Equation For Current Density Research Articles

Scattering of surface plasmons on graphene by a discontinuity in surface conductivity

The scattering of graphene surface plasmons from an arbitrary, one-dimensional discontinuity in graphene surface conductivity is treated analytically by an exact solution of the quasi-static integral equation for surface current density in the spectral domain. It is found that the reflection and transmission coefficients are not governed by the Fresnel formulas obtained by means of the effective medium approach. Furthermore, the reflection coefficient generally exhibits an anomalous reflection phase, which has so far only been reported for the particular case of reflection from abrupt edges. This anomalous phase becomes frequency-independent in the regime where the effect of inter-band transitions on graphene conductivity is negligible. The results are in excellent agreement with full-wave electromagnetic simulations, and can serve as a basis for the analysis of inhomogeneous graphene layers with a piecewise-constant conductivity profile.

Characterization of barrier heights in Nd0.7Sr0.3MnO3/Nb : SrTiO3 junctions with current–voltage characteristics

Barrier heights in heterojunctions composed of Nd0.7Sr0.3MnO3 and Nb doped SrTiO3 have been characterized with current–voltage characteristics by using various methods. It is revealed that an inappropriate assumption of the transport mechanism would usually lead to the underestimation of the barrier height. Provided that the transport mechanism is correctly identified the barrier height deduced with current–voltage characteristics could be in accordance with Anderson’s model and typical internal photoemission results. It is suggested that for manganite–titanate heterojunctions introducing the ideality factor in the thermionic emission saturation current density equation might largely counteract the underestimation of the barrier height.

LIGHT SCATTERING FROM TWO-DIMENSIONAL PERIODIC ARRAYS OF NOBLE-METAL DISKS AND COMPLEMENTARY CIRCULAR APERTURES

Numerical solution is presented for light scattering from two kinds of free-standing periodic arrays, that is, disks made of noble-metal and circular apertures perforated in a thin noble-metal sheet. The shapes of them are complementary to each other, and the circular areas are allocated along two orthogonal coordinates with the same periodicity. Using the generalized boundary conditions of the surface impedance type, we formulate the boundary value problem into a set of integral equations for unknown electric and magnetic current densities defined over the circular area. Employment of the method of moments allows us to solve the integral equations and give the expansion coefficients of the current densities, from which we can find reflected, transmitted, and absorbed powers. Dependence of the powers on the array parameters and wavelength is discussed in detail from the viewpoint of grating resonance. Special attention is paid to the extraordinary transmission which occurs in the arrays of apertures of sub-wavelength size by analytical derivation of the quasi-static solutions.

Quantum corrected drift-diffusion model for terahertz IMPATTs based on different semiconductors

The authors have developed a quantum corrected drift-diffusion model for impact avalanche transit time (IMPATT) devices by coupling the density gradient model with the classical drift-diffusion model. A large-signal simulation technique has been developed by incorporating the quantum potentials in the current density equations for the analysis of double-drift region IMPATT devices based on different semiconductors such as Wurtzite---GaN, InP, type-IIb diamond (C), 4H---SiC and Si deigned to operate at different millimeter-wave (mm-wave) and terahertz (THz) frequencies. It is observed that, the RF power output and DC to RF conversion efficiency of the devices operating at higher mm-wave ($$>$$>140 GHz) and THz frequencies reduce due to the incorporation of quantum corrections in the model; but the effect of quantum corrections are negligible for the devices operating at lower mm-wave frequencies ($$\le $$≤140 GHz).

Virtual resistive network and conductivity reconstruction with Faradayʼs law

A network-based conductivity reconstruction method is introduced using the third Maxwell equation, or Faradayʼs law, for a static case. The usual choice in electrical impedance tomography is the divergence-free equation for the electrical current density. However, if the electrical current density is given, the curl-free equation for the electrical field gives a direct relation between the current and the conductivity and this relation is used in this paper. Mimetic discretization is applied to the equation, which gives the virtual resistive network system. Properties of the numerical schemes introduced are investigated and their advantages over other conductivity reconstruction methods are discussed. Numerically simulated results, with an analysis of noise propagation, are presented.

