一种时延范德波尔电磁系统中的复杂行为(Ⅱ)——时空混沌图案动态

对于一个由线性无损传输线加非线性边界条件组成的简单无穷维电磁系统，应用行波理论确定了电压反射波的局部映射关系.数值仿真结果表明，当系统参数发生变化时，传输线沿线电压存在着非常丰富的时空非线性现象.通过描绘出空间振幅变化图和时空行为发展图，定性分析了传输线沿线电压的时空混沌图案动态，为研究和理解时空混沌提供了一种良好的可求解模型. 关键词： 图案 时空混沌 无穷维系统 时延范德波尔电磁系统     

Quantum Scars in Microwave Dielectric Photonic Graphene Billiards

In the band structure of graphene,the dispersion relation is linear around a Dirac point at the corners of the Brillouin zone.The closed graphene system has proven to be the ideal model to investigate relativistic quantum chaos phenomena.The electromagnetic material photonic graphene(PG) and electronic graphene not only have the same structural symmetry,but also have the similar band structure.Thus,we consider a stadium shaped resonant cavity filled with PG to demonstrate the relativistic quantum chaos phenomenon by numerical simulation.It is interesting that the relativistic quantum scars not only are identified in the PG cavities,but also appear and disappear repeatedly.The wave vector difference between repetitive scars on the same orbit is analyzed and confirmed to follow the quantization rule.The exploration will not only demonstrate a visual simulation of relativistic quantum scars but also propose a physical system for observing valley-dependent relativistic quantum scars,which is helpful for further understanding of quantum chaos.     

Quantum aspects of chaos for three-level atoms interacting with two harmonic oscillators

We treat a simple generalization of the Jaynes-Cummings model to three-level atoms interacting with two harmonic oscillators. The model allows for classical chaos even in the rotating wave approximation, as was recently shown by Shepelyanski. Under conditions most favorable for classical chaos we find linear level repulsion à la Wigner.     

Dynamic chaotization of the electronic subsystem in graphene superlattice

d'Alembert equation written for the electromagnetic waves propagating in the graphene superlattice is discussed. The chaotic behavior of the electrons in graphene superlattice is studied by the Melnikov method. Dynamic chaos of electron in graphene superlattice is shown to appear for certain intervals of amplitudes of preset alternate current. The frequency dependence of the critical amplitude of alternate current above which would be a chaos is investigated.     

Absorption and generation of electromagnetic waves by structural inhomogeneities of solid

The integrability conditions of the electromagnetic field equations in a continuum with defects and their wave solutions are found. The following dislocation effects on the electromagnetic wave propagation in a continuous medium are investigated: the change in the direction of the electromagnetic wave propagation in a continuous medium; the rotation of the polarization plane of electromagnetic field wave in a continuous medium; the excitation of longitudinal components of the electromagnetic wave in a continuous medium and the change in the electromagnetic wave intensity related to this phenomenon. The energy balance equation for the electromagnetic field in a continuum with a stationary distribution of dislocation is found and it is shown that an electromagnetic wave excites exciton modes localized at dislocations in the solid.     

Spatial distribution of the electromagnetic field near the surface of a dielectric medium

A boundary problem of linear classical optics is solved in which the behavior of the electromagnetic field near the surface of a dielectric medium is studied. It is shown that including the discrete structure of a medium into the analysis has the most substantial effect on the behavior of the electromagnetic field at distances smaller than 2a ₀, where a ₀ is the lattice constant. This fact makes it possible to obtain numerical estimates of the size of the region where the reflected and transmitted waves are formed.     

Ultranarrow optical beams in quadratically nonlinear media

The vector Maxwell equations for the first-and second-harmonic planar beams are solved with allowance made for the nonlinear diffraction that weakens quadratic nonlinearity. The structure of the transverse and longitudinal components of the electromagnetic field of a parametric soliton is calculated for different values of the wave vector and phase mismatch. Exact analytic expressions are obtained for the self-similar profiles of extremally narrow solitons, and it is shown that the width has a fundamental limit of the order of a wavelength in a linear medium.     

