Electric-field Equation Research Articles

A Triple-Tunable Dual-Band Metamaterial Absorber Based on Dirac Semimetal and InSb

The dynamically triple-tunable dual-band metamaterial absorber that can be electrically, thermally, and magnetically controlled is proposed in this paper. The absorber is composed of bulk Dirac Semimetal (BDS), SiO2, and InSb layers. The physical absorption mechanism can be analyzed theoretically by the equivalent circuit model (ECM) and electric field intensity distributions at absorption peaks. In the absence of applied magnetic field, based on the bright–bright coupling effect, the average absorption rate of dual-band absorber can reach 99.4% when the Fermi energy of the BDS is 0.13 eV and the temperature of the InSb is 475 K. When the applied magnetic field is along the X axis, the absorption frequencies and rates of dual-band absorber can be electrically tuned by adjusting the BDS Fermi energy and thermally and magnetically controlled by adjusting the InSb temperature and magnetic field. Furthermore, the impacts of parameters in dual-band absorbers and the application prospects of the dual-band absorber model as a refractive index sensor are further discussed. This work provides a theoretical basis for the designs of triple-tunable absorbers and sensors.

Molecular dynamics of deformation and fragmentation processes in liquid droplets under pulsed electric field

The deformation and breakup of droplets are widely observed in various aspects of production and daily life. Using molecular dynamics simulations, this study primarily investigated the deformation and breakup of droplets in a nitrogen environment under pulsed electric fields of different frequencies. The results indicate that the droplet deformation undergoes periodic changes under the influence of the pulsed electric field. At equivalent electric field strengths, droplets are more likely to break under a 6.25 GHz pulsed electric field compared to a 25 GHz pulsed electric field, where droplet deformation remains stable without breaking. At every frequency, the bond energy of water molecules consistently decreases. The solvent-accessible surface area changes with the electric field at 6.25 GHz. Furthermore, the minimum value of hydrogen bond quantity reached under high-frequency pulsed fields is higher than that under low-frequency fields. The change in hydrogen bond quantity is inversely proportional to the solvent-accessible surface area. These findings provide insights into the microscopic mechanisms of droplet deformation and breakup, offering a reference for future studies.

Terahertz magneto-optical sampling in quartz glass.

In this Letter, we demonstrate terahertz (THz) magnetic field detection in fused silica with sensitivity that can be easily controlled by sample tilting (for both amplitude and polarization). The proposed technique remains in the linear regime at magnetic fields exceeding 0.3 T (0.9 MV/cm of equivalent electric field) and allows the use of low-cost amorphous materials. Furthermore, the demonstrated effects should be present in a wide variety of materials used as substrates in different THz-pump laser-probe experiments and need to be considered in order to disentangle different contributions to the measured signals.

Enhancement of Charge-Discharge Properties and Temperature Stability of (Ba0.975Na0.05)Ti0.99Nb0.01O3 Ceramic by Doping High-Entropy Oxide

A bidirectional optimization strategy was adopted to fabricate (1-x)(Ba0.975Na0.05)Ti0.99Nb0.01O3)-xBi(Zn0.2Mg0.2Al0.2Sn0.2Zr0.2)O3(abbreviated as (1-x)BNNT-xBZMASZ, x = 0.02–0.10) ceramics, aimed to improve the energy storage performance. X-ray diffraction results revealed that Bi2+ cations entered the A site and the multiple cations occupied the B site of BNNT, thereby decreased the remnant polarization intensity and refined the hysteresis loop. Scanning electron microscopy images showed uniform morphologies with clear grain boundaries of the ceramics, and the average size decreased with x increasing. The substitution of multiple cations at the B-site induced the splitting of macroscopic ferroelectric domains into smaller polar nanodomains, leading to the formation of high-dynamic polar nanoregions and accelerating the transition from BNNT to relaxor ferroelectrics, thus improving relaxation properties of the material. The excellent energy storage density (Wrec ∼ 2.80 J cm−3) and efficiency (∼90.0%) can be obtained under 200 kV cm−1. Moreover, the discharge-charge testing revealed excellent current density (∼589.5 A cm−2), high power density (∼20.63 MW cm−2), and extremely short discharge time (t0.9 ∼ 50.4 ns), along with exceptional temperature stability and cycling stability under the equivalent electric field of 120 kV cm−1. The 0.92BNNT-0.08BZMASZ ceramic offers a new approach to the design and an improvement of pulsed dielectric capacitor materials.

