采用腔内设置限孔光阑抑制倒向波的理论分析

 氧碘化学激光器通常采用的环形腔存在着倒向波，它对正向波的输出功率以及光束质量不利，因此必须进行抑制。以对称环形共焦非稳腔为例，介绍了在腔内放置限孔光阑，通过改变倒向波与正向波经过增益介质部分的模体积比，从而抑制倒向波的方法。计算结果表明，这种方法对于负支腔倒向波的抑制效果要远远好于正支腔。     

On solutions to two-dimensional systems realizing the transition from an unstable equilibrium to a stable cycle

For a two-dimensional dynamical system at ?∞ < t < +∞, a process describing the transition from an arbitrary neighborhood of an unstable equilibrium to a stable limit cycle is studied. The system is reduced to the Poincaré normal form. An approximate solution is constructed as a polynomial of degree 2N containing only even degrees of the small parameter ε. The functional classes to which the coefficients of this polynomial belong are described. The function space containing the exact solution differing from the approximate one by O(ε^2N+1) is determined.     

Global dynamics and bifurcation of a perturbed Sigmoid Beverton–Holt difference equation

T. Wanner We investigate global dynamics of the equation where the parameters b,c, and f are nonnegative numbers with condition b + c > 0,f ≠ 0 and the initial conditions x_?1,x₀ are arbitrary nonnegative numbers such that x_?1+x₀>0. We obtain precise characterization of basins of attraction of all attractors of this equation and describe the dynamics in terms of bifurcations of period‐two solutions. Copyright © 2015 John Wiley & Sons, Ltd.     

Toward the Dark Matter of Natural Products

Considering the dynamic features of natural products, our access toward exploring the entire diversity of natural products has been quite limited. It is challenging to assess the diversity of natural products by using conventional analytical methods, even with tandem chromatographic techniques, such as LC‐MS and GC‐MS. This viewpoint is supported by the sequencing analyses of microbial genomes, which have unveiled the potential of secondary metabolite production far exceeding the number of isolated molecules. Recent advancements in metabolomics, in concert with genomics analyses, have further extended the natural product diversity, prompting growing awareness of the existence of reactive or short‐lived natural molecules. This personal account introduces some examples of the discoveries of hitherto elusive natural products, due to physico‐chemical or biological reasons, and highlights the significance of the dark matter of natural products.     

Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions

In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the Kelvin–Voigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for solutions of the problem with linear dynamic boundary conditions with initial data in the unstable set is also obtained.     

连续时间系统二维不稳定流形的异构算法

非线性系统的二维流形通常具有复杂几何结构和丰富动力学信息,因此在流形计算与可视化时存在大量的不可避免的数值计算.因此,如何高效地完成这些计算就成了关键问题.鉴于当今计算机的异构发展趋势(包含多核CPU和通用GPU),本文在兼顾精度和通用性的基础上,提出了适用于新一代计算平台的快速流形计算方法.本算法将计算任务分为轨道延伸和三角形生成两部分,前者运算量大而单一适合GPU完成,后者运算量小而复杂适合CPU执行.通过对Lorenz系统原点稳定流形的计算,表明本算法能充分发挥异构平台的综合性能,可大幅度提高计算速 关键词： 不稳定流形 流形计算 异构计算 Lorenz系统     

基于广义Foliation条件的非线性映射 二维流形计算

主要研究非线性映射函数双曲不动点的二维流形计算问题. 提出了推广的Foliation条件, 以此来衡量二维流形上的一维流形轨道的增长量, 进而控制各子流形的增长速度, 实现二维流形在各个方向上的均匀增长. 此外, 提出了一种一维子流形轨道的递归插入算法, 该算法巧妙地解决了二维流形面上网格点的插入、前像搜索, 以及网格点后续轨道计算问题, 同时插入的轨道不必从初始圆开始计算, 避免了在初始圆附近产生过多的网格点. 以超混沌三维Hénon映射和具有蝶形吸引子的Lorenz系统为例验证了算法的有效性.     

CONSTRUCTION OF MECHANISM MODES OF GEOMETRICALLY UNSTABLE SYSTEMS IN LARGE DEFORMATION

针对仅有一个自由度的几何可变体系,基于大变形机构模态的特性,提出常变、瞬变的判断方法,进而对常变体系提出大变形机构模态的二元体构建算法。该算法将问题简化为类似于一元二次方程的求解,无须求解非线性超越方程组,可给出完备的模态解答和完整的解答路径及其分叉点。本法具有原理直观、公式简洁、解答完备的优点,可作为结构力学几何构造分析教学的补充内容。     

腔内像散扰动对正支共焦腔模式影响的数值分析

 针对激光器出光过程中腔内像差扰动带来的输出光束质量和光束能量下降问题,分析了腔内像差扰动对非稳腔模式的影响,并采用数值迭代法计算了理想情形和腔内像散扰动对无源正支共焦腔输出模式强度和相位分布的影响,进一步采用Zernike模式法对光束相位进行了像差拟合,得到了前35阶Zernike像差系数、点扩散函数(PSF)分布和环围能量曲线,计算了腔内像散扰动量与远场Strehl比的关系。结果表明：对小菲涅耳数正支共焦腔,腔内像散扰动对输出光束强度和相位分布均有明显影响,相位分布中一些高阶Zernike像差也有所增大。因此在进行腔内像差校正时,应优先考虑此类像差的校正。