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An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

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Journal of Ocean Engineering and Science 2021年第1期6卷 30-39页

作者： Ved Prakash Dubey rajnesh kumar Jagdev Singh Devendra kumar Faculty of Mathematical and Statistical Sciences Shri Ramswaroop Memorial UniversityLucknow-Deva RoadUttar Pradesh-225003India Department of Applied Science and Humanities Government Engineering CollegeNawadaDepartment of Science and TechnologyBihar-805122India Department of Mathematics JECRC UniversityJaipur-303905RajasthanIndia Department of Mathematics University of RajasthanJaipur-302004RajasthanIndia

In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.

关键词： Fractional Degasperis-Procesi equation Nonlinear dispersive waves Analytical solution q-homotopy analysis method Sumudu transform

Approximate analytical solution of fractional order biochemical reaction model and its stability analysis

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International Journal of Biomathematics 2019年第5期12卷 241-261页

作者： Ved Prakash Dubey rajnesh kumar Devendra kumar Faculty of Mathematical and Statistical Sciences Shri Ramswaroop Memorial University Lucknow-Deva Road Uttar Pradesh-225003India Department of Mathematics University of Rajasthan Jaipur-302004RajasthanIndia

Approximate analytical solution of the system of coupled nonlinear Ordinary Differential Equations (ODEs) of a biochemical reaction model is much relevant due to its practical significance to biochemists.In this paper,an effective and powerful mathematical technique,viz.fractional homotopy analysis transform method (FHATM),is employed to get the numerical solutions of biochemical reaction model with time fractional derivatives.The adopted scheme is the beautiful copulation of homotopy analysis technique and Laplace transform algorithm.This paper shows that the adopted scheme is quite easy as well as computationally attractive in the context of a solution procedure.The Caputo-type fractional derivatives are considered in the present paper.Approximate results of the probability density functions of the time fractional biochemical reaction model are computed for miscellaneous fractional Brownian motions as well as for classical motion and are presented graphically.The time fractional biochemical reaction model with respect to stability analysis for various values of fractional order q is also analyzed.In the context of stability discussion,we have used the fractional Routh-Hurwitz stability criterion to establish the local stability of the biochemical reaction model of fractional order.

关键词： Biochemical reaction model FHATM Laplace transform homotopy stability analysis fractional order

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油水分离用疏水棉布的制备与表征

合成技术及应用 2019年第3期34卷 6-9页

作者：张幼维 rajnesh kumar 刘宁宇赵炯心东华大学材料科学与工程学院

采用分步乳液聚合法,合成了聚甲基丙烯酸甲酯/聚甲基丙烯酸纳米水凝胶。将其化学键接到棉布表面,制备了疏水棉布。利用动态光散射、透射电镜、扫描电镜、红外等对纳米水凝胶的尺寸和形貌,改性棉布的形貌、化学组成、疏水性等进行了表征... 详细信息

采用分步乳液聚合法,合成了聚甲基丙烯酸甲酯/聚甲基丙烯酸纳米水凝胶。将其化学键接到棉布表面,制备了疏水棉布。利用动态光散射、透射电镜、扫描电镜、红外等对纳米水凝胶的尺寸和形貌,改性棉布的形貌、化学组成、疏水性等进行了表征。结果表明,改性棉布具有良好的疏水性,可选择性吸附水下的油滴和水上的油层,并可实现油水混合物的高效分离。

关键词：聚甲基丙烯酸纳米水凝胶疏水棉布油水分离

Friction and wear behavior of Cu-4 wt.％Ni-TiC composites under dry sliding conditions

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Friction 2017年第4期5卷 437-446页

作者： Pushkar JHA Rakesh kumar GAUTAM rajnesh TYAGI Department of Mechanical Engineering Indian Institute of Technology(Banaras Hindu University)Varanasi 221005India

The present study synthesized Cu–4 wt% Ni matrix composites reinforced with different percentages of TiC (0, 2, 4, 6, and 8 wt%) through high-energy ball milling, followed by compaction and sintering. The friction and wear behavior was examined at four different normal loads of 5, 10, 15, and 20 N. A constant sliding speed of 1.25 m/s was maintained while sliding against a hardened counterface made of EN31 steel (HRC 60) under ambient conditions using a pin-on-disk test rig. The composite hardness increased until the addition of 4 wt% of TiC, beyond which it was observed to decrease. Such a trend may be attributed to the TiC agglomeration in the composites containing relatively larger amounts of TiC (i.e., 6 and 8 wt%). The wear rate linearly increased with the load. However, the composites exhibited a lower rate of wear than the matrix alloy, which may have resulted from the relatively higher hardness of composites. The observed friction and wear behavior has been explained on the basis of hardness and presence of the transfer layer on the worn surface and its nature, i.e., loose or well compacted. Addition of 4 wt% TiC showed the optimum performance in terms of friction and wear caused by its higher hardness and ability to hold a transfer layer of a relatively larger thickness compared to the other materials. The wear mechanism for the Cu4Ni matrix alloy was a mix of adhesive and oxidative wear and primarily abrasive for the composites containing hard TiC particles.

关键词： sliding wear composites TiC particles friction