Finite Conductivity Research Articles

Methodology for Accounting the Influence of Parameters of a Spherical Underlying Surface with Finite Conductivity on VLF Antennas Characteristics

Methodology for Accounting the Influence of Parameters of a Spherical Underlying Surface with Finite Conductivity on VLF Antennas Characteristics

Influence of variable viscosity and gravity fluctuation on double diffusive convection in a fluid layer with boundary slab of finite conductivity

The linear stability analysis is carried out for the onset of double-diffusive convection in a fluid layer with a boundary slab along with temperature-dependent viscosity and gravity fluctuation. The authors proposed three types of gravity fluctuation. We considered three cases of gravity field fluctuation: (a) linear and (b)parabolic and (c) cubic. An analytical solution for the subsequent problem is acquired through the perturbation technique. The findings demonstrate that the viscosity variation parameter, the thermal conductivity ratio, the gravity parameter, the depth ratio, and the soret parameter accelerate the start of convection, while the increasing Lewis number slow down the convective motion. Additionally, the system was found to be more stable for the linear type of gravity field fluctuation and more unstable for the cubic type of gravity field fluctuation.

Homogenization of Periodic Structures Using the Multimodal Transfer Matrix Method

This work presents a method for obtaining the constitutive parameters of periodic structures from the computation of their dispersion relation and average fields. The method uses the scattering parameters of multiple Bloch modes of a single unit cell. The corresponding multimodal scattering matrix is obtained with a suitable general-purpose electromagnetic software. Further post-processing of this scattering matrix is then carried out, which allows for the computation of the dispersion relation of structures with realistic finite conductivity or made of lossy dielectrics, as well as the calculation of the attenuation constant and the retrieval of the impedance, permittivity, and permeability. The proposed method is applied to homogenize some systems of interest: an artificial electric plasma built with wires, a free-space matched left-handed metamaterial based on two laterally shifted split ring resonators, a high-permittivity artificial dielectric based on densely arranged square metal patches, and a μ-near-zero metamaterial made of metallic cubes embedded in a dielectric. The retrieved material parameters are found to accurately describe the scattering of finite samples of the corresponding homogenized structures. This research is limited to orthorhombic unit cells smaller than half the free-space wavelength to avoid diffracted beams. Besides, since only one propagation direction is considered, only the transverse components of constitutive parameters are retrieved.

Reflection and transmission of both continuous and solitary waves in conductive media with Kerr-type nonlinearity

We present a theoretical study of the incidence of nonuniform waves between two dissipative media with finite conductivity and with a nonlinear response to the applied electric field, which is associated with the Kerr effect. From the Adler–Chu–Fano formulation, the complex propagation vectors, transmitted and reflected angles, and Fresnel coefficients are obtained for the two linear polarization states. In addition, the modification of the total internal reflection, the phase shift, the Goos–Hänchen effect, as well as the interface interaction with bright solitons are explored. Calculations are performed for fused silica, the chalcogenide As2S3 glass, and gold in glass media.

A review of the Kondo insulator materials class of strongly correlated electron systems: Selected systems and anomalous behavior

