326 resultados para fractional evolution equation


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In this paper, we investigate the initiation and subsequent evolution of Crow instability in an inhomogeneous unitary Fermi gas using zero-temperature Galilei-invariant nonlinear Schrodinger equation. Considering a cigar-shaped unitary Fermi gas, we generate the vortex-antivortex pair either by phase-imprinting or by moving a Gaussian obstacle potential. We observe that the Crow instability in a unitary Fermi gas leads to the decay of the vortex-antivortex pair into multiple vortex rings and ultimately into sound waves.

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In the current study, the evolution of microstructure and texture has been studied for Ti-6Al-4V-0.1B alloy during sub-transus thermomechanical processing. This part of the work deals with the deformation response of the alloy by rolling in the (alpha + beta) phase field. The (alpha + beta) annealing behavior of the rolled specimen is communicated in part II. Rolled microstructures of the alloys exhibit either kinked or straight alpha colonies depending on their orientations with respect to the principal rolling directions. The Ti-6Al-4V-0.1B alloy shows an improved rolling response compared with the alloy Ti-6Al-4V because of smaller alpha lamellae size, coherency of alpha/beta interfaces, and multiple slip due to orientation factors. Accelerated dynamic globularization for this alloy is similarly caused by the intralamellar transverse boundary formation via multiple slip and strain accumulation at TiB particles. The (0002)(alpha) pole figures of rolled Ti-6Al-4V alloy shows ``TD splitting'' at lower rolling temperatures because of strong initial texture. Substantial beta phase mitigates the effect of starting texture at higher temperature so that ``RD splitting'' characterizes the basal pole figure. Weak starting texture and easy slip transfer for Ti-6Al-4V-0.1B alloy produce simultaneous TD and RD splittings in basal pole figures at all rolling temperatures.

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The first part of this study describes the evolution of microstructure and texture in Ti-6Al-4V-0.1B alloy during sub-transus rolling vis-A -vis the control alloy Ti-6Al-4V. In the second part, the static annealing response of the two alloys at self-same conditions is compared and the principal micromechanisms are analyzed. Faster globularization kinetics has been observed in the Ti-6Al-4V-0.1B alloy for equivalent annealing conditions. This is primarily attributed to the alpha colonies, which leads to easy boundary splitting via multiple slip activation in this alloy. The other mechanisms facilitating lamellar to equiaxed morphological transformations, e.g., termination migration and cylinderization, also start early in the boron-modified alloy due to small alpha colony size, small aspect ratio of the alpha lamellae, and the presence of TiB particles in the microstructure. Both the alloys exhibit weakening of basal fiber (ND||aOE (c) 0001 >) and strengthening of prism fiber (RD||aOE (c) aOE(a)) upon annealing. A close proximity between the orientations of fully globularized primary alpha and secondary alpha phases during alpha -> beta -> alpha transformation has accounted for such a texture modification.

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A Cu-Cu multilayer processed by accumulative roll bonding was deformed to large strains and further annealed. The texture of the deformed Cu-Cu multilayer differs from the conventional fcc rolling textures in terms of higher fractions of Bs and RD-rotated cube components, compared with the volume fraction of Cu component. The elongated grain shape significantly affects the deformation characteristics. Characteristic microstructural features of both continuous dynamic recrystallization and discontinuous dynamic recrystallization were observed in the microtexture measurements. X-ray texture measurements of annealing of heavily deformed multilayer demonstrate constrained recrystallization and resulted in a bimodal grain size distribution in the annealed material at higher strains. The presence of cube- and BR-oriented grains in the deformed material confirms the oriented nucleation as the major influence on texture change during recrystallization. Persistence of cube component throughout the deformation is attributed to dynamic recrystallization. Evolution of RD-rotated cube is attributed to the deformation of cube components that evolve from dynamic recrystallization. The relaxation of strain components leads to Bs at larger strains. Further, the Bs component is found to recover rather than recrystallize during deformation. The presence of predominantly Cu and Bs orientations surrounding the interface layer suggests constrained annealing behavior.

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Friction stir processing was carried out on the Al-Mg-Mn alloy to achieve ultrafine grained microstructure. The evolution of microstructure and micro-texture was studied in different regions of the deformed sample, namely nugget zone, thermo-mechanically affected zone (TMAZ) and base metal. The average grain sizes of the nugget zone, TMAZ and base metal are 1.5 mu m +/- 0.5 mu m, 15 mu m +/- 8 mu m, and 80 mu m +/- 10 mu m, respectively. The TMAZ exhibits excessive deformation banding structure and sub-grain formation. The orientation gradient within the sub-grain is dependent on grain size, orientation, and distance from nugget zone. The microstructure was partitioned based on the grain orientation spread and grain size values to separate the recrystallized fraction from the deformed region in order to understand the micromechanism of grain refinement. The texture of both deformed and recrystallized regions are similar in nature. Microstructure and texture analysis suggest that the restoration processes are different in different regions of the processed sample. The transition region between nugget zone and TMAZ exhibits large elongated grains surrounded by fine equiaxed grains of different orientation which indicate the process of discontinuous dynamic recrystallization. Within the nugget zone, similar texture between deformed and recrystallized grain fraction suggests that the restoration mechanism is a continuous process.

