<Emphasis Type="Italic">SO</Emphasis>(3,1)-Invariant Approach to Dipole Radiation

The aim of the present work is to revisit the theory of the dipole radiation, within an SO(3,1)-gauge invariant formulation, by solving the Maxwell equations. Thus, we obtain the two interconnected components, A _B , B=1,2, of the vector potential A, in terms of Hankel and Legendre polynomials. Finally, for the pure dipole-like radiation, the observables, regarded as phasors, the Umov–Poynting vector components and the well-known Larmor formula for the effective radiated power are explicitly derived.     

Numerical modelling of the two-dimensional Fourier transformed Vlasov–Maxwell system

The two-dimensional Vlasov–Maxwell system, for a plasma with mobile, magnetised electrons and ions, is investigated numerically. A previously developed method for solving the two-dimensional electrostatic Vlasov equation, Fourier transformed in velocity space, for mobile electrons and with ions fixed in space, is generalised to the fully electromagnetic, two-dimensional Vlasov–Maxwell system for mobile electrons and ions. Special attention is paid to the conservation of the divergences of the electric and magnetic fields in the Maxwell equations. The Maxwell equations are rewritten, by means of the Lorentz potentials, in a form which conserves these divergences. Linear phenomena are investigated numerically and compared with theory and with previous numerical results.     

Solving Maxwell’s equations in singular domains with a Nitsche type method

In this paper, we propose and analyze a method derived from a Nitsche approach for handling boundary conditions in the Maxwell equations. Several years ago, the Nitsche method was introduced to impose weakly essential boundary conditions in the scalar Laplace operator. Then, it has been worked out more generally and transferred to continuity conditions. We propose here an extension to vector div–curl problems. This allows us to solve the Maxwell equations, particularly in domains with reentrant corners, where the solution can be singular. We formulate the method for both the electric and magnetic fields and report some numerical experiments.     

Quantized self-dual Maxwell field on a null surface

The canonical formalism for a self-dual Maxwell field on a null plane is reviewed. After solution of the second class constraints, the transition to the quantum theory is carried out using a representation in which the self-dual Maxwell field is diagonal. The Gauss law constraint allows us to consider the physical state vectors to be holomorphic functionals of one complex function. Application of reality conditions allows us to define an inner product such that the Hermitean adjoint operators are identified with the classical complex conjugate operators. In going over to the Fourier expansion of the operators, we find that the inner product is formally convergent for positive frequency functionals and formally divergent for the negative frequency functionals. Following similar results of Ashtekar, Rovelli, and Smolin, negative frequency states are functional distributions identified with the helicity opposite to that of the positive frequency states.     

Cohomological uniqueness of the Cauchy problem solutions for the Einstein–Maxwell equation

In this paper we analyze the Cauchy problem for the Einstein–Maxwell equation in the case of non-characteristic initial hypersurface. To find the correct notions of characteristic and Cauchy data we introduce a complex, which we call the Einstein–Maxwell complex. Then the Cauchy problem acquires correctness in terms of an associated spectral sequence. We define a Cauchy data in such way that they allow us to reconstruct a cohomologously unique formal solution.     

Unity‐Order Nonlinear Optical Index Change in Epsilon‐Near‐Zero Composite Materials of Gain Media and Metal Nanoparticles

This work reports giant optical nonlinearity of active gain composites containing metal nanoparticles. In the epsilon‐near‐zero regime, the effective index of the composite strongly depends on the magnitude of host material's saturable gain and one can obtain unity‐order nonlinear optical index change for the pump with gain saturation intensity. For pump intensity of about 100 kW/cm², the nonlinear refractive index (the refractive index change per unit pump intensity) reaches 10^?5 cm²/W, which is 6–8 orders‐of‐magnitude larger than the records recently obtained in epsilon‐near‐zero bulk materials. If the gain value of the host medium is slightly larger than a critical value, such large optical nonlinearity can be obtained without loss or even accompanying with amplification. The proposed materials also have the advantage of wide tunability of operating wavelength range from visible to infrared by changing the gain value of the host and the shape parameters and filling factors of metal nanoparticles.     

关于麦克斯韦方程组的讨论

本文讨论了麦克斯韦方程组的来龙去脉、形式和地位，对麦克斯韦主程组的教学具有一定的参考价值。     

不同功率下无工质微波推力器的推力预估

基于经典电动力学理论,从麦克斯韦方程组和麦克斯韦张量出发,推导出无工质微波推力器的推力计算方程. 应用有限元分析软件,计算了特定谐振模式下的特定圆台谐振腔在不同功率条件下的电磁场分布;根据推导出的理论计算公式,计算了不同功率条件下推力器的总推力. 计算结果表明:推力与功率成正比,而且磁场力决定着总推力的大小;圆台谐振腔消耗20–200 W电磁波功率时所产生的推力在20–250 mN范围内. 关键词： 电磁波 麦克斯韦张量     