Studies of strongly correlated electron systems have been at the forefront of research in condensed matter physics ever since the discovery of the co-existence of strong Pauli-paramagnetism and superconductivity in the archetypal heavy-fermion compound CeCu2Si2 in 1979. The construct of correlated electron physics typifies the behavior of thermal and electronic properties of a material when the Coulomb interaction between conduction electrons exceeds the electron kinetic energy at a given thermal energy and redefines in remarkable ways our understanding of the behavior of a metal near its ground state. While correlated electron behavior has by now been demonstrated in a variety of different types of materials, Kondo systems in particular are arguably the most intensively studied among these. The Kondo interaction is used to describe the effect that a spin-magnetic ion has on its environment when immersed in the conduction electron sea of a metal. The localized spin of the Kondo ion polarizes nearby conduction electrons to form a so-called Kondo cloud, which acts to screen and magnetically (partially) neutralize the localized spin. In Kondo systems, the low-temperature behavior is prone to the formation of heavy fermions, which is the term given to quasiparticle excitations that define the emergence of effective electron masses that can be up to three orders of magnitude greater than that of a free electron. The Kondo effect presents itself in three guises: first, the single-ion Kondo state which is found in a metal having only a small amount of magnetic ions dissolved into it; second, the incoherent Kondo state in materials where there is a Kondo ion in every crystallographic unit cell of the material, but the Kondo ions remain incoherent or uncoupled from each other; and third, the coherent Kondo lattice state which manifests itself toward low temperatures where the interaction between Kondo ions becomes comparable to the thermal energy of conduction electrons that mediate magnetic exchange between Kondo ions. In a small number of cases, the outcome of a material condensing into the Kondo state turns out to be the peculiar formation of a very narrow energy band gap at the metallic Fermi energy. Such a band gap has significant consequences in practically all of the physical properties of a material that stem from the behavior of conduction electrons in proximity of the Fermi energy. This is most readily seen in electrical resistivity, heat capacity, and magnetic susceptibility. The band gapping gives cause to the term Kondo insulator (also referred to as Kondo semimetal or heavy-fermion semiconductor) that is used to describe this exceptional variety of Kondo systems. The term Kondo insulator is in general use although most Kondo insulators have a small but finite electrical conduction in the low-temperature limit where Kondo screening may be accomplished to its full extent. While the Kondo lattice ground state is exemplified by a very high density of electronic states at the Fermi energy, Kondo insulators, on the other hand, have, by virtue of narrow band gapping, a low density of electronic states. It remains a counter-intuitive observation, therefore, that despite their low density of states, Kondo insulators have curiously strong spin polarization energy scales and accompanying high values of their Kondo temperature, being the defining quantity which acts as an organizing principle in their temperature-dependent physical properties. In this article, we review the fundamentals of the Kondo insulating state, and we discuss the theoretical principles of what is presently understood about the formation of a Kondo insulator. The experimental results of a selected number of examples that have gained prominence in this class of materials are compared to each other in order to seek out similarities that may help deepen our understanding of the Kondo insulating state.

Frustration shapes multi-channel Kondo physics: a star graph perspective

We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalisation group technique. Our results display the importance of ground state degeneracy in explaining various important properties like the breakdown of screening and the presence of local non-Fermi liquids (NFLs). The impurity susceptibility of the intermediate coupling fixed point Hamiltonian in the zero-bandwidth (or star graph) limit shows a power-law divergence at low temperature. Despite the absence of inter-channel coupling in the MCK fixed point Hamiltonian, the study of mutual information between any two channels shows non-zero correlation between them. A spectral flow analysis of the star graph reveals that the degenerate ground state manifold possesses topological quantum numbers. Upon disentangling the impurity spin from its partners in the star graph, we find the presence of a local Mott liquid arising from inter-channel scattering processes. The low energy effective Hamiltonian obtained upon adding a finite non-zero conduction bath dispersion to the star graph Hamiltonian for both the two and three-channel cases displays the presence of local NFLs arising from inter-channel quantum fluctuations. Specifically, we confirm the presence of a local marginal Fermi liquid in the two channel case, whose properties show logarithmic scaling at low temperature as expected. Discontinuous behaviour is observed in several measures of ground state entanglement, signalling the underlying orthogonality catastrophe associated with the degenerate ground state manifold. We extend our results to underscreened and perfectly screened MCK models through duality arguments. A study of channel anisotropy under renormalisation flow reveals a series of quantum phase transitions due to the change in ground state degeneracy. Our work thus presents a template for the study of how a degenerate ground state manifold arising from symmetry and duality properties in a multichannel quantum impurity model can lead to novel multicritical phases at intermediate coupling.

A Dual Integral Equation Approach for Evaluating the Shielding of Thick Circular Disks against a Coaxial Loop

The electromagnetic interaction between a circular disk with finite conductivity and finite thickness and a coaxial circular loop of constant current is addressed here. The finite conductivity and thickness of the material disk lead to the adoption of suitable generalized boundary conditions, and the problem is thereby reduced to the solution of two sets of dual integral equations in the Hankel transform domain. Such equations are then solved by expanding the spectral unknowns in Neumann series of Bessel functions. An alternative formulation that is valid for purely conductive screens with no magnetic properties, which is computationally much faster, is proposed as well. The magnetic shielding effectiveness of the structure is studied in detail, pointing out its dependencies and possible critical situations.

