Electromagnetic Field Equations Research Articles

Description of electromagnetic fields in uniformly accelerated frame. Revision of the radiation problem

It is shown that Maxwell equations for electromagnetic fields generated by a uniformly accelerated charge could be reduced to the Laplace equation in a co-moving frame (represented by the Łobaczewski geometry of the one-sheeted hyperboloid) for a single scalar potential. A full solution of this equation is derived. Then, the famous problem of radiation of a uniformly accelerated particle is revised. Finally, a description of the electromagnetic field on the scri is presented. Both of those approaches produce the same result, which, surprisingly, is slightly different to the well-established Larmor formula for radiation.

Interaction of electromagnetic fields with body-onboard devices

The aim of this contribution is to analyze and discuss the perturbations of body-onboard medical devices caused by electromagnetic field radiations. This involves their control via electromagnetic compatibility analysis and their protection against such perturbations. The wearable, detachable, and embedded devices are first presented and their monitoring, control, forecasting, and stimulating functions are detailed. The interaction of these devices with field exposures comprising their wireless routines is then analyzed. The perturbations control of onboard devices is investigated through the mathematical solution of governing electromagnetic field equations and their appropriate protection strategies are deliberated. The involved investigations and analyses in the contribution are supported by a literature review.

Matrix methods and teaching the fundamentals of fluid and gas mechanics in higher education institutions

Problem. The instruction of physical and mathematical disciplines in higher education institutions employing cutting-edge methods and universal approaches, which seamlessly integrate scientific and engineering activities of future specialists, remains one of the pertinent and priority tasks. The utilization of multidimensional or even infinite-dimensional spaces has become an effective and nearly indispensable tool in mathematical modeling of physical phenomena. This circumstance is directly linked to the increasing level of abstraction and the refinement of mathematical methods. The use of geometric methods inherent in vector algebra and vector analysis as the foundation for studying mechanics, despite their illustrative nature, is losing its relevance. Methods built upon matrix formalism are evolving as substitutes. The matrix framework enables the exploitation of phase space advantages to derive canonical equations of motion for continuous media and electromagnetic field equations in covariant forms. The electromagnetic potential acquires mechanical significance, allowing the utilization of electromechanical analogies at a fundamental level rather than on a merely formal basis, as done in classical electrodynamics. Goal. The aim of this research is to study and justify the advantages of matrix methods for deriving equations of motion for fluids and gases from the canonical equations of mechanics by utilizing a continuum model in phase and physical space. The research is directed towards demonstrating the connection between the internal microscopic and macroscopic motion of fluids and gases, as well as highlighting the potential of matrix formalism both in terms of modeling and the utilization of computational tools. Methodology. The methodological basis for selecting matrix methods lies in the application of tensor analysis and its generalizations for modeling the motion of fluids and gases in physical and phase space. Results. It has been demonstrated that the matrix method, previously applied to classical and relativistic mechanics, allows for the consideration of the molecular structure of the environment by folding the multidimensional phase space of the mechanical system, represented by a particle of the medium, and thereby deriving equations of motion for fluids and gases from the canonical equations of classical mechanics and the equations of momentum balance of the medium. Originality. The combination of canonical equations as a result of applying the conservation law of matter in the form of balance equations in phase space and momentum balance equations in physical space allows for elucidating the relationship between macroscopic and microscopic motions of the medium, as well as the mathematical structure of the equations of motion for fluids and gases. Practical value. The proposed method allows, while remaining within the standard mathematical training offered by technical educational institutions, to effectively formalize the equations of motion for fluids and gases and provide them with an invariant form. By guiding oneself through invariance, both fundamental laws (such as the law of universal gravitation) and partial laws (the generalized Newton's law) can be obtained.

