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This study aims to investigate the effectiveness of the lattice Boltzmann method (LBM) in studying the scattering of electromagnetic waves by curved and complex surfaces. The computation of Maxwell's equations is done by solving for a pair of distribution functions, which evolve based on a two-step process of collision and streaming. LBM bypasses the need for expansion via vector spherical harmonics and thus is amenable to scatterers with complex geometries. We have employed LBM to compute the scattering width and radiation force for perfect electrically conducting and dielectric cylinders of circular and elliptical cross sections. Both smooth and corrugated surfaces are studied, and the results are compared against known analytical and numerical solutions from other methods. To ensure the broad applicability of the method, we have explored a wide range of parameter space—the dielectric constant and particle size to the wavelength ratio spanning Rayleigh, Mie, and geometrical optics regimes. Our simulations have successfully reproduced well-known analytical and numerical solutions, confirming the accuracy and reliability of the LBM for scattering calculations by complex-shaped objects. [ABSTRACT FROM AUTHOR]

We study an air–crown glass planar interface that includes a thin layer of a cholesteric liquid crystal doped with silver spheres of nanometer size. We propose a new theoretical model for the propagation of electromagnetic waves through the liquid crystal part and use the Marcuvitz–Schwinger form of the Maxwell equations to compute guided surface wave profiles. The results suggest the presence of anisotropic surface modes with negligible attenuation. The dependence of the surface wave parameters on the liquid crystal layer parameters can be used in liquid crystal-based sensors. [ABSTRACT FROM AUTHOR]

Considering the evolution of the classical electromagnetic field inside a cavity containing a thin slab with time-dependent conductivity and dielectric permittivity, an approximate analytical solution for an infinite set of coupled ordinary differential equations for the mode amplitudes is found under certain simplifying assumptions. According to this solution, an amplification of the initial field cannot be possible, unless the dielectric permittivity can become strongly negative. [ABSTRACT FROM AUTHOR]

We present FARR (Finite-difference time-domain ARRay), an open source, high-performance, finite-difference time-domain (FDTD) code. FARR is specifically designed for modeling radio wave propagation in collisional, magnetized plasmas like those found in the Earth's ionosphere. The FDTD method directly solves Maxwell's equations and captures all features of electromagnetic propagation, including the effects of polarization and finite-bandwidth wave packets. By solving for all vector field quantities, the code can work in regimes where geometric optics is not applicable. FARR is able to model the complex interaction of electromagnetic waves with multi-scale ionospheric irregularities, capturing the effects of scintillation caused by both refractive and diffractive processes. In this paper, we provide a thorough description of the design and features of FARR. We also highlight specific use cases for future work, including coupling to external models for ionospheric densities, quantifying HF/VHF scintillation, and simulating radar backscatter. The code is validated by comparing the simulated wave amplitudes in a slowly changing, magnetized plasma to the predicted amplitudes using the WKB approximation. This test shows good agreement between FARR and the cold plasma dispersion relations for O, X, R, and L modes, while also highlighting key differences from working in the time-domain. Finally, we conclude by comparing the propagation path of an HF pulse reflecting from the bottomside ionosphere. This path compares well to ray tracing simulations, and demonstrates the code's ability to address realistic ionospheric propagation problems. [ABSTRACT FROM AUTHOR]

The document "In memoriam Alfred K Louis" published in the journal "Inverse Problems" pays tribute to the late Professor Alfred K Louis, a distinguished mathematician known for his work in inverse problems. It highlights his significant contributions to mathematics, particularly in tomography and the Radon transform, as well as his impact as a mentor and collaborator. The article details his academic journey, research achievements, and professional legacy, emphasizing his dedication to students and the field of applied mathematics. The text also acknowledges his numerous awards and honors, underscoring his profound influence on the scientific community. [Extracted from the article]

Untethered electromagnetic actuation becomes an appealing concept for developing applications in microscale motion control. Although actuator modeling is critical, there is a lack of inverse modeling methods for untethered electromagnetic actuators (EMA) for control design and implementation. Herein, we focused on a machine learning-based framework to obtain inverse models of untethered EMAs. The inverse model is defined as a model which takes a point in the workspace of EMA together with the magnetic field at that point as input and gives the current(s) and position(s) of electromagnets as output. To obtain the inverse model; initially, the Maxwell Equations are solved for the defined set of coil currents and electromagnet positions numerically. Then, the classification problem is defined by concerning the obtained magnetic field values as data and corresponding the input values (currents and positions) as labels. The Random Forest Classifier is trained to obtain an inverse model to match the given magnetic field vector at a position with input values. The proposed approach is employed for three common structures: Single, Double, and Quadruple EMA. The performance test showed that the obtained inverse model is capable of giving the required magnetic field with accuracy of 1.43% Moreover, experimental study shown that the obtained inverse model is also capable of simulating the real-time behavior of EMA systems. [ABSTRACT FROM AUTHOR]

