A novel binary effective medium model to describe the prepeak stressstrain relationship of combined bodies of rock-like material and rock

Combined bodies of rock-like material and rock are widely encountered in geotechnical engineering,such as tunnels and mines.The existing theoretical models describing the stress-strain relationship of a combined body lack a binary feature.Based on effective medium theory,this paper presents the governing equation of the“elastic modulus”for combined and single bodies under triaxial compressive tests.A binary effective medium model is then established.Based on the compressive experiment of concretegranite combined bodies,the feasibility of determining the stress threshold based on crack axial strain is discussed,and the model is verified.The model is further extended to coal-rock combined bodies of more diverse types,and the variation laws of the compressive mechanical parameters are then discussed.The results show that the fitting accuracy of the model with the experimental curves of the concretegranite combined bodies and various types of coal-rock combined bodies are over 95%.The crack axial strain method can replace the crack volumetric strain method,which clarifies the physical meanings of the model parameters.The variation laws of matrix parameters and crack parameters are discussed in depth and are expected to be more widely used in geotechnical engineering.

Factors influencing pore-pressure prediction in complex carbonates based on effective medium theory

A calculation model based on effective medium theory has been developed for predicting elastic properties of dry carbonates with complex pore structures by integrating the Kuster-Toksǒz model with a differential method.All types of pores are simultaneously introduced to the composite during the differential iteration process according to the ratio of their volume fractions.Based on this model,the effects of pore structures on predicted pore-pressure in carbonates were analyzed.Calculation results indicate that cracks with low pore aspect ratios lead to pore-pressure overestimation which results in lost circulation and reservoir damage.However,moldic pores and vugs with high pore aspect ratios lead to pore-pressure underestimation which results in well kick and even blowout.The pore-pressure deviation due to cracks and moldic pores increases with an increase in porosity.For carbonates with complex pore structures,adopting conventional pore-pressure prediction methods and casing program designs will expose the well drilling engineering to high uncertainties.Velocity prediction models considering the influence of pore structure need to be built to improve the reliability and accuracy of pore-pressure prediction in carbonates.

Optimal design of sub-wavelength metal rectangular gratings for polarizing beam splitter based on effective medium theory

A novel optimal design of sub-wavelength metal rectangular gratings for the polarizing beam splitter （PBS） is proposed. The method is based on effective medium theory and the method of designing single layer antireflection coating. The polarization performance of PBS is discussed by rigorous couple-wave analysis （RCWA） method at a wavelength of 1550 nm. The result shows that sub-wavelength metal rectangular grating is characterized by a high reflectivity, like metal films for TE polarization, and high transmissivity, like dielectric films for TM polarization. The optimal design accords well with the results simulated by RCWA method.

New assembly route for three-dimensional metamaterials obtained through effective medium theory

In this study, we illustrate the effective medium theories in the designs of three-dimensional composite metama- terials of both negative permittivity and negative permeability. The proposed metamaterial consists of random coated spheres with sizes smaller compared to the wavelength embedded in a dielectric host. Simple design rules and formulas following the effective medium models are numerically and analytically presented. We demonstrate that the revised Maxwell-Garnett effective medium theory enables us to design three-dimensional composite metamaterials through the assembly of coated spheres which are random and much smaller than the wavelength of the light. The proposed ap- proach allows for the precise control of the permittivity and the permeability and guides a facile, flexible, and versatile way for the fabrication of composite metamaterials.

High color saturation and angle-insensitive ultrathin color filter based on effective medium theory

An ultrathin angle-insensitive color filter enabling high color saturation and a wide color gamut is proposed by relying on magnesium hydride-hydrogenated amorphous silicon[MgH2-a-Si:H]lossy dielectric layer.Based on effective medium theory,the MgH2-a-Si:H layer with an ultrathin thickness can be equivalent to a quasi-homogeneous dielectric layer wit an effective complex refractive index,which can be tuned by altering the thickness of MgH2to obtain the targeted value o the imaginary part,corresponding to the realization of high color saturation.It is verified that the proposed color filte offers highly enhanced color saturation in conjunction with a wide color gamut by introducing a few-nanometer thic MgH2layer.As the MgH2-a-Si:H layer retains the advantages of high refractive index and tiny thickness,the proposed colo filter exhibits large angular tolerance up to±60°.In addition,MgH2with an unstable property can interconvert with Mg unde a dehydrogenation/hydrogenation reaction,which empowers the proposed color filter with dynamically tunable outpu color.The proposed scheme shows great promise in color printing and ultracompact display devices with high color sat uration,wide gamut,large angular tolerance,and dynamic tunability.

