Maxwell's Equations Research Articles

Next frontiers for magnetic monopole searches

Magnetic monopoles (MMs) are well-motivated hypothetical particles whose discovery would symmetrize Maxwell equations, explain quantization of electric charge, and probe the gauge structure of the unified theory. Recent models predict MMs with low masses, reinvigorating searches at colliders. However, most theories predict composite MMs, whose production in parton-parton collisions is expected to be suppressed. The Schwinger process, whereby MM pairs tunnel through the vacuum barrier in the presence of a strong magnetic field, is not subject to this limitation. Additionally, the Schwinger cross section can be calculated nonperturbatively. Together, these make it a golden channel for low-mass MM searches. We investigate the Schwinger production of MMs in heavy-ion collisions at future colliders, in collisions of cosmic rays with the atmosphere, and in decay of magnetic fields of cosmic origin. We find that a next-generation collider would provide the best sensitivity, allowing one to discover or exclude MMs with TeV-scale masses. At the same time, exploiting the infrastructure of industrial ore extraction and Antarctic ice drilling could advance the field at a faster timescale and with only a modest investment. In particular, we show with detailed calculations that the proposed experiments will be sensitive to fluxes of low-mass MMs as low as a few units of 10−22 cm−2 s−1 sr−1 in a wide range of Lorentz factors. We also propose deploying dedicated MM detectors in conjunction with cosmic ray observatories to directly investigate if the unexplained, highest-energy cosmic rays are MMs. Together, the proposed efforts would define the field of MM searches in the next decades. Published by the American Physical Society 2025

Eulerian kinetic plasma simulations via allowed deformation modes of relative probability density profile

Abstract Kinetic simulation on Vlasov-Maxwell (V-M) system have some mandatory requirements, such as non-negativity of probability density profile (f-profile) and f = 0 at v/c = ±1, to be respected. These mandatory requirements bring considerable difficulty to the simulation in Eulerian approach ,and also cause the efficiency of a simulation being affected greatly by mathematical description/expression of the f-profile. Familiar mesh expression is less efficient to correctly describe the space-time behavior of the f-profile near the v/c = ±1 regime, where mandatory requirements are easily violated for inappropriate mathematical expression. This work develops a high-efficiency simulation based on an appropriate and strict mathematical expression of the f-profile, which is favorable for fully respecting these mandatory requirements. The time evolution of a f-profile is expressed by its time-dependent local deformations at each phase space position, and fully respect these mandatory requirements.
Key words: Plasma Kinetic Simulation; Vlasov Equation; Maxwell Equation.
PACS: 52.65.-y.

Kiselev black strings: the charged rotating solutions

Abstract We investigate the properties of a charged rotating black string immersed in a Kiselev anisotropic fluid in anti-de Sitter (AdS) spacetime. The Einstein–Maxwell equations with an anisotropic stress–energy tensor and cosmological constant are analyzed and solved exactly. In this work, we calculate the Kretschmann scalar, obtaining a consistent result that agrees with the existing literature in the absence of charge and fluid. The rotating solution is obtained by applying a coordinate transformation on time and angular coordinates. The event horizon associated with specific values of the equation of state parameter wq is studied. The results show an important influence of the fluid parameters N q and w q , the charge parameter Q , and the rotation parameter a on the size of the black string horizon. In addition, we determine the conditions for the existence of closed timelike curves and compute the conserved charges, such as mass, angular momentum, and electric charge of the black string. Utilizing the Klein–Gordon equation, we employ the quantum particle tunneling approach to obtain the probability of charged scalar particles tunneling across the event horizon. We obtain the correspondent Hawking temperature as a consequence. Furthermore, we examine the thermodynamic properties, including entropy and heat capacity, to assess the effects of the quintessence field and charge on the black string. The results include particular cases such as the Lemos black string, providing a broader view of black string configurations in AdS spacetime.