A representation of Kerr-like nonlinearity for the analytical TM surface polariton solution

The TM-polarized waves propagating along the interface between a nonlinear Kerr-like material and linear cladding are investigated. We analyse the nonlinear dielectric permittivity as a function of the electromagnetic field. It is shown that an exact analytical solution of Maxwell's equations corresponding to the TM surface polariton in the form described by sech function do exist in a Kerr-like nonlinear medium with the permittivity profile given by a hypergeometric function. We compare our analytical solution and analogous exact numerical solution in a Kerr medium. The power flow down the interface between two media is also discussed.     

New approach to the defibrillation problem: Suppression of the spiral wave activity of cardiac tissue

A model of an excitable medium is considered for describing the development of fibrillation (i.e., spatiotemporal chaos) in cardiac tissue through the generation of a set of coexisting spiral waves. It is shown that a weak external point action on such a medium leads to the suppression of all spiral waves and, correspondingly, to the stabilization of the system dynamics. After reaching the regular regime, only the external source exists in the medium. The frequencies and amplitudes at which such stabilization occurs are determined. The case of the action of several point sources is considered. Analysis is performed using the Bray method to identify the number of spiral waves.     

Chaos in intrinsic motion of nuclei and its role in dissipative collective dynamics

We shall discuss the role of chaotic intrinsic motion in dissipative dynamics of the collective coordinates for nuclear systems. Using the formalism of linear response theory, it will be shown that the dissipation in adiabatic collective motion depends on the degree of chaos in the intrinsic dynamics of a system. This gives rise to a shape dependent dissipation rate for collective coordinates when the intrinsic motion is described by the independent particle model in a nucleus. The shape dependent chaos parameter measuring the degree of chaos in the intrinsic dynamics of the nuclear system will be obtained using the interpolating Brody distribution of nearest neighbour spacings in the single particle energy spectrum. A similar shape dependence is also found to be essential for phenomenological dissipation rates used in fission dynamics calculations.     

Energy Characteristics of Wave Fields Radiated from Elementary Oscillators in a Nondispersive Medium Moving with Subluminal Velocity

We study the energy characteristics of fields radiated from electric, magnetic, and toroidal dipoles in a nondispersive medium moving with velocity lower than the speed of light in this medium. The angular dependences of Abraham's energy-flux density of electromagnetic field are analyzed. In particular, it is shown that if the medium velocity is high enough, then the radial component of the vector of energy-flux density is negative in a certain angular range. Expressions for the electromagnetic energy flux through a sphere of large radius are obtained. It is shown that if the velocity of a moving medium is high enough, then the energy flux is negative and its absolute value can exceed the energy losses of sources.     

Field Structure in the Cross Section of a Ferrite Inhomogeneous Anisotropic Insert of a Rectangular Waveguide

We develop a physico-mathematical model describing excitation and distribution of electromagnetic waves in an anisotropic waveguide or resonator in the three-dimensional case. We develop a theoretical approach for discretization of the Maxwell equations in an arbitrary medium in the presence of bounding walls of a waveguide or resonator. The resulting system of linear algebraic equations for the electric-field components in an inhomogeneous anisotropic medium is solved by the method of biconjugate gradient. The results of calculating the electric field lines in the cross section of an anisotropic insert of a rectangular waveguide are presented.     

Experimental investigation of explosive plasma antennas

Explosion-produced plasma jets formed in free spece are experimentally investigated. The feasibility of emitting pulsed electromagnetic signals by plasma jets is shown, and the emitting conditions are studied. Comparison is made between the results of experiments with short and long plasma jets. When the jet passes through the field of a helix, a short-term increase in the emitted signal is detected. A linear parametric model of interaction between the plasma jet and an exciting electromagnetic signal is proposed. The operating performance of instrumentation developed for the investigation is presented.     

混沌状态下永磁同步发电机的故障诊断——LMI法研究

本文以永磁同步风力发电机为研究对象, 在两相同步旋转坐标系下建立了永磁同步发电机的数学模型. 应用时间尺度和线性仿射变换建立了系统混沌模型, 验证了系统在某些参数和工作条件下会出现混沌运动. 随后在考虑系统不确定性的情况下设计了故障观测器, 在系统发生故障时, 通过所设计的故障观测器能对混沌状态下永磁同步发电机的故障做出准确估计. 仿真结果表明基于线性矩阵不等式方法的故障观测器能够对系统故障做出快速准确的诊断. 关键词： 永磁同步发电机 混沌 非线性不确定系统 故障诊断     

