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COSET DIAGRAMS FOR A HOMOMORPHIC IMAGE OFΔ(3,3,k)

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Acta Mathematica Scientia 2008年第2期28卷 363-370页

作者： M.Ashiq q.Mushtaq Department of Basic Sciences and Humanities College of E and ME National University of Sciences and Technology RawalpindiPakistan Department of Mathematics quaid-i-Azam University IslamabadPakistan

Let q be a prime power. By PL（Fq） the authors mean a projective line over the finite field Fq with the additional point ∞. In this article, the authors parametrize the conjugacy classes of nondegenerate homomorphisms which represent actions of △（3, 3, k） = （u, v： u^3 = v^3 = （uv）^k = 1〉on PL（Fq）, where q ≡ ±1（modk）. Also, for various values of k, they find the conditions for the existence of coset diagrams depicting the permutation actions of △（3, 3, k） on PL（Fq）. The conditions are polynomials with integer coefficients and the diagrams are such that every vertex in them is fixed by （u^-v^-）^k. In this way, they get △（3, 3, k） as permutation groups on PL（Fq）.

关键词： Coset diagrams conjugacy classes nondegenerate homomorphism projec tire line and triangle groups

Reduction effect of final-pass heavy reduction rolling on the texture development,tensile property and stretch formability of ZWK100 alloy plates

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Journal of Materials Science & Technology 2022年第16期111卷 211-223页

作者： B.q.Shi L.Y.Zhao X.L.Shang B.H.Nie D.C.Chen C.q.Li Y.q.Cheng School of Materials Science and Hydrogen Energy Foshan UniversityFoshan 528000China School of Materials and Energy Guangdong University of TechnologyGuangzhouGuangdong 510006China GD Midea Air-Conditioning Equipment Co. Ltd.Foshan 528311China Guangdong Key Laboratory of Hydrogen Energy Technology Foshan 528000China YunFu(Foshan)R&D Center of Hydrogen Energy Standardization Yunfu 527326China

Obviously planar anisotropy due to‘TD split’orthotropic texture(TD indicates Transverse direction)always exist in the Rare-earth(RE)or Ca containing Mg alloy sheets,which is likely caused by the lowreduction rolling(and annealing)as revealed in our previous *** this work,the as-cast billets of a ZWK100 alloy were subjected to final-pass heavy reduction rolling(FHRR)at 500°C with different reductions(30%-70%)after rough rolling,aiming to investigate the reduction effect on the microstructure and texture *** results show that FHRR with higher reductions above 50%is in favor of shear banding formation but has little effect on the as-deformed texture components,and the excellent formability with single-pass reduction up to 70%is mainly ascribed to the activation of prismatic *** with reduction above 50%and annealing can generate uniform grain structures of~10μm and symmetrical‘oblique-line split’texture in(0001)pole figures,with basal poles tilting by about 50°from ND(Normal direction)towards some oblique-line of TD and RD(Rolling direction)as well as uniform distribution of counter lines as an annular shape,resulting in excellent elongation to failure of~50%and ultra-low planar anisotropyΔr_of~0.1 and high stretch formability(Erichsen value:8.1).The formation‘oblique-line split’texture in(0001)pole figures is mainly correlated with the preferred growth tendency of grains with■//RD,which was suggested to relate to the high mobility of some special boundaries such as 40°-45°■.The influences of starting textures on the mechanical properties,planar anisotropy and related deformation modes,as well as their correlations with the stretch formability were comparatively investigated with the‘TD split’orthotropic texture as a counterpoint.

关键词： Magnesium alloys Texture Plane anisotropy Stretch formability Rolled sheets

Calculation of Point Defects in NiAl Alloy

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Journal of Materials Science & Technology 1997年第4期13卷 280-283页

作者： Wang, BY Wang, YX Gu, q Wang, TM LANZHOU UNIV DEPT MAT SCILANZHOU 730000PEOPLES R CHINA

The potential functions of the F-S model for ordered high-temperature intermetallic compound NiAl with a B-2 structure are constructed. Using the potential, the point defects properties were studied by molecular dynamics method, the results are in good agreement with that by EAM method and the experiment values. Meanwhile, the results clarify the experiments of two recovery stages in quenched NiAl alloy, and indicate that the two stages are corresponding to the recovery of Ni vacancies and of Al vacancies.