Comparison of the Combined Shielding Effectiveness Based on Experimental Studies of Overhead Power Lines Magnetic Field 3D Model

The aim of the work is an experimental study of the efficiency of combined shielding of the magnetic field generated by transmission lines (HVPL) with single-circuit and triangular arrangements of wires and double-circuit transmission lines with a "Barrel" type of wire arrangement using an active shielding system and passive shields made in the form of solid, or multi-loop, shields. To achieve this goal, the structure of combined shields was determined, which consist of a double-loop active shield and solid or multi-loop shields. The developed combined shields provide increased efficiency in reducing the level of industrial frequency (MF) magnetic field. Designing combined shields is reduced to solving vector games in which the cost vector of the game is calculated based on solutions to Maxwell's equations in a quasi-stationary approximation using the COMSOL Multiphysics software package. The solution to these vector games is calculated based on the "particle swarm" optimization algorithms from Pareto-optimal solutions, taking into account binary preference relations. The most important results are the calculated values of the spatial arrangement coordinates of two compensation windings of the active shielding system and the values of currents and phases in these windings, as well as the parameters of solid and multi-loop passive screens, which made it possible to increase the efficiency of MF shielding inside residential buildings from that generated by single-circuit HVPL with the triangular wire arrangement and double-circuit HVPL with the "Barrel" type conductor arrangement. The significance of the obtained results is that practical recommendations are given for the justified choice of the spatial arrangement of two shielding windings of the robust active shielding system, as well as the parameters of solid and multi-loop passive screens for combined shielding systems of MF generated inside residential buildings by single-circuit HVPL with triangular wire arrangement and double-circuit HVPL with the "Barrel" type conductor arrangement. The possibility of reducing the induction level of the initial MF to the level of sanitary standards is shown.

An unconditionally stable second-order scheme for Maxwell's equations in the Cole–Cole dispersive medium

An unconditionally stable second-order scheme for Maxwell's equations in the Cole–Cole dispersive medium

A polytopal discrete de Rham complex on manifolds, with application to the Maxwell equations

A polytopal discrete de Rham complex on manifolds, with application to the Maxwell equations

P-Adaptive algorithms in discontinuous Galerkin solutions to the time-domain Maxwell's equations

The Discontinuous Galerkin time-domain method is well suited for adaptive algorithms to solve the time-domain Maxwell's equations and depends on robust and economically computable drivers. Adaptive algorithms utilize local indicators to dynamically identify regions and assign spatial operators of varying accuracy in the computational domain. This work identifies requisite properties of adaptivity drivers and develops two methods, a feature-based method guided by gradients of local field, and another utilizing the divergence error often found in numerical solution to the time-domain Maxwell's equations. Results for canonical testcases of electromagnetic scattering are presented, highlighting key characteristics of both methods, and their computational performance.

A Unified Framework for Total Variation Regularized Optimization in Fluid Dynamics and Related Physical Systems

An optimization framework is presented for minimizing the energy functional developed around a generalized equation governing physical systems such as fluid dynamics, particle transport, phase transition, and other related systems. The convexity of the energy functional is investigated to derive the necessary conditions for a smooth and global optimum solution. Furthermore, the Total Variation (TV) regularization term is introduced to gain insights into the solution space and convergence analysis of convection-dominated problems. We demonstrate the practical application of our method by applying it to some selected examples such as the Boltzmann, Navier-Stokes, and Maxwell equations.

IMPROVE OF OVERHEAD POWER LINES MAGNETIC FIELD MITIGATION EFFICIENCY BY COMBINED ACTIVE AND PASSIVE CONTOURS SHIELDING

Problem of improving of efficiency of overhead power lines magnetic field mitigation by combined active and passive contours shielding and reducing system sensitivity to uncertainty and changes in system parameters considered. Design of combined active and passive shielding reduced to solving the geometric inverse problem of magneto-quasi-static’s based on vector game solution with vector payoff calculated based on Maxwell equations solution in a quasi-stationary approximation using COMSOL Multiphysics software. Vector game solution calculated based on particles multi-swarm optimization algorithms from Pareto optimal solutions set taking into account binary preference relations. During de-sign of combined active and passive shielding number and spatial arrangement coordinates of active compensating windings and passive contours, as well as currents and phases in active compensating windings calculated. The com-puter simulation and experimental research of combined active and passive contours shielding for improving of over-head power lines magnetic field mitigation efficiency presented. References 3, figures 2.

