强外加电场与大调制度下光折变动力学光栅形成研究

强外加电场与大调制度在光折变效应的研究中已经得到了广泛应用。采用PDECOL算法,严格求解光折变带输运方程,得到外加电场时不同调制度下光折变晶体中随时间变化的空间电荷场、载流子浓度,并讨论了外加电场对它们的影响。通过将物质方程与耦合波方程联立数值求解,可得到光折变光栅形成过程中两波耦合增益系数以及光束条纹相位的变化。模拟结果表明,在强外加电场作用下,两束记录光之间的光强与相位耦合都得到了增强,而原有的解析式忽视了强外加电场与大调制度对空间电荷场相位耦合的影响,此时不再适用。同时发现折射率光栅与记录光束条纹均发生弯曲,并不再保持平行。     

Numerical evolution,linear and nonlinear,of spherically symmetric deviations from an isotropic universe

We describe an algorithm for solving 1 + 1-systems that are in symmetric hyperbolic form. It is applied to spherically symmetric deviations from ak = 0, radiation filled Isotropic universe. We compare the solution to the full Einstein equations with those of the linearized equations. For small enough initial data the evolutions are indistinguishable. However, for large data, i.e., for initial density contrasts in the 1 percent range, trapped surfaces appear and singularities form.     

稠密共振介质中近偶极-偶极相互作用的局域场效应

 为研究存在由近偶极-偶极相互作用诱导的局域场效应时超短强激光脉冲与稠密共振介质相互作用的特性,采用光与物质相互作用的半经典理论,建立了稠密二能级体系中考虑原子间近偶极-偶极相互作用的修正光学Bloch方程,并用四阶Runge-Kutta法数值求解了该方程。研究结果表明:局域场效应对稠密二能级体系中Bloch矢量的瞬态相干过程和稳态性质都具有强烈的调制作用。并由此提出了调控稳态粒子数布居的两种方案。     

稠密共振介质中近偶极-偶极相互作用的局域场效应

为研究存在由近偶极-偶极相互作用诱导的局域场效应时超短强激光脉冲与稠密共振介质相互作用的特性,采用光与物质相互作用的半经典理论,建立了稠密二能级体系中考虑原子间近偶极-偶极相互作用的修正光学Bloch方程,并用四阶Runge-Kutta法数值求解了该方程。研究结果表明:局域场效应对稠密二能级体系中Bloch矢量的瞬态相干过程和稳态性质都具有强烈的调制作用。并由此提出了调控稳态粒子数布居的两种方案。     

Exact Solutions of Atmospheric(2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

Exact solutions of the atmospheric(2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq(INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space.     

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space.     

Transport Theory and Collective Modes. I. The Case of Moderately Dense Gases

The complex spectral representation of the Liouville operator introduced by Prigogine and others is applied to moderately dense gases interacting through hard-core potentials in arbitrary d-dimensional spaces. Kinetic equations near equilibrium are constructed in each subspace as introduced in the spectral decomposition for collective, renormalized reduced distribution functions. Our renormalization is a nonequilibrium effect, as the renormalization effect disappears at equilibrium. It is remarkable that our renormalized functions strictly obey well-defined Markovian kinetic equations for all d, even though the ordinary distribution functions obey nonMarkovian equations with memory effects. One can now define transport coefficients associated to the collective modes for all dimensional systems including d = 2. Our formulation hence provides a microscopic meaning of the macroscopic transport theory. Moreover, this gives an answer to the long-standing question whether or not transport equations exist in two-dimensional systems. The non-Markovian effects for the ordinary distribution function, such as the long-time tails for arbitrary n-mode coupling, are estimated by superposition of the Markovian evolutions of the dressed distribution functions.     

Random Evolutions Are Driven by the Hyperparabolic Operators

We resolve the long-standing problem of describing the multidimensional random evolutions by means of the telegraph equations. This problem was posed by Mark Kac more than 50 years ago and has become the subject of intense discussion among researchers on whether the multidimensional random flights could be described by the telegraph equations similarly to the one-dimensional case. We give the exhaustive answer to this question and show that the multidimensional random evolutions are driven by the hyperparabolic operators composed of the telegraph operators and their integer powers. The only exception is the 2D random flight whose transition density is the fundamental solution to the two-dimensional telegraph equation. The reason of the exceptionality of the 2D-case is explained. We also show that, under the standard Kac’s condition, the governing hyperparabolic operator turns into the generator of the Brownian motion.     

边界层流动中湍斑的直接数值模拟

用Navier-Stokes方程直接数值模拟平板边界层流动中湍斑的形成和演化过程.发展了模拟湍斑的高精度、高分辨率的高效计算方法,包括推出四阶时间分裂法以提高精度;提出三维耦合差分方法,用于关于压力的泊松方程和关于速度的亥姆霍兹方程的空间离散,建立其四阶三维耦合中心差分格式;并采用四阶紧致迎风差分格式,避免了一般四阶中心差分格式不适用于边界邻域的困难和提高了分辨率;精心地处理各种边界条件,以保持精度和稳定.该方法适用于包含边界邻域的整个区域内的湍斑模拟.通过模拟平板边界层流动中湍斑的复杂演化过程,显示了湍斑的基本特征.     

Perturbative and non-perturbative evolutions of structure functions at low-x

Approximate solutions of Altarelli-Parisi equations are obtained in low-x limit and have tested them in EMC low-x and low-Q ² data. The results are compared with the phenomenological non-perturbative evolutions. Data conform to perturbative as well as non-perturbative evolutions but do not conform to the predictions of non-linear evolution.     

