基于Parareal算法的输电线路电磁暂态仿真分析

将Parareal算法运用于输电线路电磁暂态仿真以提高其计算效率。首先将输电线路的电波方程在空间上离散成一组常微分方程,再建立其动态向量模型。运用Parareal算法求解动态向量模型时,应先将整个仿真时间均分为若干个子区间,用一种较低阶的数值方法计算出一组初始值,然后借助这组初始值在每个子区间里用一种精度较高的数值方法单独进行计算,最后通过反复预估—校正的方法得到一组精细解。算例结果表明Parareal算法计算过程简单,收敛速度快,可提高输电线路电磁暂态仿真计算的效率。

Conservation Laws of a Class of Combined Equations

In this paper, we investigate conservation laws of a class of partial differential equations, which combines the nonlinear telegraph equations and the nonlinear diffusion-convection equations. Moreover, some special conservation laws of the combined equations are obtained by means of symmetry classifications of wave equations uxx = H （x）utt.

Integral Equation Method for Electromagnetic Wave Propagation in Stratified Anisotropic Dielectric-Magnetic Materials

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materialsusing the integral equation method (IEM).Based on the superposition principle, we use Hertz vector formulations ofradiated fields to study the interaction of wave with matter.We derive in a new way the dispersion relation, Snell's lawand reflection/transmission coefficients by self-consistent analyses.Moreover, we find two new forms of the generalizedextinction theorem.Applying the IEM, we investigate the wave propagation through a slab and disclose the underlyingphysics, which are further verified by numerical simulations.The results lead to a unified framework of the IEM for thepropagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.

An Analytical Approach to Thermal and Electrical Transport in a Mesoscopic Conductor

In order to consider the thermal and electrical coherent transport in a mesoscopic conductor under the influence of electron-electron interaction, in this paper, we establish a method in terms of which one can analytically obtain the Hartree self-consistent potential instead of computing it by the numerical iterative procedure as usual, which is convenient for us to describe the thermal and electric current flow through a mesoscopic conductor. If we study the electron-electron interaction at the Hartree approximation level, the Hartree potential satisfies the Poisson equation and Schroedinger equation, so when we expand the action function S（x） by Planck constant h, the self-consistent potential and the wavefunction can be solved analytically order by order, and the thermal and electrical conductance can thus be obtained readily. However, we just show the quantum corrections up to the second order.

Solitonic Information Transmission in General Relativity

An exact solution of the vacuum Einstein＇s field equations is presented, in which there exists a congruence of null geodesics whose shear behaves like a travelling wave of the KdV equation. On the basis of this exact solution, the feasibility of solitonic information transmission by exploiting the nonlinearity intrinsic to the Einstein field equations is discussed.

Frequency domain wave equation forward modeling using gaussian elimination with static pivoting

Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elimination cannot resolve the parallel computation of huge data. Therefore, we use the Gaussian elimination with static pivoting （GESP） method for sparse matrix decomposition and multi-source finite-difference modeling. The GESP method does not only improve the computational efficiency but also benefit the distributed parallel computation of matrix decomposition within a single frequency point. We test the proposed method using the classic Marmousi model. Both the single-frequency wave field and time domain seismic section show that the proposed method improves the simulation accuracy and computational efficiency and saves and makes full use of memory. This method can lay the basis for waveform inversion.

Gravitational Faraday effect in curved space-time induced by high-power lasers

Gravitational field produced by high-power laser is calculated according to the linearized Einstein field equation in weak field approximation. Gravitational Faraday effect of electromagnetic wave propagating in the above gravitational field is studied and the rotation angle of polarization plane of electromagnetic wave is derived. The result is discussed and estimated under the condition of present experiment facility.

Solution of Schrdinger Equation for Two-Dimensional Complex Quartic Potentials

We investigate the quasi-exact solutions of the Schrodinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x1 ＋ ip3, y = x2 ＋ ip4, px= p1＋ ix3, py= p2 ＋ ix4. Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetrie one, are also worked out.

Oblique Wave-free Potentials for Water Waves in Constant Finite Depth

In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform fmite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.

The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves

The dynamic behavior of two collinear cracks in magneto-electro-elastic composites under harmonic anti-plane shear waves is studied using the Schmidt method for the permeable crack surface conditions. By using the Fourier transform, the problem can be solved with a set of triple integral equations in which the unknown variable is the jump of the displacements across the crack surfaces. In solving the triple integral equations, the jump of the displacements across the crack surface is expanded in a series of Jacobi polynomials. It can be obtained that the stress field is independent of the electric field and the magnetic flux.

