有界随机媒质的等效介电常数

本文运用强扰动波动理论推导出半空间强扰动随机媒质的Dyson方程.在小尺度扰动下,给出了媒质的等效介电常数.在推导中考虑了空气-媒质分界面的影响.分析和计算结果表明:在媒质分界面处存在一过渡层,在该过渡层中,分界面对媒质的等效介电常数有较大影响,这在计算电磁波在有界随机媒质边界处的反射与折射时必须加以考虑.     

超材料电磁波有限元模拟中的相关问题 献给林群教授80华诞

超材料是指一种人工合成的纳米电磁材料,它的介电常数和磁导率对某些波频段会同时为负,从而导致其折射率为负.超材料硏究的兴起始于2000年,在过去的十多年一直是多个学科的研究热点.本文侧重介绍电磁波在超材料中传播所涉及的模型方程以及如何用有限元方法求解.本文是对过去十年来计算数学在此领域工作的一个总结.最后提出一些值得继续探讨的问题.     

电磁波经反铁磁膜层透射的多稳特性 *

分析了有损耗的反铁磁晶体对圆偏振电磁波的非线性磁化响应,得到了非线性磁化率的具体表达式.研究了红外电磁波经反铁磁膜层透射的多稳特性.理论分析表明,多稳效应的阈值主要取决于波的频率、膜厚和入射区域的介质特性,而与出射区域的介电常数无关.膜厚的增加使得功率多稳态的阈值下降、动态区域变小、阶跃值减小.系统的最大透射率为1,最小透射率与频率有关,与膜厚或入射、透射区材料的介电常数无关.     

铁电体中介电异常与长程关联的关系

利用双势阱模型研究了铁电体中介电异常的机制 ,结果表明介电常数源于外场造成的偏离中心离子在多位势中的附加的跳跃 .介电常数可分为两部分 :其一与长程关联无关 ,服从 1 /T律 ;其二由长程关联引起 ,可用关联长度很好地描述 .小尺寸样品中介电异常偏离Curie_Weiss定律源于长程关联的减弱 .     

手性环境中障碍电磁散射问题的积分方程方法

正1引言特殊介质中的电磁散射问题是一个重要的研究课题,是近些年来才开展起来的.此研究中,手性介质的电磁散射问题得到了很多关注.电磁波在手性介质中的传播是由Maxwell方程组和Drude-Born-Fedorov本构方程共同刻画的.手性介质可以由介电常数ε,磁导率μ和手性导纳β来描述.近些年来,关于手性介质中的电磁散射问题已有一些结果.Ammari,Hamdache and Nedelec~[2],Ammari and Nedelec~[3,4]给出了关于Drude-Born-Fedorov模型、表示定理,Drude-Born-Fedorov的     

多偏移距电磁波数值成像的高阶FDTD法研究

数值模拟是数据处理和反演解释的重要环节,为提高高频电磁波层析成像技术在工程勘察中的解译准确性,采用高阶时间域有限差分法(FDTD(2阶时间精度,4阶空间精度))模拟电磁波在溶洞地电模型下的数值成像,并采用多偏移距模式采集电磁波道集.分析了电磁波的波场快照图和波形剖面图,总结了电磁波在溶洞地质体中的传播规律,为实际工程勘察工作提供可靠依据.数值试验结果表明,FDTD(2,4)能高精度模拟电磁波在溶洞复杂介质中的数值成像和多偏移距采集模式具有高效性和灵活性.     

辛体系下碳纳米管阵列中太赫兹波传播特性研究

应用有效介质理论,研究了周期碳纳米管阵列中电磁波在太赫兹频段的传播特性.考虑碳纳米管阵列的非局部准静态模型,将其导入Hamilton系统的辛几何理论框架下,通过求解本征值问题得到了电磁波在碳纳米管阵列中传播的色散关系.数值计算结果给出了垂直和倾斜排列的碳纳米管阵列中电磁波传输特性.研究表明在太赫兹频段,轴向非局部空间色散对电磁波传播特性影响较小.相关研究可对太赫兹频段碳纳米管阵列波传播器件的设计提供理论参考.     

