Classical Electrodynamics Research Articles

2-D Modeling and Analysis of Time-Domain Electromagnetic Anomalous Diffusion With Space-Fractional Derivative

Recently, the electromagnetic (EM) anomalous diffusion phenomenon has been observed in time-domain EM (TDEM) surveys. Furthermore, the data interpretation accuracy has been reduced by adopting the traditional EM theory and methods. A number of models, such as random medium and roughness electrical conductivity theory, have been adopted to model the EM anomalous diffusion. However, problems such as modeling difficulty and massive discretization exist regarding characterizing the long-range correlation of EM anomalous diffusion. The space-fractional derivative has been proven to preferably describe the long-range correlation characteristic. Only a handful of studies on TDEM anomalous diffusion with space-fractional derivative have been conducted due to the difficulties in computational engineering problems. Therefore, we performed a series of studies about 2-D TDEM anomalous diffusion with space-fractional derivative. The 2-D TDEM space-fractional diffusion equation was constructed based on the space-fractional Ohm’s law model. Furthermore, the discretization and iteration forms of the control equation were derived based on the finite element method (FEM) by introducing the Riemann–Liouville (R–L)-type Riesz fractional derivatives. The 2-D mountain-shaped function and partial integration method (PIM) were combined to convert the fractional derivative into the primitive function form. Hence, the 2-D modeling of the space-fractional EM diffusion was realized. The effectiveness of our method was verified by the function construction method and wavenumber-domain analytical solution. The spatial and temporal characteristics of the space-fractional EM diffusion were analyzed by different geological models. Furthermore, we discuss the differences with the classical EM diffusion. Our method can effectively model the space-fractional EM diffusion in TDEM surveys and provide theoretical bases for improving the TDEM interpretation accuracy with complex geological conditions.

Modeling SARS-CoV-2 and preventing COVID-19 pandemic

Backgrounds: Since December 2019, COVID-19 pandemic has globally killed more than 6.602 millions, infected more than 635.2 millions of people and lasted almost three years, as of 11/22/2022. The pandemic is still killing more than 7,261 and infecting more than 2.259 millions of people per week in the whole world today. We think the rates of the fatality, infection and the long term of the pandemic are related to proliferation characteristics and biological structures of SARS-CoV-2. Methods and Objectives: We apply theories of biology, ligand field, biophysics, biochemistry, virology, classic electrodynamics, and published biological data, to model proliferation characteristics and biological structures of SARS-CoV-2. Modeling Results and Outcomes: We coin a concept: quasi identical biological objects carry the quasi identical biological information (spatial, temporal, electromagnetic and mass properties), and they cannot occupy the same biological envelope if their repulsive forces between them are stronger than the resistances. We propose two models of exclusions. Exclusion of RNA (DNA) strands: No normally and naturally replicated quasi identical RNA (DNA) strands can occupy the same virus. Exclusion of viruses: No normally and naturally proliferated quasi identical viruses can occupy the same biological host cell. For a SARS-CoV-2, we model the charged ssRNA and N proteins as a negatively charged central body, the charged proteins in the biological membrane as dynamic ligands, the electric field between the center and ligands as a dynamic ligand field. Conclusions: The biological models of exclusions of RNA strands in a virus and viruses in a host cell qualitatively respectively answer the questions why or how there is only one mature ssRNA strand inside a SARS-CoV-2 membrane envelope and the virus proliferate; it is suitable to extend or analogize the ligand field theory to illustrate the stability of SARS-CoV-2 in biophysical structures (topologic constructions). Our models could be applicable to other biological objects.