Effective medium theory of checkboard structures in the long-wavelength limit

Effective medium theory is a powerful tool to solve various problems for achieving multifarious functionalities and applications. In this article, we present a concise empirical formula about effective permittivity of checkboard structures for different directions. To verify our empirical formula, we perform simulations of checkboard periodic structures in squares, rectangles, and sectors in two dimensions. Our results show that the formula is valid in a large range of parameters. This work provides a new way to understand and design composite materials, which might lead to further optical applications in transformation optics.

Far-infrared conductivity of CuS nanoparticles measured by terahertz time-domain spectroscopy

This paper reports that terahertz time-domain spectroscopy is used to measure the optical properties of CuS nanoparticles in composite samples. The complex conductivity of pure CuS nanoparticles is extracted by applying the Bruggeman effective medium theory. The experimental data are consistent with the Drude-Smith model of conductivity in the range of 0.2 1.5 THz. The results demonstrate that carriers become localized with a backscattering behaviour in small-size nanostructures. In addition, the time constant for the carrier scattering is obtained and is only 64.3 fs due to increased electron interaction with interfaces and grain boundaries.

Research on Complex Refraction Indices of Expanded Graphite

The expanded graphite (EG) with a low density and better extinction performance can be used in military as passive jamming material in IR and MMW bands. Its complex refractive index is a significant parameter for the extinction property. This paper presents a method to calculate the complex refractive index of EG. The reflection spectra of EG pellets were measured in the 0.24-2.6μm and 2.5-25μm bands, respectively. Based on the measurement results, the complex refractive index of EG in 5-10μm band was calculated by using Kramers-Kronig(K-K) relation and Bruggeman effective medium theory, and then the errors were analyzed. The results indicate that it is feasible to calculate the complex refractive index of EG based on its IR reflection spectra data.

Homogeneous transparent device and its layered realization

Arbitrarily shaped electromagnetic transparent devices with homogeneous, non-negative, anisotropic and generic constitutive parameters are proposed based on linear transformation optics, which provides the flexibility for device design that is applicable for the practical fabrication. To remove the anisotropic property, a layered structure is developed based on effective medium theory. Simulation results show that with sufficient layers, the performance of the layered transparent device is nearly as perfect as an ideal device, and it is able to protect an antenna without sacrificing its performance. The feasibility of designing a transparent device by using natural isotropic materials instead of metamaterials would dramatically reduce the difficulty of fabrication and further promote the practicality of the device.

Giant enhancement of Kerr rotation in two-dimensional Bismuth iron garnet/Ag photonic crystals

Kerr effects of two-dimensional （2D） Bismuth iron garnet （BIG）/Ag photonic crystals （PCs） combined magnetic and plasmonic functionalities is investigated with the effective medium theory. An analytical expression of Kerr rotation angles is derived, in which the effects of the surface pasmons polaritons （SPP） on magneto--optical （MO） activities are reflected. The largest enhancement of Kerr rotation up to now is demonstrated, which is improved three orders of magnitude compared with that of BIG film. When λ 〈 750 nm all of the reflection are over 10% for the arbitrary filling ratio fl, in addition, the enhancement of Kerr rotation angles are at least one order of magnitude.

Shrinking device realized by using layered structures of homogeneous isotropic materials

We propose the practical realization of a shrinking device by using layered structures of homogeneous isotropic materials.By mimicking the shrinking device with concentric alternating thin layers of isotropic dielectrics,the permittivity and the permeability in each isotropic layer can be properly determined from the effective medium theory in order to achieve the shrinking effect.The device realized by multilayer coating with dielectrics is validated by TE wave simulation,and good shrinking performance is demonstrated with only a few layers of homogeneous isotropic materials.

Simplified triangular ground plane cloak by oblique multilayer dielectrics

Based on the effective medium theory, the triangular ground plane cloak can be realized by thin layered systems. Two solutions of parameter setting of the layered cloak are suggested to demonstrate the invisibility performance of a hybrid incoming wave. The hybrid parameters are derived from the equivalent of both anisotropies of permittivity and permeability to the Mternating layers. The performance of the designed layered cloak is validated by both TM and TE wave simulations with near-field distributions and average scattering power outflows on an observation semicircle. From the simulation results, the layered cloak with both hybrid parameters and improved hybrid parameters can reflect the incoming TM/TE waves in a specular direction, and the latter behaves with a better overall invisibility performance.

Analytical formula describing the non-saturating linear magnetoresistance in inhomogeneous conductors

The effective-medium theory(EMT)has proved successful in modeling the non-saturating linear magnetoresistance induced by inhomogeneity.However,calculating magnetoresistance using the EMT usually involves solving coupled integral equations which have no analytical solutions,and therefore,it is still difficult to directly compare the predictions of EMT with experimental data.Here we demonstrate that the linear magnetoresistance predicted by the EMT can be either exactly formulated or well approximated by a simple analytical equationΔ_(ρ)/ρ_(0)=√k^(2)B^(2)+a^(2)-a in a number of known situations.The relations between the EMT parameters and the phenomenological parameters k and a are evaluated.Our results provide a convenient and effective method for extracting the EMT parameters from experimental data.

