Electric Vector Research Articles

On gauge invariance and results for spin and orbital angular momenta and helicity densities in optical fields

The spin (sn) and orbital (ln) angular momenta and helicity (hn) densities of the electromagnetic fields are defined by introducing two types of electric (C) and magnetic (A) vector potentials defined as D = ∇ × C and B = ∇ × A for the electric (D) and magnetic (B) induction fields. The gauge invariances of sn, ln and hn for the optical field are achieved without gauge fixing by canceling out the contributions from four nablas ∇ acting on two gauge functions (GFs) (u and υ) and two scalar potentials (SPs) (Φ and ψ) which are generated by introducing A and C. As a result, it is found that sn, ln and hn can be quantized without gauge fixing, where θ and α are phase differences between A and C and between ∇u and ∇Φ or ∇υ and ∇ψ, respectively. In the fundamental aspect of gauge invariance, it was elucidated that the gauge invariance of ln works to make the phase differences θ and α to ± π/2 and 2nπ/ℓ, respectively. As its applied aspect, it is presumed to be useful in studying the behavior of the entanglement of electromagnetic waves. A new interrelationship between four nablas acting on two GFs and two SPs is established near the beam waist in paraxial approximation.

FEM Analysis of Piezoelectric Resonator Polarization Process

The polarization of the piezoelectric resonator depends on the direction of the applied electric field. The direction of the applied electric field is determined by the shape of the resonator and the position of the electrodes. In case of resonators with electrodes incompletely covering their bases, an inhomogeneous electric field is generated, which results in an inhomogeneous polarization of the resonator. The resonator will be polarized in some places either in a direction other than the desired one or not polarized at all. The aim of this work is to analyze the polarization process on resonators with electrodes incompletely covering their bases. The physical description is given by the linear piezoelectric equations, the Gaussian equation for the description of the electric field and by Newton’s law of force. On this basis, a FEM model is developed and used to analyze the polarization process. The results of the calculation of the electric field vector distribution are presented. Finally, the areas are identified in which polarization in the desired direction is achieved in the resonator as well as the ones where no polarization occurs.

Quaternion Fourier Transform spectral analysis of electrical currents for bearing faults detection and diagnosis

This paper suggests a new method for detecting and diagnosing bearing faults in three-phase asynchronous devices using the periodogram estimation of the Power Spectral Density of the three-phase electrical current space vector. Rather than a single single-phase spectral analysis or a space vector component spectral analysis using the classic Fourier Transform, The Quaternion Fourier Transform was used to do a full spectral analysis of the three-phase currents scheme. Spectral indicators are given from the Quaternion Power Spectral Density and their use suggested for accurate detection and diagnosis of bearing faults via the quaternion's formalism. To validate this approach, the proposed indicators were compared to fault indicators derived from a single-phase or inferred from the real and imaginary parts of the currents space vector. The results reveal that two of the new metrics outperform the classic ones derived from either single-phase spectral analysis or the three-phase space vector components spectral analysis (classification rates of 94.2 percent and 93.8 percent, respectively). These findings support the preference for three-phase approaches over single-phase approaches, as well as the ability to extend classical research methods developed for single-phase systems to three-phase systems using the Quaternion Fourier transform.

Calculation of the Eddy Current Losses in a Laminated Open-Type Transformer Core Based on the A→,T→−A→ Formulation

Losses due to eddy currents in an open-type transformer core are significantly reduced by the lamination of the transformer core. In order to further reduce the eddy current losses, the open-type core often has a multi-part structure, i.e., it is composed of several more slender cores. The complete homogenization of such a core is not possible when an A→,V−A→ formulation is used, where A and V represent the magnetic vector potential and electric scalar potential, respectively. On the other hand, an A→,T→−A→ formulation, where T represents the electric vector potential, enables the complete homogenization of the general open-type core, but the simulation converges poorly due to the large number of degrees of freedom. By eliminating the redundant degrees of freedom, the convergence rate is significantly improved, and is at least twice as good as the convergence rate of the simulation based on the A→,V−A→ formulation. In this paper, a method for the calculation of the eddy current losses in an open-type core based on the A→,T→−A→ formulation with the elimination of redundant degrees of freedom is presented. The method is validated by comparison with a brute force simulation based on the A→,V−A→ formulation, and the efficiency of the method is determined by comparison with the standard homogenization method based on the A→,V−A→ formulation.

