Ce Liu

Computation of conductivity and dielectric constant of periodic porous media

The static conductivity and dielectric constant of two‐component periodic composite material are calculated using the Fourier expansion technique. The composite material consists of spheres that are arranged in simple, face‐centered, or body‐centered cubic lattices. The spheres may be isolated to yield high porosity or pore space, or they may intercept each other, leaving small pore space in between. The effective static conductivity and dielectric constant of such structures are computed theoretically when the pore space is filled with a material that has a conductivity or dielectric constant which differs from that of the matrix of the structure.

Dielectric constant of two-component, two-dimensional mixtures in terms of Bergman-Milton simple poles

According to the Bergman–Milton theory [D. J. Bergman, Phys. Rep. 43, (No. 9), 377 (1978), and G. W. Milton, J. Appl. Phys. 52, 5286 (1981)], the effective dielectric constant or conductivity of a two‐component mixture is a function of the ratio of the dielectric constants (or conductivities) of those components. The function has simple poles only at some negative values of the ratio, and positions of the poles and residues are dependent only on the microgeometry of the mixture. In this study, the location of the poles and the values of the residues are found for two‐component, two‐dimensional composite materials with periodic, simple‐square lattice structures using the Fourier series expansion technique. With the locations of the poles and residues determined, the effective dielectric constants or conductivities of two‐component composite materials may be expressed in practical forms and may be predicted for composite mixtures even when the dielectric constants of the component materials are complex.

COMPUTATION OF THE EFFECTIVE DIELECTRIC CONSTANT OF TWO-COMPONENT, THREE-DIMENSIONAL MIXTURES USING A SIMPLE POLE EXPANSION METHOD

Bergman and Milton proved that the effective dielectric constant or conductivity of a two-component composite material is a function of the ratio of the dielectric constants or conductivities of the components which can be described by a series of simple poles and residues. These poles and residues are determined only by the microgeometry of the composite. In this study, we use a simplified three-dimensional Fourier series expansion method to locate the poles and residues for simple cubic, body-centered, and face-centered lattices in different concentrations. Comparison between the simple pole theory and the Fourier series expansion method shows a good agreement.

Numerical evaluation of effective dielectric properties of three-dimensional composite materials with arbitrary inclusions using a finite-difference time-domain method

In this article, we introduce a numerical procedure to evaluate effective dielectric properties of arbitrary multicomponent three-dimensional mixtures. Recognizing that many mixtures have periodic extend in all directions, we only need to analyze a unit element for effective electrical properties extraction. The numerical technique used here is a finite-difference time-domain method with a periodic boundary condition that generalizes many boundary conditions used in previous works. Several numerical examples are provided to demonstrate the effectiveness of this method. Using this developed procedure, we study the effects of frequency, inclusion shapes, inclusion volume, and inclusion conductivity on mixture’s electrical properties. It is observed that these parameters can significantly change the electrical properties of mixtures.

Numerical Modeling of Periodic Composite Media for Electromagnetic Shielding Application

This paper describes a methodology to extract effective electrical properties for periodic composite medium. The extraction algorithm is based on a periodic finite-difference time-domain (FDTD) method. The results are compared with conventional mixing theories and 3D Fourier series expansion methods. Two results show satisfactory agreement. With the extracted effective permittivity and conductivity, one can readily use these parameters to study electrical properties of composite materials with arbitrary micro-geometry and the shielding effects of using composite materials.

Study of Hc enhancement in Co‐modified γ‐Fe2O3 films

The magnetic properties and depth profiles of Co‐modified γ‐Fe2O3 films have been studied. The Hc of these films varies between 0.3 and 2.5 kOe nonmonotonically with Co concentration and depends only slightly on temperature. The non‐diffusion‐like Co‐rich layer that appears underneath the surface of the Fe‐oxide films displaying an enhanced Hc has been positively demonstrated to be responsible for the Hc enhancement.

Numerical evaluation of the effective dielectric property of multi-component three-dimensional mixtures using a finite-difference time-domain method

Summary In this paper, we introduce a novel numerical procedure to evaluate the effective dielectric property of multicomponent three-dimensional mixtures. By utilizing the properties that most mixtures can be approximated by periodic structures and the size of inclusions is normally much smaller than the wavelength, we only need to analyze a unit element for effective dielectric properties extraction. The numerical technique used in this study is a periodic finite-difference time-domain (FDTD) method. Appropriate periodic boundary conditions are required to emulate the periodicity of structures. Several numerical examples are provided to demonstrate effectiveness of this method. It is also shown that this method can be applied to analyze multi-component three-dimensional mixtures whose electrical properties cannot be evaluate by the conventional

Analysis of three-dimensional composite materials with non-isotropic or biaxial anisotropic inclusions using a finite difference method

In this paper, the FDM is extended to analyze the effective anisotropic permittivity of composite materials with non-isotropic or biaxial anisotropic inclusions. Numerical experiments have demonstrated that this technique has the ability to effectively analyze three-dimensional complex composite materials with macroscopic anisotropic dielectric properties.

Numerical Evaluation of Electrical Properties For Arbitrary Anisotropic Composite Formations

In this paper, we introduce a three-dimensional numerical procedure to evaluate anisotropic electrical properties of arbitrary three-dimensional mixtures/formations. Only a unit element with periodic condition is required in this approach since most mixtures/formations can be approximated by periodic structures. The numerical technique used here is a periodic three-dimensional finitedifference method under the electrostatic assumption. Several numerical examples are used to demonstrate effectiveness of this method. It is shown that this method can be applied to characterize medium heterogeneous properties for mixtures with anisotropies in both mixture geometries and medium electrical properties.

Comparison of Different Finite-difference Schemes of Modeling Marine Controlled-Source Electromagnetic Fields for Hydrocarbon Exploration

In this paper, two different finite difference schemes, based on vector-scalar potential formulation and direct electric field formation, are developed for modeling marine controlledsource electromagnetic survey. These methods are applied to analyze a typical hydrocarbon exploration environment. Based on the results of our simulation, we compare these two methods in terms of their numerical accuracy and efficiency. DOI: 10.2529/PIERS060906130556