This research has been conducted to analyze the free vibration behavior of a five-layered composite plate with a viscoelastic auxetic core. The plate comprises a viscoelastic auxetic core layer, functionally graded carbon nanotube reinforced composite (FG-CNTRC) interior, and magneto-electro-elastic functionally graded porous (MEE–FGP) exterior skins, which is rested on Winkler–Pasternak foundation. According to the magnetic–electric boundary conditions and Maxwell equations, the electric and magnetic potentials of the plate are determined. The macro-mechanical properties of the auxetic core have been derived based on Gibson's model; the three-parameter Zener model has also been utilized to describe its viscoelastic behavior. Additionally, the equations of motion of the plate are obtained and solved by using Reddy's third-order shear deformation theory (TSDT) and the Galerkin method, respectively. Moreover, various aspects of the current research have been validated by comparing the numerical results with those reported in the literature section. Overall, in the numerical result section, the effects of different parameters and conditions such as geometrical parameters, position of the plate's interfaces of layers (thickness of the core and face layers), various distribution patterns and volume fractions of both CNT and porosity, external work parameters of the MEE skins, boundary conditions, Winkler–Pasternak stiffness coefficients, the relaxation time, and other parameters of the viscoelastic core on the natural frequency and loss factor of the composite plate are represented. [ABSTRACT FROM AUTHOR]

A generalization of the efficient interpolation of periodic Green's functions is presented for a multilayer medium hosting transverse electric current densities and transverse equivalent magnetic current densities at different interfaces. The mathematical model is realized in terms of Maxwell's equations for multilayer media with isolated electric and magnetic equivalent current densities for large values of spectral variables or small values of spatial variables. This fact enables the use of Mixed Potential Integral Equation (MPIE) approaches in the spectral domain and provides asymptotic behaviors for Green's functions of vector and scalar potentials for both electric and magnetic sources. Consequently, the singular behaviors of the Green's functions around the source point are obtained as the spatial counterpart of the proposed spectral asymptotic behaviors. Thus, regularized multilayer periodic Green's functions are obtained, which can be efficiently interpolated over the entire unit cell using Chebyshev's polynomials. [ABSTRACT FROM AUTHOR]

In this paper, we study numerically the effect of rotation within a solvent in a cylindrical container subject to radial microwave irradiation. Two solvents with different dielectric and thermophysical properties are used: water and ethylene glycol. The samples are irradiated at a frequency of 2.45 GHz and a power of 80 W. The higher the rotation rate is, the faster the state becomes fully 3D. For water, the bifurcation occurs earlier in time due to its lower viscosity. For ethylene glycol, more susceptible to microwaves than water but with a higher viscosity, the flow remains axisymmetric for a long time and it becomes 3D when it has almost reached a stationary homogeneous maximum temperature all along the cell. We use a 3D temporal model coupling heat and momentum equations and the Maxwell equations based on spectral methods to perform the simulations. [ABSTRACT FROM AUTHOR]

Titanium–silicon (Ti–Si) alloys are widely used in aerospace, automotive manufacturing, and medical devices. A promising method to prepare these alloys involves utilizing solid wastes containing Ti and Si. However, resultant alloys often contain numerous slag particles (oxide inclusions), significantly hindering their broader application. To address this challenge, this study introduced electromagnetic separation as a novel method to remove oxygen (O) impurities from Ti–Si alloys. First, the study investigated the reasons for oxide inclusions in the alloys. Second, it explored the effects of temperature, time, and alloy composition on the preparation of low-O Ti–Si alloys. The results indicated that the residual oxide inclusions in Ti–Si alloys were primarily due to the high viscosity of the alloys while increasing Ti content in the alloy decreased the removal of O impurities. Additionally, the study investigated the influence of melt viscosity and conductivity on the electromagnetic separation of O impurities. The results indicated that with increasing Ti content in the alloy, both conductivity and viscosity increased, thereby impairing O impurity separation. Maxwell's equation and k - ε turbulent flow models were developed at a current of 29.1 A and a frequency of 3.72 kHz, with simulations conducted using COMSOL Multiphysics 6.1 software. These simulations indicated that the efficiency of electromagnetic separation was primarily affected by conductivity when Ti content ranged from 23.2 to 31.5 wt pct, while viscosity became the dominant factor when the Ti content was between 41.7 and 55.9 wt pct. This study offered valuable experimental insights into the preparation of low-O Ti–Si alloys using electromagnetic separation. [ABSTRACT FROM AUTHOR]

