Electromagnetic Field Equations Research Articles

On Maxwell Electrodynamics in Multi-Dimensional Spaces

The governing equations of Maxwell electrodynamics in multi-dimensional spaces are derived from the variational principle of least action, which is applied to the action function of the electromagnetic field. The Hamiltonian approach for the electromagnetic field in multi-dimensional pseudo-Euclidean (flat) spaces has also been developed and investigated. Based on the two arising first-class constraints, we have generalized to multi-dimensional spaces a number of different gauges known for the three-dimensional electromagnetic field. For multi-dimensional spaces of non-zero curvature the governing equations for the multi-dimensional electromagnetic field are written in a manifestly covariant form. Multi-dimensional Einstein’s equations of metric gravity in the presence of an electromagnetic field have been re-written in the true tensor form. Methods of scalar electrodynamics are applied to analyze Maxwell equations in the two and one-dimensional spaces.

Exact static spherical symmetric soliton-like solutions to the scalar and electromagnetic nonlinear induction field equations in general relativity

In this paper, we have obtained exact static spherical symmetric soliton-like solutions to the electromagnetic and scalar nonlinear induction field equations taking into account the own gravitational field of the elementary. The results show that the metric tensor functions are regular with localized energy density. Moreover, the total energy of the nonlinear induction fields is bounded and the total charge of elementary particles has a finite value. The importance of the own gravitational field of elementary particles and the role of the nonlinearity of fields in the determination of these solutions have been proved.

Sizing by optimization of line-start synchronous motor

PurposeThe purpose of this paper is to develop an algorithm and software for determining the size of a line-start permanent magnet synchronous motor (LSPMSMs) based on its optimization.Design/methodology/approachThe software consists of an optimization procedure that cooperates with a FEM model to provide the desired behavior of the motor under consideration. The proposed improved version of the genetic algorithm has modifications enabling efficient optimization of LSPMSMs. The objective function consists of three important functional parameters describing the designed machine. The 2-D field-circuit mathematical model of the dynamics operation of the LSPMSMs consists of transient electromagnetic field equations, equations describing electric windings and mechanical motion equations. The model has been developed in the ANSYS Maxwell environment.FindingsIn this proposed approach, the set of design variables contains the variables describing the stator and rotor structure. The improved procedure of the optimization algorithm makes it possible to find an optimal motor structure with correct synchronization properties. The proposed modifications make the optimization procedure faster and moreOriginality/valueThis proposed approach can be successfully applied to solve the design problems of LSPMSMs.

Electromagnetic Fields of Accelerating Charges: Applications in Lightning Strikes to a Tall Tower

The interaction of the lightning with a tall tower can be depicted by the electromagnetic field equations of a moving charge. When the equivalent moving charges are injected into the junction between the tip of tower and the bottom of lightning channel, they will travel both in the tall tower and in the channel. Along the channel, the charges will move with the return stoke speed and produce velocity field; but in the tower, they travel at the light speed without producing velocity field. At the both ends of a tower, the velocity of the moving charges will change, causing discontinuities here, and thus, the radiation fields will emit from the discontinuous ends. In such a process, the moving charges are experiencing repeatedly until the charges are fully exhausted by the channel and the ground. Based on this scenario, in this article, we proposed a method to derive the electromagnetic field radiate from the tall tower and also its current distribution by inputting the quantities of moving charges, the moving speed in the channel, the reflection and the transmission coefficient at the ends of the tower. To test the effectiveness of our method, we predict both the near-field and far-field from the tall tower struck by the lightning with three different return stroke models, i.e., transmission line (TL) model, modified TL model with exponential current decay with height (MTLE) and modified TL model with linear current decay with height (MTLL). Here, the TL model considers the velocity field and the radiation field, while MTLL and MTLE also incorporate quasi-electrostatic field produced by charges detained in the channel. Our predicted results are found to be consistent with the results from other methods. In general, our method avoids the need to incorporate the effect of current discontinuities at the return stroke frontwave compared to the extended engineering model, and could be more feasible than antenna theory method.

Covariant formulation of electrodynamics in isotropic media

The equations of electromagnetic fields in a medium are usually written in the rest frame of the medium. We outline a method of generalizing the discussion to arbitrary inertial frames. In the discussion, we also include the possibility that the medium is optically active, a possibility that is often overlooked in discussions of electromagnetic fields in an isotropic medium.