Stress Sensitivity of Proppant-Containing Fractures and Its Influence on Gas Well Productivity

Formation pressure gradually decreases with fracturing fluid flowback and gas production. Due to the stress sensitivity of the fractures, the permeability of the artificial fractures after fracturing becomes lower, which significantly affects gas well productivity. This paper focuses on two questions: (1) the stress sensitivity of proppant-containing fractures with different roughness and (2) tight gas well productivity considering stress sensitivity. Two types of artificial fracture samples, smooth and rough, are prepared and filled with different proppant concentrations. Then, the changing confining pressure method is used to quantify sample stress sensitivity. On this basis, the productivity equation for the fractured well with finite conductivity that considers fracture and matrix stress sensitivity is derived, and the influence of stress sensitivity on productivity is discussed. The results show that proppant concentration and fracture surface roughness will significantly affect fracture permeability and stress sensitivity; with increasing proppant concentration, fracture permeability increases, stress sensitivity decreases, and well productivity increases; under the same proppant concentration, the stress sensitivity is lower and the gas production is higher for smooth fracture; and when the artificial fracture changes from no proppant to proppant, the productivity of the fracturing well is improved the most.

Amalgamations subject to weakly finite conductor and P-coherence

Amalgamations subject to weakly finite conductor and P-coherence

A Pseudocomponent-Based Approach for the Formulation of Evaporation Surrogates of Practical Liquid Fuels

ABSTRACT This study proposes and demonstrates a systematic methodology to formulate surrogates that can efficiently mimic the evaporation behaviors of real fuel droplets at elevated temperatures. The surrogates were designed by employing a discrete component evaporation model, which considers finite conductivity and mass diffusivity effects in the liquid phase. In the first place, a sensitivity analysis (SA) method was applied to rigorously assess the impact of each physical property on the fuel droplet evaporation behaviors. Then, the pseudo-component approach was employed to characterize the target fuel and estimate its physical properties based on hypothetical components. Comparing each pseudo-component (PC) with alkane hydrocarbons based on the most relevant properties (as identified from the SA) led to finding the most similar alkanes to those PCs. Thus, the proposed methodology allows to choose the optimal palette in a systematic manner. The final step is to optimize the mass fractions of the different constituents to emulate the evaporation characteristics of the target fuel by means of a multi-objective genetic algorithm. The fuel droplet evaporation was modeled for those selected compositions, and the results were validated against high-temperature experimental data obtained at a single falling-droplet facility for the target fuels. The method was applied on three different practical fuels, namely diesel, Jet A and heating oil, covering therefore a broad range of real applications. In all cases, the evaporation characteristics of the surrogates designed following the systematic methodology proposed here showed remarkable similarity to the target fuels.

Heat Flow in a Periodically Forced, Thermostatted Chain II

We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the Hamiltonian equation of motion plus a reversal of the velocity of a particle occurring independently for each particle at exponential times, with rate gamma . The latter produces a finite heat conductivity. Starting with an initial probability distribution for a chain of n particles we compute the current and the local temperature given by the expected value of the local energy. Scaling space and time diffusively yields, in the nrightarrow +infty limit, the heat equation for the macroscopic temperature profile T(t, u), t>0, u in [0,1]. It is to be solved for initial conditions T(0, u) and specified T(t,0)=T_-, the temperature of the left heat reservoir and a fixed heat flux J, entering the system at u=1. |J| equals the work done by the periodic force which is computed explicitly for each n.

Second-Law Considerations in Monte Carlo Ray-Trace and Discrete Green’s Function Analysis of Coupled Radiation and Conduction Heat Transfer

Abstract A generic Monte Carlo ray-trace (MCRT) engine for computing radiation distribution factors (RDFs), working in tandem with an efficient finite volume formulation based on discrete Green’s functions (DGFs), has been used to solve a massive (2636 nodes) coupled radiation/conduction problem. Distribution factors computed using the MCRT method are known to produce unconditionally stable solutions to pure radiation problems even though the RDFs themselves do not conform exactly to the reciprocity principle. However, when these same RFDs are introduced into time-dependent finite volume conduction formulations based on DGFs, the resulting model is found to be fundamentally unstable due to inherent violations of the second law of thermodynamics. A novel approach to addressing this instability is presented and demonstrated for the case of a telescope typical of those employed to monitor the planetary energy budget from low Earth orbit.