Exploring singularity-free stellar models in f(R,T) theory: A pulsar SMC X-4 admitting electromagnetic field

In the context of [Formula: see text] gravity theory, this study formulates two new non-singular models that effectively describe anisotropic spherical structures influenced by an electromagnetic field. The modified Einstein–Maxwell equations are derived for a static charged interior spacetime. Subsequently, these equations are addressed using two distinct forms of radial metric potentials, simplifying the extraction of their solution. By employing specific types of pressure anisotropy, we derive two unique models that enhance our understanding of such stellar configurations. The differential equations are appeared in both cases whose solutions involve integration constants. We determine these constants by matching an inner and the outer Reissner–Nordström spacetimes at the spherical junction. In light of this, we also use the condition of vanishing radial pressure. Afterwards, we investigate certain conditions that, when satisfied, result in physically existing compact models. The estimated data of a star, SMC X-4 along with several parametric values are considered to perform a graphical analysis of the developed solutions. It is concluded that, for chosen parametric values, both models meet all the requirements and thus exist physically under the considered modified gravity model.

UNCOVERING UNDERGRADUATE PHYSICS PRE-SERVICE TEACHERS’ ERRORS IN ELECTROMAGNETIC INTERACTION AND ELECTROMAGNETIC EFFECTS

Electricity and magnetism are fundamental areas of physics and are integral to science curricula at various educational levels. However, this area has been reported to contain several concepts that students find challenging, leading to perspectives that diverge from scientifically accepted views. This study examines the errors made by physics pre-service teachers (PPSTs) in electromagnetic interaction and electromagnetic effects, using the De Jong and Ferguson-Hessler framework of knowledge types to classify errors into conceptual, procedural, and situational categories. An interpretivist qualitative case study design was employed. The study was conducted with a class of 86 third-year undergraduate PPSTs enrolled in a physical sciences education program. Data were collected using a test designed to assess PPSTs' understanding of key electromagnetic concepts. The test results revealed recurring errors in conceptual understanding and problem-solving techniques, particularly in interpreting electric and magnetic fields, Coulomb’s law, and applying Maxwell's equations. Findings suggest that targeted educational interventions focusing on improving students’ conceptual and procedural knowledge, along with strategic approaches to problem-solving, could reduce the frequency of these errors. Hence, this study highlights the need for more focused teacher training to address these difficulties related to electricity and magnetism and its long-term impact on physics education. Keywords: conceptual errors, electromagnetic interaction, physics pre-service teachers, procedural errors, physics education

The Fresnel equations of classical and extended electrodynamics – a review

AbstractWe study the behavior of electromagnetic waves near the interface between two media: a dielectric medium and a conducting medium leading to the so‐called Fresnel equations. We discuss analytical solutions of the problem in the framework of classical as well as extended electrodynamics. As a didactic add‐on a rational derivation of the classical Fresnel equations in conducting media by using a consistent application of vector representation for the wave vectors is presented for the benefit of the reader. The Fresnel equations obtained in the framework of extended electrodynamics are novel. We also discuss three mechanical models of electrodynamic processes in conducting media. The mathematical description of two of them allows one to obtain classical Maxwell's equations. The third model combines the two first models. Its mathematical description allows one to obtain the equations of extended electrodynamics.

Three-dimensional magneto-thermal analytical model for planar induction heater of nonmagnetic conducting materials considering transverse finite length effects

