一种处理色散介质问题的通用时域有限差分方法

色散介质的介电系数是频率的函数,使本构关系在时域成为卷积关系.这就给用时域有限差分方法计算色散介质中波的散射和传播带来了困难.现有算法往往要针对不同色散介质模型推导相应的递推公式,算法的通用性较差.本文完善和发展了移位算子-时域有限差分方法,使之成为一种处理色散介质电磁问题的通用方法.首先,证明了常见的三种色散介质模型(德拜模型、洛伦兹模型和德鲁模型)的介电系数均可以写成适于移位算子法计算的有理分式函数形式.然后,用/t代替jω,过渡到时域,再引入时域移位算子z_t代替时间微分算子来处理有理分式函数形式的介电系数,给出离散时域本构关系的表示式,进而导出时域有限差分方法当中电位移矢量和电场强度之间的关系.最后,计算了几种色散介质的电磁散射,数值结果表明了本文方法和程序的通用性和正确有效性. 关键词： 时域有限差分方法 色散介质 移位算子     

一种色散介质FDTD通用吸收边界

由单轴各向异性介质所满足的场方程出发,并根据相位匹配原理以得到介质中的色散关系和无反射条件.结合频域到时域的转换关系（即用/t代替jω）和移位算子时域有限差分（SO-FDTD）方法提出了一种适用于各向同性常见色散介质模型,包括德拜模型、洛伦兹模型、德鲁德模型等的通用UPML吸收边界.数值结果表明了该算法的通用性和高效性. 关键词： 时域有限差分 吸收边界 移位算子 色散介质     

A FDTD formulation for high order dispersive media of muscle-equivalent

In this paper, shift operator finite-difference time-domain (SO-FDTD) method is applied for the calculation of the dispersive medium. The high efficiency and accuracy of this method is verified by calculating the reflection of the plane electromagnetic wave impinging on a muscle slab. For human tissues where multiterm Debye relaxation equations must generally be used. We describe a new differential equation approach, which can be used for general dispersive media. In this method D(t) is expressed in terms of E(t) by means of a differential equation involving D, E, and their time derivatives. The method is illustrated by means of example of media for which relative permittivity is given by a multiterm Debye equation, and for an approximate two-thirds muscle-equivalent model of the human body.     

SO-FDTD Analysis on Magnetized Plasma

In this paper, a novel finite-difference time-domain (FDTD) method with recursive relationships among operators is developed for magnetized dispersive medium, named as the shift operator FDTD(SO-FDTD). The dielectric property of magnetized dispersive medium is written as rational polynomial function, the relationship between D and E is deduced in time-domain. And its high accuracy and efficiency are verified by calculating the reflection and transmission coefficients of electromagnetic waves through a collision plasma slab.     

Finite Maxwell field and electric displacement Hamiltonians derived from a current dependent Lagrangian

ABSTRACT

In the common Ewald summation technique for the evaluation of electrostatic forces, the average electric field E is strictly zero. Finite uniform E can be accounted for by adding it as a new degree of freedom in an extended Lagrangian. Representing the uniform polarization P as the time integral of the internal current and E as the time derivative of a uniform vector field A, we define such an extended Lagrangian coupling A to the total current j _t (internal plus external) and hence derive a Hamiltonian resembling the minimal coupling Hamiltonian of electrodynamics. Next, applying a procedure borrowed from nonrelativistic molecular electrodynamics the j _t · A coupling is transformed to P · D form where D is the electric displacement acting as an electrostatic boundary condition. The resulting Hamiltonian is identical to the constant-D Hamiltonian obtained by Stengel, Spaldin and Vanderbilt (SSV) using thermodynamic arguments. The corresponding SSV constant-E Hamiltonian is derived from an alternative extended Lagrangian.     

Analysis of the temperature influence on the plasma reflectance by a new FDTD method

We apply the shift-operator FDTD (SO-FDTD) method for calculating dispersive media plasmas. We write the dielectric constant of a dispersive medium as a rational fractional function and derive the relation between D and E in the time domain. For a uniform, approximately isothermic, isotropic, warm-collision-plasma slab, the reflection coefficient of electromagnetic waves can be calculated using the SO-FDTD method. We study the influence of temperature on the collisions and absorption of electromagnetic waves in the plasma and discuss the regularity of the relationships obtained.     

Theoretical Study of the Structure of the Electric Field in Helical Toroidal Plasmas

A set of transport equations is analyzed, including the bifurcation of the electric field. The structure of the electric field is studied by use of the theoretical model for the anomalous transport diffusivities. A steep gradient of the radial electric field (E _r) is obtained at the electric domain, where the electric domain is the structure of the electric field in which the ambipolar E _r spatially changes from the electron root (E _r>0) to the ion root (E _r<0). The suppression of the anomalous transport diffusivity is studied in the presence of a strong shear of the electric field. The hard transition between the multiple ambipolar solutions in the structure of the radial electric field is examined. The details of the structure of the electric domain interface are investigated.     