НИЗКОТЕМПЕРАТУРНЫЙ ЭЛЕКТРОННЫЙ ТРАНСПОРТ В ГИБРИДНЫХ ТОНКОПЛЕНОЧНЫХ НАНОСТРУКТУРАХ НА БАЗЕ ЭЛЕКТРОПРОВОДЯЩЕГО ПОЛИМЕРА

Most polymers are usually poor conductors of electric current and, accordingly, they can be classified as organic dielectrics. However, there is a special class of polymers, usually characterized by presence of conjugated pbonds, which provide electron delocalization, leading to electrical conductivity in the ground state of the system. In addition to such materials, there have been found polymers that are insulators in the ground state, but under the influence of external factors demonstrate a finite electrical conductivity. Polydiphenylenephthalide (PDP) belongs to the class of carbocyclic organic electroactive polymers that exhibit electrically conductive properties when an external electric field and/or mechanical stress is applied. The effect is explained by the nonzero density of electronic states inside the band gap. The depth of such states increases if the system accepts an additional electron, which indirectly provides electrical conductivity along the polymer chain. Accordingly, the presence of free electrons in contact region with a metal is an important condition for the appearance of final electrical conductivity in PDP. The working hypothesis that stimulates the proposed study is the assumption that superconducting correlations may arise in the electrically conductive state of an electroactive polymer. In the present work, the transport properties of thin-film lead-PDP-lead structures in two configurations are experimentally studied in a wide temperature range: a layered “sandwich” type and a quasi-planar “field-effect transistor” type. At temperatures below ~8 K, in layered samples, features of the PDP electron transport are observed, which can be explained by the effect of induced superconductivity in a thin film of a conducting polymer enclosed between two massive superconductors (lead). In the planar configuration, the electrical conductivity of the polymer in the plane of the structure does not appear. The reason for this observation may be related to the mechanism of the electrically conductive state of the PDP, characterized by formation of quasi-one-dimensional channels of electric current in the direction perpendicular to the plane of contact with the "donor" of electrons: metal in the normal or superconducting state. The effect of appearance of superconductivity in PDP requires further stidies and is potentially of significant interest for various applications in the field of practical microand nanoelectronics.

Anisotropic differential conductance of a mixed-parity superconductor/ferromagnet structure

We study the electronic transport properties of a superconductor (S) with a mixed s+p-wave pairing attached to a ferromagnetic metal (F) and a normal electrode (N) in an SFN configuration. Using the quasiclassical Green's function method, we compute the differential conductance $\sigma$ of the junction and demonstrate its dependence on the direction of the exchange field relative to the direction of the d-vector of the pair potential. If the p-wave triplet dominates the pairing, the zero bias conductance depends on the relative direction between the triplet d-vector and the exchange field. In contrast, if the s-wave singlet dominates the pairing, the zero bias conductance is isotropic with respect to the field direction. Furthermore, at zero temperature, the zero bias conductance height can only take two values as a function of $r$, the parameter quantifying the relative amount of s- and p-wave pairing, with an abrupt change at $r=1$ when the superconductor goes from a singlet to triplet dominated ground state. Moreover, we show that the relative amount of s- and p-wave pairing, can be estimated from the dependence of the finite bias conductance on the exchange field direction. Our results provide a way to characterize parity-mixed superconductors performing electrical measurements.

Lightning Electromagnetic Fields Computation: A Review of the Available Approaches

Lightning represents one of the most critical issues for electrical infrastructure. In dealing with overhead distribution line systems, indirect lightning strikes can lead to induced voltages overcoming the critical flashover value of the line, thus damaging the insulators. The computation of lightning-induced voltages requires the modeling of the lightning current, the evaluation of the lightning electromagnetic fields and the solution of the field-to-line coupling equations. The numerical calculation of the lightning electromagnetic fields is time-consuming and is strongly dependent on the lightning channel modeling and soil properties. This article presents a review of the most widely adopted methods to calculate the lightning electromagnetic fields, starting from the classical formulation, which requires numerical integration, and highlighting the most effective approaches that have been developed to reduce computational effort. This is done first for the case of a perfectly conducting ground, then the available formulations to account for the ground finite conductivity are presented together with their possible implementations in both the frequency and time domains.

