Search Results (15)

High-order harmonic generation is one of the ways to generate attosecond ultra-short pulses. In order to accurately simulate the high-order harmonic emission, it is necessary to perform fast and accurate calculations on the interaction between the atoms and strong laser fields. The accurate profile of the laser field is obtained from the propagation through the gas target. Under the conditions of longer wavelength driving lasers and higher gas densities, the calculation of the laser field becomes more challenging. In this paper, we utilize the driving laser electric field information obtained from numerically solving the three-dimensional Maxwell’s equations as data for machine learning, enabling the prediction of the propagation process of intense laser fields using an artificial neural network. It is found that the simulation based on frequency domain can improve the accuracy of electric field by two orders of magnitude compared with the simulation directly from time domain. On this basis, the feasibility of the transfer learning scheme for laser field prediction is further studied. This study lays a foundation for the rapid and accurate simulation of the interaction between intense laser and matter by using an artificial neural network scheme. Full article

This paper investigates the electromagnetic fields being scattered by a metal spherical object in a vacuum environment, providing a numerical implementation of the obtained analytical results. A time-harmonic magnetic dipole source, far enough, emits the incident field at low frequencies, oriented arbitrarily in the three-dimensional space. The aim is to find a detailed solution to the scattering problem at spherical coordinates, which is useful for data inversion. Based on the theory of low frequencies, the Maxwell-type problem is transformed into Laplace’s or Poisson’s interconnected equations, accompanied by the proper boundary conditions on the perfectly conducting sphere and the radiation conditions at infinity, which are solved gradually. Broadly, the static and the first three dynamic terms are sufficient, while the terms of a higher order are negligible, which is confirmed by the field graphical representation. Full article

Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory. Full article

In this study, the plasmon-enhanced high-order harmonic generation (HHG) of H-terminated finite-sized armchair single-walled carbon nanotubes (SWCNTs) near Ag nanoparticles is investigated systematically. Multiscale methods that combine the real-time time-dependent Hartree–Fock (TDHF) approach at the semi-empirical intermediate neglected differential overlap (INDOS) Hamiltonian level for molecular electronic dynamics with the finite-difference time-domain (FDTD) and solving Maxwell’s equations are used. It is found that for intact CNTs, HHG is significantly enhanced due to plasmon resonance. However, the nonlinear optical properties are saturated when the tube length increases enough in the inhomogeneous near-field. For long CNTs, the large gradient of a near-field is unfavorable for the nonlinear excitation of electrons. But defects can further change the properties of the spectra. The HHG of hybrid systems can be enhanced very clearly by introducing vacancy defects in CNTs. This enhancement is affected by the energy and intensity of the incident light, the near-field gradient, and the number and location of defects. Full article

In this paper, we propose a novel Maxwell dynamic vibration absorber (DVA) with lever, inerter, and grounded stiffness. Firstly, the governing equation of the coupled system is established. The analytical formula of the amplitude amplification factor of the primary system and the natural frequencies of the coupled system are derived. There are three fixed points in the amplitude–frequency response curve of the primary system, which are independent of damping. Then, based on H_∞ optimization criterion, two possible optimal parameter designs of the proposed model are obtained. Considering the practical engineering application and ensuring the stability of the system, the optimal grounded stiffness ratio is selected, and six working ranges of inerter–mass ratio are calculated. Furthermore, the performance of the vibration reduction is compared for six cases. It is found that when the values of the mass ratio, lever amplification ratio, and inerter–mass ratio change in different intervals, and the optimal grounded stiffness ratio has different cases of negative, zero, and positive results. Especially when the stiffness coefficient of the viscoelastic Maxwell model and another grounded stiffness are positive at the same time, the vibration absorption effect is better theoretically. Finally, comparing with the traditional DVAs, the performance of the novel DVA is better under harmonic excitation and random excitation. The results could provide theoretical guidance for the design of inerter-based Maxwell-type DVA with a lever component. Full article

Based on the strong field approximation theory and numerical solution of Maxwell’s propagation equations, the high–order harmonic is generated from a neon (Ne) atom irradiated by a high–intensity laser pulse whose central wavelength is 800 nm. In the harmonic spectrum, it is found that in addition to the odd harmonics of the driving laser, a new frequency peak appeared. By examining the time–dependent behavior of the driving laser, it is found that the symmetry of the laser field is broken. We demonstrated that these new spectrum peaks are caused by the intensity reduction and frequency blue shift of the high–intensity laser during propagation. Our results reveal that it is feasible to modulate the harmonics of the specific energy to produce high–intensity harmonic emission by changing the gas density and the position of the gas medium interacting with the laser pulse. Full article