Quantum drift-diffusion model for IMPATT devices

Quantum correction is necessary on the classical drift-diffusion (CLDD) model to predict the accurate behavior of high frequency performance of ATT devices at frequencies greater than 200 GHz when the active layer of the device shrinks in the range of 150---350 nm. In the present work, a quantum drift-diffusion model for impact avalanche transit time (IMPATT) devices has been developed by incorporating appropriate quantum mechanical corrections based on density-gradient theory which macroscopically takes into account important quantum mechanical effects such as quantum confinement, quantum tunneling, etc. into the CLDD model. Quantum potentials (synonymous as Bohm potentials) have been incorporated in the current density equations as necessary quantum mechanical corrections for the analysis of millimeter-wave (mm-wave) and Terahertz (THz) IMPATT devices. It is observed that the large-signal (L-S) performance of the device is degraded due to the incorporation of quantum corrections into the model when the frequency of operation increases above 200 GHz; while the effect of quantum corrections are negligible for the devices operating at lower mm-wave frequencies.

Electron spin and probability current density in quantum mechanics

This paper analyzes how the existence of electron spin changes the equation for the probability current density in the quantum-mechanical continuity equation. A spinful electron moving in a potential energy field experiences the spin-orbit interaction, and that additional term in the time-dependent Schrödinger equation places an additional spin-dependent term in the probability current density. Further, making an analogy with classical magnetostatics hints that there may be an additional magnetization current contribution. This contribution seems not to be derivable from a non-relativistic time-dependent Schrödinger equation, but there is a procedure described in the quantum mechanics textbook by Landau and Lifschitz to obtain it. We utilize and extend their procedure to obtain this magnetization term, which also gives a second derivation of the spin-orbit term. We conclude with an evaluation of these terms for the ground state of the hydrogen atom with spin-orbit interaction. The magnetization contribution is generally the larger one, except very near an atomic nucleus.

A hypersingular integral equation for current density on the surface of a microstrip vibrator

The problem of finding the current-density distribution on the surface of a microstrip vibrator (MV) in the framework of a thin ideally conducting strip, deposited on a dielectric substrate with one-sided metallization, is reduced to solution of a hypersingular integral equation (HSIE). The dependences of the input impedance on the vibrator length and substrate thickness are presented.

Proximity effect in a shielded symmetrical three-phase line

In this paper we present an approximate analysis of the proximity effect in a shielded symmetrical three-phase line with conductors of circular cross section. The system of two integral equations for current densities is solved approximately by assuming them in the form of two finite series with properly chosen basic functions. The unknown coefficients in these series are found by applying the point matching procedure. Numerical results are given for the AC to DC resistance ratio of the line conductors and for the power loss in the shield.

Simple algorithm for calculating the total electric field of high‐voltage direct current transmission lines

The basic equations of high-voltage direct current transmission lines’ ion current field are consisted of electric field Poisson equation, ion current density equation and the current continuity equation, hence, the key to calculating total electric field is to solve the non-linear differential equations, but the calculation process is very complicated. A simple algorithm is proposed to solve the problem in this study. First, the charge simulation method, an accurate numerical method, is employed to calculate the distribution of the electrical fields of a conductor. Then, the thought of emission charge is referred to calculate total electric field strength, this method does not need to adopt Deutsch hypothesis, and it avoids solving complex differential equations; hence, the calculation process can be greatly simplified. Finally, it is found that the calculated values agree satisfactorily with data measured on laboratory models and full-scale test lines.

Estimation of longitudinal dispersivity in a porous medium using self-potential signals

Abstract This paper presents several approaches to deduce the longitudinal dispersivity in a sand column during experiments oftracer tests, by measuring the output fluid concentration and the self-potential signals in the electrodes inserted into the sand. These signals have been used to obtain an estimate of longitudinal dispersivity through a coupled and an uncoupled hydrogeophysical approach. The first approach uses electrical current density and solute mass continuity equations simultaneously: the dispersivity is conditioned directly by the self-potential signals. Instead, the uncoupled approach firstly converts self-potential signals into concentration values using the Planck-Henderson equation and then estimates the dispersivity using only the transport equation. Longitudinal dispersivities calculated using self-potential signals by means of these two approaches were compared with those obtained using the concentration derived from a conductometer on the top of the column. The results show the goodness of the hydrogeophysical approaches.