Observation of a shift of the mobility threshold in the D − band of silicon in an electric field according to the photoconductivity spectra

We have discovered that the extrinsic photoconductivity spectrum of doped, uncompensated crystalline Si at liquid-helium temperatures is qualitatively different in electric fields E above a critical value E _c . Specifically, the red edge of the photoconductivity, associated with photoionization of a neutral impurity, is shifted strongly to lower frequencies. This result is explained by the appearance of a mobility threshold in the D ⁻-band (upper Hubbard band) and the shift of this threshold as E increases. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 2, 89–94 (25 January 1996)     

色散介质电磁特性时域有限差分分析的Newmark方法

根据Debye模型、Drude模型和Lorentz模型3种常见色散介质模型频域极化率的特点,利用频域到时域的转换关系jω→?/?t,将极化矢量P与电场强度E的频域关系转换成时域内关于P的二阶微分方程,其对3种色散介质模型皆适用,具有统一的形式.然后采用相比于中心差分具有更高精度的Newmark两步算法(Newmark-β-γ法)求解该方程,进而得到E→P的递推公式,再结合本构关系得到D→E的时域递推式.实现了色散介质电磁场量的时域有限差分迭代计算.数值计算结果表明该方法是适用于3种色散介质模型的通用算法,并且相比于移位算子时域有限差分方法等以中心差分为基础的离散方案具有更高的计算精度.     

FDTD analysis on the effect of plasma parameters on the reflection coefficient of the electromagnetic wave

In this paper, the dielectric constant of dispersive medium is written as rational polynomial function, and the relationship between D and E is derived in time-domain. It is named shift operator FDTD (SO-FDTD) method. Compared to the analytical solution, the high accuracy and efficiency of this method is verified by calculating the reflection coefficient of the electromagnetic wave through a cold plasma slab. The effect on reflection coefficient is calculated by using the SO-FDTD method. The result shows that some factors effect on reflection coefficient. They are as follows: plasma thickness, electron density, electron distribution and incident frequency. And on most conditions, parabola distribution helps reduce reflection coefficient more effectively than homogeneous distribution.     

基于直接离散方式的磁化铁氧体材料电磁散射的时域有限差分方法分析

根据磁化铁氧体材料的磁场强度和磁感应强度之间色散的本构关系式,利用时间微分算子/t和jω的时域和频域对应关系,将磁化铁氧体材料频域的本构关系转化为时域的本构关系,然后将时间微分算子/t在时域采用直接离散的方式,得到磁场强度和磁感应强度的时域有限差分迭代式.数值结果表明,该方法易于实现,简单可行,并节约内存. 关键词： 电磁散射 磁化铁氧体 时域有限差分方法 直接离散方法     

Bromine metallization studied by X-ray absorption spectroscopy

The experimental data carried out by M?ssbauer and magnetic resonances investigations of the structural phase transitions in K₂ZnCl₄ crystals are discussed by a simple electrostatic model, calculating, the lattice contributions to the local electric potential V(r), electric field intensity E(r) and electric field gradient tensor, (r) and taking into account both the fractional electric point charges and rigid lattice approximations. The validity of the model is proved by a good fit of the computing results and experimental data of quadrupole splitting parameters at K sites obtained by ³⁹K-NMR methods in high temperature incommensurate phase ( Pnam symmetry). The experimental results obtained by M?ssbauer and EPR methods in commensurate phase (Pna2₁ symmetry) of iron and copper doped K₂ZnCl₄ crystals are explained by relaxing the rigid lattice approximation. The insertion of probe ions appear to be done on not-exactly-Zn²⁺ site. Received 3 February 1999 and Received in final form 4 May 1999     

磁各向异性色散介质散射的Padé时域有限差分方法分析

根据矩阵Padé逼近理论，把磁化色散介质的相对磁导率张量表示成以jω为自变量的矩阵函数形式，用/t代替jω后过渡到时域，再引入离散时域移位算子代替时间微分算子.进而导出磁化色散介质中的磁感应强度B和磁场强度H在离散时域的色散关系，并将其具体应用于旋磁介质，得到了这种磁化色散介质的Padé时域有限差分方法的递推表达式.作为验证，用这种方法计算了磁化铁氧体球的后向雷达散射截面，所得结果与文献结果一致.理论推导及算例表明，该方法是正确和有效的. 关键词： 各向异性介质 色散介质 矩阵Padé逼近 时域有限差分方法     

Computational study of linear and nonlinear optical properties of substituted thiophene imino dyes using long-range corrected hybrid DFT methods