Gasdynamic characteristics of toroidal shock and detonation wave converging

Shock wave focusing is a fundamental problem in the shock wave research and the instantaneous impulse of high temperature and pressure generated at the focal points has been applied recently in industrial and medical researches[1]. There are several methods to create shock wave focusing, among which the more commonly-used one is to make a planar shock wave reflect from a concave surface, such as the elliptical or parabolic re- flector. Toroidal shock wave focusing has been proposed and investi…     

Gasdynamic characteristics of toroidal shock and detonation wave converging

The modified CCW relation is applied to analyzing the shock, detonation wave converging and the role of chemical reactions in the process. Results indicate that the shock wave is strengthened faster than the detonation wave in the converging at the same initial Mach number. Euler equations implemented with a detailed chemical reaction model are solved to simulate toroidal shock and detonation wave converging. Gasdynamic characteristics of the converging are investigated, including wave interaction patterns, observable discrepancies and physical phenomena behind them. By comparing wave diffractions, converging processes and pressure evolutions in the focusing area, the different effects of chemical reactions on diffracting and converging processes are discussed and the analytic conclusion is demonstrated through the observation of numerical simulations.     

Extended Lifetime in Computational Evolution of Isolated Black Holes

Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second-order evolution equations. Analytically the constraint equations remain solved under the action of the evolution, and one approach is to simply monitor them (unconstrained evolution). The problem of the 3-d computational simulation of even a single isolated vacuum black hole has proven to be remarkably difficult. Recently, we have become aware of two publications that describe very long term evolution, at least for single isolated black holes. An essential feature in each of these results is constraint subtraction. Additionally, each of these approaches is based on what we call “modern,” hyperbolic formulations of the Einstein equations. It is generally assumed, based on computational experience, that the use of such modern formulations is essential for long-term black hole stability. We report here on comparable lifetime results based on the much simpler (“traditional”) formulation. With specific subtraction of constraints, with a simple analytic gauge, with very simple boundary conditions, and for moderately large domains with moderately fine resolution, we find computational evolutions of isolated non-spinning black holes for times exceeding 1000 GM/c². We have also carried out a series of constrained 3-d evolutions of single isolated black holes. We find that constraint solution can produce substantially stabilized long-term single hole evolutions. However, we have found that for large domains, neither constraint-subtracted nor constrained evolutions carried out in Cartesian coordinates admit arbitrarily long-lived simulations. The failure appears to arise from features at the inner excision boundary; the behavior does generally improve with resolution.     

New solitonary solutions for the MBBM equations using Exp-function method

In this Letter we use the Exp-function method for analytic treatment for the modified Benjamin-Bona-Mahony equations. New solitonary solutions are formally derived. The change of the parameters, that will drastically change the characteristics of the equations, is examined. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving high-dimensional nonlinear evolutions in mathematical physics.     

Eulerian–Lagrangian multiscale methods for solving scalar equations – Application to incompressible two-phase flows

The present article proposes a new hybrid Eulerian–Lagrangian numerical method, based on a volume particle meshing of the Eulerian grid, for solving transport equations. The approach, called Volume Of Fluid Sub-Mesh method (VOF-SM), has the advantage of being able to deal with interface tracking as well as advection–diffusion transport equations of scalar quantities. The Eulerian evolutions of a scalar field could be obtained on any orthogonal curvilinear grid thanks to the Lagrangian advection and a redistribution of particles on the Eulerian grid. The Eulerian concentrations result from the projection of the volume and scalar informations handled by the particles. The particle velocities are interpolated from the Eulerian velocity field. The VOF-SM method is validated on several scalar interface tracking and transport problems and is compared to existing schemes within the literature. It is finally coupled to a Navier–Stokes solver and applied to the simulation of two free-surface flows, i.e. the two-dimensional buckling of a viscous jet during the filling of a square mold and the three-dimensional dam-break flow in a tank.     

Vlasov Scaling for Stochastic Dynamics of Continuous Systems

We describe a general derivation scheme for the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of realization of the proposed approach in particular models are presented.     

Multi-symplectic variational integrators for nonlinear Schrdinger equations with variable coefficients

In this paper, we propose a variational integrator for nonlinear Schrdinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrdinger equations with variable coefficients, cubic nonlinear Schrdinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.     

Coherent transient pulse propagation in two-photon resonance of a homogeneously broadened three-level medium

Pulse evolutions with SIT-like propagation are shown in spite of including the optical Stark effect and the self-phase modulation by solving numerically the two-photon Bloch equation and the coupled phase and amplitude equations.     

光学Maxwell-Bloch方程的数值算法研究及其应用

建立了高准确度快速求解均匀展宽二能级体系光学Maxwell-Bloch耦合方程的数值算法.通过与特定条件得到的解析解的比较,验证了算法所具有的高收敛性和稳定性,并可保持算法的误差阶数,因此算法是可靠并实用的.应用该算法数值求解了一般条件下的MB方程,并由计算结果分析了失谐量、弛豫时间、初始光强对光脉冲在介质中的传播及对Bloch矢量演化的影响.所建立的数值算法对MB方程以及修正的这类偏微分方程组具有普适性.     

Comments on structure functions at low-x

We present further analysis of the structure functions at low-x using the approximate solutions of Altarelli-Parisi equations recently reported by us. We also compare our results with non-perturbative and non-linear evolutions.