Polynomial Solutions of Electric Field Equations in Anisotropic Media

The time-dependent system of partial differential equations of the second order describing the electric wave propagation in electrically and magnetically anisotropic homogeneous media is considered in the paper. A method for the computation of the polynomial solutions of the initial value problem for the considered system is proposed. Symbolic computations are used and these symbolic computations are implemented in Maple. It is proved also that these polynomial solutions are approximate solutions of the considered initial value problem with smooth initial data and the inhomogeneous term. The computational experiments confirm the robustness of the suggested method for the computation of electric fields in general electrically and magnetically anisotropic media.

Energy norm error estimates and convergence analysis for a stabilized Maxwell’s equations in conductive media

The aim of this article is to investigate the well-posedness, stability of solutions to the time-dependent Maxwell’s equations for electric field in conductive media in continuous and discrete settings, and study convergence analysis of the employed numerical scheme. The situation we consider would represent a physical problem where a subdomain is emerged in a homogeneous medium, characterized by constant dielectric permittivity and conductivity functions. It is well known that in these homogeneous regions the solution to the Maxwell’s equations also solves the wave equation, which makes computations very efficient. In this way our problem can be considered as a coupling problem, for which we derive stability and convergence analysis. A number of numerical examples validate theoretical convergence rates of the proposed stabilized explicit finite element scheme.

Investigating the impact of X-ray irradiation on the SF6 gas discharge in GIS equipment

ABSTRACT Gas Insulated Switchgear (GIS) is extensively utilized in power grid systems. However, the existence of numerous photoelectrons in the SF6 gas during X-ray non-destructive testing in ultra-high-voltage (UHV) GIS equipment may induce gas streamer discharge in a strong electric field. To address this issue, in this work, the impact of X-ray irradiation on the SF6 gas discharge in GIS equipment was systematically analyzed. Firstly, one GIS engineering mode with a three-dimensional electric field was established, and a physical GIS model was established by the Geant4 and Garfield++ codes. Secondly, the electrons’ ionization, and multiplication processes in SF6 gas during the X-ray irradiation were studied. Finally, a test platform with an equivalent electric field tube, which had the same intensity as in the GIS equipment, was established to verify the physical GIS model. X-ray beams with 0.1 MeV, 0.16 MeV, 0.3 MeV, and 1.25 MeV energy were used during the test process. From our analysis, it was concluded that X-ray irradiation can cause an electron avalanche in SF6 gas and the intensity of the avalanche is low, which is far away from the appearance of the streamer discharge.

Simulation of 1D atmospheric pressure dielectric barrier discharge in argon

This work aims at modelling an atmospheric-pressure homogeneous barrier discharge in argon, using a time-dependent 1D fluid model coupled to the electric field and plasmo-chemical kinetic equations. The model is chosen to mimic a discharge when a sinusoidal 1 kV voltage at 10 MHz is applied to the terminals. Energy and mass transfer are considered for a macroscopic fluid representation, while energy transfer in molecular collisions and chemical reactions is treated at the microscopic level. The macroscopic model is represented by a set of coupled partial differential equations. Microscopic effects are studied within a discrete model for electronic and molecular collisions in the frame of ZDPlasKin, a plasma modelling numerical tool. The BOLSIG+ solver is employed in solving the electronic Boltzmann equation. An operator splitting technique is used to separate microscopic and macroscopic models. The spatial and temporal evolution of such species and electron transport parameters are presented and discussed.

