Investigation of the Effective Space–Time of the Vacuum Nonlinear Electrodynamics in a Magnetic Dipole Field

The metric tensor of the effective pseudo-Riemannian space–time for an electromagnetic wave propagating in the magnetic dipole field and the gravitational field of a neutron star is obtained within a parameterized post-Maxwellian vacuum electrodynamics. The angles of the nonlinear electrodynamic and gravitational ray bending for electromagnetic waves propagating in the magnetic equatorial plane of the star are calculated based on an analysis of isotropic geodesics of this space. We show that for all nonlinear theories whose post-Maxwellian parameters do not coincide, the velocity of the electromagnetic signal propagation in external fields and the rays along which these signals propagate depend on the polarization of the electromagnetic waves. The difference of the source-to-detector propagation time of these signals for two principal polarization states is calculated.     

Nonlinear Electrodynamic Delay of Electromagnetic Signals in a Coulomb Field

We study the motion of electromagnetic signals in the Coulomb electric field of a compact gravitating center under the laws of the parameterized nonlinear electrodynamics of the vacuum. We evaluate the deflection angles of the rays along which the electromagnetic waves of two normal modes propagate in this field. We determine the nonlinear electrodynamic delay of the electromagnetic signal of one normal mode relative to the electromagnetic signal of another normal mode during their propagation from the same source to an observer.     

Nonlinear Electromagnetic Delay of Electromagnetic Signals Propagating in the Magnetic Meridian Plane of Pulsars and Magnetars

We analyze the propagation of electromagnetic waves in the magnetic meridian planes of neutron stars with a strong magnetic field in the framework of the parameterized post-Maxwellian electrodynamics of the vacuum. The origin of these electromagnetic waves is the curvature emission of X-rays and gamma rays from high-energy electrons in the vicinity of the magnetic poles of neutron stars. We show that in the case of a slowly varying intensity of X-ray and gamma-ray emission, the delay of the slow normal mode of electromagnetic waves relative to the fast mode results in a shift of the time dependence of the intensity of the detected radiation with one polarization relative to that of the radiation with the orthogonal polarization. In the case of single X-ray or gamma-ray pulses, the delay effect results in the polarization of the detected pulse varying during the pulse length, the leading edge of all pulses being polarized normally to the magnetic equator plane of the neutron star. We note that the modern level of the experimental technique, in principle, allows observing the manifestations of the delay effect for signals of different polarizations.     

Interaction Effect of Plane Electromagnetic Waves in the Born–Infeld Nonlinear Electrodynamics

We calculate the interaction of plane electromagnetic waves in accordance with the Born–Infeld nonlinear electrodynamics in the vacuum segment of a ring laser. We show that at the present level of development in laser physics, it is possible not only to measure the direct impact of the quantum vacuum polarization effect on the generation frequencies of weak electromagnetic waves propagating in opposite directions in a ring laser but also to estimate the contribution of the Born–Infeld nonlinear electrodynamics to this effect.     

Elektrodynamik mit Spin

Atomistic equations of the electromagnetic field for a particle with spin are derived from a Lagrangian. These equations are consistent with the equations of motion for such a particle. The resulting phenomenological equations are the well-known equations of Maxwell for the electromagnetic field in matter. The atomistic field equations for a particle with spin and magnetic moment give a dipole field. This result and the corresponding quantum mechanics for a particle with spin are applied to compute the hyperfine structure of the hydrogen atom by perturbation theory.     

Neutral Fermion Having Electric and Magnetic Moments in an External Electromagnetic Field

We show that in 2+1 dimensions, the Dirac equation for a neutral fermion possessing electric and magnetic dipole moments in an external electromagnetic field reduces to the Dirac equation for a charged fermion in a external field characterized by a certain 3-pseudo-vector potential. The effective charge of the neutral fermion is determined by its dipole moments. The effects of coupling electric and magnetic moments of the neutral fermion to the external electromagnetic field seem to be inseparable in physical experiments of any type. We find an exact solution of the Dirac equation for a massive neutral fermion with electric and magnetic dipole moments in a external plane-wave electromagnetic field. We derive expressions for the fermionic vacuum current induced by neutral fermions in the presence of external electromagnetic fields.     