Development of an on-board system for diagnosing the technical condition of the tread surface of the wheels of wagons

Introduction. The aim of the study is to develop a basic configuration of the on-board system for diagnosing the technical condition of the wheels tread surface of a wagon while the train is running and to model its operation.Materials and methods. The theoretical studies are based on the methods of Lagrange's analytical mechanics, the theory of oscillations and classical electrodynamics. The simulation was carried out for a flat design scheme using numerical methods. The results were processed using the developed algorithm implemented in the programming language of the Mathcad system.Results. This article studies the problem of the negative impact of local wear of the wheel tread surface on the state of the carriage chassis of the car and the rail track, as well as on the safety of train traffic. The authors propose a basic configuration of an on-board system for diagnosing wheel pairs of a wagon with an autonomous power supply with a power of up to 10 W, which simultaneously acts as a sensor. A mathematical model of diagnostic signals for local wheel wear has been constructed, and an algorithm for their detection has been developed based on the results. A criterion for estimating the geometric parameters of wear is formulated and its threshold values for slots of various depths are calculated. Alarms have been identified that suggest a reduction in the speed of the train.Discussion and conclusion. The solution of the stated problem is important both in the operation of existing cars and in the development of new, innovative cars with an axle load of 27–30 tf and speeds of up to 140 km/h. Timely detection of local wear of the tread surface of wagon wheels will increase the level of traffic safety and reduce the cost of repairing cars and rail tracks.

Vortex Circular Dichroism: An experimental technique to assess the scalar/vectorial regime of diffraction

Background: In classical electrodynamics, light-matter interactions are modelled using Maxwell equations. The solution of Maxwell equations, which is typically given by means of the electric and magnetic field, is vectorial in nature. Yet it is well known that light-matter interactions can be approximately described in a scalar (polarization independent) way for many optical applications. While the accuracy of the scalar approximation can be theoretically computed, to the best of our knowledge, it has never been determined experimentally. Here, we show that the vectoriality of diffraction can be probed with a new technique: Vortex Circular Dichroism(VCD). Methods: We measure the differential transmission of left and right circularly polarized vortex beams through a set of single circular nano-apertures with diameters ranging from 150 to 1950 nm. We observe that VCD > 0 for smaller diameters, VCD ≲ 0 for intermediate values and VCD ≈ 0 for larger values of the diameter. We also carry out Mie Theory simulations for spheres with the same diameters as the nanoholes and observe that the theoretical and experimental VCD values follow the same trend line. Results: We relate VCD ≠ 0 to a vectorial diffraction, and VCD ≈ 0 to a scalar one. This is corroborated by the simulations, which show that a diffraction process characterized by a VCD ≈ 0 (VCD ≠ 0) is polarization-independent (polarization-dependent). Conclusions: Overall, our results give a wealth of evidence that VCD allows for the experimental assessment of the scalar/vectorial regime of diffraction.

Quantum signatures in nonlinear gravitational waves

The effective quantum field theory description of gravity, despite its non-renormalizability, allows for predictions beyond classical general relativity. As we enter the age of gravitational wave astronomy, an important and timely question is whether measurable quantum predictions that depart from classical gravity, analogous to quantum optics effects which cannot be explained by classical electrodynamics, can be found. In this work, we investigate quantum signatures in gravitational waves using tools from quantum optics. Squeezed-coherent gravitational waves, which can exhibit sub-Poissonian graviton statistics, can enhance or suppress the signal measured by an interferometer, a characteristic effect of quantum squeezing. Moreover, we show that Gaussian gravitational wave quantum states can be reconstructed from measurements over an ensemble of optical fields interacting with a single copy of the gravitational wave, thus opening the possibility of detecting quantum features of gravity beyond classical general relativity.

QED-based derivation of the general forms of the relativistic Doppler effect and of the relativistic aberration for uniformly rotating frames and for uniformly accelerated frames

This paper derives the most general form of the relativistic Doppler effect and of the relativistic aberration starting from base principles available in classical electrodynamics and from the Lorentz transforms of the energy-momentum. We derive the relativistic Doppler and the relativistic aberration formulas for the case of both source and receiver moving in arbitrary directions with respect to an inertial reference frame as viewed from either a uniformly rotating or a uniformly accelerated frame.

QED-Based Derivation of the General Forms of the Relativistic Doppler Effect and of the Relativistic Aberration

The current paper derives the most general form of the relativistic Doppler effect and of the relativistic aberration starting from base principles available in classical electrodynamics and from the Lorentz transforms of the energy-momentum. Unlike any other material before us, we derive the relativistic Doppler formula for the case of both source and receiver moving in arbitrary directions with respect to an inertial reference frame. Thus, our derivation employs three different reference frames: one commoving with the source, the second one commoving with the receiver and the third one, commoving with the observer. The general formula, once derived, allows us to tease out all the specific cases, like the one from the perspective of the receiver, the one expressing the transverse Doppler effect, and the general formula for the Doppler rotor effect. We close with the derivation of the general formula for relativistic light aberration.