Copyright of Atomic Energy Science & Technology is the property of Editorial Board of Atomic Energy Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper studies the existence and uniqueness of the invariant measure for a class of stochastic Maxwell equations and proposes a novel kind of ergodic numerical approximations to inherit the intrinsic properties. The key to proving the ergodicity lies in the uniform regularity estimates of the exact and numerical solutions with respect to time, which are established by analyzing some important physical quantities. By introducing an auxiliary process, we show that the mean-square convergence order of the discontinuous Galerkin full discretization is 1 2 in the temporal direction and 1 2 in the spatial direction, which provides the convergence order of the numerical invariant measure to the exact one in L 2 -Wasserstein distance. [ABSTRACT FROM AUTHOR]

In this paper, we study the Lagrangian structure of Vlasov-Maxwell system, that is, by using a suitable notion of flow, we prove that if the densities ρ , j are integrable in spacetime, and the charge acceleration ∂ t j and ∂ t t j (or ∇ ∂ t j) are integrable functions in spacetime, then renormalized and distributional solutions of the system are the transport of the initial condition by its flow. We study more general vector fields, with wavelike structure in the sense that it has finite speed of propagation, generalizing the vector fields studied in [6]. The result is a extension of those obtained by Ambrosio, Colombo, and Figalli [2] for the Vlasov-Poisson system, and by the author and Marcon [5] for relativistic Vlasov-systems with quasistatic approximations of Maxwell's equations. [ABSTRACT FROM AUTHOR]

Trapping molecules in strong-field-seeking states is particularly attractive to scientists in the field of molecular optics. If the external field is strong enough, all molecules are strong-field seekers. Contrary to the weak-field-seeking states, molecules trapping in strong-field-seeking states can avoid the loss caused by the inelastic collision which is a stumbling block for evaporative and sympathetic cooling. Unfortunately, the formation of a magnetostatic maximum in free space is forbidden according to Maxwell's equations and Earnshaw's theory. In this paper, a dynamic magnetic trap consisting of three pairs of Helmholtz coils is proposed. The time-sequence control is given together with the distribution of the magnetic field in space. The influence of the switching frequency and electric current flowing through the wires on the number of trapped molecules is investigated. We obtain the changes in the locations and the phase-space distribution within a switching cycle by trajectory simulation. Finally, the influence of the time during which the field is off on the performance of our trap is studied. [ABSTRACT FROM AUTHOR]

The goal of this article is to establish general principles for high frequency dispersive estimates for Maxwell's equation in the exterior of a perfectly conducting ball. We construct entirely new generalized eigenfunctions for the corresponding Maxwell propagator. We show that the propagator corresponding to the electric field has a global rate of decay in L 1 − L ∞ operator norm in terms of time t and powers of h. In particular we show that some, but not all, polarizations of electromagnetic waves scatter at the same rate as the usual wave operator. The Dirichlet Laplacian wave operator L 1 − L ∞ norm estimate should not be expected to hold in general for Maxwell's equations in the exterior of a ball because of the Helmholtz decomposition theorem. [ABSTRACT FROM AUTHOR]

As an effective geophysical tool, ground penetrating radar (GPR) is widely used for environmental and engineering detections. Numerous numerical simulation algorithms have been developed to improve the computational efficiency of GPR simulations, enabling the modeling of complex structures. The discontinuous Galerkin method is a high efficiency numerical simulation algorithm which can deal with complex geometry. This method uses numerical fluxes to ensure the continuity between elements, allowing Maxwell's equations to be solved within each element without the need to assemble a global matrix or solve large systems of linear equations. As a result, memory consumption can be significantly reduced, and parallel solvers can be applied at the element level, facilitating the construction of high-order schemes to enhance computational accuracy. In this paper, we apply the discontinuous Galerkin (DG) method based on unstructured meshes to 3D GPR simulation. To verify the accuracy of our algorithm, we simulate a full-space vacuum and a cuboid in a homogeneous medium and compare results, respectively, with the analytical solutions and those from the finite-difference method. The results demonstrate that, for the same error level, the proposed DG method has significant advantages over the FDTD method, with less than 20% of the memory consumption and calculation time. Additionally, we evaluate the effectiveness of our method by simulating targets in an undulating subsurface, and further demonstrate its capability for simulating complex models. [ABSTRACT FROM AUTHOR]