一个具有电荷和磁偶极矩黑洞的量子非热辐射及其辐射粒子射程的特征

一个稳态轴对称非Kerr-Newman黑洞时空中的粒子能级分布与电磁四维势有关，黑洞电荷和磁偶极矩的存在以及裸奇点的出现都对粒子能级分布有影响，粒子能级分布与方向有关.此黑洞的量子非热辐射及其粒子的平均射程与辐射粒子的能量范围有关。     

Electrodynamic-mechanical boundary value problems and gauge transformations in rigid dielectrics with constitutive magnetoelectric coupling

Gauge transformations are generally applied to decouple Maxwell’s equations, introducing gauge invariant vector and scalar potentials in connection with suitable gauge differential equations. This step simplifies the analytical or numerical solution of electrodynamic boundary value problems. In dielectrics, the propagation of electromagnetic waves is usually investigated restricting the problems to simple isotropic non-functional materials. On the other hand, magnetoelectric (ME) solids are of particular interest, converting electrical to magnetic energy and vice versa. The constitutive behavior of those materials has been investigated extensively, however restricting considerations to static or quasi-static loading. The goal of this paper is to combine electrodynamics in terms of the classical Maxwell equations with the constitutive behavior of ME materials. The interacting mechanisms of ME energy conversion lead to a complex behavior and are supposed to give rise to interesting phenomena influencing wave dispersion, deflection and reflection. The coupled boundary value problem is comprehensively formulated first, including mechanical stress and strain fields as well as electromagnetically induced forces. Gauge transformations are presented to decouple the electrodynamic potential equations for anisotropic ME bodies, neglecting a mechanical compliance at that point. Weak formulations are derived as a basis for numerical discretization procedures like the finite element method and simple examples demonstrate the impact of ME coupling on the phase velocity of an electromagnetic wave.     

Using the concept of natural geometry in the nonlinear electrodynamics of the vacuum

We discuss the concept of natural geometry for a physical field. We show that using this concept to solve problems of nonlinear electrodynamics allows simply studying basic effects of nonlinear electrodynamics arising when weak electromagnetic waves propagate in external electromagnetic fields.     

Amplitude Modulation of Nonlinear Waves in Fluid-Filled Tapered Tubes

We study the modulation of nonlinear waves in fluid-filled prestressed tapered tubes. For this, we obtain the nonlinear dynamical equations of motion of a prestressed tapered tube filled with an incompressible inviscid fluid. Assuming that the tapering angle is small and using the reductive perturbation method, we study the amplitude modulation of nonlinear waves and obtain the nonlinear Schrödinger equation with variable coefficients as the evolution equation. A traveling-wave type of solution of such a nonlinear equation with variable coefficients is obtained, and we observe that in contrast to the case of a constant tube radius, the speed of the wave is variable. Namely, the wave speed increases with distance for narrowing tubes and decreases for expanding tubes.     

A nonlinear stability analysis for rotating magnetized ferrofluid heated from below saturating a porous medium

A nonlinear (energy) stability analysis is performed for a rotating magnetized ferrofluid layer heated from below saturating a porous medium, in the stress-free boundary case. By introducing a generalized energy functional, a rigorous nonlinear stability result for a thermoconvective rotating magnetized ferrofluid is derived. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body force. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of linear instability analysis, and thus indicates that the subcritical instabilities are possible. However, it is noted that, in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of magnetic parameter, M ₃, medium permeability, D _a , and rotation, , on subcritical instability region has also been analyzed. It is shown that with the increase of magnetic parameter, M ₃, and Darcy number, D _a , the subcritical instability region between the two theories decreases quickly while with the increase of Taylor number, , the subcritical region expands. We also demonstrate coupling between the buoyancy and magnetic forces in the presence of rotation in nonlinear energy stability analysis as well as in linear instability analysis.      