尖劈吸波体与导引仿真用微波暗室的性能研究

首先,针对尖劈形状吸波体的性能问题,给出了直接计算法和基于镜像模型的方法,并对其进行了对比计算与仿真.其次,对于微波暗室的性能研究,针对不同的复杂度要求,建立了两种数学模型—射线追踪(Ray Tracing)模型和基于Markov链的有限元(FEM,Finite Element Model)模型.建模过程和仿真结果表明,Ray Tracing模型的计算复杂度较低,但电磁波"镜面反射"的假设过于理想,模型较为粗糙,只能用于粗略模拟实际情况.而基于Markov链的FEM模型较Ray Tracing模型更加精确.同时,相比于传统的具有高计算复杂度的FEM模型,基于Markov链的FEM模型计算更加简便,利于计算机仿真实现,而且不降低FEM模型的精确度,可以精确模拟实际情况.     

尖劈形吸波体和微波暗室中的数学模型

首先讨论电磁波在尖劈形吸波体形成的空缺中的反射问题.通过建立二维空间内两次相邻反射的数学模型,得到尖劈的几何参数和电磁波出射角、更射次数和辐射强度的关系.然后通过仿真计算出数值结果,并且将其推广到三维情况,得到了"在一定条件下,减小尖劈形吸波体顶角的大小,有利于增加反射次数,增强吸波效果"的结论.针对导弹导引试验中的仿真要求,从电磁波辐射角系数的概念出发,提出了一种计算微波暗室中静区的接收到墙面更射的功率与天线辐射的功率的比值的算法.这种算法物理意义清晰,计算过程简单,可较好的应用在导弹的导引仿真试验的分析中.     

基于粒子群优化Kriging模型的边坡可靠度分析

采用传统极限平衡法进行边坡可靠度分析时,不可避免会遇到一个问题,即边坡功能函数形式的高度非线性以及隐含性.对于隐式功能函数,传统的求解方法是通过对功能函数进行多次迭代,从而得到安全系数值.但是由于功能函数的形式较为复杂,导致迭代计算的过程变得尤为繁琐且效率低下.鉴于传统边坡可靠度分析中存在的安全系数计算繁琐耗时的问题,提出一种基于粒子群优化(PSO)算法的自动采样Kriging代理模型方法,该方法可以代替功能函数的作用进行安全系数的求解.首先用拉丁超立方抽样方法(LHS)选取少量土体参数组,并通过极限平衡法求出对应的安全系数,将土体参数组和安全系数作为初始样本建立Kriging模型;其次由粒子群优化算法将最有期望改善模型拟合精度的样本点添加到样本集合中,以逐步迭代提升Kriging模型的计算精度;最后集合经典蒙特卡洛模拟(MCS)获得边坡的破坏概率.通过一个双层的土质边坡算例分析,证明了该方法可以实现准确高效的安全系数计算,尤其是在安全系数计算量十分庞大的情况下可以大大节省计算时间,是一种有效的边坡工程稳定可靠度分析方法.     

Resonant response of a strong electromagnetic wave beam to a gravitational wave in a static magnetic field

Concrete forms of resonant response (ER) for a strong electromagnetic (EM) wave beam (photon flux) propagating in a static magnetic field to a standing gravitational wave (gravitons) are given, and the corresponding perturbation solutions and resonant conditions are obtained. It is found that perturbed EM fields (PEMFs) contain three new components with frequencies Io,* w,l and ωP_g respectively. In the case of ω_e⋙ω_g, the PEMFs are manifested as the EM wave beams with frequency ω_e and a standing EM wave with ω_g. The former and the background EM wave beam (BE-MWB) have the same propagating direction, while in the case of ω_g⋙ω_e, all PEMFs are expressed as the standing EM waves with frequency ω_g. The resonant response occurs in two cases of ω_e = 1/2 ω_g andω_e, = ω_g only. Then not only the first order perturbed energy fluxes (PEFs) propagating in the same and opposite directions of the BEMWB can be generated, but also radial and tangential PEFs which are perpendicular to the above directions can be produced. This effect might provide a new way for the EM detection of the gravitational waves (GWs). Moreover, the possible schemes of displaying perturbed effects induced by the standing GW withh = 10^-33 - 10^-35 and λ_g = 0.1 m at the level of the single photon avalanche and in a typicla laboratory dimension are reviewed.     