The covariant Hamilton–Jacobi formulation of electrodynamics is systematically derived from the first-order (Palatini-like) Lagrangian. This derivation utilizes the De Donder–Weyl covariant Hamiltonian formalism with constraints incroporating generalized Dirac brackets of forms and the associated polysymplectic reduction, which ensure manifest covariance and consistency with the field dynamics. It is also demonstrated that the canonical Hamilton–Jacobi equation in variational derivatives and the Gauss law constraint are derived from the covariant De Donder–Weyl Hamilton–Jacobi formulation after space + time decomposition. [ABSTRACT FROM AUTHOR]

In this paper, we propose a quaternion form of equations describing electromagnetic field in a homogeneous isotropic medium without dispersion. It is shown that by renormalizing the values of field inductions and sources, one can transform the asymmetrical Maxwell equations to a highly symmetric form. This provides a possibility to introduce the scalar and vector field potentials and represent the generalized equation for electromagnetic field in the form of a single second-order quaternionic wave equation. We demonstrate that this equation reduces to the system of ordinary hyperbolic wave equations for the field potentials and on the other hand, the same equation is equivalent to the system of Maxwell equations for renormalized field intensities. The symmetry of the renormalized Maxwell equations allows one to obtain the second-order relations for energy and momentum, as well as for Lorentz invariants of the renormalized fields, which formally have the same form as for the fields in a vacuum. In addition, the generalization of renormalized equations to the case of magnetic sources corresponding to the models of Dirac magnetic monopoles and Schwinger dyons is discussed. [ABSTRACT FROM AUTHOR]

The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar interface. We study spatially one-dimensional and two-dimensional reductions in the whole space R and R 2 . The dependence on the spectral parameter, i.e. the frequency, is in the dielectric function and we make no assumptions on its form. These function values determine the spectral sets. In order to allow also for non-conservative media, the dielectric function is allowed to be complex, yielding a non-self-adjoint problem. The whole spectrum consists of eigenvalues and the essential spectrum, but the various standard types of essential spectra do not coincide in all cases. The main tool for determining the essential spectra are Weyl sequences. [ABSTRACT FROM AUTHOR]

Photonic design is a process of mathematical optimization of a desired objective (beam formation, mode conversion, etc.) subject to the constraint of Maxwell's equations. Finding the optimal design is challenging: Generically, these problems are highly nonconvex and finding global optima is NP hard. Here, we show that the associated optimization problem can be transformed to a sparse-matrix, quadratically constrained quadratic program (QCQP). Sparse QCQPs can be tackled with convex optimization techniques (such as semidefinite programming) that have thrived for identifying global bounds and high-performance designs in many areas of science and engineering but seemed inapplicable to the design problems of wave physics. We apply our formulation to prototypical photonic design problems, showing the possibility to compute fundamental limits for large-area metasurfaces, as well as the identification of designs approaching global optimality. Our approach appears directly extensible to any design problem whose governing dynamics are bilinear differential equations, as arise in structural optimization, fluid dynamics, and quantum control. [ABSTRACT FROM AUTHOR]

For the first time, Levy-type solution model and the state-space concept are employed to investigate the hygrothermal bending response of a cross-ply laminated plate on a three-parameter Kerr foundation subjected to a 2D magnetic field. The displacement field is established based on Shimpi's two-variable plate theory. Based on Maxwell's equations, the magnetic body force (Lorentz force) is established. In the present analysis, two opposite edges of the plate are simply supported. While, the other two edges have arbitrary boundary conditions. For more generality and reality, the mechanical load, temperature and moisture that are applied to the upper surface of the plate are assumed to be uniformly, linearly, exponentially, and sinusoidally varied. The principle of virtual displacements is employed to derive the governing partial differential equations based on the present theory, including Lorentz magnetic force. Levy procedure is employed to obtain the nonhomogeneous ordinary differential equations. The matrix method is utilized to get the homogeneous solution. While, the particular solution is obtained by employing the method of undetermined coefficients. The effects of Kerr foundation, loading type, boundary conditions, side-to-thickness ratio, plate aspect ratio, magnetic parameter, temperature, and moisture on deflection and stresses of Levy plate are investigated. It is noted that the magnetic field and hygrothermal loads reduce the structure's strength, which leads to an increment in the deflection and stresses. [ABSTRACT FROM AUTHOR]