We investigate electromagnetic, gravitational, and plasma-related perturbations to the first order on homogeneous and hypersurface orthogonal locally rotationally symmetric (LRS) class II spacetimes. Due to the anisotropic nature of the studied backgrounds, we are able to include a non-zero magnetic field to the zeroth order. As a result of this inclusion, we find interesting interactions between the electromagnetic and gravitational variables already of the first order in the perturbations. The equations governing these perturbations are found by using the Ricci identities, the Bianchi identities, Einstein’s field equations, Maxwell’s equations, particle conservation, and a form of energy-momentum conservation for the plasma components. Using a $1+1+2$ covariant split of spacetime, the studied quantities and equations are decomposed with respect to the preferred directions on the background spacetimes. After linearizing the decomposed equations around an LRS background, performing a harmonic decomposition, and imposing the cold magnetohydrodynamic (MHD) limit with a finite electrical resistivity, the system is then reduced to a set of ordinary differential equations in time and some constraints. On solving for some of the harmonic coefficients in terms of the others, the system is found to decouple into two closed and independent subsectors. Through numerical calculations, we then observe some mechanisms for generating magnetic field perturbations, showing some traits similar to previous works using Friedmann–Lemaître–Robertson–Walker (FLRW) backgrounds. Furthermore, beat-like patterns are observed in the short wave length limit due to interference between gravitational waves and plasmonic modes. Full article

This paper is devoted to the development of generalized (for a wide range of fields (100 kV/m–1000 MV/m) and temperatures (0–1500 K) in the radio frequency range (1 kHz–500 MHz)) methods for the theoretical investigation of the physical mechanism of nonlinear kinetic phenomena during the establishment of the relaxation polarization, due to the diffusion motion of the main charge carriers in dielectrics with ionic–molecular chemical bonds (hydrogen-bonded crystals (HBC), including layered silicates, crystalline hydrates and corundum–zirconium ceramics (CZC), etc.) in an electric field. The influence of the nonlinearities equations of the initial phenomenological model of dielectric relaxation (in HBC-proton relaxation) on the mechanism for the formation of volume–charge polarization in solid dielectrics is analyzed. The solutions for the nonlinear kinetic Fokker–Planck equation, together with the Poisson equation, for the model of blocked electrodes are built in an infinite approximation (including all orders k of smallness without dimensional parameters) of perturbation theory for an arbitrary order r of the frequency harmonic of an alternating external polarizing field. It has been established that the polarization nonlinearities in ion-molecular dielectrics, already detected at the fundamental frequency, are interpreted in the mathematical model (for the first time in this work) as interactions of the relaxation modes of the volume charge density calculated on different orders of spatial Fourier harmonics. At the fundamental frequency of the field, an analytical generalized expression is written for complex dielectric permittivity (CDP), which is expressed analytically in terms of special relaxation parameters, which are quite complex real functions in the fields of frequency and temperature. The theoretical CDP and the dielectric loss tangent spectra studied depend on the nature of the relaxation processes in the selected temperature range (Maxwell and diffusion relaxation; thermally activated and tunneling relaxation), which is relevant from the point of view of choosing exact calculation formulas when analyzing the optimal operating modes of functional elements (based on dielectrics and their composites) for circuits of instrumentation, radio engineering and power equipment in real industrial production. Full article

The use of fractional derivatives and integrals has been steadily increasing thanks to their ability to capture effects and describe several natural phenomena in a better and systematic manner. Considering that the study of fractional calculus theory opens the mind to new branches of thought, in this paper, we illustrate that such concepts can be successfully implemented in electromagnetic theory, leading to the generalizations of the Maxwell’s equations. We give a brief review of the fractional vector calculus including the generalization of fractional gradient, divergence, curl, and Laplacian operators, as well as the Green, Stokes, Gauss, and Helmholtz theorems. Then, we review the physical and mathematical aspects of dielectric relaxation processes exhibiting non-exponential decay in time, focusing the attention on the time-harmonic relative permittivity function based on a general fractional polynomial series approximation. The different topics pertaining to the incorporation of the power-law dielectric response in the FDTD algorithm are explained, too. In particular, we discuss in detail a home-made fractional calculus-based FDTD scheme, also considering key issues concerning the bounding of the computational domain and the numerical stability. Finally, some examples involving different dispersive dielectrics are presented with the aim to demonstrate the usefulness and reliability of the developed FDTD scheme. Full article