Probing the percolation in the quantum anomalous Hall insulator

The percolation plays an essential role in the physics of plateau transition, localization, and breakdown in quantum Hall (QH) systems. In practice, it always exists probably due to sample imperfections and has to be addressed before realizing the full potentials of topological electronics and qubits. Here, we investigate the cause, distribution, and number of the percolation in a quantum anomalous Hall (QAH) insulator of an anti-Hall bar geometry with two perimeters, which allows for probing both the inter- and intra-perimeter percolations by injecting currents into either or both perimeters. We discover the dual-QAH effect with opposite chiralities from these two perimeters, which exhibits linear modulations by the currents applied to both perimeters. By solving the formulation of such modulations with the Landauer–Büttiker formalism, the distribution and number of the inter-perimeter percolative channels could be identified. Strikingly, a dissipative constituent is detected in the transport of the QAH state, as revealed by the linear scalings in longitudinal conductivities versus the sum of currents injected to both perimeters, similar to that in the trivial-insulating state. Such a behavior unveils the quasi-2D nature of the intra-perimeter percolation, which superimposes onto and perturbs the dissipationless chiral edge transport. The formation of percolations is ascribed to the joint effect of the electric field, finite conductivity, and sample imperfections.

Heat Flow in a Periodically Forced, Thermostatted Chain

We investigate the properties of a harmonic chain in contact with a thermal bath at one end and subjected, at its other end, to a periodic force. The particles also undergo a random velocity reversal action, which results in a finite heat conductivity of the system. We prove the approach of the system to a time periodic state and compute the heat current, equal to the time averaged work done on the system, in that state. This work approaches a finite positive value as the length of the chain increases. Rescaling space, the strength and/or the period of the force leads to a macroscopic temperature profile corresponding to the stationary solution of a continuum heat equation with Dirichlet-Neumann boundary conditions.

Alpha tensor and dynamo excitation in turbulent fluids with anisotropic conductivity fluctuations

AbstractA mean‐field theory of the electrodynamics of a turbulent fluid is formulated under the assumption that the molecular electric conductivity is correlated with the turbulent velocity fluctuation in the (radial) direction, . It is shown that for such homogeneous fluids a strong turbulence‐induced field advection anti‐parallel to arises almost independently of rotation. For rotating fluids, an extra effect appears with the known symmetries and with the expected maximum at the poles. Fast rotation, however, with Coriolis number exceeding unity suppresses this term. Numerical simulations of forced turbulence using the nirvana code demonstrate that the radial advection velocity, , always dominates the term. We show finally with simplified models that dynamos are strongly influenced by the radial pumping: for the solutions become oscillatory, while for they become highly exotic if they exist at all. In conclusion, dynamo models for slow and fast solid‐body rotation on the basis of finite conductivity–velocity correlations are unlikely to work, at least for dynamos without strong shear.

Modeling the Magnetic Field of the Inner Corona in a Radially Expanding Solar Wind

The magnetic field in the interplanetary medium is formed by the action of magnetic field sources on the photosphere of the Sun and currents in the expanding atmosphere of the Sun and the solar wind. In turn, the high-speed plasma flow changes the configuration of the magnetic field lines. The problem of determining the parameters of the magnetic field near the Sun is thus a three-dimensional problem of the interaction of the magnetic field and the plasma of the solar wind. We present analytical expressions for calculating the total magnetic field vector B→(r, θ, ϕ) (in spherical coordinates) for a radially expanding solar wind flow of finite conductivity. The parameters of the solar wind are given in the form of a dimensionless magnetic Reynolds number given as an arbitrary function of the radius, r: Rm = rσμv=ξ(r), where σ, μ, and v denote, respectively, the conductivity, magnetic permeability, and velocity of the solar wind. The solution for the magnetic field components is obtained in the form of a decomposition in spherical functions and a radial part depending on the distance from the Sun. Examples of calculations of the configuration of magnetic fields and structures of the solar corona for the solar eclipse of 21 August 2017 are given.

S-finite Conductor Rings

Recently, Anderson and Dumitrescu’s S-finiteness has attracted the interest of several authors. Inspired by the work done by S. Glaz (See [8]), in this paper, we introduce and study a new concept called S-finite conductor rings, as an extension of the classical notion of finite conductor rings. Knowing that the latter is closely linked to the notion of weakly finite rings, so for compatibility reasons, it is convenient to define and study an extension of the concept of finite presentation, we will call it weakly S-finite conductor rings.