In this study, the stability and vibration analyses of a spinning smart nanotube under electrical loads are examined for the first time. The smart nanotube structure is made from a single-walled zinc oxide nanotube (SWZnONT) due to its extraordinary piezoelectric and magnetic properties, which have great potential for use as a rotating component in nanoelectromechanical systems (NEMS). To achieve this aim, nonlocal strain gradient theory and Maxwell's electrostatic equations are used to capture the structure's small-scale and piezoelectric effects, respectively. In addition, the nanotube's structural model is based on the Euler–Bernoulli beam theory, deriving governing equations and boundary conditions via the Hamilton principle. A technique employing Galerkin-based closed-form solutions is utilized to solve the equations of motion and get the vibration response of the spinning smart nanotube. Finally, the effects of the material length scale, nonlocal parameter, rotating speed, external voltage, and boundary conditions on natural frequency and critical rotational speed are investigated. The study results indicate that applying an external voltage to spinning SWZnONT effectively adjusts the critical speed and enhances structural stability. [ABSTRACT FROM AUTHOR]

The coupling coefficient determines the transfer efficiency of the wireless power transfer (WPT) system. The magnetic leakage can be reduced, and the coupling coefficient of the coil can be enhanced by adding a magnetic shield. Thus, the transfer efficiency of the WPT system can be improved. However, when the receiving coil is added with magnetic shield and occurs horizontally misaligned, the coupling coefficients between the coils with the magnetic shield can only be calculated by finite element simulation, and there is no calculation method for the coupling coefficient of two circular coils with bilateral finite magnetic shield at horizontal misalignment. Therefore, based on Maxwell's equations and Bessel's function, the formula of the coupling coefficient between circular coils at coaxial is derived by the subdomain hierarchical analysis (SHA) method. On this basis, the coupling coefficient calculation formula between circular coils at horizontal misalignment is further derived by using the boundary vector equivalence (BVE) method. The results show that the maximum experimental error is not more than 5.58%, and the longest average time of the algorithm is not more than 1.282 s, which verifies the effectiveness and rapidity of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method for locating discontinuities in grounding grids using a multistatic radar. The objective is to determine the fault position in the structure by injecting an ultra-wideband pulse (Gaussian monocycle) at one of the corners of the grid and analyzing the transient signals obtained at two sensors and at the transceiver. To perform the analysis and validation of the developed method, simulations based on the finite-difference time-domain (FDTD) technique were carried out to numerically solve Maxwell's equations. The voltage signals obtained in an intact grounding grid are used as a reference. Differences between these reference voltages and the voltages obtained with the faulty grid are calculated. With these difference signals, the parameters of the radar ellipses and circle are obtained, which delimit the area where the fault can be found. These parameters depend on the wave propagation speed and the arrival times of the signals at the sensors and the transceiver. The results show that the proposed method is able to reduce the estimated fault location area to a range of 2% to 19% of the total grid area. In addition, the average distance between the actual fault and the center of the estimated region varies between 3.0 and 4.0 m. [ABSTRACT FROM AUTHOR]

The article explores the phenomenon of reflection, focusing on Fresnel's equations to understand the interaction of light with different materials. By using polarized light from cell phones, the study demonstrates reflection with respect to viewing angles. The research delves into the reflectivity of various materials, including dielectrics, semiconductors, and metals, showcasing how refractive indices influence reflection intensity. The study provides insights into how different materials exhibit varying levels of reflection based on their refractive indices, shedding light on the optical properties of common solid materials. [Extracted from the article]

In this work, we propose an a posteriori goal-oriented error estimator for the harmonic |$\textbf{A}$| - |$\varphi $| formulation arising in the modeling of eddy current problems, approximated by nonconforming finite element methods. It is based on the resolution of an adjoint problem associated with the initial one. For each of these two problems, a guaranteed equilibrated estimator is developed using some flux reconstructions. These fluxes also allow to obtain a goal-oriented error estimator that is fully computable and can be split in a principal part and a remainder one. Our theoretical results are illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