The current research involves an analytical method of electromagnetic wave scattering by an impenetrable spherical object, which is immerged in an otherwise lossless environment. The highly conducting body is excited by an arbitrarily orientated time-harmonic magnetic dipole that is located at a reasonable remote distance from the sphere and operates at low frequencies for the physical situation under consideration, wherein the wavelength is much bigger than the size of the object. Upon this assumption, the scattering problem is formulated according to expansions of the implicated magnetic and electric fields in terms of positive integer powers of the wave number of the medium, which is linearly associated to the implied frequency. The static Rayleigh zeroth-order case and the initial three dynamic terms provide an excellent approximation for the obtained solution, while terms of higher orders are of minor significance and are neglected, since we work at the low-frequency regime. To this end, Maxwell’s equations reduce to a finite set of interrelated elliptic partial differential equations, each one accompanied by the perfectly electrically conducting boundary conditions on the metal sphere and the necessary limiting behavior as we move towards theoretical infinity, which is in practice very far from the observation domain. The presented analytical technique is based on the introduction of a suitable spherical coordinated system and yields compact fashioned three-dimensional solutions for the scattered components in view of infinite series expansions of spherical harmonic modes. In order to secure the validity and demonstrate the efficiency of this analytical approach, we invoke an example of reducing already known results from the literature to our complete isotropic case. Full article

The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. Here, the average helicity is derived using the conformally invariant inner product for Maxwell fields. Several equivalent integral expressions in momentum space, in $(\mathbf{r},t)$ space, and in the time-harmonic $(\mathbf{r},\omega )$ space are obtained, featuring Riemann–Silberstein-like fields and potentials. The time-harmonic expressions can be directly evaluated using the outputs of common numerical solvers of Maxwell equations. The results are shown to be equivalent to the well-known volume integral for the average helicity, featuring the electric and magnetic fields and potentials. Full article

In this paper, we study the regularity of the weak solution of the coupled system derived from the microwave heating model with frequency variable. We first show that the weak solution $\mathbf{E}$ of the system is Hölder continuous near the boundary of $S=\partial \Omega$ . The main idea of the proof is based on the estimation of linear degenerate system in Campanato space. Then we show that the solution u of the heat conduction equation is Hölder continuous with exponent $\frac{\alpha }{2}$ . Finally, under the appropriate conditions we show that the coupled system with microwave heating has a weak solution. Moreover the regularity of the weak solution is studied. Full article

A two-degree-of-freedom direct-drive induction motor (2DoFDDIM), whose solid rotor is coated with a copper layer, is capable of linear, rotary, and helical motions and has widespread applications. For solid-rotor motors, the calculation and analysis of rotor total eddy current loss (TECL) are crucial in studying the factors causing such a loss and possible loss reduction methods. In this study, a new nonlinear analytical method considering the saturation of the rotor core is proposed to solve the fundamental magnetic field. The new method divides the time period into segments. The magnetic field distribution at any time is obtained using Maxwell equations. The eddy current losses in the copper layer and rotor core caused by the fundamental magnetic field are calculated. The surface eddy current losses in the copper layer and rotor core caused by harmonics are calculated using a 2D analytical method. TECL is determined by the sum of eddy current and surface eddy current losses. Coefficients are utilized to consider eddy, saturation, and end-region effects when calculating the rotor core TECL. The new method is verified using 3D FEM, and the results show the proposed method has higher accuracy than the original method. The errors of the rotor core and copper layer TECLs are less than $6\%$ and $7.3\%$ , respectively. Full article

The theory of generalized locally Toeplitz (GLT) sequences is a powerful apparatus for computing the asymptotic spectral distribution of matrices $A_n$ arising from virtually any kind of numerical discretization of differential equations (DEs). Indeed, when the mesh fineness parameter n tends to infinity, these matrices $A_n$ give rise to a sequence ${\left\{A_n\right\}}_n$, which often turns out to be a GLT sequence or one of its “relatives”, i.e., a block GLT sequence or a reduced GLT sequence. In particular, block GLT sequences are encountered in the discretization of systems of DEs as well as in the higher-order finite element or discontinuous Galerkin approximation of scalar DEs. Despite the applicative interest, a solid theory of block GLT sequences has been developed only recently, in 2018. The purpose of the present paper is to illustrate the potential of this theory by presenting a few noteworthy examples of applications in the context of DE discretizations. Full article

In this work, we develop a numerical method for solving the three dimensional hydrodynamic electron fluid Maxwell equations that describe the electron gas dynamics driven by an external electromagnetic wave excitation. Our numerical approach is based on the Finite-Difference Time-Domain (FDTD) method for solving the Maxwell’s equations and an explicit central finite difference method for solving the hydrodynamic electron fluid equations containing both electron density and current equations. Numerical results show good agreement with the experiment of studying the second-harmonic generation (SHG) from metallic split-ring resonator (SRR). Full article