Homogeneous Conductivity Research Articles

General Solution of the Inhomogeneous Div-Curl System and Consequences

We consider the inhomogeneous div-curl system (i.e. to find a vector field with prescribed div and curl) in a bounded star-shaped domain in $$\mathbb {R}^3$$ . An explicit general solution is given in terms of classical integral operators, completing previously known results obtained under restrictive conditions. This solution allows us to solve questions related to the quaternionic main Vekua equation $$DW=(Df/f)\overline{W}$$ in $$\mathbb {R}^3$$ , such as finding the vector part when the scalar part is known. In addition, using the general solution to the div-curl system and the known existence of the solution of the inhomogeneous conductivity equation, we prove the existence of solutions of the inhomogeneous double curl equation, and give an explicit solution for the case of static Maxwell’s equations with only variable permeability.

Analytical solution of electromagnetic radiation by a vertical electric dipole inside the earth and the effect of atmospheric electrical conductivity inhomogeneity

In this paper, the effect of atmospheric electrical conductivity on the electromagnetic waves radiated by a vertical electric dipole located in the earth, near the surface of the earth, is investigated. As far as electrical conductivity is concerned, the atmosphere is divided into three areas, in which the electrical conductivity changes with altitude. The Maxwell equations in these areas are investigated as well. Using the differential transform method, the differential equation is solved in a way that atmospheric electrical conductivity is variable. Solving the problem in these areas indicates that electrical conductivity in the middle and lower areas of atmosphere may be ignored. However, in the upper areas of atmosphere, the magnitude of the magnetic field in the ionosphere at a frequency of 10kHz at night is five times smaller when electrical conductivity is considered compared to when it is neglected.

Quantitative Approach for Thickness and Conductivity Measurement of Monolayer Coating by Dual-Frequency Eddy Current Technique

A new approach is proposed to measure the coating material’s thickness and its conductivity simultaneously by using the eddy current technique. The proposed approach can be used for a coating material with unknown or inhomogeneous conductivity. This is achieved by exploring an inverse algorithm to investigate the relationship between the thickness and the perpendicular component of the magnetic flux density for different coating conductivities. The measured average relative error is less than 10%, which makes the monitoring of the coating thickness possible under variation of the conductivity due to the applied loads and the manufacturing process.

The study of the interactions between graphene and Ge(001)/Si(001)

The interaction between graphene and germanium surfaces was investigated using a combination of microscopic and macroscopic experimental techniques and complementary theoretical calculations. Density functional theory (DFT) calculations for different reconstructions of the Ge(001) surface showed that the interactions between graphene and the Ge(001) surface introduce additional peaks in the density of states, superimposed on the graphene valence and conduction energy bands. The growth of graphene induces nanofaceting of the Ge(001) surface, which exhibits well-organized hill and valley structures. The graphene regions covered by hills are of high quality and exhibit an almost linear dispersion relation, which indicates weak graphene–germanium interactions. On the other hand, the graphene component occupying valley regions is significantly perturbed by the interaction with germanium. It was also found that the stronger graphene–germanium interaction observed in the valley regions is connected with a lower local electrical conductivity. Annealing of graphene/Ge(001)/Si(001) was performed to obtain a more uniform surface. This process results in a surface characterized by negligible hill and valley structures; however, the graphene properties unexpectedly deteriorated with increasing uniformity of the Ge(001) surface. To sum up, it was shown that the mechanism responsible for the formation of local conductivity inhomogeneities in graphene covering the Ge(001) surface is related to the different strength of graphene–germanium interactions. The present results indicate that, in order to obtain high-quality graphene, the experimental efforts should focus on limiting the interactions between germanium and graphene, which can be achieved by adjusting the growth conditions.