On the analogy between stochastic electrodynamics and nonrelativistic quantum electrodynamics

I expose nonrelativistic quantum electrodynamics in the Weyl–Wigner representation. Hence, I prove that an approximation to first order in Planck constant has a formal analogy with stochastic electrodynamics (SED), that is classical electrodynamics of charged particles immersed in a random radiation filling space. The analogy elucidates why SED agrees with quantum theory for particle Hamiltonians quadratic in coordinates and momenta, but fails otherwise.

Ionization-induced optical heterogeneity and ion-like direct emission in 1-nm silicon nanoparticle grains: Prospect for fast optical modulation

Silicon, a highly symmetric and homogeneous material, does not exhibit fast optical modulation. Recent classical electrodynamics simulations, however, demonstrated transient optical heterogeneity in silicon nanostructures, in which a high-density of excitonic electron–hole pair plasma and charge is created. The phenomenon, however, requires a specific particle size (∼100 nm diameter) and a high-density (1023/cc) plasma. We examine here the quantum aspect of the heterogeneity in 1-nm Si nanoparticles. Due to the small number of atoms, 1 nm nanoparticles are amenable to the Hartree–Fock first principle atomistic quantum theory simulations procedure, while single ionization events are sufficient to provide high charge density (2 × 1021/cc). The simulations show that the charge distribution in singly charged 1-nm particles is nonlinear and heterogeneous, accompanied with structural distortion that produces an electric dipole moment. Electronically, the simulations show that the single charge induces stationary Coulomb states that riddle the bandgap of the neutral particle, with dipole-allowed transitions, effectively inducing partial conducting-like behavior. Optically, when the charge is produced by ionizing UV radiation, the ionized particle survives and exhibits both extended (wide-band) as well as atomic- or ion-like sharp emission, in agreement with infrared polarimetry and spectroscopy observations in the solar coronal holes, as well as under synchrotron irradiation. Not only do ionized Si nanoparticles (charged nanosilicon grains) afford fast optical modulations, but they may also prove pivotal for understanding features of interstellar medium, observed throughout the Milky Way and other galaxies, including spectroscopic and material composition, as well as neutral hydrogen abundancy.

The expanded Maxwell’s equations for a mechano-driven media system that moves with acceleration

In classical electrodynamics, by motion for either the observer or the media, it is always naturally assumed that the relative moving velocity is a constant along a straight line (e.g., in inertia reference frame), so that the electromagnetic behavior of charged particles in vacuum space can be easily described using special relativity. However, for engineering applications, the media have shapes and sizes and may move with acceleration, and recent experimental progresses in triboelectric nanogenerators have revealed evidences for expanding Maxwell’s equations to include media motion that could be time and even space dependent. Therefore, we have developed the expanded Maxwell’s equations for a mechano-driven media system (MEs-f-MDMS) by neglecting relativistic effect. This paper first presents the updated progresses made in the field. Second, we extensively investigated Faraday’s law of electromagnetic induction for a media system that moves with an acceleration. We concluded that the newly developed MEs-f-MDMS are required for describing the electrodynamics inside a media that has a finite size and volume and move with and even without acceleration. The classical Maxwell’s equations are to describe the electrodynamics in vacuum space when the media in the nearby move.

Is neutrino lensing possible?

Neutrino is a fundamental neutral stable particle. Neutrino is unique because of its extremely high penetrating power. Finding out the mysterious nature of neutrinos seems to be one of the most interesting tasks of elementary particle physics. Let's consider properties of neutrinos, which can be described in the framework of classical electrodynamics.

