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On certain new exact solutions of the Einstein equations for axisymmetric rotating fields

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Chinese Physics B 2013年第10期22卷 73-78页

作者： Lakhveer kaur r.k.gupta School of Mathematics and Computer Applications Thapar University

We investigate the Einstein field equations corresponding to the Weyl-Lewis-Papapetrou form for an axisymmetric rotating field by using the classical symmetry method. Using the invafiance group properties of the governing system of partial differential equations （PDEs） and admitting a Lie group of point transformations with commuting infinitesimal generators, we obtain exact solutions to the system of PDEs describing the Einstein field equations. Some appropriate canonical variables are characterized that transform the equations at hand to an equivalent system of ordinary differential equations and some physically important analytic solutions of field equations are constructed. Also, the class of axially symmetric solutions of Einstein field equations including the Papapetrou solution as a particular case has been found.

关键词： Einstein equations symmetry analysis exact solutions

Corrosion Behavior and Hardness of Al-M (M:Mo,Si,Ti,Cr) Alloys

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Acta Metallurgica Sinica(English Letters) 2017年第4期30卷 333-341页

作者： J.Esquivel r.k.gupta Department of Chemical and Biomolecular Engineering The University of Akron Akron OH 44325-3906 USA

The corrosion behavior of Al-5 at.% Cr, A1-5 at.% Si, Al-5 at.% Mo and Al-5 at.% Ti produced via casting and Al-5 at.% Cr produced by high-energy ball milling and subsequent consolidation by cold pressing was studied using potentiodynamic polarization and surface analysis following constant immersion tests. Alloys were characterized using a scanning electron microscope coupled with the energy-dispersive X-ray spectroscopy and X-ray diffraction analysis. Hardness, a representative of the strength, was also measured. The alloys produced by casting contained coarse intermetallics and therefore exhibited poor corrosion resistance. Al-5 at.% Cr alloy produced by high-energy ball milling exhibited a significantly improved corrosion resistance and hardness, which was attributed to the grain refinement to nanoscale and extended solid solubility of Cr in AL The study indicated that the high-energy ball milling was capable of producing Al alloys with improved corrosion behavior and hardness.

关键词： Corrosion Mechanical alloying Casting Aluminum alloys

Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion–advection equation with variable coefficients

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Chinese Physics B 2014年第3期23卷 71-76页

作者： Vikas kumar r.k.gupta ram Jiwari Department of Mathematics D.A.V.College Pundari School of Mathematics and Computer Applications Thapar University

In this paper, the variable-coefficient diffusion-advection （DA） equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended （Gl/G）-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.

关键词： diffusion-advection equation Lie group analysis numerical solutions extended (G'/G)-expansion method

Painlev Analysis,Lie Symmetries and Exact Solutions for Variable Coefficients Benjamin-Bona-Mahony-Burger (BBMB) Equation

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Communications in Theoretical Physics 2013年第8期60卷 175-182页

作者： Vikas kumar r.k.gupta ram Jiwari School of Mathematics and Computer Applications Thapar UniversityPatiala147004PunjabIndia

In this paper, a variable-coefficient Benjarnin-Bona-Mahony-Burger （BBMB） equation arising as a math- ematical model of propagation of small-amplitude long waves in nonlinear dispersive media is investigated. The inte- grability of such an equation is studied with Painlevd analysis. The Lie symmetry method is performed for the BBMB equation and then similarity reductions and exact solutions are obtained based on the optimal system method. Further- more different types of solitary, periodic and kink waves can be seen with the change of variable coefficients.

关键词： BBMB equation Painleve analysis Lie symmetric analysis exact solutions

Corrosion Protective Conversion Coatings on Magnesium Disks Using a Hydrothermal Technique

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Journal of Materials Science & Technology 2014年第1期30卷 47-53页

作者： r.k.gupta k.Mensah-Darkwa D.kumar Department of Chemistry Pittsburg State University Engineering research Center for revolutionizing Metallic Biomaterials(ErC-rMB) Department of Mechanical EngineeringNorth Carolina A&T State University

A uniform, compact, and well adherent conversion coating of magnesium hydroxide has been formed on bioresorbable magnesium disks by means of a hydrothermal technique. Electrochemical results indicate that the coating brings about a significant reduction in magnesium corrosion in phosphate buffered saline （PBS） solution. It is also observed that corrosion resistance of the coating increases with an increase in treatment time, which in turn, increases the coating thickness. The protective behavior of magnesium hydroxide coating is attributed to its chemical inertness in PBS solution. The coatings are found to be free from pores that reduce the direct contact between corroding media and underlying magnesium.