The investigation of the optics of shock‐compressed strongly correlated plasma

AbstractRare gas plasmas at high temperatures and pressures, produced by explosive shock fronts, are explored using laser diagnostics. The analysis of the response of a dense plasma to an electromagnetic wave of moderate‐intensity proves successful for investigating properties and the validity of physical models describing the behaviour of dense and non‐ideal plasmas. We present new experimental data for the reflectivity of oblique incidence of polarized electromagnetic waves on the front of shock‐compressed xenon plasmas. The optical properties of strongly correlated plasma were studied in the near‐infrared and green spectral regions at a plasma mass density ρ = 0.83 g/cm3 and temperature T = 32900 K. The spatial parameters of the plasma transition shock‐front layer are determined by solving numerically the electromagnetic field equations.

Tuning surface waves in graphene-covered metamaterial by varying the chemical potential of graphene

In this work, we have studied the surface waves propagating on the interface of graphene-covered metamaterial in GHz range. We have used the equations of electromagnetic field and impedance boundary condition approach to obtain the characteristic equation. The surface waves are not supported in all frequency ranges, and the dispersive curves of TM and TE polarized wave do not overlap in same wave vector spaces. The numerical solution can explain the propagation behavior of electromagnetic waves very well. The results show that it is able to tune surface waves through changing the chemical potential of graphene. We also have discussed the effective wavenumber and the propagation length as the chemical potential is changed. TM polarized waves is more sensitive when changing the chemical potential.

Hyperbolicity of velocity–stress–electromagnetic field equations for waves in anisotropic magnetoelectroelastic solids with hexagonal symmetry

This paper reports on a theoretical framework to analyse coupled wave propagation in magnetoelectroelastic solids of hexagonal symmetry. The constitutive equations contain the effective properties of micromechanics to model piezoelectric–piezomagnetic composites. The Mori–Tanaka scheme is used. The governing equations include the elastodynamic equations of motions and unique forms of the Maxwell equations for electromagnetics. The result is a set of fifteen first-order, fully coupled, hyperbolic partial differential equations with velocities, elastic stress components, and electromagnetic fields as the unknowns and as the components of the state vector. The structural analysis of the introduced equation set is performed, and the hyperbolicity is formally proved. The physics of coupled acoustic–electromagnetic wave propagation are fully described by the eigenstructure of matrices included in the considered system of equations. In particular, the eigenvalues of the main matrix pencil are the wave speeds, and a part of the left eigenvectors represents the coupled-wave polarization. The spectrum of the main matrix pencil shows the two-scale structure with the gap between mainly electromagnetic and mainly acoustic coupled modes. The analysis of the two-scale system dynamics is also performed. The small parameter is identified, and the slow–fast decomposition is obtained. The slow subsystem in the two-time-scale model is identified as the so-called quasi-static approximation of the magnetoelectroelastic continuum dynamics.

Numerical modeling and optimal design of microwave-heating falling film evaporation

Microwave-heating falling film evaporation (MFFE) has demonstrated the ability to promote the separation of polar/nonpolar mixtures, but it still faces the challenges of low energy efficiency and uneven heating. The present study optimizes the geometry/operating parameters and flow pattern of MFFE process by coupling the equations of electromagnetic field, fluid flow, heat transfer and liquid evaporation. The accuracy of simulating results is verified experimentally. On the optimization of geometry/operating parameters, the highest energy efficiency is obtained when the liquid film is located at the cylindrical cavity center and only one microwave port is employed. On the design of flow pattern, we employ a rotating spiral falling film flow to MFFE, where the fluid flows along the designed channels. This flow pattern disperses the overheating domains and therefore overcomes the problem of uneven heating. The obtained results can provide guidance for the design and optimization of novel MFFE devices.

Three-dimensional magnetotelluric modeling in general anisotropic media using nodal-based unstructured finite element method

Magnetotelluric sounding is an efficient and economical method for detecting Earth's deep structure because of its large surveying depth. We use a finite element approach to solve magnetotelluric fields in three-dimensional general anisotropic media based on the vector–scalar potentials and unstructured meshes. The implementation of a three-dimensional unstructured mesh generator TetGen with high-quality local mesh refinement can easily handle complicated models with high performance. The electromagnetic field equations are expressed in terms of Coulomb-gauged vector–scalar potentials, and the nodal-based finite element method can be used to compute the electromagnetic fields with high efficiency. The symmetric successive over-relaxation preconditioned conjugate gradient solver is used to solve the resulting linear equation system. The magnetotelluric responses in one-, two-, and three-dimensional medias are computed through our proposed approach. These results are then compared with the analytical solutions, two- and three-dimensional adaptive finite element solutions. Numerical examples demonstrate that these results are in good agreement. Because an unstructured mesh is incorporated in this approach, it has great potential for simulating the magnetotelluric responses in geometrically complicated situations.

