Components Of Permeability Tensor Research Articles

Analytical and numerical modeling of the work of a perfect well in anisotropic homogeneous soil formation

The extraction of oil and gas reservoirs in complex geological structures is constantly increasing. Thus, it is obvious that the reliable mathematical models governing such porous media must be of interest. The problem is concerned with the work of a well in anisotropic soil formation in the case of a random smooth (piecewise-smooth) external boundary of reservoir. The permeability of the soil is described by an asymmetric second-rank tensor. To find a solution to the problem is difficult because of the complicated form of the basic equation. The solution can be simplified if the equation is transformed into the Laplace equation. To do this, we turn on the auxiliary plane using homeomorphic (affine) transformation. In a special case when the external boundary of reservoir of the auxiliary plane takes the form of a circle, we arrive at a closed-form (analytical) solution. These analytic solutions are useful in testing numerical codes. In the general case, the problem is reduced to a system of integral equations with Cauchy kernel and the integral relation. The system is solved by the method of discrete singularities. Convergence of the algorithm is studied. Convergence solutions are improved with an increase in the number of division points. The convergence solutions with a piecewise-smooth (square) external boundary of reservoir are slightly worse compared with the smooth (circular) ones. Soil anisotropy greatly affects the production rate and can strongly change the production rate compared to the rate of the well in an isotropic soil. Permeability tensor components located on the main diagonal have a major impact on the rate of flow in the anisotropic soil. This method can be used to solve different problems in filtering anisotropic porous medium.

Determination of thickness and permeability tensor using the combination (models-neural networks)

The purpose of this paper is to describe an improved microwave method for predicting the material’s thickness and the saturation magnetization and the damping factor through the neural networks. These characteristics provide the permeability tensor components using the combination between theoretical models and neural network. Neural networks learn the relationship between the scattering parameters and the outputs. The networks’ performances result from both simulation and measurement thin ferrite samples.

Tunable all-angle negative refraction using antiferromagnets

We show how all-angle negative refraction can occur in a uniaxial antiferromagnet close to the magnon resonance frequency. This behavior is based on the fact that, in such cases, the antiferromagnet acts as an indefinite permeability medium, i.e., not all its permeability tensor components are of the same sign. If an external magnetic field is applied, the angle of refraction becomes tunable, and can be made to change sign. We illustrate these effects using the example of MnF${}_{2}$ at low temperature, and show that in this system negative refraction should occur with a large figure of merit.

Generation of Guiding Modes by Surface Modes in Anisotropic Metamaterial Waveguide

We explore the possibility of the existence of guiding modes generated by surface modes in a three-layer waveguide composed of anisotropic single-negative metamaterial. The conditions for generation of even or odd guiding modes are deduced in eight subcases of single-negative (SNG) metamaterials with a different combination of positive or negative components of permittivity and permeability tensors, including the requirements for real propagation of surface and guiding modes as well as a solvable dispersion equation. The theoretical prediction is verified by simulation results, and the generated guiding modes are much more controllable and practicable in the three-layer symmetric waveguide consists of anisotropic SNG metamaterial.

A probabilistic model for the interaction of microwaves with 3-dimensional magnetic opal nanocomposites

The complex diagonal and off-diagonal components of the effective permeability tensor were calculated for the case of a realistic 3D opal, infiltrated with Ni0.7Zn0.3Fe2O4 nanoparticles. First, an accurate electrodynamic effective medium permeability tensor approach is formulated. Next, Maxwell`s equations were solved rigorously for the case of an interacting systems of ferrite particles in the opal matrix, having a normal distribution of the ferromagnetic resonance fields. The method is demonstrated by calculating the bias field dependence of the components of the complex permeability tensor at 26 GHz, and a good agreement with recent experimental data was obtained.

Phase constant peculiarities of cylindrical zero-index anisotropic metamaterial waveguide

Here, we present the phase constant dependencies of propagating eigenmodes of an open cylindrical anisotropic metamaterial waveguide when the metamaterial permittivity and permeability tensor components may accept values close or equal to zero. Dispersion characteristics of rod and hollow-core waveguides with the radii 0.5, 2.5, and 5 mm at the left-handed polarization of the microwave are shown here. There are unusual shapes of eigenmode dispersion characteristics and anomalous sectors of the characteristics at certain frequencies. The first eigenmode of the rod waveguide with the lowest cutoff frequency is a particularly important mode because it is a single one in the frequency range 1.0–1.9 GHz, and some small variations on the frequency produce large changes in the phase constant. We can observe packages of dispersion characteristic branches when their cutoff frequencies closed to the metamaterial electric and magnetic plasma frequencies between 1.9 and 3.5 GHz. There are only three modes in the hollow core anisotropic metamaterial waveguide at the frequency range 1.4–2.8 GHz.

