuir and dust-acoustec wave in a multicomponent dusty plasma, possesses rogue waves in the form of the rational solutions. Here a hierarchy of rational solutions, the Peregrine breather and the second-order rational solution are given by means of the Hirota technique. Also, it is worth noting that the electric field exhibits bright rogue wave feature while electrostatic potential plays a role of dark rogue wave. Meanwhile, in comparison with rogue wave of nonlinear Schrödinger equation, some novel features of rogue waves are presented in their second order rational solutions. Secondly, rational solution of the coupled Higgs equation is taken into account by utilizing Hirota technique and the existence condition of rogue wave for this system is discussed. © 2012 The Physical Society of Japan.

Qin Z.,Fudan University | Qin Z.,University of Michigan | Mu G.,Qujing Normal University
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012

We report new types of matter rogue waves of a spinor (three-component) model of the Bose-Einstein condensate governed by a system of three nonlinearly coupled Gross-Pitaevskii equations. The exact first-order rational solutions containing one free parameter are obtained by means of a Darboux transformation for the integrable system where the mean-field interaction is attractive and the spin-exchange interaction is ferromagnetic. For different choices of the parameter, there exists a variety of different shaped solutions including two peaks in bright rogue waves and four dips in dark rogue waves. Furthermore, by utilizing the relation between the three-component and the one-component versions of the nonlinear Schrödinger equation, we can devise higher-order rational solutions, in which three components have different shapes. In addition, it is noteworthy that dark rogue wave features disappear in the third-order rational solution. © 2012 American Physical Society.

He J.-H.,Soochow University of China | Li Z.-B.,Qujing Normal University
Thermal Science | Year: 2012

A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.

Li Z.-B.,Qujing Normal University | He J.-H.,Soochow University of China
Mathematical and Computational Applications | Year: 2010

Fractional complex transform is proposed to convert fractional differential equations into ordinary differential equations, so that all analytical methods devoted to advanced calculus can be easily applied to fractional calculus. Two examples are given. © Association for Scientific Research.

Chen Y.,Qujing Normal University
Journal of Physical Chemistry A | Year: 2013

The interactions between halogen-substituted s-trazine (C3H 2N3X) and halide anions (Y-) have been investigated at the MP2/aug-cc-pVDZ (aug-cc-pVDZ-PP) level. C3H 2N3X can interact with halide anions to form five types of complexes (C3H2N3X·Y-): a strong σ-type interaction complex, a weak σ-type interaction complex, an anion-π interaction complex, a hydrogen-bonding complex, and a halogen-bonding complex. The binding energies, structures, and bonding characteristics of these complexes have been discussed. The local details of potential energy surfaces around the binding sites for some selected complexes have been depicted. The results indicate that the binding behavior of F - is quite different from that of Cl-, Br-, and I-. The potential energy surface is separated into two parts, the HB-σ-π region and the XB region, by a relatively high energy barrier for complexes C3H2N3Cl·Cl-, C3H2N3Br·Cl-, and C 3H2N3I·Cl-. The HB-σ-π region is characterized by the flat potential energy surface, indicating that the binding strength is retained when the anion is held over the HB-σ-π region. The XB region is characterized by the steeper potential energy surface, indicating that the binding strength is more sensitive to the anion position in this region. The binding strength of the HB-σ-π region is stronger than that of the XB region for C3H 2N3Cl·Cl- and C3H 2N3Br·Cl-, whereas the binding strength of the XB region is stronger than that of the HB-σ-π region for C 3H2N3I·Cl-. © 2013 American Chemical Society.

A total of 10 skulls of Tibetan gazelle were utilized in this study. Craniometric measurements for 22 different parts of the skull were made. Skull indices and ratios were calculated. A skull index of 43.22±0.44, a cranial index of 58.37±0.80 and a facial index of 116.37±1.24 were obtained.

El-Nabulsi R.A.,Qujing Normal University
Computers and Mathematics with Applications | Year: 2011

The fractional Boltzmann transport equation is derived making use of the fractional Hamilton's equations based on the fractional actionlike variational approach. By simply defining a distribution function and inspecting its time derivative, many important results in statistical physics can be derived. © 2011 Elsevier Ltd. All rights reserved.

Li Z.-B.,Qujing Normal University
International Journal of Nonlinear Sciences and Numerical Simulation | Year: 2010

An extended fractional complex transform is proposed to convert some kinds of fractional differential equations with the modified Riemann-Liouville derivatives into ordinary differential equations. © Freund Publishing House Ltd.

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