Symplectic structure-preserving integrators for the two-dimensional Gross-Pitaevskii equation for BEC

Symplectic integrators have been developed for solving the two-dimensional Gross-Pitaevskii equation. The equation is transformed into a Hamiltonian form with symplectic structure. Then, symplectic integrators, including the midpoint rule, and a splitting symplectic scheme are developed for treating this equation. It is shown that the proposed codes fulfill the discrete charge conservation law. Furthermore, the global error of the numerical solution is theoretically estimated. The theoretical analysis is supported by some numerical simulations.     

Near-invariant Tori on Exponentially Long Time for Poisson systems

This paper deals with the near-invariant tori for Poisson systems. It is shown that the orbits with the initial points near the Diophantine torus approach some quasi-periodic orbits over an extremely long time. In particular, the results hold for the classical Hamiltonian system, and in this case the drift of the motions is smaller than one in the past works.     

稀疏数据非线性降维的CN-Isomap算法

针对经典的流形学习算法Isomap在非线性数据稀疏时降维效果下降甚至失效的问题,提出改进的切近邻等距特征映射算法(Cut-Neighbors Isometric feature mapping,CN-Isomap).该算法在数据稀疏的情况下首先通过有效识别样本点的"流形邻居"来剔除近邻图上的"短路"边,然后再通过最短路径算法拟合测地线距离,使得拟合的测地线距离不会偏离流形区域,从而低维嵌入映射能够正确地反映高维输入空间样本点间的内在拓扑特征,很好地发现蕴含在高维空间里的低维流形,有效地对非线性稀疏数据进行降维.通过对Benchmark数据集的实验表明了算法的有效性.CN-Isomap算法是Isomap算法的推广,不仅能有效地对非线性稀疏数据进行降维,同样也适用于数据非稀疏的情况.     

Vector Minimization of Upper Robust Mappings

1.IntroductionLetXbeatopologicalspaceandf=(f',f',...):X-Reamapping.Inthispaper,weconsiderthevectoroptimizationproblemswithrespecttothepartialorderinginducedb}'thenonnegativeorthantoftheproductspaceRe.Apointx6Xissaidtobeaegcientsolutionornondominatedsoluti…     

微分代数系统稳定性及镇定新判据

本文利用矩阵迹不等式讨论了微分代数系统的稳定性,并给出了微分代数系统容许的充分条件.提出了用此方法设计状态反馈控制器使微分代数系统容许的新方法,并设计了矩阵迹不等式组的计算机求解程序,并用例子说明了主要定理的有效性.     

用于PKU-FEL注入器的腔式BPM的设计

 设计了用于PKU-FEL注入器的腔式位置诊断装置。该BPM腔采用的偶极模TM₁₁₀模的频率与PKU-FEL主加速器的基模频率一致,都是1.3 GHz;通过在圆形腔上镶入两个完全一致的矩形腔解决了腔式BPM的Cross-Talk问题。 根据PKU-FEL的设计要求,所设计的BPM腔的最小位置响应约10 mm,动态范围大于30 mm,时间响应小于束团间距。还估算了该BPM腔引起的束团功率损耗。结果表明,BPM腔引起的束团功率损耗是可以忽略的。     

KMgF3:Cr3+的EPR参量和K+空位研究

EPR和ENDOR表明:顺磁离子取代KMgF₃中的Mg²⁺离子后,所处的环境具有轴对称。本文研究了KMgF₃:Cr³⁺的Δg=g_∥-g_⊥和零场分裂值D,证实KMgF₃:Cr³⁺中K⁺空位的存在。并且指出:由于K⁺空位,使Cr³⁺的最近邻F^-离子分 关键词：     

Nanocrystalline gold with small size: inverse Hall–Petch between mixed regime and super-soft regime

ABSTRACT

Molecular dynamics simulations were used to study the atomic mechanisms of deformation of nanocrystalline gold with 2.65–18?nm in grain size to explore the inverse Hall–Petch effect. Based on the mechanical responses, particularly the flow stress and the elastic-to-plastic transition, one can delineate three regimes: mixed (10–18?nm, dislocation activities and grain boundary sliding), inverse Hall-Petch (5–10?nm, grain boundary sliding), and super-soft (below 5?nm). As the grain size decreases, more grain boundaries present in the nanocrystalline solids, which block dislocation activities and facilitate grain boundary sliding. The transition from dislocation activities to grain boundary sliding leads to strengthening-then-softening due to grain size reduction, shown by the flow stress. It was further found that, samples with large grain exhibit pronounced yield, with the stress overshoot decrease as the grain size decreases. Samples with grain sizes smaller than 5?nm exhibit elastic-perfect plastic deformation without any stress overshoot, leading to the super-soft regime. Our simulations show that, during deformation, smaller grains rotate more and grow in size, while larger grains rotate less and shrink in size.     

北京自由电子激光摇摆磁铁场分布测量装置

我们设计加工了一套测量摇摆磁铁整体场分布的测量装置，并对北京自由电子激光（ＢＦＥＬ）摇摆磁铁进行了实际测量，定态测量误差优于１×１０￣（－４），动态测量误差５×１０￣（－４）。     

圆弧曲线的有理五次Bézier表示

给出了有理五次Bézier曲线精确表示0<2θ<2π(θ为圆心角)的圆弧及整圆的充要条件,加以了证明并给出了图例..