Purpose This paper aims to present a three-dimensional nonlinear magneto-thermal analytical model for a planar permanent-magnet induction heater, enabling the evaluation of the spatiotemporal temperature distribution in a non-magnetic conducting plate. The coupled 3D magneto-thermal problem is formulated using the sub-domain method, image theory and the equivalent thermal network. Design/methodology/approach The 3D magneto-thermal problem is solved through a nonlinear coupling between an electromagnetic analytical model and a transient thermal analysis. The electromagnetic model is derived by solving the three-dimensional Maxwell equations in Cartesian coordinates. First, the analytical expression for the heating power is determined for an infinitely wide conducting plate using a hybrid formulation. Then, the method of images is applied to account for finite-width extremity effects. The thermal model is obtained using the equivalent thermal network method. To analyze the accuracy of the magneto-thermal model, the analytical results are compared with those obtained from the 3D finite element (FE) multiphysics simulation. Findings The obtained results show the accuracy of the proposed magneto-thermal model, even for geometries with a very strong 3D edge effects. The analytical model directly takes into account the magnetic edge effects, the transverse finite width of the conducting plate, the reaction field and the temperature-dependent nonlinearity of the physical properties, without using correction factors. The use of a direct formulation of induced currents in the conducting part allowed us to determine a new analytical expression for the heating power. The magneto-thermal analytical model shows a good compromise between accuracy and computation time. Practical implications The proposed magneto-thermal model significantly reduces computation time compared to 3D FE simulations, making it a robust tool for the quick and accurate optimization and design of planar permanent-magnet induction heater systems. Originality/value A new 3D magneto-thermal analytical model for determining the spatiotemporal temperature distribution on a planar heater has been developed. This model accounts for magnetic edge effects, the finite width of the workpiece and the reaction field, while improving computation time thanks to the new analytical expression for the heating power derived from a hybrid formulation.

A geometric Particle-In-Cell discretization of the drift-kinetic and fully kinetic Vlasov–Maxwell equations

Abstract In this paper, we extend the geometric particle in cell framework on dual grids to a gauge-free drift-kinetic (DK) Vlasov–Maxwell model and its coupling with the fully kinetic (FK) model. We derive a discrete action principle on dual grids for our DK model, such that the dynamical system involves only the electric and magnetic fields and not the potentials as most DK and gyrokinetic models do. This yields a macroscopic Maxwell equation including polarization and magnetization terms that can be coupled straightforwardly with a FK model.

Relativistic approach to manipulating angular distribution of charged particles via kinetic equations

Deflection angles of charged particles interacting with materials play a critical role in various plasma applications. The development of a mathematically well-posed kinetic collision operator that accounts for deflection angles of strong Coulomb interactions remains a fundamental open problem. This paper presents a relativistic method for modifying the electromagnetic field in an anisotropic and adjustable manner to manipulate a system of charged particles, specifically by the transfer of angular momentum from a superluminal wave source to particles at specific times and locations. The method provides a mechanism to influence the scattering outcomes of strong interactions by manipulating the angular distribution of particles, and thus the deflection angles of their interactions with a solid surface, without requiring detailed knowledge of the kinetic collision operator. To this end, we demonstrate how a specific type of singularity, generated by Maxwell's equations for a superluminal wave source at the boundary of the plasma, can modify the electromagnetic field in a highly directional manner. The proposed method can lead to the development of novel approaches for controlling interactions of charged particles with a material in plasma systems. Published by the American Physical Society 2025

The VEM for Time-Harmonic Maxwell Equations in Inhomogeneous Media with Lipschitz Interface

The VEM for Time-Harmonic Maxwell Equations in Inhomogeneous Media with Lipschitz Interface

Transient dynamics and stress evolution under moving heat flux: A coupled magneto-electro-thermoelastic framework for smart hybrid plates resting on viscoelastic foundation

Transient coupled magneto-electro-thermoelastic responses of multiferroic hybrid plates exposed to a distributed moving heat flux are investigated in this article with an overarching aim of controlling undesirable stresses through an inclusive design framework. The structure is considered to rest on a two-parameter viscoelastic Winkler-Pasternak foundation with the moving heat flux acting on the top surface, and the study assumes simply supported boundary conditions for numerical demonstration. The governing equations for the motion of each layer are derived following an orthotropic laminated model based on the generalized three-dimensional coupled thermoelasticity theory of Lord-Shulman, coupled with electrostatic and magnetostatic Maxwell equations for the present multi-physical simulations. In this regard, the powerful state space technique and the transfer matrix are exploited. The key parameters of the dynamic response are calculated based on Durbin’s numerical Laplace inversion algorithm. Previous studies have typically analyzed the thermal stresses of structures using classical uncoupled theories. These theories assume an infinite heat propagation rate and ignore the wave-like heat propagation that occurs in reality. The proposed computational framework based on Lord Shulman’s theory considers wave-like behavior in thermal propagation. Comprehensive numerical results concerning temporal and spatial variations of temperature, displacement, and stress fields are presented for various critically influencing parameters such as volume fraction index, open or closed-circuit conditions, heat flux speed and length, and smart layer thickness. The coupled computational framework along with the numerical findings presented in this article would lead to efficient designing and intelligent control of hybrid and smart structures under thermal loading.