Improved DC flashover performance of epoxy insulators in SF6 gas by direct fluorination

In order to prove the effectiveness of direct fluorination in improving dc flashover performance of epoxy insulators in SF6 gas and also to provide evidence for the importance of surface conductivity of solid insulators, sheet-shaped and truncated cone epoxy samples were prepared and were fluorinated in a laboratory stainless vessel using a F2/N2 mixture with 12.5% F2 by volume at 0.1 MPa and 85 °C for 30 min. Physicochemical characteristics of the fluorinated surface layer were evaluated by ATR-FTIR and SEM techniques, and the results showed substantial chemical modification of the surface layer, which has a thickness of 0.89 μm and a roughened surface. Further, as expected on the basis of previous studies, measurements of surface electrical properties of the surface fluorinated sample, compared to the unfluorinated one, revealed a four orders of magnitude higher surface conductivity and a much more rapid decay of surface potential after corona charging. Dc flashover tests were performed on the truncated cone samples in SF6 gas at 0.1 MPa with a stepwise increasing voltage before and after the fluorination. The flashover test results showed a definite improvement in dc flashover voltage. For example, the flashover voltage at 63.2% probability or the mean flashover voltage for 2 min duration of the voltage step increased by 13.8% or 13.6% after the fluorination. The performance improvement is mainly attributed to easy leakage and dispersion of the charge deposited on the surface fluorinated sample from the gas phase, due to high conductivity of the fluorinated layer. The flashover test results also showed the influences of the duration of the voltage step on the flashover voltage and on the increase rate of flashover voltage. This means that even the time constant of the fast gas phase charging should be larger than 2 min, and that there should be different influences of the inhomogeneous surface conduction between the virgin sample and the fluorinated sample.

Phase coexistence and dynamical behavior inNdNiO3ultrathin films

Rare-earth nickelates exhibit several temperature-driven phase transitions that are tunable by the size of the rare-earth ions, pressure, epitaxial strain in ultrathin films, etc. We investigate the metal-insulator and Neel transitions in a series of NdNiO3 thin films with varying degrees of lattice mismatch using ultralow frequency electrical noise measurements. The noise magnitude follows a 1/f behavior and is Gaussian in the high temperature paramagnetic metallic phase of the films, however deviations are seen in the low temperature paramagnetic and antiferromagnetic insulating phases. The noise magnitude increases by orders of magnitude at temperatures below the metal-insulator transition and is indicative of inhomogeneous electrical conduction arising from phase separation. The inhomogeneous nature of conduction is corroborated by the presence of a large non-Gaussian noise signature in the low temperature phases. Well below the Neel temperature, the noise behavior evolves between Gaussian and non-Gaussian over several hours pointing to dynamically competing ground states with subtle variations within the antiferromagnetic insulating phase.

Electric field distribution during polarization reversal in lithium niobate with inhomogeneous bulk conductivity

ABSTRACTWe propose a method for direct observation of the spatial distribution of electric field in the bulk of lithium niobate (LN) single crystals. The experimental configuration allows revealing simultaneously domain kinetics due to polarization reversal. The complex analysis of the evolution of spatial field distribution and the stages of domain kinetics during polarization reversal in LN crystals with inhomogeneous modification of the bulk conductivity enables revealing the 3D growth of the charged domain walls. It opens new opportunities for creation of the charged domain walls in the single crystals of LN family.

RETRACTED ARTICLE: Small perturbation of a surface: full Maxwell’s equations

In this paper, we derive high-order terms in the asymptotic expansions of the boundary perturbations of the electromagnetic fields resulting from small perturbations of the shape of an inhomogeneity with -boundary in for . For such solutions we provide a rigorous derivation that extends those already derived for small volume conductivity inhomogeneities. Our formulas may be expected to develop effective algorithms, aimed at determining certain properties of the shape of an object based on electromagnetic boundary measurements.