Special Relativity in Six Dimensions

In the four-dimensional spacetime theory of special relativity, the space coordinate is time contracted along the motion, while perpendicular coordinates are invariant and time varies with position. This leads to a velocity transformation valid at speed of light and used in showing invariance electric and magnetic fields which are invariant along x-axis but change occur along y, and z-axes, contrary to the classical electrodynamics. In this work we introduce a new six-dimensional spacetime theory which allows time (position) change of position (time) in three coordinate axes and still satisfy the Lorentz invariance conditions of metric and Maxwell’s wave equations between two frames. We derive a new velocity transformation rule which is valid at any relative speed of massive frames moving with respect to each other. We derived expressions for relativistic mass, energy, Doppler shift, time dilation, length contraction, photon rest mass, and used the conservation of relativistic power to prove that the electric and magnetic fields and consequently, Maxwell wave equations are Lorentz invariant between two massive frames with and without nonzero photon mass in vacuum and materials medium. Calculated photon mass is in excellent agreement with the measured and observed upper bounds of 1.24x10-54 kg and1.75x 10-53 kg, respectively.

Review of rationales for the introduction of the “Geophysical electrodynamics” term

Background. The article provides arguments for the introduction of the “geophysical electrodynamics” term.Aim. To justify the introduction of a new term “geophysical electrodynamics”.Methods of substantiation. The limits of the applicability of Maxwell’s equations are studied. Additionally, some concepts are introduced, in particular, about a new paradigm in electrodynamics, about new equations in geophysical electrodynamics, about the differences between new electrodynamics and Maxwell’s electrodynamics, about the sources of toroidal and poloidal electromagnetic fields, about toroidal currents in Maxwell’s equations, about non-power electromagnetic fields, about the quantum effect in non-power electromagnetic fields, toroidal fields in the core of the Earth, mathematical achievements in the new paradigm, about the reproduction of sources of the electromagnetic field of the Earth, and effects in classical electrodynamics explained by geophysical electrodynamics.Results. Responses to the above justifications were received.Conclusion. Physical and mathematical justifications for the introduction of the term “geophysical electrodynamics” find confirmation both in the natural electromagnetic field of the Earth, and in a number of long-known classical effects in the standard Maxwell’s electrodynamics. Small but fundamental differences of one electrodynamics from another will reduce the number of effects unexplained from the standpoint of Maxwell’s equations, encountered in both theory and experiments on Earth.

The Paradox that Induced Electric Field has Energy in Maxwell’s Theory of Classical Electromagnetic Field is Shown and Solved

The Paradox that Induced Electric Field has Energy in Maxwell’s Theory of Classical Electromagnetic Field is Shown and Solved

The complex Maxwell stress tensor theorem: The imaginary stress tensor and the reactive strength of orbital momentum. A novel scenery underlying electromagnetic optical forces

We uncover the existence of a universal phenomenon concerning the electromagnetic optical force exerted by light or other electromagnetic waves on a distribution of charges and currents in general, and of particles in particular. This conveys the appearence of underlying reactive quantities that hinder radiation pressure and currently observed time-averaged forces. This constitutes a novel paradigm of the mechanical efficiency of light on matter, and completes the landscape of the optical, and generally electromagnetic, force in photonics and classical electrodynamics; widening our understanding in the design of both illumination and particles in optical manipulation without the need of increasing the illuminating power, and thus lowering dissipation and heating. We show that this may be accomplished through the minimization of what we establish as the reactive strength of orbital (or canonical) momentum, which plays against the optical force a role analogous to that of the reactive power versus the radiation efficiency of an antenna. This long time overlooked quantity, important for current progress of optical manipulation, and that stems from the complex Maxwell theorem of conservation of complex momentum that we put forward, as well as its alternating flow associated to the imaginary part of the complex Maxwell stress tensor, conform the imaginary Lorentz force that we introduce in this work, and that like the reactive strength of orbital momentum, is antagonistic to the well-known time-averaged force; thus making this reactive Lorentz force indirectly observable near wavelengths at which the time-averaged force is lowered. The Minkowski and Abraham momenta are also addressed.

Revisit the Poynting vector in P T-symmetric coupled waveguides.