关键词： Nickel alloys

Multi-scale simulation of columnar-to-equiaxed transition during laser selective melting of rare earth magnesium alloy

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Journal of Materials Science & Technology 2022年第24期119卷 11-24页

作者： W.L.Wang W.q.Liu X.Yang R.R.Xu q.Y.Dai School of Metallurgical Engineering Xi’an University of Architecture and TechnologyXi’an 710055China

A model of coupling macro finite volume method(FVM) and cellular automata(CA) is proposed in this paper to explore the columnar-to-equiaxed transition(CET) during selective laser melting(SLM) of rare earth magnesium *** into account the impact of recoil pressure and Marangoni convection on the molten pool temperature field,the grain structure is *** suggested by the simulation results,with the undissolved Zr serving as heterogeneous nucleation sites,the liquid undercooled layer under the combined action of forced cooling,the temperature gradient and the liquid solute concentration gradient leads to *** considering the dissolution of Zr in magnesium matrix,the results demonstrate that the dissolution of element Zr is effective in significantly inhibiting the growth of columnar crystals and ensuring the sufficient constitutional supercooling(CS) required for *** addition,to raise the preheating temperature contributes to enhancing the outcome of nucleation and incresing the grain *** the interdependence model(IM),with the cooling rate gradually increasing in the SLM process of magnesium alloy,the nucleation-free zone(NFZ) reduces by decreasing the solute diffusion layer in the front of the solid/liquid(SL) interface and the temperature *** reduction in temperature gradient can promote undercooling for nucleation and facilitate the development of equiaxed *** simulation results are qualitatively verified as highly consistent through experimentation.

关键词： Multi-scale simulation Columnar-to-equiaxed transition Selective laser melting Rare earth magnesium alloy Constitutional supercooling

Deformation behavior of laser bending of circular sheet metal

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Chinese Optics Letters 2011年第5期9卷 47-51页

作者： q.Nadeem S.J.Na Department of Mechanical Engineering KAIST

The application of a thermal source in non-contact forming of sheet metal has long been used. However, the replacement of this thermal source with a laser beam promises much greater controllability of the process. This yields a process with strong potential for application in aerospace, shipbuilding, automobile, and manufacturing industries, as well as the rapid manufacturing of prototypes and adjustment of misaligned components. Forming is made possible through laser-induced non-uniform thermal stresses. In this letter, we use the geometrical transition from rectangular to circle-shaped specimen and ring-shaped specimen to observe the effect of geometry on deformation in laser forming. We conduct a series of experiments on a wide range of specimen geometries. The reasons for this behavior are also analyzed. Experimental results are compared with simulated values using the software ABAqUS. The utilization of line energy is found to be higher in the case of laser forming along linear irradiation than along curved ones. We also analyze the effect of strain hindrance. The findings of the study may be useful for the inverse problem, which involves acquiring the process parameters for a known target shape of a wide range of complex shape geometries.

关键词： Deformation behavior of laser bending of circular sheet metal

Multi-soliton solutions of a two-component Camassa–Holm system:Darboux transformation approach

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Communications in Theoretical Physics 2020年第4期72卷 23-28页

作者： Gaihua Wang Nianhua Li q P Liu Department of Mathematics China University of Mining and TechnologyBeiing100083China School of Mathematical Sciences Huaqiao UniversityQuanzhouFujian 362021China

We propose and develop another approach to constructing multi-soliton solutions of an integrable two-component Camassa–Holm(CH2)*** the help of a reciprocal transformation and a gauge transformation,we relate the CH2 system to a negative flow of the Broer–Kaup or twoboson *** solutions of this negative flow are given in terms of Wronskians via Darboux *** the multi-soliton solutions of the CH2 system are recovered in parametric form by inverting the reciprocal transformation and the gauge transformation.