Influence of powerful nanosecond electrical pulses on an array of double-walled nanotubes

We obtain a system of equations for the surface current density by taking the effect of intershell tunneling in the array of double-walled carbon nanotubes in the presence of a nonstationary electrical pulse into account. We show that if there is no tunneling, then the resonance frequency of surface currents for the symmetric mode increases by a factor of approximately \(\sqrt 2 \) in addition to the twofold increase in their concentration in the direction transverse to the nanotube axis as compared with single-walled nanotubes. We show that bending the carbon nanotube surfaces does not affect the electrical conduction in the millimeter range of generated radiation. We discuss the influence of the nonstationary electrical pulse on the asymmetric mode of longitudinal surface currents.

On a New Equation for Critical Current Density Directly in Terms of the BCS Interaction Parameter, Debye Temperature and the Fermi Energy of the Superconductor

Recasting the BCS theory in the larger framework of the Bethe-Salpeter equation, a new equation is derived for the temperature-dependent critical current density jc(T) of an elemental superconductor (SC) directly in terms of the basic parameters of the theory, namely the dimensionless coupling constant [N(0)V], the Debye temperature θD and, additionally, the Fermi energy EF—unlike earlier such equations based on diverse, indirect criteria. Our approach provides an ab initio theoretical justification for one of the latter, text book equations invoked at T = 0 which involves Fermi momentum; additionally, it relates jc with the relevant parameters of the problem at T ≠ 0. Noting that the numerical value of EF of a high-Tc SC is a necessary input for the construction of its Fermi surface—which sheds light on its gap-structure, we also briefly discuss extension of our approach for such SCs.

Electromagnetic fields of time-dependent magnetic monopole

Dirac-Maxwell's equations, retained for magnetic monopoles, are generalized by introducing magnetic scale field. It allows the magnetic monopoles to be time-dependent and the potentials to be Lorentz gauge free. The non-conserved part or the time-dependent part of the magnetic charge density is responsible to produce the magnetic scalar field which further contributes to the magnetic and electric vector fields. This contribution makes possible to create an ideal square wave magnetic field from an exponentially rising and decaying magnetic charge. The Maxwell-Heaviside equations prescribe both open dissipative systems having coefficient of performance (COP) > 1 and equilibrium systems having COP 1, by functioning as open dissipative systems freely receiving and using excess energy from the active vacuum. To study the open dissipative systems the potentials are to be made Lorentz gauge free. While studying such systems, Anastasovski et al (2) obtained equations for vacuum current density and vacuum charge density and proposed to pick up by a receiver and use to generate huge electrical energy. Similar results have been deduced by Lehnert (3-6) and Lehnert and Scheffel (7) from the condition of a nonzero charge density from vacuum fluctuations in combination with the requirement of Lorentz invariance. By another approach Teli and Jadhav (8) removed the Lorentz condiction on potentials by introducing scalar potentials in the Generalized Dirac- Maxwell's equations which made the electrical charges time varying in nature. These charges then did not satisfy the continuity equation. The non-conserved part of the charge density was accommodated in terms of a scalar field. They obtained electromagnetic fields of non-conserving electric charged particle. However, magnetic monopoles, elementary particles with a net magnetic charge, have been a curiosity for physicists and many believe they ought to exist. Our attempt is to find out the fields of non-conserving magnetic monopoles

Theoretical study of armchair single-walled carbon nanotubes in the presence of a strong laser field: high harmonic generation

The nonlinear optical response of armchair single-walled carbon nanotubes under high-intensity laser irradiation is investigated theoretically and numerically because the generation of high harmonics requires a strong laser field and come from the nonlinear motion of π electrons in carbon nanotubes. A nonperturbative approach is performed to investigate the effect of group velocity on the high harmonics spectrum by nanotubes. A set of the quantum kinetic equations is derived, which includes coupled equations for the density matrix. By solving the density matrix and the current density equations numerically, we have studied the high-order harmonic generation from metallic carbon nanotubes driven by an electromagnetic external field.