Electromagnetic interaction of moving conductors with magnets: kinematic solutions for infinitely long square and cylindrical geometries

The electromagnetic drag force on a point dipole near a moving conductor caused by the induced electric currents is investigated by numerical and analytical computations. Our focus is on prototypical configurations for Lorentz force velocimetry, i.e. velocity measurement from the electromagnetic drag force on the dipole. We examine the particular cases of conducting infinite bars of square or round cross-section, which are moving with constant velocity in the field of arbitrary oriented magnetic dipole. In addition, we study the laminar liquid-metal flow in a square duct. The motion of the conductor is prescribed. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sufficient Global Stability Condition for a Model of the Synchronous Electric Motor under Nonlinear Load Moment

We study a model of the synchronous electric motor, which is described by a system of ordinary differential equations, including equations for electric currents in the windings of the rotor. The load moment is assumed to be a nonlinear function of the angular velocity of the rotor, allowing a linear estimate. The system of differential equations under consideration has a countable number of stationary solutions corresponding to the operating mode of uniform rotation of the rotor with the angular velocity equal to the angular velocity of rotation of the magnetic field in the stator. An effective sufficient condition is derived under which any motion of the rotor of the synchronous electric motor tends with time to uniform rotation.     

Developing the eikonal method in nonlinear electrodynamics based on the geometrization principle

We derive the eikonal equation for an electromagnetic wave propagating in an external electromagnetic field according to the laws of nonlinear electrodynamics. Based on Logunov’s geometrization principle, we determine the metric tensors of the effective Riemannian spaces for the Born-Infeld electrodynamics, nonlinear Heisenberg-Euler electrodynamics, and a parameterized post-Maxwellian electrodynamics. We analyze the main properties of these nonlinear electrodynamics. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 150, No. 1, pp. 112–117, January, 2007.     

A lattice Boltzmann model for Maxwell’s equations

In this paper, a lattice Boltzmann model for the Maxwell’s equations is proposed by taking separate sets of distribution functions for the electric and magnetic fields, and a lattice Boltzmann model for the Maxwell vorticity equations with third order truncation error is proposed by using the higher-order moment method. At the same time, the expressions of the equilibrium distribution function and the stability conditions for this model are given. As numerical examples, some classical electromagnetic phenomena, such as the electric and magnetic fields around a line current source, the electric field and equipotential lines around an electrostatic dipole, the electric and magnetic fields around oscillating dipoles are given. These numerical results agree well with classical ones.     

On the formation of gap solitons in nonlinear electromagnetic metamaterials

A nonlinear (Kerr‐type) electromagnetic metamaterial, characterized by a double‐Lorentz model of its frequency‐dependent linear effective dielectric permittivity and magnetic permeability, is considered. The formation of gap solitons in the low‐ and high‐frequency band gaps of this metamaterial is investigated analytically. Evolution equations governing the gap solitons, of the form of a nonlinear Klein‐Gordon and a nonlinear Schrödinger equation, are obtained, and the structure of their solutions is discussed.     

Propagation of TM waves in a Kerr nonlinear layer

TM electromagnetic waves propagating through a nonlinear homogeneous isotropic unmagnetized dielectric layer located between two homogeneous isotropic half-spaces are studied. The nonlinearity in the layer obeys the Kerr law. The problem is reduced to a system of nonlinear ordinary differential equations. A dispersion relation for the propagation constants is derived. The results are compared with those in the case of a linear layer.     

Multidimensional nonlinear wave equations with multivalued solutions

We present the theory of breaking waves in nonlinear systems whose dynamics and spatial structure are described by multidimensional nonlinear hyperbolic wave equations. We obtain a general relation between systems of first-order quasilinear equations and nonlinear hyperbolic equations of higher orders, which, in particular, describe electromagnetic waves in a medium with nonlinear polarization of an arbitrary form. We use this approach to construct exact multivalued solutions of such equations and to study their spatial structure and dynamics. The results are generalized to a wide class of multidimensional equations such as d’Alembert equations, nonlinear Klein-Gordon equations, and nonlinear telegraph equations.     

Integral and Asymptotic Properties of Solitary Waves in Deep Water

We consider two‐ and three‐dimensional gravity and gravity‐capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves like a dipole at infinity and obtain a related asymptotic formula for the free surface. We then prove an identity relating the “dipole moment” to the kinetic energy. This implies that the leading‐order terms in the asymptotics are nonvanishing and in particular that the angular momentum is infinite. Lastly we prove that the “excess mass” vanishes. © 2018 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.