Circular Dichroism in the Photoionization of Unpolarized Atoms by Two Crossing Photon Beams

The polarization dependence of the photoionization probability was analyzed in the case when a randomly oriented atom is irradiated by two crossing polarized monochromatic photon beams with the same frequency. It was found that the angular distributions of photoelectrons exhibit the effect of circular dichroism (CD), which consists of the dependence of the photoionization probability on the sign of the circular polarization degree of each beam. We demonstrate that the CD effect exists only for coherent crossing photon beams. It was shown that CD effects are strongly dependent on the phase difference between the electric field vectors of the photon beams and have a quite large magnitude. The possibilities of the experimental observation of CD effects are discussed.

Wave structure at radar irradiation of homogeneous absorbing media

The work is devoted to the study of the structure of waves excited in bordering media under radar irradiation of both smooth and rough interfaces. It is found that counter propagating waves are excited in bordering absorbing media, which determine backward reflection at the interface. On the other hand, the reflection of the counter propagating wave excites waves with a negative angle of refraction. It was found in this work that when the interface is irradiated with a plane wave during polarization, when the electric field strength vector lies in the plane of incidence, the backward reflection and the refracted wave are increases, and the specular reflection decreases. Electrodynamics models of the back reflection coefficients are developed for both the case of smooth and for the case of uneven interfaces between the media.

Inference of electric currents in the solar photosphere

Context. Despite their importance, routine and direct measurements of electric currents, j, in the solar atmosphere have generally not been possible. Aims. We aim at demonstrating the capabilities of a newly developed method for determining electric currents in the solar photosphere. Methods. We employ three-dimensional radiative magneto-hydrodynamic (MHD) simulations to produce synthetic Stokes profiles in several spectral lines with a spatial resolution similar to what the newly operational 4-meter Daniel K. Inouye Solar Telescope solar telescope should achieve. We apply a newly developed inversion method of the polarized radiative transfer equation with magneto-hydrostatic (MHS) constraints to infer the magnetic field vector in the three-dimensional Cartesian domain, B(x, y, z), from the synthetic Stokes profiles. We then apply Ampere’s law to determine the electric currents, j, from the inferred magnetic field, B(x, y, z), and compare the results with the electric currents present in the original MHD simulation. Results. We show that the method employed here is able to attain reasonable reliability (close to 50% of the cases are within a factor of two, and this increases to 60%–70% for pixels with B ≥ 300 G) in the inference of electric currents for low atmospheric heights (optical depths at 500 nm τ5∈[1, 0.1]) regardless of whether a small or large number of spectral lines are inverted. Above these photospheric layers, the method’s accuracy strongly deteriorates as magnetic fields become weaker and as the MHS approximation becomes less accurate. We also find that the inferred electric currents have a floor value that is related to low-magnetized plasma, where the uncertainty in the magnetic field inference prevents a sufficiently accurate determination of the spatial derivatives. Conclusions. We present a method that allows the inference of the three components of the electric current vector at deep atmospheric layers (photospheric layers) from spectropolarimetric observations.

Association of electrical bioimpedance vectors with the nutritional classification of vulnerable multiethnic children.