Comparison of linear and non-linear monotonicity-based shape reconstruction using exact matrix characterizations

Detecting inhomogeneities in the electrical conductivity is a special case of the inverse problem in electrical impedance tomography, that leads to fast direct reconstruction methods. One such method can, under reasonable assumptions, exactly characterize the inhomogeneities based on monotonicity properties of either the Neumann-to-Dirichlet map (non-linear) or its Fréchet derivative (linear). We give a comparison of the non-linear and linear approach in the presence of measurement noise, and show numerically that the two methods give essentially the same reconstruction in the unit disk domain. For a fair comparison, exact matrix characterizations are used when probing the monotonicity relations to avoid errors from numerical solution to PDEs and numerical integration. Using a special factorization of the Neumann-to-Dirichlet map also makes the non-linear method as fast as the linear method in the unit disk geometry.

Inhomogeneity and complexity in defining fractionated electrograms

Ablation strategies targeting areas of complex fractionated atrial electrograms are not successful for treatment of atrial fibrillation. Fractionation of atrial electrograms may have multiple causes of both pathologic and nonpathologic origin. In order to gain insight into the definitions used for determining areas of fractionation, a literature search was performed using a systematic approach. A PubMed search for studies describing fractionation during human atrial electrophysiologic measurements resulted in 348 articles that were screened for new definitions of fractionation. The 24 studies remaining after screening described 11 different visual definitions for fractionation, 3 automated complex fractionated atrial electrogram detection programs, and 7 new parameters for measuring fractionation. Five different definitions for continuous electrical activity were presented. Electrode properties were often not described, and endocardial bipolar recordings in recent studies used electrode diameters ranging from 1 to 8 mm with interelectrode distance of 2-5 mm. In summary, no uniform definition or recording method is used for measuring fractionation of cardiac atrial electrograms. The different electrophysiologic causes of fractionation and the influence of recording device properties on fractionation complicate identification of true pathologic inhomogeneous conduction. The first step in discrimination between origins of fractionation may be accomplished by relating electrogram morphology to spatial patterns of activation. Before revisiting ablation of areas with fractionated electrograms, we need to determine the correct method for identifying pathologic fractionation.

Thermal convection in electrochemical cells. Boundaries with heterogeneous thermal conductivity and implications for scanning electrochemical microscopy.

We investigate the heat transfer in a cylinder-shaped electrochemical cell with solid, thermally insulating walls. The cell is filled with a liquid and a solid substrate that is thermostated from below is situated at its base. The initial temperature of the liquid is different from that of the substrate so as to mimic imperfect thermostating in an electrochemical experiment; as heat transfer acts to diminish the temperature difference between the two, natural convection ensues. The influence of inhomogeneities in the thermal conductivity of the solid is studied - numerical simulations of the heat transfer in the system are conducted for substrates that are comprised of a thermally conductive material, an insulating one or a combination thereof. It is shown that the substrate structure strongly influences the structure and intensity of the natural convective flows emerging in the system. The present work demonstrates that under the idealized conditions under consideration, depending on the substrate structure, natural convection due to imperfect solution thermostating may give rise to flows whose local velocity can reach values as high as 10-3 m s-1. Moreover, as comparison between cells of two different radii shows, both the intensity and the temporal evolution of the flows arising in this system are highly sensitive to the precise geometry of the experimental cell. These results can have far-reaching consequences for the interpretation of results from experimental techniques such as scanning electrochemical microscopy.

Simulation of local ion transport in lamellar block copolymer electrolytes based on electron micrographs

ABSTRACTA method is presented to relate local morphology and ionic conductivity in a solid, lamellar block copolymer electrolyte for lithium batteries, by simulating conductivity through transmission electron micrographs. The electrolyte consists of polystyrene‐block‐poly(ethylene oxide) mixed with lithium bis(trifluoromethanesulfonyl) imide salt (SEO/LiTFSI), where the polystyrene phase is structural phase and the poly(ethylene oxide)/LiTFSI phase is ionically conductive. The electric potential distribution is simulated in binarized micrographs by solving the Laplace equation with constant potential boundary conditions. A morphology factor, f, is reported for each image by calculating the effective conductivity relative to a homogenous conductor. Images from two samples are examined, one annealed with large lamellar grains and one unannealed with small grains. The average value of f is 0.45 ± 0.04 for the annealed sample, and 0.37 ± 0.03 for the unannealed sample, both close to the value predicted by effective medium theory, 1/2. Simulated conductivities are compared to published experimental conductivities. The value of fUnannealed/fAnnealed is 0.82 for simulations and 6.2 for experiments. Simulation results correspond well to predictions by effective medium theory but do not explain the experimental measurements. Observation of nanoscale morphology over length scales greater than the size of the micrographs (∼1 μm) may be required to explain the experimental results. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017, 55, 266–274