The molecular structures, linear and nonlinear optical properties of a series constituted by four R-substituted thiophene imino dyes, namely A(R?=?SO₂Me), B(R?=?SO₂Ph), C(R?=?NO₂), and D(R?=?C₂(CN)₃) were analysed using CAM-B3LYP, ωB97XD and LC-ωPBE hybrid DFT functionals in combination of the 6-311++G(d,p) standard basis set. The dipole moments, polarisabilities, HOMO-LUMO energy gaps, maximum absorption wavelengths and first hyperpolarisabilities were calculated in the gas phase and the obtained results are in good agreement with experimental NLO activity order A?<?B?<?C. Compared to synthesised dyes A-C, the designed dye D presents a longer maximum absorption wavelength and a lower HOMO-LUMO gap because of the appreciable stabilisation of its LUMO energy. These results were confirmed by the calculation of the total second-order stabilisation energy E⁽²⁾ defined in the context of the NBO population analysis. Consequently, dye D is predicted to exhibit a higher first hyperpolarisability in comparison with dyes A-C. This result can be justified by the enhanced intramolecular charge transfer in dye D due to the stronger electron-withdrawing ability and the cumulative action of the long π-conjugation of the tricyanovinyl moiety. The very high total hyperpolarisability (27 times greater than that of para-nitroaniline) of the designed dye D suggests its promising use in organic NLO devices.     

The effect of polymer type on electric breakdown strength on a nanosecond time scale

Based on the concepts of fast polarization, effective electric field and electron impact ionization criterion, the effect of polymer type on electric breakdown strength (E_BD) on a nanosecond time scale is investigated, and a formula that qualitatively characterizes the relation between the electric breakdown strength and the polymer type is derived. According to this formula, it is found that the electric breakdown strength decreases with an increase in the effective relative dielectric constants of the polymers. By calculating the effective relative dielectric constants for different types of polymers, the theoretical relation for the electric breakdown strengths of common polymers is predicted. To verify the prediction, the polymers of PE (polyethylene), PTFE (polytetrafluoroethelene), PMMA (organic glass) and Nylon are tested with a nanosecond-pulse generator. The experimental result shows E_BD (PTFE) > E_BD (PMMA) > E_BD (Nylon) > E_BD (PE). This result is consistent with the theoretical prediction.     

An approximate expression for the galvanomagnetic tensor

Using the iterative solution to the Boltzmann equation for electrons in d.c. electric and magnetic fields, an expression for the resistivity tensor can be obtained in the form of an infinite series. This series can be approximated by retaining only the first two terms. In the cases where relaxation times exist — in the sense that the collision term in the Boltzmann equation can be written asg(k)/τ(k), whereτ(k) is the relaxation time, andf (k) = f _E(ɛ k) + [∂f _E(εk)/∂ε]·g(k) the distribution function for electrons with wavevectork — this approximation is exact. For polyvalent metals in the one-OPW approximation, the complete galvanomagnetic tensor can be obtained using this approximation and the result differs from that obtained by using a time of relaxation given by an expression suggested byZiman. A calculation for a simple model Fermi surface, with screened Coulomb scattering, is carried out and the results compared with those of the relaxation time approximation.     

Appearance of a band of delocalized D − states in uncompensated silicon in an electric field

The impurity photoconductivity spectra of uncompensated silicon at liquid-helium temperatures under conditions of strongly suppressed background radiation (background) are studied in different electric fields E. It is established that the delocalization arising in the D ⁻ band as E increases is not associated with any changes of the fluctuation potential and is due to the direct action of the field E. A delocalization band of finite width appears abruptly at a critical value E _c (∼100 V/cm) of E. The critical field E _c increases with the density of charged centers in the sample. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 56–59 (10 January 1997)     

First principles calculations of alloying element diffusion coefficients in Ni using the five-frequency model

The diffusion coefficients of several alloying elements(Al,Mo,Co,Ta,Ru,W,Cr,Re) in Ni are directly calculated using the five-frequency model and the first principles density functional theory.The correlation factors provided by the five-frequency model are explicitly calculated.The calculated diffusion coefficients show their excellent agreement with the available experimental data.Both the diffusion pre-factor(D 0) and the activation energy(Q) of impurity diffusion are obtained.The diffusion coefficients above 700 K are sorted in the following order:DAl>DCr>DCo>DTa>DMo>DRu>DW>D Re.It is found that there is a positive correlation between the atomic radius of the solute and the jump energy of Ni that results in the rotation of the solute-vacancy pair(E 1).The value of E 2-E 1(E 2 is the solute diffusion energy) and the correlation factor each also show a positive correlation.The larger atoms in the same series have lower diffusion activation energies and faster diffusion coefficients.