Gravitational and Electromagnetic Field of an Isolated Rotating Charged Particle

A charged isolated particle with spherically symmetry is considered at origin in empty space. The particle has both mass and charge; therefore it is under the influence of both gravitational and electro-magnetic field. So to find out a line element especial attention is given in Einstein’s gravitational and Maxwell’s electro-magnetic field equations. Initially Einstein’s field equations are considered individually for gravitational and electro-magnetic fields in empty space. In this work initially starts with Schwarzschild like solution and then a simple elegant, systematic method is used. In these methods the e-m field tensor is also used from Maxwell’s electro-magnetic field equations. Finally thus a new metric is found for both positive and negative charged particles. The new metric for electron is not same as the metric is devised by Reissner and Nordstrom. The new metric for proton is used to find another new metric for rotating charged particle. The new metric is extended for the massive body and gives us some new information about the mass required to stop electro-magnetic interaction. It gives interesting information that planet having mass more than 1.21 times of Jupiter mass, live cannot survive. Also gives information that the mass greater than the aforesaid mass there is no electrically charged body in the universe.

Convolutional Neural Network 기반 EBG 구조 설계를 통한 고속 PCB 노이즈 저감

With rapid advances in technology, the operating frequencies of digital systems have increased to several GHz bands. This has led to an increase in simultaneous switching noise(SSN). To reduce SSN, electromagnetic bandgap(EBG) structures have been intensively studied. One of the critical steps in the design of an EBG structure is to predict the stopband that reduces SSN. Existing methods include using a 3D electromagnetic field simulation program or equations based on the Floquet theory. However, these have limitations. In this study, we verified a new method for predicting the stopband using a convolutional neural network(CNN). Specifically, a CNN architectural model was used to compare structures that perform well in predicting the stopband. It was also used to confirm that the DenseNet showed high performance.

Gravitational and Electromagnetic Field of a Non-rotating and Rotating Charged Mass

A new alternative method is presented here to find out a metric for an isolated charged mass situated at the origin in empty space. Since the charged mass has the both gravitational and electromagnetic field, therefore at first a crude line element or metric is considered for the mass, and then another crude line element is considered for the electric charge of the body. The both line elements are the functions of the distance, therefore combined the both line elements and a most general form of line element is found. To solve this metric Einstein’s gravitational and Maxwell’s electromagnetic (e-m) field equations are used. In the method of solutions e-m field tensor is also used which is found from Maxwell’s e-m field equations. After a rigorous derivation the metrics are found for both positively charged and negatively charged massive particles. The new metric for an electron is different as the metric is devised by Reissner and Nordstrom. The metric for a proton is extended for the massive body and which gives some new interesting information about the mass required to stop e-m interaction. This means that above the aforesaid mass there is no electrically charged body in the universe. On the other hand we can say that life cannot survive in those massive planets which masses are greater than 1.21 times of Jupiter mass. The metric found for proton is used to find another new metric for rotating charged massive body.

Axion-radiation conversion by super and normal conductors

We have proposed a method for the detection of dark matter axion. It uses superconductor under strong magnetic field. As is well known, the dark matter axion induces oscillating electric field under magnetic field. The electric field is proportional to the magnetic field and makes charged particles oscillate in conductors. Then, radiations of electromagnetic fields are produced. Radiation flux depends on how large the electric field is induced and how large the number of charged particles is present in the conductors. We show that the electric field in superconductor is essentially identical to the one induced in vacuum. It is proportional to the magnetic field. It is only present in the surface because of Meissner effect. On the other hand, although the magnetic field can penetrate the normal conductor, the oscillating electric field is only present in the surface of the conductor because of the skin effect. The strength of the electric field induced in the surface is equal to the one in vacuum. We obtain the electric field in the superconductor by solving equations of electromagnetic fields coupled with axion and Cooper pair described by Ginzburg-Landau model. The electric field in the normal conductor is obtained by solving equations of electromagnetic fields in the conductor coupled with axion. We compare radiation flux from the cylindrical superconductor with that from the normal conductor with same size. We find that the radiation flux from the superconductor is a hundred times larger than the flux from the normal conductor. We also show that when we use superconducting resonant cavity, we obtain radiation energy generated in the cavity two times of the order of the magnitude larger than that in normal conducting resonant cavity.

