Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system

This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits. We also propose a kinetic formulation for the Hall-MHD equations which contains as fluid closure different variants of the Hall-MHD model. Then, we prove the existence of global weak solutions for the incompressible viscous resistive Hall-MHD model. We use the particular structure of the Hall term which has zero contribution to the energy identity. Finally, we discuss particular solutions in the form of axisymmetric purely swirling magnetic fields and propose some regularization of the Hall equation

Growth and characterization of Ni_xCu_1_-_x alloy films, Ni_xCu_1_-_x/Ni_yCu_1_-_y multilayers, and nanowires

It was found that it is possible to grow Ni_xCu_1_-_x alloy systems of arbitrary composition by electrodepositing well-defined sub-monolayer quantities of Ni and Cu in alternation using a new method based on that used previously to prepare potentiostatically deposited magnetic multilayers from a single sulphamate-based electrolyte. Following growth, the chemical composition of Ni_xCu_1_-_x alloy films was obtained by ZAF-corrected energy dispersive X-Ray (EDX) analysis and less than a 4% difference between the nominal and actual composition was observed. The structure of the films was investigated by high-angle X-ray diffractometry (HAXRD) and transmission electron microscopy (TEM). The films grown on polycrystalline Cu substrates had (100) texture, while those grown on Au-coated glass had (111) texture. Some evidence of Ni clustering was obtained by vibrating sample magnetometry (VSM). Self-organisation of the deposited metal was suggested for Ni potentials more positive than #approx#-1.4V. The transition from a Ni/Cu multilayer to a Ni_xCu_1_-_x alloy was also studied and an interesting aspect, namely a plateau region in a plot of magnetisation as a function of Ni layer thickness was observed, suggesting a preferred Ni cluster size in these alloy films. Anisotropic magnetoresistance (AMR) of the films decreased with increasing Cu content at 300K and 77K. SQUID measurements for Ni_0_._5_2Cu_0_._4_8 and Ni_0_._6_2CU_0_._3_8 films showed that they become much more strongly ferromagnetic at low temperatures. Evidence for blocked -superparamagnetic behaviour above a blocking temperature (T_B) of the films was obtained from zero-field-cooled (ZFC) and field-cooled (FC) magnetic susceptibility measurements. Ni_xCu_1_-_x/Ni_yCu_1_-_y alloy/alloy multilayer films with short repeat distance were successfully fabricated using this method. Up to third order satellite peaks observed in HAXRD showed that the interface is sharp. Room temperature longitudinal magnetoresistance measurements showed that Ni_xCu_1_-_x/Ni_yCu_1_-_y multilayers with certain layer thicknesses and compositions exhibit giant magnetoresistance (GMR) at room temperature which switched to AMR at 77K. This is a magnetotransport behaviour that is only possible through materials engineering. As another application of the new pulse-plating method Ni_xCu_1_-_x alloy nanowires were successfully electrodeposited into nuclear track-etched polycarbonate membranes. The current profiles recorded during deposition showed three different stages of growth: nucleation onto the Au substrate, steady growth in the pores, and growth of the wires in three dimensions. The structural analysis of the nanowires by TEM showed the grain length varied in the range 5-100nm, while its width varied between a few nm and the full width of the wire. The actual length and diameter of the wires were measured to be #approx#5#mu#m and (80#+-#5)nm respectively. The chemical compositions of the nanowires were obtained by EDX analysis. (author)SIGLEAvailable from British Library Document Supply Centre-DSC:DXN049385 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Fabrication of electrodeposited Ni-Cu/Cu multilayered films and study of their nanostructures before and after annealing

In this work electrodeposited Ni-Cu/Cu metallic multilayered films with different thicknesses of Ni and Cu were prepared on (100) polycrystalline Cu substrates. The nanostructure of the multilayers was studied using XRD. The existence of satellite peaks in the XRD patterns showed that the multilayered films have superlattice structures. The difference between the intensity of ML(200) and ML(111) peaks showed that the multilayers have a strong texture of (100) as their substrate structures which confirms the epitaxial growth. The morphology of the films was studied by SEM. The SEM images showed that the surface of the films is rough. The samples were also analyzed using EDX and the results showed that the real content of Ni is less than its nominal content this refers to the current efficiency which is less than unity due to hydrogen evolution. In the second stage of the work some identical samples which have the highest order of satellite peaks were electrodeposited. The samples were annealed at different temperatures and times. Their structures were then studied by XRD. The XRD patterns of the annealed samples showed that if the temperature and time of annealing increase, the satellite peaks begin to disappear. It means by increasing these two parameters, the sharpness of the bilayer interface decreases and the multilayered structure tends to become alloy structure. The morphology of the samples was also studied by SEM. The SEM images showed that the surface of the annealed films becomes approximately uniform due to the diffusion of Ni and Cu atoms to Cu and Ni layers, respectively