Solving unsteady Korteweg–de Vries equation and its two alternatives

This paper aims to present the generalized Kudryashov method to find the exact traveling wave solutions transmutable to the solitary wave solutions of the ubiquitous unsteady Korteweg–de Vries equation and its two famed alternatives, namely, the regularized long‐wave equation and the time regularized long‐wave equation. The exact analytic solutions of the studied equations are constructed explicitly in three forms, namely, hyperbolic, trigonometric, and rational function. The validity of our solutions is verified with MAPLE by putting them back into the original equation and found correct. Moreover, it has shown that the generalized Kudryashov method is an easy and reliable technique over the existing methods. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of quantization and positron concentration on shielding potentials in electron-positron-ion plasma

The kinetic theory of plasma has been employed to compute the test-charge potential distributions accounting for quantization effects in magnetized electron-positron-ion (EPI) plasmas. In this regard, the degenerate positrons and electrons are assumed to follow the Fermi-Dirac distribution, while inertial ions are modelled by Maxwellian velocity distribution. By solving the Fourier-transformed Vlasov–Poisson equations, a modified dielectric function and electrostatic potential is obtained. By imposing various constraints on the test-charge speed, the potential profile has been analysed in terms of Debye–Hückel (DH), far-field (FF), and wake-field (WF) potentials. It has been found that the amplitude of DH and FF potentials increases by the inclusion of quantization effects, and it becomes the opposite for the WF potential profile. Furthermore, the variation of positron concentration significantly affects the DH, FF, and WF potentials. The present findings are important to understand the shielding phenomenon in degenerate multi-species plasmas.     

Alfvén waves in temperature anisotropic Cairns distributed plasma

The dispersion relations and Landau damping of Alfven waves in kinetic and inertial limits are studied in temperature anisotropic Cairns distributed plasma.In the case of kinetic Alfven waves(KAWs),it is found that the real frequency is enhanced when either the electron perpendicular temperature or the non-thermal parameter A increases.For inertial Alfven waves(IAWs),the real frequency is slightly affected by the electron temperature anisotropy and A.Besides the real frequency,the damping rate of KAWs is reduced when the electron perpendicular temperature or A increases.In the case of IAWs,the temperature anisotropy and A either enhance or reduce the damping rate depending upon the perpendicular wavelength.These results may be helpful to understand the dynamics of KAWs and IAWs in space plasmas where the non-Maxwellian distribution of particles are routinely observed.     

Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: a Galerkin approach

This article concerns the analysis of an unsteady stagnation point flow of Eyring-Powell nanofluid over a stretching sheet. The influence of thermophoresis and Brownian motion is also considered in transport equations. The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations. The numerical experiments are performed using the Galerkin scheme. A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme (RK-4) is available to show the credibility of the Galerkin method. The numerical exploration is carried out for various governing parameters, namely, Brownian motion, steadiness, thermophoresis, stretching ratio, velocity slip, concentration slip, thermal slip, and fluid parameters, and Hartmann, Prandtl and Schmidt numbers. The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing, but the behavior is reversed for assisting cases. The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases (assisting and opposing). The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter. All the outcomes and the behavior of emerging parameters are illustrated graphically. The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method. It is concluded that said method could be extended to other problems of a complex nature.     

A new fractional analytical approach via a modified Riemann–Liouville derivative

This work suggests a new analytical technique called the fractional homotopy perturbation method (FHPM) for solving fractional differential equations of any fractional order. This method is based on He’s homotopy perturbation method and the modified Riemann–Liouville derivative. The fractional differential equations are described in Jumarie’s sense. The results from introducing a modified Riemann–Liouville derivative in the cases studied show the high accuracy, simplicity and efficiency of the approach.     