Relativity Theory for All Velocities v<c, v = c, v>c Based on Single Transformation Law for 4-Vectors and Tensors

Relativity theory based on a single transformation law (STL) for 4-vectors and tensors under universal rotation matrix (URM) on a unit circle satisfies principle of relativity, conservation laws and new symmetry valid for v<c, v = c and v>c. This model can be called as relativity theory for all velocities (RTAV). The framework of relativity theory under universal Lorentz transformation matrix (ULTM) on a unit hyperbola gave form invariance of spacetime laws of physics for v<c only. URM is the inverse of ULTM. In this model, time and space components remain equal at v = c and reciprocate at v<c and v>c such that spacetime as a whole remains same for all observers. We consider the transformation of electrodynamic laws consisting of electromagnetic field (EMF), Maxwell’s equations (ME) and conservation law in tensor components form. STL under URM gives rise to new symmetry of EMF, ME and conservation law along their diagonals. These terms constitute structure of zero-point electrodynamics (ZPE). Matrix method and Einstein’s summation convention method (ESCM) are employed. Both methods agree up to the transformation of EMF, ME but differ in the transformation of conservation law. Usual electrodynamics remains same for all observers without being affected by ZPE. Conservation law in matrix method holds as usual. In ESCM, zero-point conservation appears as 4D EM wave while conservation law itself becomes 7D EM wave. In quantum theory zero-point energy violates conservation law whereas in our model ZPE is necessary to validate form invariance of spacetime laws and conservation law. This model of relativity is equally valid for noninertial frame.

Sayed`s Theory on Unification of Electromagnetism and Gravity Forces: Innovative Correlation of Electrodynamics and Gravity with Inevitable Violation of E=mc

The unified universe is a function in the only Great Creator, Allah. The unification of the weak nuclear force and electromagnetism was achieved in 1979 by Noble laureates. This article is a theory and outstanding approach for unification of electromagnetism and gravity forces. The Sayed`s electromagnetic-gravity force (SEMGF) equations were derived and generated by fusion of Newton, Einstein, Planck, Maxwell equations and Coulomb law. The violation of E=mc2 is remarkably concluded. The unified equations lead to introduce the effect of electromagnetic gravity force on the measured and calculated speed of light. The acceleration, wavelength, gravitational constant, Planck constant, and speed of light were also integrated to develop Maxwell`s equations. The magnetic to electric field ratio was postulated to be π. To verify some universal constants taking into consideration the electromagnetic gravity force, speed of light was served to be violated: ~ 6 x1016 m/s. The Planck force and acceleration were found to be in concordance with the calculated by SEMGF; 1.21029x1044 N and 5.6077x1051 m/s2 respectively. The calculated gravitational constant (G) and electrostatic charge (e) values are; 6.67 x 10-11 Nm2/kg2 and 1.602x10-19 C. Some values show differences that could be due to mutual and overlapping effect of the gravity and electromagnetism forces. It is a deep step for unification of gravity and electromagnetism.

New interpretation of the original charged BTZ black hole spacetime

Abstract In their seminal 1992 paper, Bañados, Teitelboim and Zanelli (BTZ) proposed a simple charged generalization of what is now known as the spinning BTZ black hole, the proposal being that a rotating metric can be supported by a `static vector' potential.
While with such an ansatz the Einstein equations are satisfied, and the corresponding energy-momentum tensor is divergence-less, the Maxwell equations do not (due to the special degenerate form of the corresponding field strength) hold. More recently, Deshpande and Lunin have proposed a generalized `Einstein--Maxwell' system which yields analytic rotating black holes in all odd dimensions. In this paper, we show that the original charged BTZ solution can be re-interpreted as a solution of the Deshpande--Lunin theory. Moreover, as we shall explicitly illustrate on an example of regularized conformal electrodynamics, similar construction also works for any non-linear electrodynamics in 3-dimensions.