Three types of a-C:Co/Si samples were fabricated using the pulsed laser deposition: Co2-C98/8i with Co dispersed in the a-C film, Co2-C98/Si with Co segregated at the interface, and a-C/Co/Si with Co continuously dist...Three types of a-C:Co/Si samples were fabricated using the pulsed laser deposition: Co2-C98/8i with Co dispersed in the a-C film, Co2-C98/Si with Co segregated at the interface, and a-C/Co/Si with Co continuously distributed at the a-C/Si interface. Both types of Co2-C98/Si samples had the positive bias-voltage-dependent magnetoresistance (MR) at 300 K, and all MRs had saturated behavior. The study on the electrotransport properties indicated that the MR appeared in the diffusion current region, and the mechanism of MR was proposed to be that the applied magnetic field and local random magnetic field caused by the superparamagnetic Co particles modulate the ratio of singlet and triplet spin states, resulting in the MR effect. In addition, the very different physical and structural properties of all samples revealed that Co played a crucial role in the room-temperature positive MR of a-C:Co/Si system.展开更多
This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a sig...This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations.展开更多
基金support given by the National Natural Science Foundation of China (Grant Nos. U0734001 and 50772054)the Ministry of Science and Technology of China (Grant Nos. 2008CB617601 and 2009CB929202)
文摘Three types of a-C:Co/Si samples were fabricated using the pulsed laser deposition: Co2-C98/8i with Co dispersed in the a-C film, Co2-C98/Si with Co segregated at the interface, and a-C/Co/Si with Co continuously distributed at the a-C/Si interface. Both types of Co2-C98/Si samples had the positive bias-voltage-dependent magnetoresistance (MR) at 300 K, and all MRs had saturated behavior. The study on the electrotransport properties indicated that the MR appeared in the diffusion current region, and the mechanism of MR was proposed to be that the applied magnetic field and local random magnetic field caused by the superparamagnetic Co particles modulate the ratio of singlet and triplet spin states, resulting in the MR effect. In addition, the very different physical and structural properties of all samples revealed that Co played a crucial role in the room-temperature positive MR of a-C:Co/Si system.
基金supported by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE(No.EP/E035027/1)the UK EPSRC Award to the EPSRC Centre for Doctoral Training in PDEs(No.EP/L015811/1)+1 种基金the National Natural Science Foundation of China(No.10728101)the Royal Society-Wolfson Research Merit Award(UK)
文摘This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations.