Multiphysics simulation of two-phase viscous fluid flow steered by electric field for jetting of microdroplets

In this research, we delve into the intricacies of viscous fluid flow with electric field coupling by employing the Finite Element Method (FEM) in tandem with the level set method. We generate a weak form for satisfying governing equations for electric field and fluid velocity while two phases are tracked by the level set function. The primary focus of this study is the complex interactions between free-falling jet and electric field, and the behavior of droplet encompassing deformation, fission, and fusion under the influence of electric field. The main contribution of this paper is given a new implement by using the P1/P1 scheme to directly solve the weak forms of coupled governing equations, which significantly improves calculation efficiency compared to the P2/P1 scheme, and we open source the code. This implement is verified by comparing with the experimental results of oil droplets deforming under an electric field. Computations are performed by FEniCS open-source packages. The phenomena documented underscore the multifaceted relationship between electrodynamic forces and fluid mechanics, accentuated distinctly under non-uniform electric field conditions.

A NUMERICAL ANALYSIS ON THE SUBMICRON- AND MICRON-SIZED PARTICLE SEDIMENTATION IN A WIRE-TO-PLATE ELECTROSTATIC PRECIPITATOR

Electrostatic precipitators (ESPs) are frequently utilized in collecting fine organic and inorganic materials from continuous liquid with few moving parts and high efficiency using electrically charging the particles. In this study, cross-sectional 2D geometry of a wire-to-plate electrostatic precipitator the parametric data of which originally published elsewhere was numerically modeled and validated to investigate submicron-micron particle charging in terms of diffusion and field charging mechanisms and precipitation behavior of particles with detailed electric field properties. Electric field, gas flow, and particle trajectory equations are coupled and solved in a multiphysics solver. Particle tracking is realized with the Lagrangian approach. Results indicate variations in electric field strength and space charge density between corona electrodes, with space charge present in the entire precipitation channel. Between two different charging mechanisms, diffusion charging prevails for charge accumulated on submicron particles, whereas field charging becomes dominant for particles larger than 1μm diameter. However, for the ESP configuration considered in this study, particles reach a charge saturation in less than 0.7 seconds, regardless of their size. Although calculated precipitation efficiencies for micron-sized particles can reach to 100%, efficiencies for submicron particle range drop with increasing particle size, as diffusion charging rapidly loses its effectiveness, in 50-250nm range.

Design and theoretical analysis of a tunable bifunctional metasurface absorber based on vanadium dioxide and photoconductive silicon.

A tunable bifunctional metasurface absorber based on vanadium dioxide (VO2) and photoconductive silicon (PSi) is proposed in a terahertz (THz) band. When the conductivities of VO2 (σvo2) and PSi (σPSi) are 10 S m-1 and 1 × 105 S m-1, the designed absorber has a function of dual-broadband absorption. The absorptivity rate of over 90% is in the dual-broadband of 2.47-3.71 THz and 8.90-10.62 THz, corresponding to relative bandwidths (RBs) of 40.13% and 17.62%, respectively. When σvo2 and σPSi are equal to 2 × 105 S m-1 and 1 × 105 S m-1, the proposed design has a function of single-broadband absorption. More than 90% absorptivity is achieved in 4.69-7.72 THz (RB = 48.83%). Furthermore, the absorptivity under the dual- and single-broadbands is manipulated by changing σPSi. An impedance matching theory, equivalent transmission-line (TL) model and electric field distribution are used to reveal the tunable bifunctional absorption mechanism. The influences of structure parameters, polarization mode and incidence angle on the dual- and single-broadband absorption are investigated. The dual- and single-broadband absorption performances are maintained within the incident angles of 55° and 60°, which also possess polarization insensitivity. The proposed absorber has a potential application value in multifunctional devices such as modulation, sensing and electromagnetic (EM) stealth.