Maxwell-Schrödinger equations in singular electromagnetic field

Maxwell-Schrödinger equations in singular electromagnetic field

Entanglement between Micro-Magnetism, electromagnetism and the Tensor Magnetic Phase Theory (TMPT) – Symmetry, conservation and invariance laws analysis at low frequency

Ferromagnetic materials show magnetic structures with domains and walls. Thanks to decades of research regarding the origin and behaviour of magnetic domains, we now possess a general foundation which has been verified experimentally in single crystals and powders. The governing equations at the microscopic scale were built in the 1960 s when Brown published calculations of the magnetic moments distribution inside domain walls. This micromagnetic theory uses the so called LLG ‘Landau-Lifshitz-Gilbert’ equation and can include the damping effects. The LLG equation requires a coupling to the field derived from energy contributions: exchange, anisotropy, magnetostriction, stray-field … and the anti-eddy field. At the macroscopic scale, such behaviours are lumped in a homogenized magnetization law for the electromagnetic field equations inside larger polycrystals. Therefore, the inhomogeneous magnetic material nature is always ignored. The Tensor Magnetic Phase Theory (TMPT) describes the magnetic structure and the magnetization thanks to a tensor variable at a mesoscopic scale. The material structuring is then explained thanks to an energy balance which will be discussed.This paper presents the results of investigations on entangled relationships between the micromagnetic theory, the electromagnetic theory and what is called the Tensor Magnetic Phase Theory (TMPT), which statistically describes the magnetic structures of soft ferromagnetic materials. It examines a connection between the TMPT and the LLG by deriving the main energy terms. Then, the TMPT must stay compatible and coupled to the Maxwell equations at low frequencies with volume and surface connections. Additionally, this paper investigates the way to derive the domains structuring and magnetization laws through the Lagrange principle and the corresponding conservation laws with invariants linked to the Nœther theorem. Finally, the TMPT must be discussed while checking its coherence and formulation when changing the reference frame.

RÓWNANIA POLA ELEKTROMAGNETYCZNEGO W ŚRODOWISKU NIELINIOWYM

The paper proposes electromagnetic field equations from the point of view of their adaptation to numerical methods. Maxwell's equations with partial derivatives are used, written concerning field vectors, which most fully reproduce the picture of physical processes in electrical engineering devices. The values of these vectors provide comprehensive information about the field at any spatio-temporal point. The concept of creating mathematical models of electrical devices adequate to physical processes has been developed. Mathematical transformations are carried out according to the rules of differential calculus. Dynamic processes in the elements of electrotechnical devices were analyzed using the apparatus of mathematical modeling. An algorithm for implementing differential equations with partial derivative numerical methods using computer simulation was implemented. The obtained results made it possible to understand the nature of electromagnetic phenomena in nonlinear media. The paper provides calculations of the field parameters in a flat ferromagnetic plate and the groove of the rotor of an electric machine.

Quasinormal modes of Einstein–scalar–Gauss–Bonnet black holes

In this paper, we investigate quasinormal modes of scalar and electromagnetic fields in the background of Einstein–scalar–Gauss–Bonnet (EsGB) black holes. Using the scalar and electromagnetic field equations in the vicinity of the EsGB black hole, we study nature of the effective potentials. The dependence of real and imaginary parts of the fundamental quasinormal modes on parameter p (which is related to the Gauss–Bonnet coupling parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}) for different values of multipole numbers l are studied. We analyzed the effects of massive scalar fields on the EsGB black hole, which tells us the existence of quasi-resonances. In the eikonal regime, we find the analytical expression for the quasinormal frequency and show that the correspondence between the eikonal quasinormal modes and null geodesics is valid in the EsGB theory for the test fields. Finally, we study grey-body factors of the electromagnetic fields for different multipole numbers l, which deviates from Schwarzschild’s black hole.

Electrodynamics of Superconductors: From Lorentz to Galilei at Zero Temperature.

We discuss the derivation of the electrodynamics of superconductors coupled to the electromagnetic field from a Lorentz-invariant bosonic model of Cooper pairs. Our results are obtained at zero temperature where, according to the third law of thermodynamics, the entropy of the system is zero. In the nonrelativistic limit, we obtain a Galilei-invariant superconducting system, which differs with respect to the familiar Schrödinger-like one. From this point of view, there are similarities with the Pauli equation of fermions, which is derived from the Dirac equation in the nonrelativistic limit and has a spin-magnetic field term in contrast with the Schrödinger equation. One of the peculiar effects of our model is the decay of a static electric field inside a superconductor exactly with the London penetration length. In addition, our theory predicts a modified D'Alembert equation for the massive electromagnetic field also in the case of nonrelativistic superconducting matter. We emphasize the role of the Nambu-Goldstone phase field, which is crucial to obtain the collective modes of the superconducting matter field. In the special case of a nonrelativistic neutral superfluid, we find a gapless Bogoliubov-like spectrum, while for the charged superfluid we obtain a dispersion relation that is gapped by the plasma frequency.