Radial infusion models for permeability measurements of compressed fibrous beds

A summary, new development on analytic solutions of models of the Darcy problem for liquid progression through porous media, and some experimental results obtained by these models are presented. Two anisotropic cases, 2D in-plane and 3D axisymetric transverse injection, are analyzed and compared with a reference case that is represented by the widely used closed-form solution of radial in-plane injection. The analytic solutions of the two analyzed models were originally interpreted as the approximate ones, since they were derived assuming that one component of pressure gradients, in the governing equations, may be neglected. It is shown that the assumption regarding pressure gradients in both cases may be released, that the original results present closed-form solutions of the imposed quasi-steady models, and through numerical experiments, that these models are not sensitive to the radius of the injection port within the range in which relevant parameters usually vary in experiments. With these findings and the results obtained experimentally, it is also show that the two models are equally accurate and reliable as the reference one. They can be employed for the evaluation of all three permeability tensor components utilizing a relatively simple apparatus and as such may be utilized as standard models.

Application of multilayer perceptron neural networks for predicting the permeability tensor components of thin ferrite films

A novel characterization method using artificial neural networks is presented. This method allows one to determine the intrinsic permeability tensor of ferrite thin-films from S -parameters measurements. Neural networks, efficient to solve inverse problems, are used to compute the permeability tensor components μ and k. This optimization technique is used to find extremely complex functions between inputs and outputs and can be successfully applied on our magnetic thin-film characterization problem. Results of our networks are compared to a theoretical model. A great number of both simulated and measured tests have been performed on many magnetic thin-films. Neural network processing leads to a rapid and robust method for predicting the magnetic characterization of thin-films in microwave range.

Controllable Metamaterial-Loaded Waveguides Supporting Backward and Forward Waves

Rectangular waveguides loaded by anisotropic metamaterials are analyzed to assess the controllability of transmission characteristics of the involved electromagnetic waves. Dispersion relations of TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m0</sub> modes in the metamaterial-loaded waveguide (MLW) are theoretically investigated. It is shown that all propagating modes (the forward wave, the backward wave and the evanescent wave) in the MLW can be realized below the cut-off frequency by changing transverse and longitudinal components of permeability tensors of the loading metamaterials. Numerical simulations are carried out to verify the proposed theory and the controllability. Transmission characteristics and effective constitutive parameters of three MLWs with different cells, which should theoretically support forward waves, backward waves and evanescent waves, respectively, are numerically calculated. Dispersion curves and magnetic field distribution for the backward wave MLW and the forward wave MLW are simulated. It is shown that the simulated results are in a good agreement with theoretical predictions. Implementation of the controllable MLW was achieved by using axially rotating control rods. Rotating the control rods can reconfigure the metamaterial and make propagating modes in the MLW switch from backward waves to forward waves or evanescent waves.

Electromagnetic analysis of arbitrarily shaped pinched carpets

We derive the expressions for the anisotropic heterogeneous tensors of permittivity and perme- ability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map a non convex region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components, and this may lead to some broadband cloaking.

Generalized Measurement Method for the Determination of the Dynamic Behavior of Magnetic Materials in Any Magnetization State

broad-band characterization method based on the junction of the full-wave analysis of a nonreciprocal strip transmission line with a predictive permeability tensor model is presented. The aim of this method is the direct measurement of the permeability tensor components spectra of magnetized thick samples, whatever their magnetization state is. The propagation constants of the dominant transverse electromagnetic (TEM) and higher order modes inside the measurement cell are obtained along with its scattering parameters (S-parameters). The apparition of magnetostatic modes and the nonreciprocal nature of the structure are probed. Procedures based on the use of this method to find accurate values of gyromagnetic resonance and the resonance line width (?H) are proposed. The direct analysis is validated by comparison of the calculated S-parameters with those obtained with an electromagnetic field simulator based on finite element methods (FEM).

