We present a rigorous homogenization approach for elcient computation of a class of physical problems in a one-dimensional periodic heterogeneous material. This material is represented by a spatially periodic array of...We present a rigorous homogenization approach for elcient computation of a class of physical problems in a one-dimensional periodic heterogeneous material. This material is represented by a spatially periodic array of unit cells with a length of More specifically, the method is applied to the diffusion, heat conduction, and wave propagation problems. Heterogeneous materials can have arbitrary position-dependent continuous or discontinuous materials properties （for example heat conductivity） within the unit cell. The final effective model includes both effective properties at the leading order and high-order contributions due to the microscopic heterogeneity. A dimensionless heterogeneity parameter ~ is defined to represent high-order contributions, shown to be in the range of [-1/12, 0], and has a universal expression for all three problems. Both effective properties and heterogeneity parameter 13 are independent oft, the microscopic scale of heterogeneity. The homogenized solution describing macroscopic variations can be obtained from the effective model. Solution with sub-unit-cell accuracy can be constructed based on the homogenized solution and its spatial derivatives. The paper represents a general approach to obtain the effective model for arbitrary periodic heterogeneous materials with position-dependent properties.展开更多
In this review,we review the progress of research on ZnO-and In2O3-based diluted magnetic oxides(DMOs).Firstly,we present the preparation and characterization of DMOs.The former includes the preparation methods and co...In this review,we review the progress of research on ZnO-and In2O3-based diluted magnetic oxides(DMOs).Firstly,we present the preparation and characterization of DMOs.The former includes the preparation methods and conditions,and the latter includes the characterization techniques for measuring microstructures.Secondly,we introduce the magnetic and transport properties of DMOs,as well as the relationship between them.Thirdly,the origin and mechanism of the ferromagnetism are discussed.Fourthly,we introduce other related work,including computational work and pertinent heterogeneous structures,such as multilayers and magnetic tunnel junctions.Finally,we provide an overview and outlook for DMOs.展开更多
文摘We present a rigorous homogenization approach for elcient computation of a class of physical problems in a one-dimensional periodic heterogeneous material. This material is represented by a spatially periodic array of unit cells with a length of More specifically, the method is applied to the diffusion, heat conduction, and wave propagation problems. Heterogeneous materials can have arbitrary position-dependent continuous or discontinuous materials properties （for example heat conductivity） within the unit cell. The final effective model includes both effective properties at the leading order and high-order contributions due to the microscopic heterogeneity. A dimensionless heterogeneity parameter ~ is defined to represent high-order contributions, shown to be in the range of [-1/12, 0], and has a universal expression for all three problems. Both effective properties and heterogeneity parameter 13 are independent oft, the microscopic scale of heterogeneity. The homogenized solution describing macroscopic variations can be obtained from the effective model. Solution with sub-unit-cell accuracy can be constructed based on the homogenized solution and its spatial derivatives. The paper represents a general approach to obtain the effective model for arbitrary periodic heterogeneous materials with position-dependent properties.
基金supported by China National Funds for Distinguished Young Scientists(Grant No.51025101)the National Natural Science Foundation of China(Grant Nos.11274214,11104173 and 61204097)+1 种基金the Research Fund for the Doctoral Program of Higher Education(Grant No. 20101404120002)the Youth Science Foundation of Shanxi Province (Grant Nos.2011021021-1,2011021021-2 and 2012021020-2)
文摘In this review,we review the progress of research on ZnO-and In2O3-based diluted magnetic oxides(DMOs).Firstly,we present the preparation and characterization of DMOs.The former includes the preparation methods and conditions,and the latter includes the characterization techniques for measuring microstructures.Secondly,we introduce the magnetic and transport properties of DMOs,as well as the relationship between them.Thirdly,the origin and mechanism of the ferromagnetism are discussed.Fourthly,we introduce other related work,including computational work and pertinent heterogeneous structures,such as multilayers and magnetic tunnel junctions.Finally,we provide an overview and outlook for DMOs.