We show that the time-averaged Poynting vector of S→=E→×H→∗/2 in parity-time (P T) symmetric coupled waveguides is always positive and cannot explain the stopped light at exceptional points (EPs). In order to solve this paradox, we must accept the fact that the fields E→ and H→ and the Poynting vector in non-Hermitian systems are in general complex. Based on the original definition of the instantaneous Poynting vector S→=E→×H→, a formula on the group velocity is proposed, which agrees perfectly well with that calculated directly from the dispersion curves. It explains not only the stopped light at EPs, but also the fast-light effect near it. This investigation bridges a gap between the classic electrodynamics and the non-Hermitian physics, and highlights the novelty of non-Hermitian optics.

The Disappearance and Reappearance of Potential Energy in Classical and Quantum Electrodynamics

In electrostatics, we can use either potential energy or field energy to ensure conservation of energy. In electrodynamics, the former option is unavailable. To ensure conservation of energy, we must attribute energy to the electromagnetic field and, in particular, to electromagnetic radiation. If we adopt the standard energy density for the electromagnetic field, then potential energy seems to disappear. However, a closer look at electrodynamics shows that this conclusion actually depends on the kind of matter being considered. Although we cannot get by without attributing energy to the electromagnetic field, matter may still have electromagnetic potential energy. Indeed, if we take the matter to be represented by the Dirac field (in a classical precursor to quantum electrodynamics), then it will possess potential energy (as can be seen by examining the symmetric energy-momentum tensor of the Dirac field). Thus, potential energy reappears. Upon field quantization, the potential energy of the Dirac field becomes an interaction term in the Hamiltonian operator of quantum electrodynamics.

Critical review of classical electrodynamics

In this paper, we will review classical electrodynamics, where our main concern will be exclusively the propagation of electromagnetic waves in the vacuum and the interaction of these waves with free charges. We will examine the reasons why the classical Maxwell's equations are not complete and consistent. We will show that there are three kinds of waves propagating in the vacuum, namely, transverse waves, longitudinal waves, and helicoidal waves. We will particularly review the theoretical and experimental aspects of longitudinal waves whose existence seems to be proven.

Orbital-free methods for plasmonics: Linear response.

Plasmonic systems, such as metal nanoparticles, are widely used in different areas of application, going from biology to photovoltaics. The modeling of the optical response of such systems is of fundamental importance to analyze their behavior and to design new systems with required properties. When the characteristic sizes/distances reach a few nanometers, nonlocal and spill-out effects become relevant and conventional classical electrodynamics models are no more appropriate. Methods based on the Time-Dependent Density Functional Theory (TD-DFT) represent the current reference for the description of quantum effects. However, TD-DFT is based on knowledge of all occupied orbitals, whose calculation is computationally prohibitive to model large plasmonic systems of interest for applications. On the other hand, methods based on the orbital-free (OF) formulation of TD-DFT can scale linearly with the system size. In this Review, OF methods ranging from semiclassical models to the Quantum Hydrodynamic Theory will be derived from the linear response TD-DFT, so that the key approximations and properties of each method can be clearly highlighted. The accuracy of the various approximations will then be validated for the linear optical properties of jellium nanoparticles, the most relevant model system in plasmonics. OF methods can describe the collective excitations in plasmonic systems with great accuracy and without system-tuned parameters. The accuracy of these methods depends only on the accuracy of the (universal) kinetic energy functional of the ground-state electronic density. Current approximations and future development directions will also be indicated.

How to measure the magnetic field in relativistic heavy-ion collisions

The intense magnetic field created in heavy-ion collisions has often been calculated with classical electrodynamics. This description is thought to be accurate if the occupation number of every field mode is high enough. However, this hypothesis has never been tested. Recently, we have studied a process involving the magnetic field, which we believe to be the simplest: pion production in ultraperipheral collisions. We have started using the classical approximation to study the forward pion production by the magnetic excitation of nucleons through the process N → Δ → N + π. Then, in a subsequent work, we have replaced this classical field by a flux of photons and have calculated the cross section for photoproduction of pions, which is the quantum version of magnetic excitation. We compared the cross sections obtained with both formalisms, which turned out to be compatible with each other. In this note, we review those works, enlarge the discussion and suggest some improvements that can be done to make our results more accurate. We emphasize that these pions could be detected by the ZDC’s installed at ATLAS and ALICE. Since the theoretical uncertainties are under control, this detection could be used to perform an indirect measurement of the magnetic field intensity.