关于结构非概率可靠性模型中安全评估

考虑区间变量非概率可靠性模型，采用非概率可靠性指标、安全系数和集合可靠度三类确定性参数描述结构的可靠性和安全程度。通过几何描述，明确地给出了三类参数的物理意义，指出了各自的取值范围和实用区间。从设计思想、度量方法及表现形式方面分析了三类度量的区别，并建立了它们之间的函数关系。研究结果拓展了结构非概率设计理论，并通过具体优化算例对三类度量所得到的结果进行了讨论。     

光晶格中超流费米气体的能隙孤子

研究了一维光晶格中超流费米气体的能隙孤子. 应用平均场理论和超流费米气体的流体动力学模型, 利用变分法得到了在整个跨越区超流费米气体在光晶格中存在带隙孤子的条件, 即原子间的非线性相互作用项与系统化学势以及晶格深度的相互关系. 通过对超流费米气体的基态能隙孤子空间分布的分析与对比, 揭示了在一维情况下超流费米气体能隙孤子的存在并发现超流费米气体能隙孤子在整个跨越区当系统从Bose-Einstein凝聚端跨越到BCS端时孤子存在的条件与孤子空间分布存在明显的差别.     

Variational Approach to Study PT-Symmetric Solitons in a Bose–Einstein Condensate with Non-locality of Interactions

Considering the non-locality of interactions in a Bose–Einstein condensate, the existence and stability of solitons subject to a PT-symmetric potential are discussed. In the framework of the variational approach, we investigate how the non-locality of interactions affects the self-localization and stability of a condensate with attractive two-body interactions. The results reveal that the non-locality of interactions dramatically influences the shape,width, and chemical potential of the condensate. Analytically variational computation also predicts that there exists a critical negative non-local interaction strength(p_c 0) with each fixed two-body interaction(g_0 0),and there exists no bright soliton solution for p_0 p_c. Furthermore, we study the effect of the non-locality interactions on the stability of the solitons using the Vakhitov–Kolokolov stability criterion. It is shown that for a positive non-local interaction(p_0 0), there always exist stable bright solitons in some appropriate parameter regimes.     

Modulational Instability of Dipolar Bose-Einstein Condensates in Optical Lattices with Three-Body Interactions

Motivated by the recent experiment [Nature 530(2016) 194] in which a stable droplet in a dipolar quantum gas has been created by the interaction-induced instability, we focus on the modulation instability of an optically-trapped dipolar Bose-Einstein condensate with three-body interaction. Within the mean-field level, we analytically solve the discrete cubic-quintic Gross-Pitaevskii equation with dipole-dipole interaction loaded into a deep optical lattice and show how combined effects of the three-body interaction and dipole-dipole interaction on the condition of modulational instability. Our results show that the interplay of the three-body interaction and dipole-dipole interaction can dramatically change the modulation instability condition compared with the ordinary Gross-Pitaevskii equation. We believe that the predicted results in this work can be useful for the future possible experiment of loading a Bose-Einstein condensate of ~(164)Dy atoms with strong magnetic dipole-dipole interaction into an optical lattice.     

嵌入式粒子群-遗传算法的水质COD检测特征波长优化算法

基于紫外-可见光谱法的水质测量中,光谱信号易受到系统噪声干扰、悬浮物散射干扰,且存在信息冗余、多重共线性等特征,导致水质COD测量中特征波长的选取产生较大偏差。因此,提出了基于嵌入式粒子群-遗传（EPSO_GA）算法的水质COD检测特征波长优化算法,以提高波长选择精度。为验证检测特征波长优化算法的可行性,采集了某高校池塘水样、生活污水和排水沟水样的光谱数据,利用EPSO_GA算法对预处理后的光谱数据选取特征波长。EPSO_GA算法采用实数编码方法实现了粒子群（PSO）优化算法和遗传（GA）优化算法的统一编码,在PSO算法中更新粒子时嵌入GA算法的选择、交叉、变异等操作,改善了这两种算法各自在光谱波长特征选取问题上的局限性。将EPSO_GA算法选取的特征波长结合偏最小二乘法（PLS）构建了EPSO_GA_PLS的水质COD预测模型,并且与传统的PSO算法、GA算法选取特征波长建立的PSO_PLS、GA_PLS和全光谱构建的PLS水质COD预测模型做了对比。结果表明：与PSO_PLS,GA_PLS和全光谱构建的PLS水质COD预测模型相比,EPSO_GA改善了PSO算法和GA算法在光谱特征波长选择中早熟和收敛速度慢的问题,降低了全光谱构建PLS水质COD预测模型的复杂度,提高了模型的预测精度。基于EPSO_GA算法建立的EPSO_GA_PLS水质COD预测模型,均方根误差降到了0.212 3,预测精度增加到0.999 3,可以快速定量检测水质COD,为紫外-可见光谱法测COD提供了更好的预测模型。     

Effects of three-body interaction on dynamic and static structure factors of an optically-trapped Bose gas

We investigate how three-body interactions affect the elementary excitations and dynamic structure factor of a Bose- Einstein condensate trapped in a one-dimensional optical lattice. To this end, we numerically solve the Gross-Pitaevskii equation and then the corresponding Bogoliubov equations. Our results show that three-body interactions can change both the Bogoliubov band structure and the dynamical structure factor dramatically, especially in the case of the two-body interaction being relatively small. Furthermore, when the optical lattice is strong enough, the analytical results, combined with the sum-rule approach, help us to understand that： the effects of three-body interactions on the static structure Ihctor can be significantly amplified by an optical lattice. Our predictions should be observable within the current Bragg spectroscopy experiment.     

Dynamic Structure Factor of an Optically Trapped Dipolar Bose–Einstein Condensate

Motivated by the recent experimental achievements in using the Bragg spectroscopy to measure the excitation spectrum of an ultra-cold atomic system with long-range interactions, we investigate the dynamic structure factor of a cigar-shaped dipolar Bose condensate trapped in a one-dimensional optical lattices. Our results show that the Bogoliubov bands of the system, particularly the lowest one, can be significantly influenced when one tunes the dipole orientation. Consequently, the calculated static structure factor of an optically trapped dipolar Bose gas shows marked difference from the non-dipolar one. Moreover, we show that the effects of dipole-dipole interaction on the dynamic structure factor is also strongly affected by the strength of the optical confinement.