关键词： Magnesium Polarization Electrochemical impedance spectroscopy (EIS) Scanning electron microscopy (SEM) Conversioncoating Corrosion

Mechanical and Corrosion Properties of Magnesiume-Hydroxyapatite (MgeHA) Composite Thin Films

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Journal of Materials Science & Technology 2013年第9期29卷 788-794页

作者： k.Mensah-Darkwa r.k.gupta D.kumar Engineering research Center of revolutionizing Metallic Biomaterials Department of Mechanical Engineering North Carolina A & T State University Department of Chemistry Pittsburg State University

Magnesium(Mg)-hydroxyapatite(Ca10(PO4)6(OH)2,abbreviated as HA) composite films have been grown on Mg plates using a pulsed laser deposition *** property measurements and analysis have indicated that hardness and Young’s modulus of nMge(100e n)HA composite coatings increase with Mg content in the coatings and reach a maximum at a 70Mge 30HA composition.n and 100e n in the nMge(100e n)HA represent the relative number of laser pulses impinging on Mg and HA targets,*** current potentiodynamic polarization studies have shown that the corrosion of Mg plate(control) decreases with an increase in the HA ratio in the composite *** example,the corrosion current density of Mg plate reduces by w350 times after coating the Mg plate with 10Mge 90HA composite *** reduction in corrosion current density of Mg plates was also accompanied by a positive shift in the corrosion potential(w6%) due to this *** mechanism behind the reduction in corrosion behavior of Mg plates due to nMge(100e n) HA composite coatings has been understood by electrochemical impedance spectroscopy.

关键词： Magnesium Hydroxyapatite Scanning electron microscopy Pulsed laser deposition Corrosion Impedance spectroscopy

Effect of Pressure and Temperature on Phase Transformation and Properties of Titanium Aluminide Obtained through reaction Synthesis

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Journal of Materials Science & Technology 2010年第8期26卷 693-704页

作者： r.k.gupta Bhanu Pant Vijaya Agarwala r.C.Agarwala P.P.Sinha Vikram Sarabhai Space Centre ISROTrivandrum-695 022India Indian Institute of Technology Roorkee

reaction synthesis process has been used to develop γ titanium aluminide using elemental powders. Powder mixture of Ti-48 at. pct AI was prepared in ball mill and reaction synthesis was carried out in hot press with varying temperature and pressure. Titanium aluminide synthesized under high pressure and temperature resulted in better properties with respect to densification, homogenization response, mechanical properties and oxidation resistance as compared to that synthesized under low pressure and temperature. AI rich phases were observed in as-synthesized condition in all the experiments. However, some Ti rich phases were also found in high pressure-temperature synthesized samples. Density, hardness and tensile strength have been correlated with applied pressure through empirical relations. Variation in density with pressure is found to be logarithmic whereas hardness and tensile strength variation with pressure is polynomial.

关键词： Titanium aluminide reaction synthesis Phase transformation

The influence of spark plasma sintering temperatures on the microstructure,hardness,and elastic modulus of the nanocrystalline Al-xV alloys produced by high-energy ball milling

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Journal of Materials Science & Technology 2022年第27期122卷 68-76页

作者： J.Christudasjustus C.S.Witharamage Ganesh Walunj T.Borkar r.k.gupta Department of Materials Science and Engineering North Carolina State UniversityRaleighNC 27606United States Department of Mechanical Engineering Cleveland State UniversityClevelandOH 44115United States

Al-xV alloys(x=2 at.%,5 at.%,10 at.%)with nanocrystalline structure and high solid solubility of V were produced in powder form by high-energy ball milling(HEBM).The alloy powders were consolidated by spark plasma sintering(SPS)employing a wide range of temperatures ranging from 200 to 400°*** microstructure and solid solubility of V in Al were investigated using X-ray diffraction analysis,scanning electron microscope and transmission electron *** microstructure was influenced by the SPS temperature and V content of the *** alloys exhibited high solid solubility of V–six orders of magnitude higher than that in equilibrium state and grain sizermation of Al3V intermetallic was detected at 400℃.Formation of a V-lean phase and bimodal grain size was observed during SPS,which increased with the increase in SPS *** hardness and elastic modulus,measured using nanoindentation,were significantly higher than commercial *** example,Al-V alloy produced by SPS at 200℃ exhibited a hardness of 5.21 GPa along with elastic modulus of 96.21 *** evolution of the microstructure and hardness with SPS temperatures has been discussed.

关键词： Spark plasma sintering Aluminum alloys Nanocrystalline alloys High-energy ball milling Nanoindentation Hardness Elastic modulus

Spark plasma sintering of a high-energy ball milled Mg-10 wt% Al alloy

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Journal of Magnesium and Alloys 2020年第2期8卷 319-328页

作者： M.U.F.khan A.Patil J.Christudasjustus T.Borkar r.k.gupta Department of Chemical Biomolecularand Corrosion EngineeringThe University of AkronAkronOH 44325United States Department of Mechanical Engineering Washkevicz College of EngineeringCleveland State UniversityClevelandOH 44115United States

The influence of spark plasma sintering(SPS)temperature on microstructure,hardness and corrosion behavior of a high-energy ball milled Mg-10wt%Al alloy was investigated in this *** holding time and sintering pressure for SPS were kept constant while varying the sintering temperature from 200 to 350℃.The grain size and microstructure were studied using X-ray diffraction analysis,scanning electron microscopy,energy dispersive X-ray spectroscopy,and Archimedes'based density *** behavior was investigated using potentiodynamic polarization *** nanocrystalline regime(grain sizer SPS up to 350℃.The density of the alloy increased with increasing the SPS ***'hardness and corrosion performance improved up to 300℃ followed by a decrease after SPS at 350℃.Possible reasons for densification,strengthening,and corrosion behavior have been discussed in the light of reduced porosity and microstructural changes.

关键词： Nanocrystalline alloy Magnesium High energy ball milling Spark plasma sintering Corrosion