Regional, Single Point, and Global Blow-Up for the Fourth-Order Porous Medium Type Equation with Source

Blow-up behaviour for the fourth-order quasilinear porous medium equation with source,ut=-（｜u｜^nu）xxxx＋｜u｜^p-1u in R×R＋,where n 〉 0, p 〉 1, is studied. Countable and finite families of similarity blow-up patterns of the form us（x,t）=（T-t）^-1/p-1f（y）,where y=x/（T-t）^β＇ β=p-（n＋1）/4（p-1）,which blow-up as t → T^- 〈∞ are described. These solutions explain key features of regional （for p = n＋1）, single point （for p 〉 n＋1）, and global （for p ∈ （1,n＋1））blowup. The concepts and various variational, bifurcation, and numerical approaches for revealing the structure and multiplicities of such blow-up patterns are presented.     

激光大气闪烁的间歇特征

 以小波变换法观察了湍流大气中激光光强起伏的间歇特征, 并用奇性测度进行了定量的描述。根据间歇性参量的周日变化规律发现：激光大气闪烁的间歇性存在于所有的时间和起伏条件下,并且保持稳定,间歇性参量约为0.1,基本不随起伏条件和时间变化。     

湍流大气中高斯光束焦移的数值模拟研究

采用数值模拟方法对聚焦高斯光束在湍流大气中传输的焦移进行了研究.结果表明:湍流大气中高斯光束的焦点不再位于真空焦点位置,而是向发射点移动,且前移的幅度随湍流强度的增大而增大,这与理论预计结果一致.引用焦深概念描述光束在焦点附近的准直特性,结果显示:在弱起伏和中等强度起伏情况下,光束的焦深随着湍流强度的增大而增大,焦点附近光束准直度提高;在中等和强起伏情况下,光束在焦点附近高度准直.     

激光湍流大气传输数值模拟中计算参量的选取

根据抽样原则、湍流介质特性、湍流效应和光传播效应等全面分析了网格间距、相屏间距和网格数目等关键计算参量选取的基本要求.通过数值计算,分析各种要求的可行性,表明在具体的数值模拟过程中,并非所有要求都能同时满足,若严格按照要求选择计算参量,所需的计算量常超出计算机负荷范围.结合具体数值计算,综合考虑计算机承受能力和计算准确度,给出了一种可靠实用的计算参量选取思路和方案.     

The dynamical mixing of light and pseudoscalar fields

We solve the general problem of mixing of electromagnetic and scalar or pseudoscalar fields coupled by axion-type interactions L _int = g _ϕ ϕε _μναβ F ^μν F ^αβ . The problem depends on several dimensionful scales, including the magnitude and direction of background magnetic field, the pseudoscalar mass, plasma frequency, propagation frequency, wave number, and finally the pseudoscalar coupling. We apply the results to the first consistent calculations of the mixing of light propagating in a background magnetic field of varying directions, which show a great variety of fascinating resonant and polarization effects.      

Epidemic spreading in complex networks

The study of epidemic spreading in complex networks is currently a hot topic and a large body of results have been achieved. In this paper, we briefly review our contributions to this field, which includes the underlying mechanism of rumor propagation, the epidemic spreading in community networks, the influence of varying topology, and the influence of mobility of agents. Also, some future directions are pointed out.      

Time reversal for obstacle location in elastodynamics from acoustic recording

The Note is concerned with a feasibility study of time reversal in a non-homogeneous elastic medium, from data recorded in an acoustic medium. Our aim here is to determine the presence and some physical properties of elastic “inclusions” (unknown, not observable solid objects, characterized by their elastic properties) from partial observations of acoustic waves scattered by these inclusions. A finite element numerical method, based on a variational acousto-elastodynamics formulation, is derived and used to solve the forward, and then, the time-reversed problem. A criterion, derived from the reverse time migration framework, is introduced, to help construct images of the inclusions to be determined. Numerical illustrations on configurations that mimic the breast cancer configuration are proposed, and show that one can differentiate between two inclusions, even with different properties.     

Chebyshev spectral variational integrator and applications

The Chebyshev spectral variational integrator(CSVI) is presented in this paper. Spectral methods have aroused great interest in approximating numerically a smooth problem for their attractive geometric convergence rates. The geometric numerical methods are praised for their excellent long-time geometric structure-preserving properties.According to the generalized Galerkin framework, we combine two methods together to construct a variational integrator, which captures the merits of both methods. Since the interpolating points of the variational integrator are chosen as the Chebyshev points,the integration of Lagrangian can be approximated by the Clenshaw-Curtis quadrature rule, and the barycentric Lagrange interpolation is presented to substitute for the classic Lagrange interpolation in the approximation of configuration variables and the corresponding derivatives. The numerical float errors of the first-order spectral differentiation matrix can be alleviated by using a trigonometric identity especially when the number of Chebyshev points is large. Furthermore, the spectral variational integrator(SVI) constructed by the Gauss-Legendre quadrature rule and the multi-interval spectral method are carried out to compare with the CSVI, and the interesting kink phenomena for the Clenshaw-Curtis quadrature rule are discovered. The numerical results reveal that the CSVI has an advantage on the computing time over the whole progress and a higher accuracy than the SVI before the kink position. The effectiveness of the proposed method is demonstrated and verified perfectly through the numerical simulations for several classical mechanics examples and the orbital propagation for the planet systems and the Solar system.     

含孔隙混凝土二维细观建模方法研究

根据混凝土的细观组成和结构特点,对传统二维建模方法加以继承与改进,提出了一种高效的分步入侵判定算法.将孔隙直观地反映在模型中,建立了不同的含孔隙混凝土细观模型.对含圆形、椭圆形、多边形骨料与圆形、椭圆形孔隙的混凝土标准试件分别进行了建模研究,结果表明本文的算法具有较强适用性.同时,通过对不同面积率与多种形状骨料/孔隙混凝土的大量建模进一步验证了该算法的效率.模拟了混凝土试件在单轴压缩下的准静态力学性能,分析了混凝土内部孔隙对其裂纹扩展的主要路径、破坏模式以及宏观力学性能的显著影响.     

激光系统组件化仿真软件EasyLaser

针对国内一直以来缺乏一套能够对复杂激光系统进行全面仿真模拟工具的问题,在成熟仿真模块的基础上,基于组件化建模仿真思想研发了通用易用的激光系统仿真软件EasyLaser。它由通用的组件化建模仿真支撑平台SciSimu和8个仿真组件库构成,具备对光束的光学元件间传输、大气传输、电视成像、自适应光学校正、识别提取跟踪等复杂过程的建模与仿真能力。详细介绍了EasyLaser的物理仿真能力和软件特色,并利用EasyLaser软件搭建仿真光路模型,进行自适应光学系统对大气湍流效应的校正效果的分析和研究。