Monitoring growth and body composition in childhood is vital for early detection of health and nutrition problems during child development. The bioelectrical impedance vector analysis (BIVA) revealed its effectiveness as an indicator of nutritional status. This study aimed to measure the bioimpedance vectors of a sample of multiethnic children and evaluate the utility of BIVA for the classification of the nutritional status in a group of children with greater vulnerability, including in the presence of obesity. This is a cross-sectional study that analyzed the bioelectrical impedance of a sample of 321 children from public daycare centers, aged 1-4 years, using the RXc graph method (tetrapolar analysis at 50kHz frequency). The 95%, 75%, and 50% tolerance ellipses were plotted by age group. The Z-scores of bioimpedance parameters (Xc/H-Z and R/H-Z) were calculated regarding age, which were used to build reference tolerance ellipses for a single group, regardless of age. Such ellipses were evaluated for their ability to recognize the pattern and classify the deviations, using individual vectors of obese children. The mean impedance vectors showed progressively higher reactances and lower resistances with age. In the group of obese children, the individual vectors located outside the 95% baseline tolerance ellipse were 12.5%, 18.75%, and 11.1% of the cases for the WHZ, WAZ, and BMIZ criteria, respectively, all above the expected 5%, but much below expectations. This may be a problem with the obesity criteria used, as WHZ, WAZ, and BMIZ do not differentiate fat from lean mass. Bioimpedance vector analysis reflects differences in the bioelectric patterns of children classified as obese. Provided the obesity criteria are constructed based on fat measurements, rather than lean mass, the use of tolerance ellipses in the BIVA chart is promising as a tool for monitoring nutritional status where measuring body composition is difficult, because constant tissue hydration cannot be assumed.

Selectively doped piezoelectric ceramics with tunable piezoelectricity via suspension-enclosing projection stereolithography

The macroscopic piezoelectric properties of piezoelectric materials can be regulated via localized control of microstructures to introduce site-specific electric displacement vectors, but much of the current research is centered around design and manipulation of meso-scale architectural units that are inherently limited in achieving high functionality. In this study, we propose a stereolithography-based additive manufacturing (AM) strategy to spatially tune the properties of piezoelectric ceramics at a grain-microstructural scale through selectively incorporating dopants into the ceramic materials for tailoring the grain development. The effects of different doping parameters (including ceramic solid loading, dopant type, and dopant concentration) on the microstructures and properties of printed piezoelectric ceramics are investigated. The thermodynamics and kinetics of different doping additives in the dopant-ceramic interaction are experimentally and numerically studied to enable location-specific inhibition of microstructures. Our results indicate that a doping concentration of 2 wt% promoted the homogeneity of local grain growth, resulted in a higher compressive strength and lower porosity, and improved dielectric permittivity and piezoelectric voltage constant in printed piezoelectric ceramics. Moreover, our results suggest that thermochemically stable particles (e.g., ZrO2) with a high melting point and a low vapor pressure exhibited micro-scale diffusion behaviors, in contrast to millimeter-scale diffusion behaviors of common doping additives (e.g., ZnO), which are more suitable as a locally incorporated dopant for achieving location-specific property tuning. Test cases of selectively doped piezoelectric components in predefined patterns highlight the potential of the proposed approach in creating novel piezoelectric materials with programmable location-specific properties.

Polarization vector formalism of plasma weak turbulence

This paper formulates the plasma weak turbulent theory based on the unit electric field polarization vector. This concept is not intrinsically new, and partial formulations of weak turbulence processes based on the polarization vector approach are found in the literature. However, the present paper applies such a method uniformly to all the relevant processes for the first time, thus unifying the existing formalisms. The present result potentially provides many advantages including the fact that it facilitates the complex manipulations of various tensor coupling coefficients that dictate the wave–wave and nonlinear wave–particle interactions. To demonstrate its validity, the limit of unmagnetized plasmas is considered, and it is shown that the known results are recovered. The present formalism can be extended to more complex situations including magnetized plasmas, which is a subject of future work.

Effect of a perfectly conducting corner space on the PAFs for an absorptive dielectric circular cylinder

The photophoretic asymmetry factors (PAFs) for an absorptive dielectric circular cylinder, located near a perfectly conducting and totally reflecting corner space are derived and computed. The method used in this analysis relies on the modal expansion method in cylindrical coordinates, the classical method of images, and the translational addition theorem of cylindrical wave functions. Initially, the components of the internal electric field vector are obtained stemming from an analysis of the scattering. Subsequently, the solution is used to integrate to the normalized intensity function over the cylinder’s volume to obtain the longitudinal (L) and transverse (T) PAFs. Both TM- and TE-polarized plane progressive waves with arbitrary incidence (in the polar plane) are considered. Attention is given to varying the dimensionless size parameter of the cylinder, the angle of incidence of the incoming waves, and the dimensionless distance parameters from the corner space. Numerical examples illustrate the analysis and demonstrate the net effect of the totally reflecting corner space on the L- and T-PAFs, where negative, positive, and neutral values have been predicted. The results are relevant in applications related to the emergence of the photophoretic force and torque on an absorptive particle located near surfaces and topics in electromagnetic/optical scattering, particle manipulation and assembly, optically bound matter, light–matter interactions, and photopheresis.