Generation of acoustic solitons by a single-mode electromagnetic field

Mechanisms of acoustic pulse generation by a single-mode electromagnetic field propagating in a photoelastic material are analyzed. The anisotropy induced by acoustic excitations in an isotropic medium leads to nonlinear coupling between the polarization components of a single-mode electromagnetic field. For different conditions, it is shown that the acoustic-electromagnetic wave interaction due to mixing of the polarization components of light and acoustic waves can give rise to soliton-like coherent acoustic excitations in a thin crystal plate. When spatial dispersion is ignored, the governing system of equations for unidirectional acoustic solitons can be reduced to an integrable model. It is shown that qualitatively different scenarios of formation of acoustic solitons are possible, depending on the directions of deformation and field polarization.     

Generation of pulses upon nonresonant acousto-electromagnetic interaction

New mechanisms of generation of acoustic and electromagnetic soliton-like pulses in an optoelastic medium upon nonlinear nonresonant interaction of the polarization components of an electromagnetic field with acoustic oscillations in the medium are considered. It is shown that the acousto-electromagnetic interaction in such a system may lead to the formation of coherent soliton excitations in a thin crystal plate. It is found that a modulation instability occurs in an extended medium, which is caused by the spatial effects and leads to the generation of transverse sound waves. The evolution of a light field in a one-dimensional extended periodic optoelastic medium is also considered. It is shown that acoustic and electromagnetic solitons can be generated due to the mixing of direct and backward optical waves and their nonresonant interaction with a sound wave.     

Bands of Localized Electromagnetic Waves in 3D Random Media

Anderson localization of electromagnetic waves in three-dimensional disordered dielectric structures is studied using a simple yet realistic theoretical model. An effective approach based on analysis of probability distributions, not averages, is developed. The disordered dielectric medium is modeled by a system of randomly distributed electric dipoles. Spectra of certain random matrices are investigated and the possibility of appearance of the continuous band of localized waves emerging in the limit of an infinite medium is indicated. It is shown that localization could be achieved without tuning the frequency of monochromatic electromagnetic waves to match the internal (Mie-type) resonances of individual scatterers. A possible explanation for the lack of experimental evidence for strong localization in 3D as well as suggestions how to make localization experimentally feasible are also given. Rather peculiar requirements for setting in localization in 3D as compared to 2D are indicated.     

A study of constraints on the constitutive relationships of electro magnetic medium based on generally acknowledged truths

1 Introduction With the new synthetic material coming forth, many scholars pay more and more at-tention to the issue of the probable forms of electromagnetic (EM) medium constitutive relationships. These constitutive relationships must objectively reflect the relationships between microscopic physical quantities, but the constitutive relationships obtained through mathematical methods may be not physically realizable, or conflict with the generally acknowledged truths (such as energy conservat…     

Propagation of a short electromagnetic pulse in a linear medium with frequency and spatial dispersion: Direct integration of the Maxwell equations by the finite difference method

The specific features of the propagation of a short (on the order of ten oscillations) electromagnetic pulse in an isotropic linear medium with frequency and spatial dispersion, which were established via integration of a system of Maxwell equations by the finite-difference time-domain method using an auxiliary differential equation, are discussed. The variation of the direction of the electric field-strength vector oscillations that occurs in an optically active medium upon propagation of a linearly polarized ultrashort pulse incident on it is shown to be significantly different from the rotation of the polarization plane (proportional to the propagation coordinate) in the case of the incidence of a long pulse.     

Division of the energy and of the momentum of electromagnetic waves in linear media into electromagnetic and material parts

We defend a natural division of the energy density, energy flux and momentum density of electromagnetic waves in linear media in electromagnetic and material parts. In this division, the electromagnetic part of these quantities have the same form as in vacuum when written in terms of the macroscopic electric and magnetic fields, the material momentum is calculated directly from the Lorentz force that acts on the charges of the medium, the material energy is the sum of the kinetic and potential energies of the charges of the medium and the material energy flux results from the interaction of the electric field with the magnetized medium. We present reasonable models for linear dispersive non-absorptive dielectric and magnetic media that agree with this division. We also argue that the electromagnetic momentum of our division can be associated with the electromagnetic relativistic momentum, inspired on the recent work of Barnett [Phys. Rev. Lett. 104 (2010) 070401] that showed that the Abraham momentum is associated with the kinetic momentum and the Minkowski momentum is associated with the canonical momentum.