A stability estimate for a solution to an inverse problem of electrodynamics

We consider the integrodifferential system of equations of electrodynamics which corresponds to a dispersive nonmagnetic medium. For this system we study the problem of determining the spatial part of the kernel of the integral term. This corresponds to finding the part of dielectric permittivity depending nonlinearly on the frequency of the electromagnetic wave. We assume that the support of dielectric permittivity lies in some compact domain Ω ⊂ ℝ³. In order to find it inside Ω we start with known data about the solution to the corresponding direct problem for the equations of electrodynamics on the whole boundary of Ω for some finite time interval. On assuming that the time interval is sufficiently large we estimate the conditional stability of the solution to this inverse problem.     

Maxwell's equations in an unbounded structure

This paper is concerned with the mathematical analysis of the electromagnetic wave scattering by an unbounded dielectric medium, which is mounted on a perfectly conducting infinite plane. By introducing a transparent boundary condition on a plane surface confining the medium, the scattering problem is modeled as a boundary value problem of Maxwell's equations. Based on a variational formulation, the problem is shown to have a unique weak solution for a wide class of dielectric permittivity and magnetic permeability by using the generalized Lax–Milgram theorem. Copyright © 2016 John Wiley & Sons, Ltd.     

Microscopic model of a non-Debye dielectric relaxation: The Cole-Cole law and its generalization

Based on a self-similar spatial-temporal structure of the relaxation process, we construct a microscopic model for a non-Debye (nonexponential) dielectric relaxation in complex systems. In this model, we derive the Cole-Cole expression for the complex dielectric permittivity and show that the exponent ?? involved in that expression is equal to the fractal dimension of the spatial-temporal self-similar ensemble characterizing the structure of the medium and the relaxation process occurring in it. We find a relation between the macroscopic relaxation time and the micro- and mesoparameters of the system. We obtain a generalized Cole-Cole expression for the complex dielectric permittivity involving log-periodic corrections that occur because of a discrete scaling invariance of the fractal structure generating the relaxation process on the mesoscopic scale. The found expression for the dielectric permittivity can be used to interpret dielectric spectra in disordered dielectrics.     

Nonlinear stability of an axial electric field: Effect of interfacial charge relaxation

We introduce a nonlinear perturbation technique to third order, to study the stability between two cylindrical inviscid fluids, subjected to an axial electric field. The study takes into account the relaxation of electrical charges at the interface between the two fluids. At first order, a linear dispersion relation is obtained. Analytical and numerical results for the overstability and incipient instability conditions are given. For perfect dielectric fluids, the electric field has a stabilizing influence, while for leaky dielectric fluids, the electric field can have either a stabilizing or a destabilizing influence depending on the conductivity and permittivity ratios of the two fluids. At higher order, a nonlinear dispersion relation (nonlinear Ginzburg–Landau equation) is derived, describing the evolution of wave packets of the problem. For leaky dielectric fluids near the marginal state, a nonlinear diffusion equation (nonlinear incipient instability) is obtained. For perfect dielectric fluids, two cubic nonlinear Schrödinger equations are obtained. One of these equations to determine a nonlinear cutoff electric field separating stable and unstable disturbance, whereas the other is used to analyze the stability of the system. It is found that the nonlinear stability criterion depending on the ratio of permittivity, Such effects can only be explained successfully in the nonlinear sense, as the linear analysis unsuccessful to inform about them.     