A modified volume integral equation for anisotropic elastic or conducting inhomogeneities: Unconditional solvability by Neumann series

This work addresses the solvability and solution of volume integrodifferential equations (VIEs) associated with 3D free-space transmission problems (FSTPs) involving elastic or conductive inhomogeneities. A modified version of the singular volume integral equation (SVIE) associated with the VIE is introduced and shown to be of second kind involving a contraction operator, i.e. solvable by Neumann series, implying the well-posedness of the initial VIE. Then, the solvability of VIEs for frequency-domain FSTPs (modelling the scattering of waves by compactly-supported inhomogeneities) follows by a compact perturbation argument. This approach extends work by Potthast (1999) on 2D electromagnetic problems (transverse-electric polarization conditions) involving orthotropic inhomogeneities in a isotropic background, and contains recent results on the solvability of Eshelby's equivalent inclusion problem as special cases. The proposed modified SVIE is also useful for iterative solution methods, as Neumannn series converge (i) unconditionally for static problems and (ii) on some inhomogeneity configurations for which divergence occurs with the usual SVIE for wave scattering problems.

Two alternatives for magnetic resonance electrical impedance tomography: injected or induced current

In this paper, the abilities of injected current magnetic resonance electrical impedance tomography (MREIT) and induced current magnetic resonance electrical impedance tomography (ICMREIT) systems to differentiate a conductivity perturbation from an otherwise uniform conductivity distribution are compared. The sensitivity of MREIT measurements changes as a function of distance to the electrodes used for current injection. The sensitivity of ICMREIT measurements is related to the radial location, being a minimum for concentrically located small conductivity perturbations. The very low sensitivity of ICMREIT to conductivity perturbations at central locations seems to be the major drawback of the method compared with MREIT. When the diameter of a concentric and/or an eccentric circular conductivity inhomogeneity inside an otherwise homogeneous circular conductor is close to half of the diameter of the conductor region, the distinguishability of the perturbation by MREIT increases. MREIT is more sensitive to perturbations with lower conductivity with respect to background conductivity (resistive perturbations) than to conductive perturbations. In the case of ICMREIT, concentric inhomogeneities are equally distinguishable for conductive and resistive conductivity perturbations. Eccentric resistive inhomogeneities are more distinguishable then conductive inhomogeneities. Distinguishability increases with the size and number of conductivity perturbations.

Detecting Thermal Cloaks via Transient Effects.

Recent research on the development of a thermal cloak has concentrated on engineering an inhomogeneous thermal conductivity and an approximate, homogeneous volumetric heat capacity. While the perfect cloak of inhomogeneous κ and inhomogeneous ρcp is known to be exact (no signals scattering and only mean values penetrating to the cloak’s interior), the sensitivity of diffusive cloaks to defects and approximations has not been analyzed. We analytically demonstrate that these approximate cloaks are detectable. Although they work as perfect cloaks in the steady-state, their transient (time-dependent) response is imperfect and a small amount of heat is scattered. This is sufficient to determine the presence of a cloak and any heat source it contains, but the material composition hidden within the cloak is not detectable in practice. To demonstrate the feasibility of this technique, we constructed a cloak with similar approximation and directly detected its presence using these transient temperature deviations outside the cloak. Due to limitations in the range of experimentally accessible volumetric specific heats, our detection scheme should allow us to find any realizable cloak, assuming a sufficiently large temperature difference.