The Effect of the Under-dense Magnetized Plasma on Electron Density Distribution and Field Profile

Propagation of a high frequency electromagnetic wave in under-dence plasma in presence of an external magnetic field is investigated. When a constant magnetic field perpendicular to the motion of electrons is applied, then the electrons rotate around the magnetic field lines and generate electromagnetic part in the wake with a nonzero group velocity. Using of the Maxwell equations and nonlinear differential equation for the electric field a direct one dimensional （ID） procedure for calculating wake equations are developed and the electric and magnetic field profile in the plasma are investigated.

Exact Solution to the Equation of Motion of a Charged Particle Driven by an Electrostatic Wave

An exact solution is derived for the equation of motion of a charged particle driven by an electrostatic wave.The explicit expression of particle velocity is obtained,and the trapping condition of the charged particle in the electrostatic wave is also derived exactly.The interaction between the charged particle and the electrostatic wave is discussed,which is a supplement to the existing textbook of plasma physics.The results are of interest to particle accelerators,microwave tubes,and basic plasma processes.

The form-invariance of wave equations without requiring a priori relations between field variables

According to the principle of relativity,the equations describing the laws of physics should have the same forms in all admissible frames of reference,i.e.,form-invariance is an intrinsic property of correct wave equations.However,so far in the design of metamaterials by transformation methods,the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation.The main contribution of this paper is to give general proofs of form-invariance of electromagnetic,sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables.The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant,but traditional elastodynamic equations are not.As a by-product,one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media.The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak.These findings are important for solving inverse scattering problems in many fields such as seismology,nondestructive evaluation and metamaterials.

Klein Paradox of Two-Dimensional Dirac Electrons in Circular Well Potential

We study two-dimensional massive Dirac equation in circular well potential. The energies of bound states are obtained. We demonstrate the Klein paradox of this relativistic wave equation:For large enough potential depth, the bound states disappear from the spectra. Applications to graphene systems are discussed.

Cylindrical and Spherical Electron-Acoustic Shock Waves in Electron-Positron-Ion Plasmas with Nonextensive Electrons and Positrons

Electron-acoustic shock waves （EASWs） in an unmagnetized four-component plasma （containing hot elec- trons and positrons following the q-nonextensiv.e distribution, cold mobile viscous electron fluid, and immobile positive ions） are studied in nonplanar （cylindrical and spherical） geometry. With the help of the reductive perturbation method, the modified Burgers equation is derived. Analytically, the effects of nonplanar geometry, nonextensivity, relative number density and temperature ratios, and cold electron kinematic viscosity on the basic properties （viz. amplitude, width, speed, etc.） of EASWs are discussed. It is exarmined that the EASWs in nonplanar geometry significantly differ from those in planar geometry. The results of this investigation can be helpful in understanding the nonlinear features of EASWs in various astrophysical plasmas.

A Theoretical Model to Explain the Mechanism of Electromagnetic Wave Propagation Along Cylindrical Micelles

A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.

solitary waves shock waves dust charge variation dusty plasma

The nonlinear propagation of dust acoustic waves is investigated in four-component plasmas consisting of positively charged dust grains, trapped ions, nonthermal electrons, and photoelectron due to ultraviolet irradiation.We use generalized viscoelastic hydrodynamic model for strongly coupled dust grain. In the weak nonlinearity limit, a modified Kadomstev–Petviashvili（KP） equation and a modified KP-Burger equation, which have a damping term coming from nonadiabatic charge variation, have been derived in the kinetic regime and hydrodynamic regime, respectively. With the increasing of UV photon flux, the hydrodynamic regime changes to kinetic regime. The approximate analytical line soliton and shock solutions are investigated in the kinetic regime and hydrodynamic regime, respectively.

Nonlinear Structures of Lower Hybrid Wave in Collision Plasmas

Nonlinear structures of lower hybrid wave in collision plasmas are studied using the two-fluid theory.The oscillatory shock wave is observed due to the effects of the electron-neutral collision and the density inhomogeneity.In the cold electron limit,the oscillatory shock wave becomes the ordinary shock wave.In the collisionless limit,the dominated equation becomes Kd V equation and the lower hybrid solitons arise.The amplitude of the nonlinear structure is depressed by the plasma inhomogeneity,but is hardly affected by the electron-neutral collision.