The variational approach to estimation of the dielectric permittivity of a unidirectional fibrous composite

Based on the dual variational formulation of an electrostatic problem in an inhomogeneous anisotropic dielectric, we construct two-side bounds for possible values of second rank tensor components for the dielectric permittivity of a unidirectional fibrous composite taking into account mutual positions of anisotropic reinforcing fibers in the plane perpendicular to their axes. We consider variants of arrangement of cross sections of fibers such that the composite is transversal-isotropic or orthotropic relative to the property of dielectric permittivity. Some estimates of the greatest error appearing in the choice of true values of each component of the dielectric permittivity tensor of the composite in the form of a half-sum of its boundary values are obtained. A successive improvement of two-side bounds for domains where the components of this tensor should lie is carried out. A quantitative analysis of calculation dependencies is presented.     

One-way propagation in electromagnetic materials

Approaches to the characterization of the direction of wave propagation are examined, in the frequency and in the time domains, for electromagnetic materials with memory. In the frequency domain, the direction is characterized through the sign of the energy flux which is shown to decay as the wave propagates. In the time domain, a review is given of the wave-splitting approach for a dispersive dielectric. The result is a pair of decoupled equations, one being regarded to represent a forward propagating wave and the other a backward propagating wave, both of them involving an appropriate convolution kernel. To establish a connection between the two approaches, the Fourier components associated with the wave-splitting equations are examined. Owing to a thermodynamic restriction on the permittivity, the energy flux criterion, as well as the phase and amplitude criteria, implies that the direction is forward or backward depending on the value of the cosine transform of the convolution kernel and hence on the frequency.     

A LOW-FREQUENCY ELECTROMAGNETIC NEAR-FIELD INVERSE PROBLEM FOR A SPHERICAL SCATTERER

The interior low-frequency electromagnetic dipole excitation of a dielectric sphere is uti- lized as a simplified but realistic model in various biomedical applications. Motivated by these considerations, in this paper, we investigate analytically a near-field inverse scatter- ing problem for the electromagnetic interior dipole excitation of a dielectric sphere. First, we obtain, under the low-frequency assumption, a closed-form approximation of the series of the secondary electric field at the dipole＇s location. Then, we utilize this derived approx- imation in the development of a simple inverse medium scattering algorithm determining the sphere＇s dielectric permittivity. Finally, we present numerical results for a human head model, which demonstrate the accurate determination of the complex permittivity by the developed algorithm.     

Existence and uniqueness theorems in electromagnetic diffraction on systems of lossless dielectrics and perfectly conducting screens

New vector problem of electromagnetic wave diffraction by a system of non-intersecting three-dimensional inhomogeneous dielectric bodies and infinitely thin screens is considered in a quasiclassical formulation as well as the classical problem of diffraction by a lossless inhomogeneous body. In both cases, the original boundary value problem for Maxwell’s equations is reduced to integro-differential equations in the regions occupied by the bodies (and on the screen surfaces). The integro-differential operator is treated as a pseudodifferential operator in Sobolev spaces and is shown to be zero-index Fredholm operator. Uniqueness of solutions is proved under the realistic hypothesis of discontinuity of the dielectric permittivity the boundary of a volume scatterer. This result allowed to establish invertibility of the integro-differential operator in sufficiently broad spaces. For the problem of diffraction on dielectrics and surface conductors, theorem on smoothness of a solution is proved under assumption of data smoothness. The latter implies equivalence between the differential and integral formulations of the scattering problem. The matrix integro-differential operator is proved to be a Fredholm invertible operator. Thus, the existence of a unique solution to both problems is established.     

Towards modelling the curing process in particle-filled electro-active polymers

A large actuation voltage is required to produce a desired mechanical deformation in dielectric elastomers. To reduce the amount of the actuation voltage, several mechanisms can be applied and the inclusion of high dielectric permittivity fillers in the matrix material in the uncured stage is one of them. Moreover, to obtain a maximum advantage from the high dielectric permittivity fillers, an electric field is applied during the curing process which helps the particles to align in a preferred direction. The stiffness gaining during curing is modelled by an appropriate constitutive relation where the temporal evolution of the material parameters is considered. In this paper we present a phenomenologically-inspired large strain framework for simulating the curing process of polymers that can work under the use of an electro-mechanically coupled load. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)