熵、麦克斯韦妖与生命

熵的概念来自物理学研究，但是它的应用早已超过物理学的范畴，对许多自然科学领域产生了重要的影响，本文研究生命现象中的熵，期望对丰富熵的内涵从而理解生命过程能有所裨益。     

Kinetic Approach to Long time Behavior of Linearized Fast Diffusion Equations

We show that the rate of convergence towards the self-similar solution of certain linearized versions of the fast diffusion equation can be related to the number of moments of the initial datum that are equal to the moments of the self-similar solution at a fixed time. As a consequence, we find an improved rate of convergence to self-similarity in terms of a Fourier based distance between two solutions. The results are based on the asymptotic equivalence of a collisional kinetic model of Boltzmann type with a linear Fokker-Planck equation with nonconstant coefficients, and make use of methods first applied to the reckoning of the rate of convergence towards equilibrium for the spatially homogeneous Boltzmann equation for Maxwell molecules.     

Superradiance in a dense open Λ-system

We show that the excitation threshold for the on-set of superradiance in the Λ-system depends on the initial state of coherence between the atomic lower levels. Furthermore, we find the characteristics of the superradiant radiation as function of the degree of excitation, the atomic relaxation times, the incoming seed-field area and the local field correction term.     

Note on “Domain wall universe in the Einstein–Born–Infeld theory” [Phys. Lett. B 679 (2009) 160]

The interaction between bulk and dynamic domain wall in the presence of a linear/non-linear electromagnetism make energy density, tension and pressure on the wall all variables, depending on the wall position. In Lee et al. (2009) [1] this fact seems to be ignored.     

Free‐Electron Gas Spectrum Uniqueness in the Mixture of Noble Gases

Gas mixtures can reach the Maxwell's specter shape in case of low‐ionized mono‐atomic mixtures in the weak electric field. The parameters pertaining to the Maxwell spectrum of free electrons' gas straightforwardly settle on the insulating characteristics of the examined gas mixture at the fundamental level. In this paper, a condition for breakdown has been accomplished taking as a starting point the ionization coefficients derived accordingly, as well as the conditions for breakdown in keeping with the Townsend mechanism. The dc breakdown voltage value of noble gases mixture has been measured in the experimental part of the paper. The hypothesis that the free‐electron gas spectrum is unique in the noble gas mixture and is of Maxwell's type has been verified. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of the Electromagnetic Lagrangian from a System of Poisson Brackets

The Lagrangian and Hamiltonian formulations of electromagnetism are reviewed and the Maxwell equations are obtained from the Hamiltonian for a system of many electric charges. It is shown that three of the equations which were obtained from the Hamiltonian, namely the Lorentz force law and two Maxwell equations, can be obtained as well from a set of postulated Poisson brackets. It is shown how the results derived from these brackets can be used to reconstruct the original Lagrangian for the theory aided by some reasoning based on physical concepts.     

The interaction of electricity and magnetism in Einstein–Maxwell theory

I consider stationary axially symmetric solutions of the Einstein–Maxwell equations. These show that, in general, time-independent electric and magnetic fields acting together cause rotational effects in the spacetime. An electric charge placed on the axis of a magnetic dipole induces a region of closed timelike curves.     

Dynamics of Light in Teleparallel Bianchi-Type I Universe

In the present study, using the Fourier analysis method and considering the Bianchi-type I spacetime, we investigate the dynamics of photon in the torsion gravity, and show that the free-space Maxwell equations give the same results. Furthermore, we also discuss the harmonic oscillator behavior of the solutions.     

The Proof that Maxwell Equations with the 3D E and B are not Covariant upon the Lorentz Transformations but upon the Standard Transformations: The New Lorentz Invariant Field Equations

In this paper the Lorentz transformations (LT) and the standard transformations (ST) of the usual Maxwell equations (ME) with the three-dimensional (3D) vectors of the electric and magnetic fields, E and B, respectively, are examined using both the geometric algebra and tensor formalisms. Different 4D algebraic objects are used to represent the usual observer dependent and the new observer independent electric and magnetic fields. It is found that the ST of the ME differ from their LT and consequently that the ME with the 3D E and B are not covariant upon the LT but upon the ST. The obtained results do not depend on the character of the 4D algebraic objects used to represent the electric and magnetic fields. The Lorentz invariant field equations are presented with 1-vectors E and B, bivectors E_Hv and B_Hv and the abstract tensors, the 4-vectors E^a and B^a. All these quantities are defined without reference frames, i.e., as absolute quantities. When some basis has been introduced, they are represented as coordinate-based geometric quantities comprising both components and a basis. It is explicitly shown that this geometric approach agrees with experiments, e.g., the Faraday disk, in all relatively moving inertial frames of reference, which is not the case with the usual approach with the 3D bf E and B and their ST.