Determination of the Brewster angle of the wave reflected from a plate with dielectric losses

In free space, the permittivity of materials is usually determined by the value of the Brewster angle using the angular dependences of the amplitude and phase of the wave reflected from the material plate. An expression corresponding to materials without dielectric and magnetic losses is used as a calculation model. Experimental studies of the parameters of the wave reflected from dielectric materials show the discrepancies with theoretical calculations known as deviations from the Fresnel laws. We present the results of determining the Brewster angle of the wave reflected from a plate made of a material with dielectric losses. The angular dependences of the amplitude and phase of the reflected wave were calculated using the numerical solution of the problem of falling at an arbitrary angle of a plane linearly polarized wave with an electric field vector lying in the plane of incidence on a plate of a dielectric material with complex values of the dielectric and magnetic permittivity. They were used to determine the angles corresponding to the minimum reflection coefficient depending on the dielectric losses of the plate material. The differences between the numerical calculations and the data obtained using the Brewster angle formula were noted, which increased with increasing dielectric losses of the material. From the condition that the modulus of the reflected wave amplitude is equal to zero, a different formula for calculating the Brewster angle for a material with losses is analytically obtained. The results of calculations using this formula coincided with the calculations for the reflected wave when solving the classical problem of the inclined incidence of a plane wave on a plate of a dielectric material in the framework of geometric optics. The results obtained can be used to determine the Brewster angle for a wave reflected from a plate with magnetic and dielectric losses.

Observing electric field and neutral wind with EISCAT 3D

Abstract. Measurements of height-dependent electric field (E) and neutral wind (u) are important governing parameters of the Earth's upper atmosphere, which can be used to study, for example, how auroral currents close or how energy flows between the ionized and neutral constituents. The new EISCAT 3D (E3D) incoherent scatter radar will be able to measure a three-dimensional ion velocity vector (v) at each measurement point, which will allow less stringent prior assumptions about E and u to be made when estimating them from radar measurements. This study investigates the feasibility of estimating the three-dimensional electric field and neutral wind vectors along a magnetic field-aligned profile from E3D measurements, using the ion momentum equation and Maxwell's equations. The uncertainty of ion drift measurements is estimated for a time and height resolution of 5 s and 2 km. With the most favourable ionospheric conditions, the ion wind at E region peak can be measured with an accuracy of less than 1 m/s. In the worst case, during a geomagnetically quiet night, the uncertainty increases by a factor of around 10. The uncertainty of neutral wind and electric field estimates is found to be strongly dependent on the prior constraints imposed on them. In the lower E region, neutral wind estimates have a lower standard deviation than 10 m/s in the most favourable conditions. In such conditions, also the F region electric field can be estimated with uncertainty of about 1 mV/m. Simulated measurements of v are used to demonstrate the ability to resolve the field-aligned profile of E and u. However, they can only be determined well at the heights where they dominate the ion drift, that is above 125 km for E and below 115 km for u. At the other heights, the results are strongly dependent on the prior assumptions of smoothness.

If We Postulate Atomic and ± Subatomic Particles are Size Particles and Satisfy the Schrodinger Equation, what will be the Inferences?