Investigation of energetic ion-induced mixing in Bi/Ge system

The present study is carried out for the investigation of energetic ion beam mixing in the Bi/Ge system, induced by electronic excitation. The system Ge/Bi/C was deposited on Si substrate at room temperature in the high vacuum deposition system and irradiated using Au ions of 120?MeV at the fluences 1?×?10¹³, 5?×?10¹³ and 1?×?10¹⁴?ions/cm². The top layer of carbon was deposited as the protecting layer to avoid oxidation. The swift heavy ions (SHI)-induced interface mixing was studied by Rutherford backscattering spectroscopy (RBS) for depth profiles and compositions, grazing incidence X-ray diffraction (GIXRD) for phase identification and atomic force microscopy (AFM) for surface roughness. We have calculated the mixing rate, mixing efficiency and inter-diffusion coefficient for the Bi/Ge system. We observed that the thickness of the mixed region increased with increasing fluence. In the GIXRD pattern, no new crystalline phase formation was observed after irradiation, the mixed region may be in an amorphous form. The mixing effect is explained in the framework of the thermal spike model.     

New class of generating functions associated with generalized hypergeometric polynomials

In this paper authors prove a general theorem on generating relations for a certain sequence of functions. Many formulas involving the families of generating functions for generalized hypergeometric polynomials are shown here to be special cases of a general class of generating functions involving generalized hypergeometric polynomials and multiple hypergeometric series of several variables. It is then shown how the main result can be applied to derive a large number of generating functions involving hypergeometric functions of Kampé de Fériet, Srivastava, Srivastava-Daoust, Chaundy, Fasenmyer, Cohen, Pasternack, Khandekar, Rainville and other multiple Gaussian hypergeometric polynomials scattered in the literature of special functions.     

Intelligent reversible watermarking technique in medical images using GA and PSO

The advances in recording, editing, and broadcasting multimedia contents in digital form motivate to protect these digital contents from illegal use, such as duplication, manipulation, and redistribution. However, watermarking algorithms are designed to satisfy requirements of applications, as different applications have different concerns. We intend to design a watermarking algorithm for applications which require high embedding capacity and imperceptibility, to maintain the integrity of the host signal as well as embedded information. Reversible watermarking is a promising technique which satisfies our requirements. In this paper, we concentrate on improving the watermark capacity and reducing the perceptual degradation of an image. We investigated the Luo's [1] additive interpolation-error expansion algorithm and enhanced it by incorporating with two intelligent techniques: genetic algorithm (GA), and particle swarm optimization (PSO). Genetic algorithm is applied to exploit the correlation of image pixel values to obtain better estimation of neighboring pixel values, which results in optimal balance between information storage capacity and imperceptibility. Particle swarm optimization (intelligent technique) is also applied for the same purpose. Experimental results show that PSO and GA nearly give the same results, but GA outperforms the PSO. Experimental results also reveal that the proposed strategy outperforms the state of art works in terms of perceptual quality and watermarking payload.     

利用原位红外光谱与微分电化学质谱联用技术研究在Pt以及PtRu电极上发生的甲醇氧化反应

利用电化学衰减全反射原位傅里叶变换红外光谱与微分电化学质谱联用技术,在流动电解池环境以及恒电位条件下研究了Pt电极和Pt电极通过表面电沉积Ru形成的PtRu电极(Pt_xRu_y)上发生的甲醇氧化反应(反应电解质溶液为0.1 mol/L HClO₄+0.5 mol/L MeOH). 在0.3～0.6 V(参比电极为可逆氢参比)实验用到的所有电极上,CO是唯一能从红外光谱观察到的与甲醇相关的表面吸附物;在Pt_0.56Ru_0.44电极上可以观察到CO吸附在Ru原子形成的岛上和CO线式吸附在Pt电极表面红外波段,而其他电极上只能观察到Pt表面上线式吸附的CO;甲醇氧化活性按Pt_0.73Ru_0.27>Pt_0.56Ru_0.44>Pt_0.83Ru_0.17>Pt的顺序递减;在0.5 V 时,甲醇在Pt_0.73Ru_0.27电极上的氧化反应的CO₂电流效率达到了50%.