Generalization of London equations with space-time sedeons

We discuss the generalization of phenomenological equations for electromagnetic field in superconductor based on algebra of space-time sedeons. It is shown that the combined system of London and Maxwell equations can be reformulated as a single sedeonic wave equation for the field with nonzero mass of quantum, in which additional conditions are imposed on the scalar and vector potentials, relating them to the deviation of charge density and currents in the superconducting phase. Also, we considered inhomogeneous equations including external sources in the form of charges and currents of the normal phase. In particular, a screening of the Coulomb interaction of external charges in a superconducting media is discussed.

Asymptotically massive-BTZ black holes with nonlinear electrodynamics in massive gravity theory

The field equations of Einstein-massive gravity theory has been solved in a three-dimensional spherically symmetric spacetime, and in the presence of three alternative theories of nonlinear electrodynamics, separately. As the result, three novel classes of nonlinearly charged black holes have been obtained in massive gravity theory, which are asymptotically massive-BTZ black holes. The solutions of gravitational and electromagnetic field equations recover their corresponding quantities in the Einstein–Maxwell-massive theory, when the nonlinearity parameters are chosen very large. The conserved and thermodynamic quantities of the black holes such as mass, charge, temperature, entropy and electric potential have been calculated, and it has been shown that the thermodynamical first law is valid for all of new black holes. Thermodynamic stability and phase transition of the black holes have been analyzed by applying the canonical ensemble and thermodynamic geometry approaches, and noting the heat capacities and thermodynamic Ricci scalars. Then results of these alternative approaches have been compared. Finally, global stability and Hawking–Page phase transition of the black holes have been studied making use of the grand canonical ensemble and regarding the Gibbs free energies.

Polarization of propagated light with optical solitons along the fiber in de-sitter space [formula omitted

In this article, we present transformation equations for electromagnetic fields of polarized light ray traveling by magnetic optical fiber on De Sitter space S12. Some applications have been supervised by applying the new spherical frame of some Lorentzian spherical systems that are illustrated simultaneously with coiled magnetic optical fiber in De Sitter space S12. Also, we introduce perturbed new solitons for some nonlinear Schrödinger's transformation equations that manages propagation of solitons by electromagnetic fields M,E. Finally, we present some analytical reproductions to complement the analytical conclusions.

Nonlinear Numerical Analysis of The Plate Based on Thermo-Magneto-Mechanical Coupling

The thermo-magneto-elastic problems of the thin rectangular plate under the interaction of mechanical field, temperature field, and electromagnetic field are studied. On the basis of the geometric equations, physical equations, kinetic equations, and electrodynamics equations of the plate, the thermo-magneto-elastic basic equations of a thin rectangular plate are developed. According to Joule’s heat effect in the electromagnetic field and thermal equilibrium equation, temperature field in the thin rectangular plate, integral eigenvalues are derived. Adopting the difference, the quasi-linearization methods, quasilinear differential equations are obtained. Change rules of the stresses, temperatures, and deformations in the thin rectangular plate with electromagnetic parameters are analysed. It is confirmed that the stresses, strains, and temperatures in the plates can be dominated by altering electromagnetic and mechanical parameters through an example calculation.

Charged particle motion around non-singular black holes in conformal gravity in the presence of external magnetic field

We consider electromagnetic fields and charged particle dynamics around non-singular black holes in conformal gravity immersed in an external, asymptotically uniform magnetic field. First, we obtain analytic solutions of the electromagnetic field equation around rotating non-singular black holes in conformal gravity. We show that the radial components of the electric and magnetic fields increase with the increase of the parameters L and N of the black hole solution. Second, we study the dynamics of charged particles. We show that the increase of the values of the parameters L and N and of magnetic field causes a decrease in the radius of the innermost stable circular orbits (ISCO) and the magnetic coupling parameter can mimic the effect of conformal gravity giving the same ISCO radius up to omega _{mathrm{B}}le 0.07 when N=3.

On the interaction between tripod-type four-level atom and one-mode field in the presence of a classical homogeneous gravitational field

In this paper, we investigate the effects of gravitational field on the dynamical behaviour of nonlinear atom–field interaction. We consider a moving tripod-type four-level atom interacting with a single mode field in the presence of a classical homogeneous gravitational field. The analytical solution of the model is calculated by using the Schrodinger equation for a coherent electromagnetic field and when the atom is in its excited state. The influence of the detuning parameter and the classical homogeneous gravitational field on the temporal behaviour of atomic inversion, Mandel Q-parameters, purity of the atomic system and concurrence is studied. Our proposal has many advantages over the previous optical schemes and can be realised in several multiple experiments, such as quantum gravity. The results show that the gravity parameter has an important effect on the properties of these phenomena. Finally, conclusions and some features and comments are given.