Enhanced energy storage performance in Na(Nb,Ta)O3-doped Ba(Ti,Ca)O3-based ceramics through bidirectional optimization strategy

(1-x)(0.9Ba1.003Ti0.97Ca0.03O3–0.1(Bi0.51Na0.47)0.94Ba0.06TiO3)-xNa(Nb0.85Ta0.15)O3 (x = 0.03–0.15) ceramics were designed and fabricated through a bidirectional optimization strategy using traditional solid reaction method. The results revealed that the introduction of Na(Nb0.85Ta0.15)O3 increased the vacancy concentration at the A site, conducing to improved polarization and reduced grain size. The substitution at the B site disrupted the long-range ordered ferroelectric domains and generated polar nanodomains, leading to enhanced relaxation behavior. The optimum energy storage density of 3.57 J/cm3 and efficiency of 87.5% were simultaneously achieved under the electric field of 220 kV/cm in the sample with x = 0.09. Moreover, it also exhibits extremely high-power density (∼57 MW/cm3), ultrafast discharge time (∼103 ns), high discharge density (1.35 J/cm3), along with excellent temperature (30‒120 °C) and frequency stability (1‒100 Hz) under the equivalent electric field of 120 kV/cm. This novel design strategy provides theoretical guidance for the development of advanced electrical energy storage devices.

Effect of electrode configuration on minichannel heat sink with EHD vortex generators

A numerical study has been performed to understand the effects of electrode spacing on thermo-hydraulic performance in a minichannel assisted with electrohydrodynamics (EHD) based active vortex generation. A minichannel design with alternate high voltage and grounded electrodes flushed to the walls of the channel is considered. Multiple cases with different combinations of electrode length and spacing (pitch) at Reynolds number varying from 200 to 1000 are investigated. The numerical framework consisting of the two-way coupled governing equations for flow, thermal, charge, and electric potential fields is developed in the open-source finite-volume framework of OpenFOAM®. Applying an electric field induces the Onsager–Wien effect, producing flow vortices from electrode pairs. The EHD vortices disrupt the inherent laminar flow structure in the minichannel. The flow morphology is characterized by alternate vortex and shear dominant zones near the top and bottom walls. The EHD vortex dominant zones near the channel wall disrupt the laminar boundary layers. Thus, fluid mixing and heat transfer in the minichannel are enhanced. Electrode size and spacing influence the electric field distribution in the flow domain. As a result, electrode length and the inter-electrode spacing notably influenced the flow structure and the resulting heat transfer in the minichannel. The electrode spacing or the pitch decides the number of electrode pairs in the minichannel. An increase in pitch leads to fewer electrode pairs; thus, the electric field intensity is weak. Hence, EHD vortices in configurations with wider electrode spacing are weaker in strength. Longer electrodes produced stronger electric fields due to increased charge accumulation. Therefore, EHD vortices generated by longer electrodes are prominent and influential. The influence of EHD vortices on flow disruption and heat transfer is significant at lower Reynolds numbers. Cases with smaller electrodes perform well at higher Reynolds numbers, whereas usage of bigger electrodes exhibits higher performance at lower Reynolds numbers. Within the parameter space of this study, a minimum of 38.1% and a maximum of 60.6% enhancement in heat transfer is observed. A maximum performance factor of 1.46 is obtained in the present study using an electric current of 30μA with an electric power consumption of 30.1mW, which are notably low. Thus, the results of the present study exhibit that EHD vortex generation using the Onsager–Wien effect is a viable and economical option for thermo-hydraulic performance enhancement in a minichannel. Insights provided in the present study will be helpful to engineers and researchers in designing minichannel heat sinks with EHD-based performance improvement.

An Efficient Parallel Iterative Solver for Controlled-source Electromagnetic 3-D Adaptive Forward Modeling in General Anisotropic Media

Controlled-source electromagnetic (CSEM) surveys are moving increasingly toward realistic and complicated scenarios where the survey region may contain undulated topography, complex geometries, and electrical anisotropy media. In this paper, the adaptive finite element numerical method is employed to discrete the total electric field equation, which can provide precise electromagnetic (EM) responses even with a coarse initial mesh. The unstructured tetrahedral grid is employed to effectively address arbitrary irregular geometry and mountain terrain. Then, the flexible generalized minimum residual solver (FGMRES), auxiliary-space Maxwell pre-conditioner, and grid division technique were used to solve the large-scale linear system of equations, which can stably solve ill-conditioned problems using fewer computing resources. Finally, we conducted a numerical experiment via our newly proposed forward modeling scheme on a synthetic model with multi-contrast electrical anisotropy. It validated that accurate EM fields could be obtained against the semi-analytic solutions, and this iterative solver has good robustness for various anisotropic media. As a result, we have developed a state-of-the-art 3D CSEM anisotropic forward modeling engine, which can quickly and accurately deal with large-scale and complex geo-models.