Non-uniform magnetic fields for single-electron control.

Controlling single-electron states becomes increasingly important due to the wide-ranging advances in electron quantum optics. Single-electron control enables coherent manipulation of individual electrons and the ability to exploit the wave nature of electrons, which offers various opportunities for quantum information processing, sensing, and metrology. Here we explore non-uniform magnetic fields, which offer unique mechanisms for single-electron control. Considering the modeling perspective, conventional electron quantum transport theories are commonly based on gauge-dependent electromagnetic potentials. A direct formulation in terms of intuitive electromagnetic fields is thus not possible. In an effort to rectify this, a gauge-invariant formulation of the Wigner equation for general electromagnetic fields has been proposed [M. Nedjalkov et al., Phys. Rev. B, 2019, 99, 014423]. However, the complexity of this equation requires the derivation of a more convenient formulation for linear electromagnetic fields [M. Nedjalkov et al., Phys. Rev. A, 2022, 106, 052213]. This formulation directly includes the classical formulation of the Lorentz force and higher-order terms, depending on the magnetic field gradient, that are negligible for small variations of the magnetic field. In this work, we generalize this equation in order to include a general, non-uniform electric field and a linear, non-uniform magnetic field. The thus obtained formulation has been applied to investigate the capabilities of a linear, non-uniform magnetic field to control single-electron states in terms of trajectory, interference patterns, and dispersion. This has led to the exploration of a new type of transport inside electronic waveguides based on snake trajectories and the possibility of splitting wavepackets to realize edge states.

Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions

All non-equivalent solutions of vacuum Maxwell equations are found for the case when space-time manifolds admit simply transitive four-parameter groups of motions [Formula: see text]. The potentials of the admissible electromagnetic fields admit the existence of the algebra of motion integrals of the Hamilton–Jacobi and Klein–Gordon–Fock equations which is isomorphic to the algebra of the group operators for the same group [Formula: see text].

3D forward modeling and response characteristics of low-resistivity overburden of the CFS-PML absorbing boundary for ground-well transient electromagnetic method

This study used the stable and convergent Dufort-Frankel method to differentially discretize the diffusion equation of the ground-well transient electromagnetic secondary field. The absorption boundary condition of complex frequency-shifted perfectly matched layer (CFS-PML) was used for truncation so that the low-frequency electromagnetic wave can be better absorbed at the model boundary. A typical three-dimensional (3D) homogeneous half-space model was established and a low-resistivity cube model was analyzed under the half-space condition. The response patterns and drivers of the low-resistivity cube model were discussed under the influence of a low-resistivity overburden. The absorption boundary conditions of CFS-PML significantly affected the low-frequency electromagnetic waves. For a low-resistivity cube around the borehole, its response curve exhibited a single-peak, and the extreme point of the curve corresponded to the center of the low-resistivity body. When the low-resistivity cube was directly below the borehole, the response curve showed three extreme values (two high and one low), with the low corresponding to the center of the low-resistivity body. The total field response of the low-resistivity overburden was stronger than that of the uniform half-space model due to the low-resistivity shielding effect of electromagnetic waves. When the receiving-transmitting distance gradually increased, the effect of the low-resistivity overburden was gradually weakened, and the response of the low-resistivity cube was strengthened. It was affected by the ratio of the overburden resistivity to the resistivity of the low-resistivity body.

Full-band modeling of AM and FM interband cascade laser frequency combs

A numerical model for the simulation of frequency combs in interband cascade lasers is developed. The approach is based on slowly varying amplitude approximation for electromagnetic field and semiconductor Bloch equations for the electron gas. The electron gas nonequilibrium distribution function is computed explicitly. Effects of both radiative and nonradiative recombination are considered. The model is applied to both amplitude modulated and frequency modulated combs.