Method of radar detection and identification of metal and dielectric objects with resonant sizes located in dielectric medium

Mathematical model of a radar detection and identification system to be used for finding different objects buried in the ground or in other dielectric media is considered. In the suggested model scattering characteristics of 3D resonant objects are calculated by solving 2nd kind Fredholm integral equations for equivalent current densities on the object’s surface. Based on the obtained results we derive a method of detection and identification for specific types of objects which incorporates analysis of their natural resonant frequencies. Potentialities of the developed method for detection and identification of different types of mines are estimated.

Modeling the pre-earthquake electrostatic effect on the F region ionosphere

This paper presents the results of modeling the ionospheric effect of the seismogenic electrostatic field (SEF) seen at the earth’s surface as a perturbation of the vertical atmospheric electrostatic field in the earthquake preparation zone. The SEF distribution at ionospheric altitudes is obtained as an analytical solution of the continuity equation for the electric current density. It is shown that at night, the horizontally large scale SEF can efficiently penetrate into the ionosphere and produce noticeable changes in the horizontal distribution of the F region electron density. The results suggest that the seismogenic electrostatic field could be a possible source for the ionospheric variations observed over Taiwan before the strong Chi Chi earthquake of September 21, 1999.

Wave-diffusion theory of spin transport in metals after ultrashort-pulse excitation

Spin and charge-current dynamics after ultrafast spin-polarized excitation in a normal metal are studied theoretically using macroscopic wave-diffusion equations for spin-resolved carrier and current densities. It is shown analytically how this set of equations yields a unified description of ballistic and diffusive properties of spin and charge transport, including the intermediate regime between these two limits. In the framework of the wave-diffusion approach, ultrafast excitation of spin-polarized carriers in thin gold films is modeled assuming slightly spin-dependent momentum relaxation times along with standard parameters (Fermi velocity, spin and momentum relaxation times). The unified treatment of diffusive and ballistic transport yields robust signatures in the spin and charge dynamics that are in qualitative agreement with recent experimental results [Melnikov et al., Phys. Rev. Lett. 107, 076601 (2011)]. The influence of boundary effects on the temporal signatures of spin transport is also studied.

Pole discontinuity removal using artificial neural networks for microstrip antenna design

This article presents the use of artificial neural networks for the evaluation of integrals with finite number of pole singularities while formulating the integral equation for the electric surface current density. A feed-forward single-layer back-propagated artificial neural network (ANN) model has been trained to approximate the discontinuous integrand function. Generation of a soft continuous function obtained from the ANN model and closed-loop expressions for the evaluation of the integrals are presented. The proposed technique is applied to compute the input impedance of microstrip antenna and results have been compared with IE3D. Integration has been performed using n-point Gaussian quadrature rule for evaluating the reaction matrix.

Modelling and simulation of self-ordering in anodic porous alumina

Real-time evolution of pre-textured anodic porous alumina growth during anodization is numerically simulated in two-dimensional cases based on a kinetic model involving the Laplacian electric field potential distribution and a continuity equation for current density within the oxide body. Ion current densities governed by the Cabrera–Mott equation in high electric field theory are formed by ion migration within the oxide as well as across the metal/oxide (m/o) and oxide/electrolyte (o/e) interfaces, and the movements of the m/o and o/e interfaces due to oxidation and electric field assisted oxide decomposition, respectively, are governed by Faraday's law. Typical experimental results, such as linear voltage dependence of the barrier layer thickness and pore diameter, time evolution of the current density, scalloped shape of the barrier layer, and the extreme difference in the reaction rates between pore bottoms and pore walls, are successfully predicted. Our simulations revealed the existence of a domain of model parameters within which pre-textured porous structures which do not satisfy self-ordering configurations are driven into self-ordering configurations through a self-adjustment process. Our experimental results also verify the existence of the self-adjustment process during anodization.