Analysis of characteristics of electric field-enhanced multi-gradient of solid particles in oil

Lubricating oil is easily polluted by solid particles, causing it to deteriorate; therefore, solid particles must be separated from the oil. Furthermore, as conventional filtration devices cannot meet both filtration accuracy and service life requirements, an oil and solid separation method for multi-gradient filtration enhanced by an electric field is proposed. A numerical model for multi-gradient separation was established by coupling the governing equations of electric and flow fields, the particle-wall collision equation, and the discrete phase-tracking equation. Enhanced by an electric field, the characteristics of the multi-gradient filtration of solid particles in oil were investigated using finite element method. The effects of the main control parameters on the filtration performance were analyzed. The results indicate that using the electric field-enhanced multi-gradient filtration method can achieve highly efficient separation of solid particles from the oil. When the electric field strength was increased from 0 kV/mm to 2 kV/mm, the deposition concentration of particles was 2.5 times higher and filtration efficiency of the system increased to 97.46%. Additionally, the deposition concentration and filtration efficiency decreased from 0.15 m/s to 0.3 m/s, while gradually increased from 0.3 m/s to 0.5 m/s, for a particle size range of 10–40 µm.

Diffusiophoresis of a highly charged rigid colloid in a hydrogel incorporating ion steric interactions

Diffusiophoresis, mediated by an imposed ionic concentration gradient, is a useful technique in directed migration of colloids. Theoretical studies on diffusiophoresis in a polymer hydrogel medium are rather limited owing to the presence of nonlinear terms in the fluid transport equations. The hydrogel creates a hydrodynamic interaction and short-range steric interaction to the dispersing particle and macromolecules. The volume exclusion due to a finite ion size consideration is important in the context of a highly charged particle. In this study, we consider the finite ion size effects on diffusiophoresis of a charged particle with ζ≥1 in a hydrogel medium. The modified ion transport equations coupled with the Brinkman equation for fluid flow and the Poisson equation for electric field are solved numerically in a coupled manner through a control volume approach. Our results based on the Brinkman model incorporating only the hydrodynamic interactions deviate from the existing experimental results. A close comparison with this experimental data is established when the computed mobility is modified to incorporate the short-range steric factor. We have considered the impact of the hindered diffusivity of ions in the gel medium. Our results show that the modification in the ionic diffusivity is significant for low porosity and high charge density situations. The impact of the finite ion size effect is found to be significant when the bulk ionic concentration is large enough to create an electric double layer thinner than the particle size. We have analyzed the size dependency of the mobility in the gel medium. A simplified expression for the mobility in a hydrogel medium is proposed.

Extension of Maxwell’s Equations for Determination of Relativistic Electric and Magnetic Field

This paper presents the transformation of four Maxwell’s equation into relativistic electromagnetism via the partial differential equation of electric and magnetic field with respect to spatial and temporal coordinates. The relativistic form of magnetic field is developed based on Gauss’s law for magnetism and Ampere’s law while the relativistic form of electric field is developed based on Gauss’s law for electricity and Faraday’s law, where and are rest magnetic and electric field. We can easily explain theoretically about the various properties of electromagnetic waves (EM waves) with help of this relativistic formula such as; 1) Why EM waves are not deflected by electric and magnetic field as they have both oscillating electric and magnetic field? ;2) why can’t light travel faster than the speed of light? In this highly interesting topic, the particular purpose is not to enter into the merits of existing theory of relativistic electromagnetism, but rather to present a succinct and carefully reasoned account of new aspect of Maxwell’s equation which properly describe the relativistic nature of magnetic and electric Field.

