求解大规模矛盾方程组的最小二乘支持向量机算法

房价预测、共享单车出租数量预测、空气污染情况预测等常涉及矛盾方程组求解,对其数值求解方法研究具有重要的理论意义与应用价值。当矛盾方程组规模过大时,用传统的最小二乘法求解,不仅计算量大,而且由于误差积累使最终结果的准确性不高。鉴于此,采用机器学习中的最小二乘支持向量机（least squares support vector machine,LS-SVM）算法求解大规模矛盾方程组,并分别针对线性、非线性、单变量、多变量矛盾方程组进行了数值求解。数值结果表明,数据类型和数据量的变化对结果的影响不大,因此只要选取适当的参数就可建立合适的模型,得到高精度的预测结果。     

Pattern formation in superdiffusion Oregonator model

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction–diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.     

激光辐照氮化硅陶瓷光谱信息研究北大核心CSCD

氮化硅陶瓷具备耐腐蚀、耐磨损和耐高低温冲击的优良性能,常用于高超声速飞行器的热防护材料,激光武器是未来高超声速目标拦截和打击的主要技术手段。采用Nd3+:YAG固体脉冲激光器作为辐照源,热压烧结氮化硅陶瓷为靶材,中阶梯光栅光谱仪为探测器搭建实验系统,采集激光波长1064 nm,脉宽15 ns,不同能量(50 mJ~500 mJ)作用靶材的辐射光谱。基于美国标准技术与研究院原子光谱数据库对谱线指认,利用玻尔兹曼斜线法计算得到等离子体电子温度范围为6203 K~6826 K,斯塔克展宽法计算等离子体电子密度范围为8.40×10^(15)cm^(−3)~1.14×10^(16)cm^(−3),等离子体电子振荡频率为8.23×10^(11)Hz~9.58×10^(11)Hz,随着激光能量增加电子温度整体呈上升趋势,电子密度变化存在波动。     

Rotation of a single vortex in dusty plasma

A single vortex is obtained in radio-frequency capacitive discharge in argon gas. The dust subsystem is confined in the horizontal plane with an asymmetrical saw structure placed on the lower electrode. The vortex rotates as a whole along the long side of the saw-teeth. Asymmetry of the saw structure plays an important role in the rotation of the vortex. Nonzero curl of the total force resulting from the local ion flow and the electric field in the plasma sheath could be attributed to the persistent rotation of vortex.     

Formation and dissociation of dust molecules in dusty plasma

Dust molecules are observed in a dusty plasma experiment.By using measurements with high spatial resolution,the formation and dissociation of the dust molecules are studied.The ion cloud in the wake of an upper dust grain attracts the lower dust grain nearby.When the interparticle distance between the upper dust grain and the lower one is less than a critical value,the two dust grains would form a dust molecule.The upper dust grain always leads the lower one as they travel.When the interparticle distance between them is larger than the critical value,the dust molecule would dissociate.