3D Electromagnetic Forward Modeling in Anisotropic Medium Using the Secondary Field Formula

The electromagnetic (EM) method is an essential geophysical method to detect underground geological structures. With the increasing requirements for the reliability of data interpretation, we need an accurate anisotropic forward algorithm, which is applied several times in the inversion. At the same time, modeling the anisotropic response is an advantageous method for designing actual survey lines. In this paper, we utilize the quadratic field formulation in anisotropic media to derive the governing equations for electromagnetic fields. The governing equation is discretized using the finite difference method. Experimental results indicate that our algorithm is able to accurately model both the magnetotelluric (MT) and the controlled-source electromagnetic (CSEM) response.

Numerical model of a gaseous inductive discharge in oxygen, taking into account the complete scheme of the vibrational kinetics of O2 molecules

In this work, the two-dimensional model of inductively coupled plasma discharge in oxygen was developed. The model includes hydrodynamic equations in drift-diffusion approximation for describing the kinetics of charged (electrons and ions) and neutral plasma particles, Maxwell’s equations for electromagnetic fields, and equations for the temperature and neutral gas flow as well as a detailed scheme of plasma-chemical reactions. The model was tested against theoretical and experimental data in a simple cylindrical chamber. The electron density and temperature distributions were obtained over a wide range of powers deposited in the plasma (100–500 W) and compared with literature data. Also, the complete scheme of the vibrational kinetics of O2 molecules was included in the model. The vibrational distribution function was calculated in low-pressure inductive discharge as well as spatial distributions of plasma parameters (density and temperature of electrons, excited components, neutral gas temperature, etc.) and flows of charged and active neutral particles at the reactor walls.

On the mathematical structure of Einstein field equations and the existence of dark fields

In this work, we examine the possible existence of dark fields by showing that an energy‐momentum tensor associated with a dark field can be introduced into Einstein field equations of general relativity, in which the trace of the energy‐momentum of the dark field is identified with the cosmological constant. The introduction of dark fields into Einstein field equations is made possible by establishing field equations for the Ricci curvature tensor, which have similar mathematical structure to Maxwell field equations of electromagnetism. We also establish a system of field equations for the Riemann curvature tensor and investigate the possibility to represent physical systems consisting of dark fields and observable fields as spaces of constant scalar curvature, which are maximally symmetric spaces that admit the maximal number of Killing vectors. As an illustration, we show that if a dark field is considered as a dark fluid, then the pressure associated with the dark field can take negative values if the cosmological constant is assigned with positive values.

Three Serious Mistakes in Einstein’s Original Paper of Special Relativity in 1905

It is revealed in this paper that there were three serious mistakes in the Einstein’s original paper in 1905. Einstein did not prove that the motion equation of classical electromagnetic field could satisfy the invariance of the Lorentz coordinate transformation. The Einstein’s derivations on the formulas of transverse and longitudinal masses, as well as the calculation on the mass-energy relation are wrong. 1. In order to prove that the classical Maxwell electromagnetic field equation satisfied the invariance of Lorentz transformation in free space without charged and current, Einstein introduced the transformations of electromagnetic fields themselves, called the Einstein’s transformations of electromagnetic fields. However, these transformations are completely different from the Lorentz transformations of electromagnetic fields themself, which leads to contradiction and does not hold. 2. For the electromagnetic field equations in non-free space with charge and current, the Einstein’s transformations can not make the electromagnetic fields unchanged under the Lorentz transformation. 3. The constitutive equations of electromagnetic theory in the medium do not satisfy the invariance of the Lorentz transformation too. Therefore, the classical electromagnetic field equations have no the invariance of the Lorentz transformation actually, and the most important theoretical and experimental basis of special relativity do not exist. 4. The Einstein's derivations on the formulas of transverse and longitudinal masses have a series of elementary mistakes in mathematics and physics. Einstein took the relative speed between two reference frames as the arbitrary moving velocity of a particle, and the obtained formulas were completely different from the existing mass-velocity of special relativity. 3. When Einstein derived the mass-energy relationship, he only calculated the work done by the force in the x-axis direction of particle’s motion, ignoring the work done by the force at the y- and z-axes directions. Meanwhile, the constant relative motion velocity between two reference frames was misused as the variable arbitrary velocity of a particle. Therefore, Einstein had not derived the mass-velocity formula and mass-energy relationship used in the present special relativity.