Anisotropy effects in two-phase flows through porous media

Effects manifested in two-phase flows through anisotropic porous reservoirs with monoclinic and triclinic characteristics are analyzed. It is shown that in two-phase flows through media with monoclinic and triclinic symmetries of flow characteristics the position of the principal axes of the phase permeability tensors depends on the saturation and does not coincide with the position of the principal axes of the absolute permeability tensor in single-phase flows and that going over from single-to two-phase flow may lead to a change in the symmetry group of the flow characteristics. A general representation of the phase permeability tensor components is presented and formulas are given for the diagonal and nondiagonal components of the relative phase permeabilities, which are universal and can be used for anisotropic media with any type of anisotropy (symmetry) of flow characteristics. A complex of laboratory tests for finding the nondiagonal components of the phase and relative phase permeability tensors is discussed.

MICROWAVE DIFFRACTION CHARACTERISTIC ANALYSIS OF 2D MULTILAYERED UNIAXIAL ANISOTROPIC CYLINDER

Here we present the rigorous electrodynamical solution of microwave scattering by a multilayered electrically or (and) magnetically anisotropic circular cylinder. The number and thickness of layers may be arbitrary. We present the solution when all area of multilayered cylinder can be made of difierent uniaxial anisotropic or isotropic materials. The multilayered cylinder media can be of strongly lossy materials. The signs of the complex permittivity and permeability tensor components can be positive or negative in difierent combinations. Here we present the numerical dependencies of the Poynting vector radial component P‰ that is responsible for the scattered and absorbed powers when the incident microwave impinges on the anisotropic Lithium Niobate (LiNbO3) cylinder as well as on two single isotropic cylinders. The permittivity tensor components of the anisotropic cylinder are t = 43ii0:0005, p = 28ii0:0005 as well as for the isotropic cylinders the permittivities are t = p = 43ii0:0005 and t = p = 28 i i0:0005. We show here the pattern of the value P‰ inside and outside of the LiNbO3 and two isotropic cylinders when the polar angle ' changes from 0 to 360 degrees with the step equal to one degree. We present here our calculations when the incident microwave has perpendicular or parallel polarization at

Effective permeability tensor and double resonance of interacting bistable ferromagnetic nanowires

We present a model for the effective permeability tensor of nonsaturated arrays of axially magnetized bistable ferromagnetic wires based on a Maxwell-Garnett formalism generalized to include the case of two oppositely magnetized wire populations. Explicit expressions for the complex diagonal and off-diagonal components of the effective permeability tensor are derived to describe the magnetic response of the array and its dependence upon microwave frequency and external magnetic field. The model accounts for the geometrical parameters and the static magnetic configuration of the array, as well as the shape and intrinsic properties of the wires. We incorporate the effect of the static and dynamic interwire dipolar interactions and obtain explicit expressions for the position and relative amplitude of the two ferromagnetic resonance peaks associated with the effective permeability of nonsaturated arrays. The two absorption peaks arise due to the presence of the up and down wire populations, which are predominantly excited by the right-handed and left-handed circularly polarized magnetic field components of the electromagnetic wave propagating inside the array. Excellent agreement is found between the model and experimental results obtained from $S$-parameter broadband microstrip line measurements. Small discrepancies when the array is magnetically unsaturated or when the peaks are close to each other are discussed and attributed to spatial variations of the local interaction field not accounted for by the present model.

Transport properties of heterogeneous materials. Combining computerised X-ray micro-tomography and direct numerical simulations

Feasibility of a method for finding flow permeability of porous materials, based on combining computerised X-ray micro-tomography and numerical simulations, is assessed. The permeability is found by solving fluid flow through the complex 3D pore structures obtained by tomography for actual material samples. We estimate overall accuracy of the method and compare numerical and experimental results. Factors contributing to uncertainty of the method include numerical error arising from the finite resolution of tomographic images and the rather small sample size available with the present tomographic techniques. The total uncertainty of computed values of permeability is, however, not essentially larger than that of experimental results. We conclude that the method provides a feasible alternative for finding fluid flow properties of the kind of materials studied. It can be used to estimate all components of permeability tensor and is useful in cases where direct measurements are not achievable. Analogous methods can be applied to other modes of transport, such as diffusion and heat conduction.