In this study, we investigate the Cauchy problem for the Vlasov-Maxwell-Fokker-Planck system near a global Maxwellian in low regularity space. We establish the existence of global mild solutions to the system by employing the energy method, provided that the perturbative initial data is sufficiently small. Moreover, despite the absence of zeroth-order dissipation for the magnetic field, we are able to derive exponential decay estimates for solutions in higher-order regularity space. This is achieved by leveraging the higher-order dissipation properties of the magnetic field, which are deduced from the Maxwell equation. [ABSTRACT FROM AUTHOR]

This paper presents a fast and robust numerical method for reconstructing point-like sources in the time-harmonic Maxwell's equations given Cauchy data at a fixed frequency. This is an electromagnetic inverse source problem with broad applications, such as antenna synthesis and design, medical imaging, and pollution source tracing. We introduce new imaging functions and a computational algorithm to determine the number of point sources, their locations, and associated moment vectors, even when these vectors have notably different magnitudes. The number of sources and locations are estimated using significant peaks of the imaging functions, and the moment vectors are computed via explicitly simple formulas. The theoretical analysis and stability of the imaging functions are investigated, where the main challenge lies in analyzing the behavior of the dot products between the columns of the imaginary part of the Green's tensor and the unknown moment vectors. Additionally, we extend our method to reconstruct small-volume sources using an asymptotic expansion of their radiated electric field. We provide numerical examples in three dimensions to demonstrate the performance of our method. [ABSTRACT FROM AUTHOR]

The article from Physics Today discusses the historical development and recent progress in quantum electrodynamics, comparing it to classical electrodynamics. It explains the challenges faced by physicists in reconciling theoretical predictions with experimental results, particularly regarding the field reaction force on electrons. The article highlights the importance of experimental validation in shaping and refining scientific theories, drawing parallels between the evolution of classical electrodynamics and quantum electrodynamics. The author, F. J. Dyson, emphasizes the need for a new, simpler description of electrons in quantum electrodynamics to further advance our understanding of elementary particles. [Extracted from the article]

We investigate the possibility of upgrading of the evolutionary approach to solving vector initial-boundaryvalue problems for the Maxwell equations and solve the equation of forced oscillations in a cylindrical resonator by using the upgraded approach. In addition, the potential for extending the approach to the theory of laser dynamics is discussed. [ABSTRACT FROM AUTHOR]

We consider the eigenfrequency problem of the magnetic field of Maxwell's equation in a domain Ω of $ \mathbb {R}^3 $ R 3 with an inclusion O under perturbation $ O_\delta $ O δ , which is a thin layer at the wall boundary (skin depth) $ \partial O_\delta $ ∂ O δ . We write the asymptotic formula in terms of the function modelling: the oscillation and the electric permittivity. We establish the convergence of the solution and then we justify a rigorous asymptotic formula for the eigenfrequency. [ABSTRACT FROM AUTHOR]

A Hertz radiator's Sommerfeld boundary value problem is considered for the case when its electric moment is directed horizontally relative to the plane interface between two media with different values of magnetic permeability. An integral representation of the exact expression for the Hertz potential, which generalizes the classical solution for non-magnetic media, both in cylindrical and spherical coordinate systems, is obtained. The corresponding expressions for the scattered wave fields are given in the form of Sommerfeld integrals. It is shown that the potential components can be represented as the sum of an infinite series in powers of the Green function. [ABSTRACT FROM AUTHOR]

Quantitative interpretation of the data from controlled‐source electromagnetic methods, whether via forward modelling or inversion, requires solving a considerable number of forward problems, and multigrid methods are often employed to accelerate the solving process. In this study, a new extrapolation cascadic multigrid method is employed to solve the large sparse complex linear system arising from the finite element approximation of Maxwell's equations using secondary potentials. The equations using secondary potentials are discretized by the classic nodal finite element method on nonuniform rectilinear grids. The resulting linear systems are solved by the extrapolation cascadic multigrid method with a new prolongation operator and preconditioned Stabilized bi‐conjugate gradient method smoother. High‐order interpolation and global extrapolation formulas are utilized to construct the multigrid prolongation operator. The extrapolation cascadic multigrid method with the new prolongation operator is easier to implement and more flexible in application than the original one. Finally, several synthetic examples including layered models, models with anisotropic anomalous bodies or layers, are used to validate the accuracy and efficiency of the proposed method. Numerical results show that the extrapolation cascadic multigrid method improves the efficiency of 3D controlled‐source electromagnetic forward modelling a lot, compared with traditional iterative solvers and some state‐of‐the‐art methods or software (e.g., preconditioned flexible generalized minimal residual method, emg3d) in the considered models and grid settings. The efficiency benefit is more evident as the number of unknowns increases, and the proposed method is more efficient at low frequencies. The extrapolation cascadic multigrid method can also be used to solve systems of equations arising from related applications, such as induction logging, airborne electromagnetic, etc. [ABSTRACT FROM AUTHOR]