Illusion thermal device based on material with constant anisotropic thermal conductivity for location camouflage

Thermal metamaterials and devices based on transformation thermodynamics often require materials with anisotropic and inhomogeneous thermal conductivities. In this study, still based on the concept of transformation thermodynamics, we designed a planar illusion thermal device, which can delocalize a heat source in the device such that the temperature profile outside the device appears to be produced by a virtual source at another position. This device can be constructed by only one kind of material with constant anisotropic thermal conductivity. The condition which should be satisfied by the device is provided, and the required anisotropic thermal conductivity is then deduced theoretically. This study may be useful for the designs of metamaterials or devices since materials with constant anisotropic parameters have great facility in fabrication. A prototype device has been fabricated based on a composite composed by two naturally occurring materials. The experimental results validate the effectiveness of the device.

Convergence and regularization for monotonicity-based shape reconstruction in electrical impedance tomography

The inverse problem of electrical impedance tomography is severely ill-posed, meaning that, only limited information about the conductivity can in practice be recovered from boundary measurements of electric current and voltage. Recently it was shown that a simple monotonicity property of the related Neumann-to-Dirichlet map can be used to characterize shapes of inhomogeneities in a known background conductivity. In this paper we formulate a monotonicity-based shape reconstruction scheme that applies to approximative measurement models, and regularizes against noise and modelling error. We demonstrate that for admissible choices of regularization parameters the inhomogeneities are detected, and under reasonable assumptions, asymptotically exactly characterized. Moreover, we rigorously associate this result with the complete electrode model, and describe how a computationally cheap monotonicity-based reconstruction algorithm can be implemented. Numerical reconstructions from both simulated and real-life measurement data are presented.

Mathematical framework for multi-frequency identification of thin insulating and small conductive inhomogeneities

We are aiming to identify the thin insulating inhomogeneities and small conductive inhomogeneities inside an electrically conducting medium by using multi-frequency electrical impedance tomography. The thin insulating inhomogeneities are considered in the form of a tubular neighborhood of a curve and small conductive inhomogeneities are regarded as circular disks. Taking advantage of the frequency dependent behavior of insulating objects, we give a rigorous derivation of the potential along thin insulating objects at various frequencies. Asymptotic formula is given to analyze relationship between inhomogeneities and boundary potential at different frequencies. In numerical simulations, spectroscopic images are provided to visualize the reconstructed admittivity at various frequencies. For the view of both kinds of inhomogeneities, an integrated reconstructed image based on principal component analysis is provided. Phantom experiments are performed by using Swisstom EIT-Pioneer Set.

On Parameterization of the Global Electric Circuit Generators

We consider the problem of generator parameterization in the global electric circuit (GEC) models. The relationship between the charge density and external current density distributions inside a thundercloud is studied using a one-dimensional description and a three-dimensional GEC model. It is shown that drastic conductivity variations in the vicinity of the cloud boundaries have a significant impact on the structure of the charge distribution inside the cloud. Certain restrictions on the charge density distribution in a realistic thunderstorm are found. The possibility to allow for conductivity inhomogeneities in the thunderstorm regions by introducing an effective external current density is demonstrated. Replacement of realistic thunderstorms with equivalent current dipoles in the GEC models is substantiated, an equation for the equivalent current is obtained, and the applicability range of this equation is analyzed. Relationships between the main GEC characteristics under variable parameterization of GEC generators are discussed.

Small perturbation of a surface: Full Maxwell's equations

In this paper, we derive high-order terms in the asymptotic expansions of the boundary perturbations of the electromagnetic fields resulting from small perturbations of the shape of an inhomogeneity with Cd-boundary in Rd, for d=2,3. For such solutions we provide a rigorous derivation that extends those already derived for small volume conductivity inhomogeneities. Our formulas may be expected to develop effective algorithms, aimed at determining certain properties of the shape of an object based on electromagnetic boundary measurements.