HIGH-FREQUENCY RESPONSE AND VOLTAGE NOISE IN MAGNETIC NANOCOMPOSITES

We study the noise spectra and high-frequency permeability of inhomogeneous magnetic materials consisting of single-domain magnetic nanoparticles embedded into an insulating matrix. Possible mechanisms of 1/f voltage noise in phase-separated manganites is analyzed. The material is modelled by a system of small ferromagnetic metallic droplets (magnetic polarons or ferrons) in insulating antiferromagnetic or paramagnetic matrix. The electron transport is related to tunnelling of charge carriers between droplets. One of the sources of the 1/f noise in such a system stems from fluctuations of the number of droplets with extra electron. In the case of strong magnetic anisotropy, the 1/f noise can arise also due to the fluctuations of the magnetic moments of ferrons. The high frequency magnetic permeability of nanocomposite film with magnetic particles in insulating non-magnetic matrix is studied in detail. The case of strong magnetic dipole interaction and strong magnetic anisotropy of ferromagnetic granules is considered. The composite is modelled by a cubic regular array of ferromagnetic particles. The high-frequency permeability tensor components are found as a functions of frequency, temperature, ferromagnetic phase content, and magnetic anisotropy. The results demonstrate that magnetic dipole interaction leads to a shift of the resonance frequencies towards higher values, and nanocomposite film could have rather high value of magnetic permeability in the microwave range.

Electrodynamic model for low loss microwave nanocomposite magnets using autonomous blocks with Floquet channels

The diagonal and off-diagonal components of the effective permeability tensor and the effective permittivity of three-dimensional (3D) periodic magnetic nanosystems, depending on the size and separation of the magnetic nanoparticles, were calculated using the computed values of the propagation constants and the dispersion relations of clockwise and counterclockwise polarized electromagnetic waves (EMWs), as well as for the ordinary and extraordinary modes in the gyromagnetic medium. The propagation constants of EMWs in a 3D periodic array of 150 nm iron nanospheres in a dielectric matrix, depending on the ratio of the period of the array to the radius of the nanospheres, were obtained at a frequency f=30 GHz for longitudinal and transverse orientations of the bias magnetic field. It is shown that the magnetic and dielectric losses of weakly interacting systems are lower than that of yttrium iron garnet (YIG); however, losses increase due to spin wave (SW) excitations upon reduced separation.

A reference specimen for permeability measurements of fibrous reinforcements for RTM

The capability to simulate the flow of resin through a porous reinforcement by FE modelling has become very important for designing RTM production processes for high-performance composite parts. The key parameter in RTM flow simulations is the fibre reinforcement permeability. The measurement of this material parameter is still not standardized and many different set-ups have been proposed. Recently, a stereolithography technique was used to produce a textile-like solid specimen with anisotropic permeability, designed as a reference for calibration and comparison of permeability measurement set-ups and for validation of numerical permeability computation software. Unlike real textiles, the permeability properties of such reference specimens do not vary from test to test. Excellent repeatability of the experiments is achieved. When used for benchmarking, any discrepancy between different measurements on this specimen must be attributed to the set-up and data processing. This paper presents the first experimental measurements of the permeability of such reference specimens, obtained with a 2D central injection rig. The measured values, with principal components of the 2D permeability tensor of 2.47 ± 0.09 × 10 −9 m 2 and 5.44 ± 0.22 × 10 −9 m 2, are in good agreement with the values predicted using numerical permeability computation software. Statistics from a series of measurements using the same set-up show that the precision of the permeability identification depends on the data processing procedure. An approach which incorporates a numerical model that is also valid after the fluid reached an edge of the reinforcement performs significantly better than the approach, based on an analytical approximation, which was used before.

2D permeability tensor identification of fibrous reinforcements for RTM using an inverse method

A fast and robust mixed numerical/experimental technique is presented, that allows with a single experiment to determine all components of the in-plane permeability tensor, needed for process simulation of resin transfer molding . This technique combines the highly automated “PIERS” (permeability identification using electrical resistance sensors) central injection rig with a customized numerical simulation of the experiment, and uses an iterative inverse method to identify permeability values for which the simulation agrees with the experiment. It is shown that, for reinforcements that are not approximately isotropic, the numerical simulation in the inverse method significantly improves the precision of the parameter identification, compared to inverse methods with models that are valid only until the injected fluid reaches an edge of the reinforcement.

FDTD STUDY ON WAVE PROPAGATION IN LAYERED STRUCTURES WITH BIAXIAL ANISOTROPIC METAMATERIALS

The Gaussian beam propagation in multi-layered structures that include indefinite anisotropic metamaterial (AMM) are simulated with shift operator method in Finite-Difference Time-Domain method (FDTD). The excitations of backward and forward surface affected by the types of biaxial AMM are investigated. Numerical results show that the directions of the guided wave excited are influenced by the sign of z component of relative permeability tensor of AMM that determines the energy flow is positively refracted or negatively refracted. Positive or negative Goos-Hanchen shift associated with Total Cutoff media are also shown.