On modal decomposition as surrogate for charge-conservative EHD modelling of Taylor Cone jets

The dynamics of the interface of a fluid jet subjected to an external electrostatic field forming a Taylor cone jet is investigated using a numerical approach. A charge-conservative electrohydrodynamic model is used. In this model, the reduced form of Maxwell’s equations for an electrostatic field, a transport equation for electric charges and the Navier–Stokes equations for a laminar flow are solved. The connection between the electric field and the hydrodynamic flow is established by the Maxwell stress tensor, which ensures the description of the electric surface forces. A fluid volume model based on surface compression provides an efficient and robust modulation of the overall behaviour of the electric drive of immiscible flows. Test cases from the literature López-Herrera et al. (2011); Roghair et al. (2015) help us to validate the numerical model. The order of accuracy of the spatial and temporal discretization of the electric field equations is computed through a quasi one-dimensional test case. The primary decay of a Taylor cone beam is then simulated with uniform droplet emission. This simulation is validated with experimental results from the literature Taylor (1969). To analyse the dynamics of the flow, it is proposed to use decomposition methods such as Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD) using snapshots of the flow field. The dynamic structures formed by the velocity field and the dynamics of the electric charge determine the fundamental dynamics of the droplet emission. An analysis of the sensitivity of the modes to the sampling frequency is performed. The influence of different inlet velocities on the decomposition is analysed in the spatial and frequency domain. A reduced-order model (ROM) is interpolated from the base POD, and we demonstrate that it can be used to successfully construct the velocity and electric charge along the field. We anticipate numerous applications of this new type of ROM, such as for accelerating electrohydrodynamic calculations as surrogate models in digital twins.

Water-Induced Bandgap Engineering in Nanoribbons of Hexagonal Boron Nitride.

Different from hexagonal boron nitride (hBN) sheets, the bandgap of hBN nanoribbons (BNNRs) can be changed by spatial/electrostatic confinement. It is predicted that a transverse electric field can narrow the bandgap and even cause an insulator-metal transition in BNNRs. However, experimentally introducing an overhigh electric field across the BNNR remains challenging. Here, it istheoretically and experimentally demonstrated that water adsorption greatly reduces the bandgap of zigzag-oriented BNNRs (zBNNRs). Ab initio calculations show that water molecules can be favorably assembled within the trench between two adjacent BNNRs to form a polar ice layer, which induces a transverse equivalent electric field of over 2Vnm-1 accounting for the bandgap reduction. Field-effect transistors aresuccessfully fabricated from zBNNRs with different widths. The conductance of water-adsorbed zBNNRs canbe tuned over 3 orders in magnitude via modulation of the equivalent electrical field at room temperature. Furthermore, photocurrent response measurements aretaken to determine the optical bandgaps of zBNNRs with water adsorption. The zBNNR with increased width can exhibit a bandgap down to 1.17eV. This study offers fundamental insights into new routes toward realizing electronic/optoelectronic devices and circuits based on hexagonal boron nitride.

A FEM in frequency domain for a transient electric field in non-sinusoidal steady state under the non-sinusoidal periodic voltage

PurposeThis paper aims to focus on the finite element method in the frequency domain (FD-FEM) for the transient electric field in the non-sinusoidal steady state under the non-sinusoidal periodic voltage excitation.Design/methodology/approachFirstly, the boundary value problem of the transient electric field in the frequency domain is described, and the finite element equation of the FD-FEM is derived by Galerkin’s method. Secondly, the constrained electric field equation on the boundary in the frequency domain (FD-CEFEB) is also derived, which can solve the electric field intensity on the boundary and the dielectric interface with high accuracy. Thirdly, the calculation procedures of the FD-FEM with FD-CEFEB are introduced in detail. Finally, a numerical example of the press-packed insulated gate bipolar transistor under the working condition of the repetitive turn-on and turn-off is given.FindingsThe FD-CEFEB improves numerical accuracy of electric field intensity on the boundary and interfacial charge density, which can be achieved by modifying the existing FD-FEMs’ code in appropriate steps. Moreover, the proposed FD-FEM and the FD-CEFEB will only increase calculation costs by a little compared with the traditional FD-FEMs.Originality/valueThe FD-CEFEB can directly solve the electric field intensity on the boundary and the dielectric interface with high accuracy. This paper provides a new FD-FEM for the transient electric field in the non-sinusoidal steady state with high accuracy, which is suitable for combined insulation structure with a long time constant.