In quantum mechanics, atomic and subatomic particles are treated as waves. The idea of wave function and wave function collapse brought us great success but left us different opinions. Is there a way it can avoid the different opinions and give us more? We try to postulate directly that these particles are size particles and satisfy the Schrodinger equation. Start from the general solution of free particle’s Schrodinger equation, we will prove: (i) To satisfy the Schrodinger equation, the size particle must possess a circular polarized structure of the plane vector（a complex number）like the electric vector E in the circular polarized light; its modular is mass density. (ii) These particles fall into two categories: they have the same sign of negative charge e or positive charge e, but different directions of mass density and charged helices, like left handed electron and right handed electron etc. (iii) The spin of the particle has its mechanism, it is formed by the motion of the helices structure of mass plus intrinsic self rotation. (iv) Negative charge e (or positive charge e) distributes double helically on the particle side boundary. It produces and carries a circular polarized electric field E with the same velocity of the particle. It forms a circular polarized E-wave. This wave will be proved is just the de Broglie wave and the E-wave function is just the particle’s state function in quantum mechanics. Such charged particle is consisted of the particle itself and the de Broglie wave; they form a particle-wave hybrid structure. The E- wave exhibits all possible states with possibility in the atom, molecule or interference pattern; as for the particle itself, it cannot split into two or move with two velocity at the same time. It can only locate at one basic state any moment, such as in an eigen state of the atom or at a point in the interference pattern. It is the self-interference of the hybrid structure of the particle makes the one after one single particle form double-slits interference.

Ways to Improve Wear Resistance and Damping Properties of Radial Bearings Taking into Account Inertial Forces

This article considers a radial sliding bearing of infinite length whose moving part consists of the support, the porous layer, and the liquid lubricant. The analysis of the existing design calculation methods for such sliding bearings shows that they are very approximate because they do not consider the inertial forces applied, the electric conductivity of the lubricant, the permeability anisotropy, as well as the impacts of the electric field vector, magnetic induction vector, and incomplete filling of the working gap (pre-accident condition). The authors demonstrate how these factors impact the stable operation of the device facilitating the hydrodynamic regime. The authors find the asymptotic solution for the zero, first, and second approximation taking into account the inertial forces for the “thin layer”. By solving the produced equations using the Gauss-Seidel method, the authors determine the key operating parameters of the friction couple in question: the carrying capacity and the friction force. The authors provide an impact assessment for the parameters characterizing the permeability of the porous coating, the electric conductivity, and viscosity of the lubricant, as well as the length of the loaded area and the impacts of inertial forces on the carrying capacity and the friction force.

Spherical harmonics based model of electric field effects on neocortical neurons

Abstract Transcranial electrical stimulation (tES) techniques generate electric fields in the brain whose effects on single neurons can be approximated from the cable equation as a membrane potential perturbation that is proportional to the membrane length constant (lambda). This is referred to as the lambda-E model and is a simple mechanistic approach that assumes that the membrane perturbation can be modeled as the dot product of a vector parallel to the orthodromic direction of cortical neurons with the electric field, multiplied by lambda. We propose a more general way to represent the model of the membrane perturbation as a function of the magnitude and angular orientation of the E-field, using a spherical harmonics expansion that can capture the dependence of the perturbation on electric field direction. In this representation, the lambda-E model corresponds to the first-order degree (l=1) term of the expansion. This approach can represent the three-dimensional response of a specific cell part, obtained experimentally. Here we employ it using synthetic data from realistic neocortical cell models in a DC field in the tDCS regime, fitting the coefficients for the membrane responses. We use realistic reconstructions of the somatosensory cortex from the Blue Brain Project to simulate the response of different pyramidal cells and interneurons to electric fields of 1 V/m as a function of the orientation of the field with respect to the cell using the NEURON simulation environment. We report membrane perturbation values comparable to those in the literature, extend it to different cell types, and provide the spherical harmonic coefficient profile for each neuron. Finally, we provide an azimuth-independent version of the model providing an averaged response that only depends on the electric field vector and the cortical surface. We believe this method can improve the accuracy and detail of real life simulation-based stimulation. Keywords: Electric field coupling, Multicompartment models, tES, NEURON

A comparison between current-based integral equations approaches for eddy current problems

In this paper, a comparison between two current-based Integral Equations approaches for eddy current problems is presented. In particular, the very well-known and widely adopted loop-current formulation (or electric vector potential formulation) is compared to the less common J-φ formulation. Pros and cons of the two formulations with respect to the problem size are discussed, as well as the adoption of low-rank approximation techniques. Although rarely considered in the literature, it is shown that the J-φ formulation may offer some useful advantages when large problems are considered. Indeed, for large-scale problems, while the computational efforts required by the two formulations are comparable, the J-φ formulation does not require any particular attention when non-simply connected domains are considered.