In this paper, we study a numerical scheme to solve the nonlinear Maxwell's equations. The discrete scheme is based on the triangular spectral element method (TSEM) in space and the exponential time differencing fourth-order Runge-Kutta (ETDRK4) method in time. TSEM has the advantages of spectral accuracy and geometric flexibility. The ETD method involves exact integration of the linear part of the governing equation followed by an approximation of an integral involving the nonlinear terms. The RK4 scheme is introduced for the time integration of the nonlinear terms. The stability region of the ETDRK4 method is depicted. Moreover, the contour integral in the complex plan is utilized and improved to compute the matrix function required by the implementation of ETDRK4. The numerical results demonstrate that our proposed method is of exponential convergence with the order of basis function in space and fourth order accuracy in time. • The spatial discrete scheme is based on the triangular spectral element method. • The exponential time differencing fourth-order Runge-Kutta method is employed in time. • The stability region of the time discrete scheme is analyzed. • The contour integral in the complex plan is utilized to calculate the matrix function. • The novel scheme is of spectral accuracy in space and fourth order accuracy in time. [ABSTRACT FROM AUTHOR]

In wireless power transfer systems, the relative positional misalignment between transmitting and receiving coils significantly impacts the system's mutual inductance characteristics, thereby constraining the system's output power stability and transmission efficiency optimization potential. Hence, accurate formulas for calculating mutual inductance are crucial for optimizing coil structures and achieving mutual inductance stability. This study focuses on the mutual inductance characteristics of rectangular coils under positional misalignment conditions in a dual-sided electromagnetic shielding environment. Initially, the research deduces the incident magnetic flux density induced by the current in rectangular coils through the dual Fourier transform and magnetic vector potential method. Subsequently, Maxwell's equations and boundary conditions are employed to analytically examine the induced eddy currents within the shielding layer, allowing for the calculation of reflected magnetic flux density. Based on these analyses, the study derives a formula for mutual inductance using the magnetic flux density method. A prototype was built for experimental verification. The experiment results show that the maximum error between the measured mutual inductance and the calculated result is less than 3.8%, which verifies the feasibility and the accuracy of the proposed calculation method. Simulations and empirical validation demonstrate the superior accuracy and practicality of the proposed formula. This research not only offers an innovative technological pathway for enhancing the stability and efficiency of wireless power transfer systems but also provides a solid theoretical foundation and guiding framework for coil design and optimization. [ABSTRACT FROM AUTHOR]

The efficient mixing of fluids at microscale dimensions presents challenges due to the dominant laminar flow regime which restricts convective mixing. This study introduces a numerical analysis of a novel microrobotic mixing system with a levitated propeller robot, driven by magnetic fields, within a Y-shaped microchannel with a square cross-section (500 × 500 μm). Our research investigates the fluid mixing effectiveness facilitated by the microrobot through various levitation heights and orientations to enhance the mixing index (MI). This index is tested under different conditions by leveraging the dynamics of the propeller robot, characterized by adjustable roll and pitch angles and varying levitation heights. The numerical simulations, conducted using COMSOL® (Finite Element Method, FEM) software, integrate Maxwell's equations for magnetic field interaction with momentum and transport-diffusion equations to analyze fluid dynamics within the microchannel. Results indicate that the propeller robot can achieve an MI of up to 98.94% at a 150 μm levitation height and 1500 rpm propeller speed within 3 s. Additionally, the study examines the impact of propeller speed, Reynolds number, and robot length on mixing performance, providing comprehensive guidance for optimizing microscale fluid mixing in lab-on-a-chip applications. [ABSTRACT FROM AUTHOR]