Vapor Sensing Theoretical Study on Optical Microcavities

When the organic vapors absorbed to the surface of porous silicon(PS), capillary condensation takes place due to the porous structure of the PS layer, accordingly resulting in the effective refractive index changing. For PS multi-layer microcavities, the different resonant peaks shift in the reflectivity spectrum of porous silicon microcavities(PSMs). The optical sensing model is set up by applying Bruggeman effective medium approximation theory, capillary condensation process and transfer matrix theoretically analytical method of one-dimensional photonic crystals. At the same time, comprehensively researched on are the sensing characteristics of PSMs which are exposed to give concentration organic vapors. At last, made is the theoretical simulation for sensing model of the PSMs in case of saturation by using computer numerical calculation, and found is the linearity relation between the refractive index of organic solvent and the peak-shift. At the same time deduced is the peak-shift as a function of the concentration of ethanol vapors.

Designing nonlinear thermal devices and metamaterials under the Fourier law: A route to nonlinear thermotics

Nonlinear heat transfer can be exploited to reveal novel transport phenomena and thus enhance people’s ability to manipulate heat flux at will.However,there has not been a mature discipline called nonlinear thermotics like its counterpart in optics or acoustics to make a systematic summary of relevant researches.In the current review,we focus on recent progress in an important part of nonlinear heat transfer,i.e.,tailoring nonlinear thermal devices and metamaterials under the Fourier law,especially with temperature-dependent thermal conductivities.We will present the basic designing techniques including solving the equation directly and the transformation theory.Tuning nonlinearity coming from multi-physical effects,and how to calculate effective properties of nonlinear conductive composites using the effective medium theory are also included.Based on these theories,researchers have successfully designed various functional materials and devices such as the thermal diodes,thermal transistors,thermal memory elements,energy-free thermostats,and intelligent thermal materials,and some of them have also been realized in experiments.Further,these phenomenological works can provide a feasible route for the development of nonlinear thermotics.

Thermal transport in organic/inorganic composites

Composite materials, which consist of organic and inorganic components, are widely used in various fields because of their excellent mechanical properties, resistance to corrosion, low-cost fabrication, etc. Thermal properties of organic/inorganic composites play a crucial role in some applications such as thermal interface materials for micro-electronic packaging, nano-porous materials for sensor development, thermal insulators for aerospace, and high-performance thermoelectric materials for power generation and refrigeration. In the past few years, many studies have been conducted to reveal the physical mechanism of thermal transport in organic/ inorganic composite materials in order to stimulate their practical applications. In this paper, the theoretical and experimental progresses in this field are reviewed. Besides, main factors affecting the thermal conductivity of organic/ inorganic compositcs are discussed, including the intrinsic properties of organic matrix and inorganic fillers, topolo- gical structure of composites, loading volume fraction, and the interfacial thermal resistance between fillers and organic matrix.

Design of diamond-shaped transient thermal cloaks with homogeneous isotropic materials

Transformation thermodynamics as a major extension of transformation optics has recently received considerable attention. In this paper, we present two-dimeusional （2D） and three-dimensional （3D） diamond-shaped transient thermal cloaks with non-singular homogeneous material parameters. The absence of singularity in the parameters results from the fact that the linear coordinate transformation is performed by expanding a line segment rather than a point into a region, while the mechanism behind the homogeneity is the homogeneous stretching and compression along orthogonal directions during the transformation. Although the derived parameters remain anisotropic, we further show that this can be circumvented by considering a layered structure composed of only four types of isotropic materials based on the effective medium theory. Numerical simulation results confirm the good performance of the proposed cloaks.

Analysis of influence factors of negative refraction phenomenon in particulate composite

The effective optical constants that describe the interaction between electromagnetic wave and particulate composite are calculated based on effective medium theory and Mie theory.The negative refractive phenomenon is compared between the Ge-particle-dispersed LiTaO 3 composites and Ag-particle-dispersed LiTaO 3 composites.It is indicated that the negative refraction phenomenon for semiconductor Ge particulate composite occurs in higher frequency range than that of noble Ag particulate composite.By take the Ge particulate composite as an example,the influence of size and number density of spherical particles on the negative refraction phenomenon is analyzed.It is indicated that the frequency range where negative refraction phenomenon occurs can be shifted to higher frequency by adjusting these two influencing factors.