Nearly Zero Ultra-Flattened Dispersion in Octagonal Photonic Crystal Fiber

The low confinement losses, relatively high nonlinearity, and wideband ultra-flattened chromatic dispersion are the crucial properties of the PCFs. Thus, in this research, a comprehensive study has been conducted to design a novel Octagonal PCF (Photonic Crystal Fiber) microstructure with an ultra-flattened dispersion profile through a vast range of optical communication band wavelengths with a large negative dispersion of nearly 0.6635 ps/nm/km at 1550 nm. This PCF design and simulative study have been made by using COMSOL multi-physics. The guiding features of the fiber have been analyzed numerically to solve the Maxwell equation of electromagnetic field by using the full vector finite element method with cylindrically perfect to match layer for strongly absorb the outgoing waves from the computational region. Moreover, Octagonal rings in the cladding region provide better confinement and flattened dispersion in O-band (1260 nm-1360 nm) and C-band (1530 nm-1565 nm) in comparison to honeycomb or hexagonal lattice structures. Our proposed model has a nearly zero ultra-flattened dispersion of ± 0.3028 ps/nm/km in a 1290 nm to 1620 nm with wavelength range (320 nm flat band) and low confinement loss is less than 10-7 dB/km in the entire band of interest. Furthermore, this research has been presented a 7.2 μm2 effective area which is smaller than other reported fibers at 1550 nm wavelength.

Negative Velocity Characteristics in Electromagnetism

Newton mechanics is great, Newton's contribution is indelible. But from Newton's classical mechanics, the definition of velocity (=) must mean that this physical parameter is a vector, so "negative velocity" only means the opposite direction of motion, no other meaning. It is difficult to understand negative velocity within the framework of classical mechanics. However, wave is a special form of material motion, wave mechanics has a unique method and meaning, and its concept and connotation are significantly different from classical mechanics. For example, wave velocity (whether phase velocity or group velocity) is a scalar quantity. "Negative wave velocity" does not mean that the direction of motion is reversed, but a special phenomenon that does not accord with causality from the surface view. In any case, research in recent decades has shown that negative wave velocity is not only theoretically possible, it has also been repeatedly shown to exist experimentally. Moreover, negative wave velocity is a special form of superluminal speed; The wave with negative velocity is the advanced wave. It corresponds to the leading solution of the basic equation of electromagnetic field and electromagnetic wave. The past practice (discarding the advanced solution) is wrong! As for causality, scientists have provided a new definition and interpretation. In short, both wave mechanics and quantum optics take a different approach from classical mechanics.
 This paper points out that it is unusual for the 2022 Nobel Prize in Physics to be awarded to Alain Aspect and two others, since Aspect's experiments on the Bell inequality were completed in 1982, Which still stands today as a crucial experiment that proved Einstein's EPR paper wrong and quantum mechanics (QM) correct. Aspect's award in 2022 showed that mainstream physical community had been forced to accept that quantum entanglement existed and that the "light-speed limit" theory of SR was a mistake.
 This paper discusses the proposition "negative characteristic motion of electromagnetic wave" put forward by the author in 2013, pointing out that it is an inherent physical phenomenon reflecting symmetry in nature. In this paper, the faster-than-light motion of waves found in the near-field of antennas is discussed. In addition, the realizability of "time travel" is also discussed.

Exact Solutions of Maxwell Equations in Homogeneous Spaces with the Group of Motions G3(VIII)

The problem of the classification of the exact solutions to Maxwell’s vacuum equations for admissible electromagnetic fields and homogeneous space-time with the group of motions G3(VIII) according to the Bianchi classification is considered. All non-equivalent solutions are found. The classification problem for the remaining groups of motion, G3(N), has already been solved in other papers. All non-equivalent solutions of empty Maxwell equations for all homogeneous spaces with admissible electromagnetic fields are now known.

Wave equations for electromagnetic field based on quaternion algebra

Wave equations for electromagnetic field based on quaternion algebra