We study a class of dynamic control systems described by nonlinear fractional stochastic degenerate evolution equations in Hilbert spaces. We investigate the possibility of replacing a degenerate Cauchy problem by an equivalent problem in the factor space H ⊥ = H \ Ker (L) . The core of this paper is to factorize the degenerate Cauchy problem, to derive a mild solution of stochastic system based on the perturbation theory for linear operators and to study approximate controllability results. Using fixed point technique, fractional calculations, stochastic analysis technique and methods adopted directly from deterministic control problems, a new set of sufficient conditions for approximate controllability of fractional stochastic degenerate evolution equations is formulated and proved. In particular, we discuss the approximate controllability of nonlinear fractional stochastic degenerate control system under the assumption that the corresponding linear system is approximately controllable. As an application, the abstract results are illustrated by the application in complex media electromagnetic. In addition, the fractional stochastic partial differential equations (fractional SPDEs) are discussed and approximate controllability results are proved by verifying main assumptions. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Shanghai Jiao Tong University (1006-2467) is the property of Journal of Shanghai Jiao Tong University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Nowadays, there has been a notable surge in the utilization of piezoelectric materials at the micro and nano scales, manifesting across various branches of science through the development of diverse microstructures. On the other hand, given the deployment of microstructures in environments subject to temperature fluctuations or in close proximity to heat sources, it is imperative to thoroughly examine the thermal impacts at a micro scale, particularly concerning piezoelectric materials. This paper delves into the investigation of wave propagation within a micro-scale piezoelectric layer experiencing thermal shock. This study represents the exploration of thermo-electro-elastic wave propagation within the micro dimension. For the first time, it incorporates size-dependent modeling (non-classic continuous theory) along with the application of Lord Shulman's theory to analyze the behavior of the piezoelectric layer. In the modeling process, Maxwell's three equations governing energy, motion, and electrostatics were extracted, subsequently coupled together, and finally, they were reformulated into a dimensionless form. The differential quadrature method was employed to solve the equations, and the coupled equations were resolved. Houbolt's method is employed for solving the equations in the time domain. Ultimately, the findings concerning a micro-scale piezoelectric layer under thermal shock are presented. The findings highlight the significance of size effects at the micro scale, emphasizing the necessity of considering them in analyses and applications. [ABSTRACT FROM AUTHOR]

The Maxima computer algebra system, the open-source successor to MACSYMA, the first general-purpose computer algebra system that was initially developed at the Massachusetts Institute of Technology in the late 1960s and later distributed by the United States Department of Energy, has some remarkable capabilities, some of which are implemented in the form of add-on, "share" packages that are distributed along with the core Maxima system. One such share package is itensor, for indicial tensor manipulation. One of the more remarkable features of itensor is functional differentiation. Through this, it is possible to use itensor to develop a Lagrangian field theory and derive the corresponding field equations. In this paper, we demonstrate this capability by deriving Maxwell's equations from the Maxwell Lagrangian, and exploring the properties of the system, including current conservation. [ABSTRACT FROM AUTHOR]

Coupling the averaged L1 scheme and the Crank–Nicolson scheme for temporal derivatives, we study Maxwell's equations in the Cole–Cole dispersive medium. A rigorous analysis is carried out to show that the proposed scheme is unconditionally stable and has a second-order convergence in time for sufficiently smooth solutions. We avoid using the mathematical induction method, which simplifies the analysis than the existing schemes. A fully discrete scheme with a finite difference method at Yee's grid is proposed. Numerical experiments are carefully designed to illustrate our theoretical analysis. • We applied the averaged L1 scheme to the Maxwell's equation in Cole-Cole dispersive medium. • Due to the semi-positivity property of the average L1 scheme, we analyse the discrete energy stability. • The dissipation law with the modified energy is proved. • We also rigorously analyse the convergence in time and space. • Ample numerical experiments illustrated the accuracy of our theoretical analysis. [ABSTRACT FROM AUTHOR]

In the field of high-frequency magnetic impedance (MI) research, accurately describing the MI effect in multilayer nanostructured thin films remains a challenging task. A model to accurately describe high-frequency magnetoimpedance in the FeNi/Co/Cu/Co/FeNi five-layer nanostructured thin film is developed. The GMI response was obtained through the simultaneous solution of Maxwell's equations and the Landau-Lifshitz equation. Through the induction of an effective bias field in the soft magnetic layer, the magnetostatic coupling between the soft and hard magnetic layers is taken into account. At frequencies up to GHz magnitude, symmetrically structured nanofilms are capable of obtaining a greater MI ratio through magnetic coupling. Furthermore, we demonstrate that modifying film properties and manipulating the bias field can lead to improved sensing performance. This study not only fills the gap in the theoretical model of five-layer nanostructured symmetrical films but also provides a theoretical foundation for the design and optimization of high-performance magnetic sensors operating at high frequencies. The findings presented in this paper hold potential to advance the development of high-frequency magnetic impedance sensors. [ABSTRACT FROM AUTHOR]