关键词： Darboux transformation reciprocal transformation two-component Camassa–Holm system multi-soliton solutions

Fluid flow driven along microchannel by its upper stretching wall with electrokinetic effects

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Applied Mathematics and Mechanics(English Edition) 2018年第3期39卷 395-408页

作者： Hang XU I.POP q.SUN Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration State Key Lab of Ocean EngineeringSchool of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong University Department of Mathematics Babe§-Bolyai University Particulate Fluids Processing Centre Department of Chemical EngineeringThe University of Melbourne

We develop a mathematical model to describe the flow in a microchannel driven by the upper stretching wall of the channel in the presence of electrokinetic effects. In this model, we avoid imposing any unphysical boundary condition, for instance, the zero electrostatic potential in the middle of the channel. Using the similarity transformation, we employ the homotopy analysis method （HAM） to get the analytical solution of the model. In our approach, the unknown pressure constant and the integral constant related to the electric potential are solved spontaneously by using the proper boundary conditions on the channel walls, which makes our model consistent with the commonly accepted models in the field of fluid mechanics. It is expected that our model can offer a general and proper way to study the flow phenomena in microchannels.

关键词： microchannel electrokinetic effect stretching wall electro-viscous flowmodel

Stability and local bifurcation of parameter-excited vibration of pipes conveying pulsating fluid under thermal loading

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Applied Mathematics and Mechanics(English Edition) 2015年第8期36卷 1017-1032页

作者： Demin ZHAO Jianlin LIU C.q.WU Department of Mechanics College of Pipeline and Civil Engineering China University of Petroleum Department of Mechanical and Manufacturing Engineering University of Manitoba

The parametric excited vibration of a pipe under thermal loading may occur because the fluid is often transported heatedly. The effects of thermal loading on the pipe stability and local bifurcations have rarely been studied. The stability and the local bifurcations of the lateral parametric resonance of the pipe induced by the pulsating fluid velocity and the thermal loading are studied. A mathematical model for a simply supported pipe is developed according to the Hamilton principle. Two partial differential equations describing the lateral and longitudinal vibration are obtained. The singularity theory is utilized to anMyze the stability and the bifurcation of the system solutions. The transition sets and the bifurcation diagrams are obtained both in the unfolding parameter space and the physical parameter space, which can reveal the relationship between the thermal field parameter and the dynamic behaviors of the pipe. The frequency response and the relationship between the critical thermal rate and the pulsating fluid velocity are obtained. The numerical results demonstrate the accuracy of the single-mode expansion of the solution and the stability and local bifurcation analyses. It also confirms the existence of the chaos. The presented work can provide valuable information for the design of the pipeline and the controllers to prevent the structural instability.

关键词： thermal load parameter excited local bifurcation,unfolding parameterspace physical parameter space

Crack Initiation Mechanism of Z3CN20.09M Duplex Stainless Steel during Corrosion Fatigue in Water and Air at 290 °C

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Journal of Materials Science & Technology 2015年第11期31卷 1144-1150页

作者： H.C.Wu B.Yang Y.Z.Shi q.Gao Y.q.Wang State Key Laboratory for Advanced Metals and Materials University of Science and Technology Beijing Collaborative Innovation Center of Universal Iron & Steel Technology School of Materials Science and Engineering Anhui University of Technology

The crack initiation mechanism of a Z3CN20.09M duplex stainless steel （DSS） during corrosion fatigue （CF） in water and air at 290 ℃ was investigated by using a CF cracking machine and a scanning electron microscopy （SEM）. The cracks were initiated successively at the persistent stip bands （PSBs）, phase boundaries （PBs） and pitting corrosion points （PCPs） of the specimens when they were tested in water at 290 ℃, while in airat 290 ℃ the cracks were only initiated at the PSBs and PBs. And the cracks were found mainly to initiate at the PSBs and PBs when the specimens were tested in water and air at 290 ℃, respectively. The results also reveal that the cracks were likely to be initiated at the first 20% of fatigue life of the specimens tested in water at 290 ℃. However, the cracks were not found until 50% of fatigue life when tested in air at 290 ℃. Moreover, the crack numbers of the specimens tested in water at 290 ℃ were much more than those tested in air at 290 ℃.

关键词： Duplex stainless steel Corrosion fatigue Crack initiation High temperature water