In this paper, we analytically discuss the scaling properties of the average square end-to-end distance <R2> for anisotropic random walk in D-dimensional space ( D ≥ 2), and the returning probability Pn(ro) for...In this paper, we analytically discuss the scaling properties of the average square end-to-end distance <R2> for anisotropic random walk in D-dimensional space ( D ≥ 2), and the returning probability Pn(ro) for the walker into a certain neighborhood of the origin. We will not only give the calculating formula for <R2> and Pn (ro), but also point out that if there is a symmetric axis for the distribution of the probability density of a single step displacement, we always obtain <R2⊥n> ～ n, where ⊥ refers to the projections of the displacement perpendicular to each symmetric axes of the walk; in D-dimensional space with D symmetric axes perpendicular to each other, we always have <R2n> ～ n and the random walk will be like a purely random motion; if the number of inter-perpendicular symmetric axis is smaller than the dimensions of the space, we must have <R2n> ～ n2 for very large n and the walk will be like a ballistic motion. It is worth while to point out that unlike the isotropic random walk in one and two dimensions, which is certain to return into the neighborhood of the origin, generally there is only a nonzero probability for the anisotropic random walker in two dimensions to return to the neighborhood.展开更多
The equilibrium magnetization configuration, the inducing field and the coercive field in trilayer magnetic materials having an out-of-plane anisotropy defect interlayer between two in-plane anisotropy layers are disc...The equilibrium magnetization configuration, the inducing field and the coercive field in trilayer magnetic materials having an out-of-plane anisotropy defect interlayer between two in-plane anisotropy layers are discussed by both analytical and numerical calculations based on a micromagnet approach. It is shown that the above physical parameters strongly depend on the defect layer such as its thickness and exchange stiffness etc., as well as on the applied fields. It is found that there is a special thickness of defect layer, in which the inducing effect begin to occur, and the critical behavior of inducing field in the vicinity of the special thickness is linearly characterized. Particularly, the magnetic hysteresis shows typical soft hysteresis shape, even though the host material is composed of hard magnets, and the coercivity increases with increasing the thickness of the interlayer.展开更多
文摘In this paper, we analytically discuss the scaling properties of the average square end-to-end distance <R2> for anisotropic random walk in D-dimensional space ( D ≥ 2), and the returning probability Pn(ro) for the walker into a certain neighborhood of the origin. We will not only give the calculating formula for <R2> and Pn (ro), but also point out that if there is a symmetric axis for the distribution of the probability density of a single step displacement, we always obtain <R2⊥n> ～ n, where ⊥ refers to the projections of the displacement perpendicular to each symmetric axes of the walk; in D-dimensional space with D symmetric axes perpendicular to each other, we always have <R2n> ～ n and the random walk will be like a purely random motion; if the number of inter-perpendicular symmetric axis is smaller than the dimensions of the space, we must have <R2n> ～ n2 for very large n and the walk will be like a ballistic motion. It is worth while to point out that unlike the isotropic random walk in one and two dimensions, which is certain to return into the neighborhood of the origin, generally there is only a nonzero probability for the anisotropic random walker in two dimensions to return to the neighborhood.
文摘The equilibrium magnetization configuration, the inducing field and the coercive field in trilayer magnetic materials having an out-of-plane anisotropy defect interlayer between two in-plane anisotropy layers are discussed by both analytical and numerical calculations based on a micromagnet approach. It is shown that the above physical parameters strongly depend on the defect layer such as its thickness and exchange stiffness etc., as well as on the applied fields. It is found that there is a special thickness of defect layer, in which the inducing effect begin to occur, and the critical behavior of inducing field in the vicinity of the special thickness is linearly characterized. Particularly, the magnetic hysteresis shows typical soft hysteresis shape, even though the host material is composed of hard magnets, and the coercivity increases with increasing the thickness of the interlayer.
