Addendum to “Spatiotemporal evolution in a (2+1) -dimensional chemotaxis model” [Physica A 391 (2012) 107–112]

After our article, Physica A 391 (2012) 107–112, had been published online, T. Hillen told us about a theorem by Osaki, relevant for our numerical simulations.     

On Default Priors for Robust Bayesian Estimation with Divergences

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.     

On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

We generalize the Jensen-Shannon divergence and the Jensen-Shannon diversity index by considering a variational definition with respect to a generic mean, thereby extending the notion of Sibson’s information radius. The variational definition applies to any arbitrary distance and yields a new way to define a Jensen-Shannon symmetrization of distances. When the variational optimization is further constrained to belong to prescribed families of probability measures, we get relative Jensen-Shannon divergences and their equivalent Jensen-Shannon symmetrizations of distances that generalize the concept of information projections. Finally, we touch upon applications of these variational Jensen-Shannon divergences and diversity indices to clustering and quantization tasks of probability measures, including statistical mixtures.     

能见度仪探测光束平行度检测方法

为实现能见度计算中消光系数的正确测量,论述了光源平行度在能见度测量中的重要作用,设计了探测光束发散角检测方法与测量装置。该装置包括定焦成像系统和移动光源的直线系统,利用成像关系与空间几何关系推导了发散角表达式。以紫外LED作为实验光源,设计完成了测量系统成像装置与控制软件,计算得到水平方向与垂直方向发散角,利用所得发散角分析探测光束。实验结果表明,紫外LED光源的光束发散角水平与垂直方向分别为7.8和6.9,经比较得到未加入平行度的能见度与加入后的比值为0.51。该方法测得的能见度值更接近于实际值。     

固体介质间隔层激光标准具性能的影响因素研究

针对固体介质间隔层的镀膜标准具, 以1 064 nm激光镀膜标准具为例, 首先研究了反射膜堆数对反射带宽、基底厚度以及对自由光谱区的影响:标准具的带宽随着膜层堆数增加而减小, 自由光谱区随着基板厚度的增加而减小;其次研究了基底误差对标准具中心波长定位和透过率的影响, 通过定量数值计算证明了基底误差可通过标准具的使用角度补偿;针对典型的H(LH)^m/Substrate/(HL)^mH和L(LH)^m/Substrate/(HL)^mL两个膜系结构, 研究了入射激光发散角对标准具中心波长偏移、通带半宽度、中心波长透过率和最大透过率的影响。随着激光发散角的增加, 中心波长向短波方向移动, 通带半宽度、中心波长透过率和最大透过率呈现下降的趋势, 并且第二个膜系结构的标准具性能优于第一个膜系结构的标准具。     

The inverse problem of the calculus of variations for scalar fourth-order ordinary differential equations

A simple invariant characterization of the scalar fourth-order ordinary differential equations which admit a variational multiplier is given. The necessary and sufficient conditions for the existence of a multiplier are expressed in terms of the vanishing of two relative invariants which can be associated with any fourth-order equation through the application of Cartan's equivalence method. The solution to the inverse problem for fourth-order scalar equations provides the solution to an equivalence problem for second-order Lagrangians, as well as the precise relationship between the symmetry algebra of a variational equation and the divergence symmetry algebra of the associated Lagrangian.

     

发散光束抽运的宽带光参量啁啾脉冲放大系统的理论研究

对发散光束抽运的光参量啁啾脉冲放大器的增益带宽进行了系统的理论研究.采用空间傅里叶变换和四阶Runge-Kutta算法，分别模拟了非衍射极限情况下的高斯光束和空间频谱为矩形的发散光束作为抽运光时的增益曲线.结果表明：不管是在可见光或是在近红外光谱区，用发散光束均可以明显地改善光参量啁啾脉冲放大系统的增益带宽.选取合适的发散角和抽运光强，可以获得高增益、宽谱带的信号光输出. 关键词： 光参量啁啾脉冲放大 增益带宽 发散角 高斯光束     

用于激光驱动质子束测量的腔式束流位置探测器模拟研究

根据激光驱动质子束流低发射度、短脉冲、单束团低电量的性质,研究腔式束流位置探测器(BPM)测量激光加速器产生的质子束团横向位置的可行性问题。针对质子束团的大横向分布和发散角问题,推导了其通过腔式BPM的输出信号,结果表明该信号与集中从束团对称中心、倾斜一定角度通过的束流产生的输出信号相同。依据上述原理,使用CST软件进行了腔式BPM的设计和仿真,确定了矩形谐振腔波导耦合的方案。讨论了该方案的腔式BPM对于激光加速束流的适用性和不同激光驱动质子束流参数的分辨率,并针对PW级激光加速系统进行了分辨率估算。     

相空间路径积分中的Feynman规则和广义Ward恒等式

基于Green函数的相空间生成泛函,导出了广义正则Ward恒等式.指出无须作出相空间生成泛函中对正则动量的路径积分,即可求得树图近似下的Feynman规则.对场的拉氏量添加一个四维散度项后,场的传播子发生了改变.     

高温下夸克场真空图中的红外发散

用热传播子的实时形式对高温条件下夸克(忽略质量)场三圈真空图进行了详细地计算,找出了其中和费米–狄拉克统计因子有关的红外发散积分的类型,并对这种发散积分进行了正规化,进一步把真空图中的红外发散全部孤立出来了.