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Hot deformation of pearlitic steel was carried out to examine the overall deformation response to microstructural evolution. To understand the mechanisms operative during hot deformation, compression tests were carried out at various temperatures in the range 400(-)600 degrees C and strain rates in the range 0.001-10 s(-1). The flow curves were analyzed to examine the occurrence of dynamic recrystallization. The evolution of microstructure in hot deformed samples is analysed using EBSD.

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In this work, the effect of hybridizing micro-Ti with nano-SiC particulates on the microstructural and the mechanical behaviour of Mg-5.6Ti composite were investigated. Mg materials containing micron-sized Ti particulates hybridized with different amounts of nano-size SiC particulates were synthesized using the disintegrated melt deposition method followed by hot extrusion. The microstructural and mechanical behaviour of the developed Mg hybrid composites were studied in comparison with Mg-5.6Ti. Microstructural characterization revealed grain refinement attributed to the presence of uniformly distributed micro-Ti particles embedded with nano-SiC particulates. Electron back scattered diffraction (EBSD) analyses of Mg-(5.6Ti + 1.0SiC)(BM) hybrid composite showed relatively more localized recrystallized grains and lesser tensile twin fraction, when compared to Mg-5.6Ti. The evaluation of mechanical properties indicated that the best combination of strength and ductility was observed in the Mg-(5.6Ti + 1.0SiC)(BM) hybrid composites. The superior strength properties of the Mg-(5.6Ti + x-SiC)(BM) hybrid composites when compared to Mg-5.6Ti is attributed to the presence of nano-reinforcements, the uniform distribution of the hybridized particles and the better interfacial bonding between the matrix and the reinforcement particles, achieved by nano-SiC addition.

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We extend our analysis of transverse single spin asymmetry in electroproduction of J/psi to include the effect of the scale evolution of the transverse momentum dependent (TMD) parton distribution functions and gluon Sivers function. We estimate single spin asymmetry for JLab, HERMES, COMPASS, and eRHIC energies using the color evaporation model of charmonium production, using an analytically obtained approximate solution of TMD evolution equations discussed in the literature. We find that there is a reduction in the asymmetry compared with our predictions for the earlier case considered by us, wherein the Q(2) dependence came only from DGLAP evolution of the unpolarized gluon densities and a different parametrization of the TMD Sivers function was used.

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A systematic study of the evolution of the microstructure and crystallographic texture during free end torsion of a single phase magnesium alloy Mg-3Al-0.3Mn (AM30) was carried out. The torsion tests were done at a temperature of 250 degrees C to different strain levels in order to examine the progressive evolution of the microstructure and texture. A detailed microstructural analysis was performed using the electron back-scattered diffraction technique. The observed microstructural features indicated the occurrence of continuous dynamic recovery and recrystallization, starting with the formation of subgrains and ending with recrystallized grains with high angle boundaries. Texture and microstructure evolution were analysed by decoupling the effects of imposed shear and of dynamic recrystallization. Microstructure was partitioned to separate the deformed grains from the recovered/recrystallized grains. The texture of the deformed part could be reproduced by viscoplastic self-consistent polycrystal simulations. Recovered/recrystallized grains were formed as a result of rotation of these grains so as to reach a low plastic energy state. (C) 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

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This paper deals with the evolution of microstructure and texture during hot rolling of hafnium containing NiTi based shape memory alloy Ni49.4Ti38.6Hf12. The formation of the R-phase has been associated with the precipitation of (Ti,Hf)(2)Ni phase. The crystallographic texture of the parent phase B2 as well as the product phases R and B19' have been determined. It has been found that the variant selection during the B2 -> R phase transformation is quite strong compared to the case of the B2 -> B19' transformation. During deformation, the texture of the austenite phase evolves with strong Goss and Bs components. After transformation to martensitic structure, it gives rise to a 011]parallel to RD fiber. Microstructure and texture studies reveal the occurrence of partial dynamic recrystallization during hot rolling. Large strain heterogeneities that occur surrounding (Ti,Hf)(2)Ni precipitates are relieved through extended dynamic recovery instead of particle stimulated nucleation.

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In this study, we present a new computational approach for studying the effect of melt convection on solidification at the micro-scale level. Models for dendritic and eutectic growth are developed on the basis of the enthalpy technique and incorporate the presence of flow in the domain. Simulation results show the growth and motion of dendrites and evolution of eutectic lamellae and their interaction with melt flow. The present study provides the foundation for development of an efficient generalized micro-scale solidification model, which can potentially be coupled with system-scale models based on the same framework.