Study of a dielectric internal laser accelerating structure

High acceleration gradients can be realized in dielectric laser accelerators (DLAs) due to their high damage thresholds; hence, they are promising candidates for miniaturized particle accelerators. In this study, we present a new type of DLA, in which the accelerating laser is generated inside the accelerating structure, by etching the grating of the acceleration structure and a Brewster window on the semiconductor dielectric material, and the acceleration region is within the internal structure of the laser resonator. The consistency of the electric vector oscillation direction of the laser with the direction of the beam motion is maintained by passing through the Brewster window. The internal laser is used as the excitation source; hence, the need of high power laser distribution can be mitigated, and the complete DLA device is more compact. Particle-in-cell (PIC) simulation is employed to investigate the energy gain of the electron in this structure.

The pseudo-null geometric phase along optical fiber

In this study, a pseudo-null space curve in Minkowski 3-space is used to describe an optical fiber that is injected into monochromatic linear polarized light. The direction of the electric field vector with respect to the Frenet frame of a pseudo-null curve determines the state polarization of a monochromatic linearly polarized light wave traveling along an optical fiber. For the Frenet frame of a pseudo-null curve in Minkowski 3-space, the polarization vector [Formula: see text] is assumed to be perpendicular to the tangent vector [Formula: see text] with respect to anholonomic coordinates. Anholonomic coordinates for the Frenet frame of a pseudo-null curve are used to describe pseudo-null electromagnetic curves in the normal and binormal directions along an optical fiber. For the Frenet frame of the pseudo-null curve, Lorentz force equations in the normal and binormal directions along the optical fiber are presented. Pseudo-normal and binormal Rytov parallel transport laws for electric fields in the normal and binormal directions along with the optical fiber for the Frenet frame of the pseudo-null curve via anholonomic coordinates are presented. For anholonomic coordinates in Minkowski 3-space, rotations of the polarization planes of a light wave traveling in the normal and binormal directions along with the optical fiber with respect to the Frenet frame of the pseudo-null curve are obtained. Finally, a pseudo-null curve’s Maxwellian evolution is determined.

Azygous Vein Coil Implantation in Left Ventricular Assist Device Patients: A Hands-on Approach.

Recently, there have been reports of left ventricular assist device (LVAD) patients presenting with multiple ineffective implantable cardioverter-defibrillator (ICD) shocks. In such patients, the placement of an azygous vein coil by providing an alternative anteroposterior trajectory of the electrical shock vector can enable successful defibrillation. This review discusses a hands-on approach to azygous vein coil implantation. Additionally, we compare our tools and technique to those that have been previously described by other operators. From 2018 to 2021, eight patients were identified who underwent azygous vein coil implantation at MedStar Washington Hospital Center using a specific technique and tools. Demographic and procedural data were obtained by a retrospective review of patient charts, procedure logs, fluoroscopy, and venography performed during coil implantation. The indication for azygous vein coil implantation was ineffective ICD shocks in seven patients. The presenting rhythm was ventricular fibrillation in six (75%) cases and sustained ventricular tachycardia in two (25%) cases. Using the approach described, we were able to successfully implant an azygous vein coil in all eight (100%) patients. There were no procedure-related complications. Postimplantation, defibrillation threshold (DFT) testing was successfully performed in six of eight (75%) patients. One patient failed DFT testing despite placement of an azygous vein coil. In another patient, DFT testing was not performed because the patient was in atrial fibrillation and was not systemically anticoagulated. In conclusion, the placement of an azygous vein coil in LVAD patients with failed ICD shocks using the tools and technique described in this report is safe and highly efficacious (successful in 100% of cases).